AU2020201562B2 - Jet-turbine and jet-ventilator - Google Patents

Abstract

The invention describes a biconvex wing, a two-humped wing, and a tandem of two airfoil bodies, each sharing a novel cross-sectional area profile defined in terms of a gradual monotonic smooth M velocity profile. Embodiments include a jet-rotor, a jet-turbine, a jet-ventilator, a jet-propeller and a jet-transformer. 9/17 800 820 811 8221-+r-8 810 833 823 335 834 _ 810b 834 824 812 Fig. 8a Fig. 8b

Description

9/17

800 820 811

810 833 8221-+r-8

823 335 834 _ 810b 834 824 812

Fig. 8a

Fig. 8b

Jet-Turbine and Jet-Ventilator

FIELD OF THE INVENTION

The invention relates generally to fluid dynamics and to use of jet-effect, applied to headway motions in fluids, and, more particularly, to use for designing either: U a jet-turbine, and/or * a jet-ventilator, and/or * a jet-propeller; the all having a rotor comprising novel airfoil wings playing the role of blades.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of 2018204546 22-Jun-2018 further indicated by AU03, which, in turn, is divisional of 2017206155 - 17-July-2017 further indicated by AU01.

BACKGROUND OF THE INVENTION

A widened BACKGROUND OF THE INVENTION may be referred to the mentioned AU03, which (the widened BACKGROUND OF THE INVENTION) i not narrated herein for brevity. Instead, a reduced background of the invention is repeated, wherein the reduced background of the invention comprising aspects introducing directly to the claims of the present divisional patent application. The disclosures of AU03 and AU01 are herein incorporated by reference in their entirety. The inventor points out again to a diversity of manifestations of the Venturi effect and the Coanda-effect, both resulting in a phenomenon of convective self-acceleration, and emphasizes again features of lift-force and jet-thrust occurring when airflow moves near convex surfaces of B-Point of Sail and above a convexity of an airfoil wing, and, especially, when the airflow moves near convexities of a biconvex wing having a profile similar to a profile of a wing of bird.

Preamble and Terminology (reduced)

The well-known and widely-used jet-effect provides for the effect of gas extension and thereby acceleration. Accelerated flow is widely applied to propelling some kinds of vehicles having jet-engines usually supplied by either converging or convergent-divergent nozzles, to which the term "jet-nozzle" is also applied to emphasize the jet-effect importance. US Patent 6,981,366 by Sharpe overviews numerous modifications of the jet-effect implementation.

Page 1 of 75

In US 2008/0061559 Al patent application, Hirshberg points out that the jet-effect is accompanied by decreasing static pressure and temperature, and suggests applying the phenomenon as a trigger for vapor-to-water condensation. In US Patents 8,268,030 "Wind Energy Use" and 8,221,514 "Ecologically Clean Method and Apparatus for Water Harvesting from Air", Abramov points out that a long cascade of streamlined nozzles provides a convergence of a wider front of fluid flow, and provides for an adaptation of the jet-effect use for big-scale devices. In this invention, the equation of fluid motion is generalized to correspond to the kinetic theory of matter, wherein, in particular, it is shown that a consideration of a fluid, defined as composed of molecules in accordance with the kinetic theory of matter, provides for solving a series of confusing paradoxes, following from the definitions, restricted in the frames of the continuum mechanics. In relation to the molecular fluid, to analyze the equation of the molecular fluid motion, for the purposes of the present invention, the term "jet-effect" is used in a wide sense as the effect of fluid flow portion convective acceleration at the expense of fluid portion internal heat energy. In particular, the jet-effect occurs when the fluid portion moves adjacent to configured walls and is subjected to the walls accelerating action, as seemingly "negative drag". For example, the fluid is gas and the walls are configured to form a converging or convergent-divergent nozzle. In particular, the term "jet-effect" is applied to the well-known and widely-used effect of convective acceleration of a wind-portion, which is flowing over a convex upper surface of an airplane wing and is thereby being subjected to the varying of flow front cross-section in an imaginary convergent-divergent nozzle. Another example is a case, wherein the fluid is water and the configured walls have a hydrophobic surface. Thus, the term "jet-effect", used here in a wide sense, assumes that the process of gas extension may be insignificant or latent. For the purposes of the present invention, the term "imaginary wall", applied to flowing fluid streamlines, should be understood as a material (but not virtual) wall, formed by the fluid's matter, forcedly-bordering a portion of the flowing fluid. I.e. the material but optionally invisible by the human eye and thereby imaginary wall acts on adjoining fluid portions, enforcing the fluid portions to move along the streamlines, i.e. in alignment with the imaginary wall. When flowing plasma is subjected to an action of a magnetic field, "imaginary walls" are formed by the magnetic field's force-lines defining the streamlines of the flowing plasma. When considering the electromagnetic field, "imaginary walls" should be understood as formed by the electromagnetic field's force-lines. The jet-effect is the nature of the well-known Coanda-effect, defined as a tendency of a fluid jetstream to be attracted to and aligned with a nearby airfoil surface, i.e. to be specifically

Page 2 of 75 accelerated at the expense of the fluid warmth. For the purposes of the present patent application, to emphasize the jet-effect nature of the Coanda-effect, the term "Coanda-jet-effect" is also applied as equivalent to the commonly known term "Coanda-effect". Looking ahead, the term "airfoil" will be specified as "actually-airfoil" in contrast to "seemingly-airfoil". For the purposes of the present patent application: " the term "velocity of a flying body" should be understood as the body motion velocity relative to a stationary fluid; and vice-versa, the term "flow velocity" should be understood as the fluid flow velocity relative to the considered body submerged in the flowing fluid. These two terms are interrelated according to Galilean relativity; U the term "M-velocity" should be understood as the fluid velocity measured in Mach numbers, or identically, velocity normalized to the temperature-dependent velocity of sound in the fluid; and " the well-known terms "low-subsonic", "high-subsonic", "transonic", "supersonic", and "hypersonic" are used to specify the flow velocity ranges as the following: (a) the low-subsonic velocity range is defined as the M-velocity range comprising M velocities lower than 0.3 Mach; (b) the high-subsonic velocity range is defined as the M-velocity range comprising M velocities higher than 0.3 Mach and lower than 0.8 Mach; (c) the transonic velocity range is defined as the M-velocity range comprising M velocities higher than 0.8 Mach and lower than 1.2 Mach; (d) the supersonic velocity range is defined as the M-velocity range comprising M velocities higher than 1Mach and lower than 5 Mach; and (e) the hypersonic velocity range is defined as the M-velocity range comprising M velocities higher than 5 Mach. Moreover, for the purposes of the present patent application, the term "specific M-velocity" is introduced to separate the terms "low M-velocities", associated with M-velocities lower than the specific M-velocity indicated by M,, and "high M-velocities", associated with M-velocities higher than the specific M-velocity M,. The value of the specific M-velocity M, will be defined hereinbelow by a specific molecular structure of fluid. Furthermore, the term "essential M-velocity range" is defined as an M-velocity range comprising the specific M-velocity M". For the purposes of the present patent application, the term "molecular fluid" should be understood as a fluid substance composed of randomly moving and interacting molecules, according to the kinetic theory of matter. Referring to the defined term "molecular fluid", the earlier

Page 3 of 75 defined term "flow velocity" is further specified as a measure of the molecular fluid molecules motion in a prevalent direction in addition to the random Brownian motion. For instance, the air is considered as a molecular fluid, and the wind is considered as a natural process, bringing fresh portions of air, storing at least both: the heat energy of molecules Brownian random motion and the kinetic energy of wind motion. Normally, in nature, when the wind is of 10 m/sec, the proportion is such that 99.96% is the heat energy [i.e. warmth] and only 0.04% is the kinetic energy. A phenomenon of a transformation of warmth into a hurricane power is well-known; however, the warmth of ambient natural air remains unused in the world industry. Possession of a technology to control the transformation of the surrounding air and/orwater warmth into a directional motion of the fluid could provide a renewable cycle, comprising: " transformation of the flowing fluid heat-power into acquired kinetic-power of an arisen jetstream (and/or into acquired wave power of an arisen wave); " conversion of the jetstream kinetic-power into useful electric-power; and " consumption of the electric power, in the final analysis, inevitably dissipating back into the warmth of the surrounding matter. There is, therefore, a need in the art for a method and apparatus to provide proper analysis and optimal design of a system, implementing a controllable jet-effect appropriate for use in industry.

Venturi Effect

Reference is now made to prior art Fig. 1b. Fig. 1b is a schematic illustration of an airfoil shaped convergent-divergent nozzle 102, pipe-section in a sagittal plane. The shape can be described as comprising an inlet part 103 constricting into a narrow throat 104, further followed by a divergent outlet part 105. When a fluid 106 flows slowly through convergent-divergent nozzle 102, a jet-effect is observed in an adiabatic process, i.e. velocity increases in narrow throat 104 at the expense of the static pressure in fluid 106. Speedometers 1071, 1072, 1073 and barometers 1081, 1082, 1083 illustrate the interrelated behavior of the velocity and static pressure. This jet-effect is known also as the Venturi effect. Thus, the Venturi acceleration effect is observed in the case of a slow and converging flow, and the Venturi retarding effect is observed in the case of slow and divergent flow. The inventor points out and emphasizes that the phenomenon of the Venturi effect is the self-acceleration and self-retarding of an airflow portion, i.e. is the airflow velocity self-oscillation,

Page 4 of 75 at the expense of the air portion's warmth. I.e., in other words, the Venturi effect of the airflow velocity self-oscillation (as well as the Coanda-jet-effect) has the jet-effect nature. When observing a freely falling water jetstream, one explains a conic constriction of the waterjetstream by the Venturi effect, where the accelerated jetstream becomes accompanied by a decrease of the cross-sectional area.

De Laval Effect

Reference is now made to prior art Figs. 1c and 1d. Fig. 1c shows schematically a pipe 100 referred to the de Laval nozzle that, in principle, is similar to pipe 102 shown in Fig. 1b, but now the incoming fluid-flow 101 is sufficiently fast such that fluid 101 becomes substantially compressible-expandable. In this case, in an adiabatic process, the de Laval effect is observed. This is the effect of the extension of fluid 101 in the divergent outlet part 142 resulting in a further decrease of the static pressure and temperature and a correlated increase of the flow velocity.

Fig. 1d illustrates schematically graphics of distributions of the fluid-flow 101's (Fig. 1c) three parameters: velocity 150, static pressure 160, and temperature 170, each along the length of nozzle 100. A standard rocket convergent-divergent jet-nozzle 100 can be modeled as a cylinder 140 that leads to a constriction 141, known as the "throat", which leads into a widening "exhaust bell" 142 open at the end. The location of the narrowest cross-section of the throat is called as the "critical condition" point 180. High speed and therefore compressible-expandable hot fluid 101 flows through throat 141, where the velocity picks up 151 and the pressure and temperature fall, 161 and 171 correspondingly. Hot fluid 101 exits throat 141 and enters the widening exhaust bell 142. It expands rapidly, and this expansion drives the velocity up 152, while the pressure and temperature continue to fall, 162 and 172 correspondingly. This jet-effect phenomenon of fluid 101 extra-acceleration at the expense of the fluid 101 heat energy, defined by the static pressure, temperature, and density, is applied to jet-engines, particularly to accelerate a rocket. A sharp slope of the static pressure, observed in throat 141, results in pressure waves, called Mach waves. An undesired influence of the Mach waves in the de Laval nozzle is described, for example, in US Patent 8,611,787 "Rocket nozzles for unconventional vehicles" by Bulman. Looking ahead, the enhanced jet-effects: the de Laval jet-effect and the de Laval retarding effect, both will be conceptually embodied in the present invention.

Ordinary Blowing Ventilator

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Fig. 1eis a prior art schematic drawing of ordinary blowing ventilator 110 operating in open airspace. Ordinary blowing ventilator 110, defined by the main functionality to launch a jetstream characterized by the flow headway-motion kinetic-power, has an inherent engine [not shown here] consuming either a power of burned fuel or electrical power. Ordinary blowing ventilator 110 comprises blades 112, having an asymmetrical shape such that, when forcedly rotating in frontal plane 119 and covering effective cross-section 114, suck air portions 115.A from space "Al" located upstream-afore effective cross-section 114 and convert air portions 115.A into an accelerated jetstream 115.B entering space "B1" located downstream-behind effective cross section 114. Space "Al",comprising air portions 115.A subjected to the sucking and motion through effective cross-section 114, is bordered by streamlines, forming imaginary contours 116.A. The imaginary contours 116.A separate space "Al"from space "C", comprising air portions 115.C, drawn by moving air portions 115.A and flowing toward frontal plane 119 out of effective cross-section 114. Space "B1", comprising jetstream 115.B, is bordered bystreamlines, forming imaginary contours 116.B. The imaginary contours 116.B separate space "B1" from space "D1", comprising air portions 115.D, drawn by jetstream 115.B and flowing downstream behind frontal plane 119. A complicated motion of air portions 115.A, 115.B, 115.C, and 115.D comprises both: a headway-motion, i.e. a laminar component of motion aligned with the imaginary contours 116.A and 116.B having a prevalent direction along imaginary sagittal axis 111, and a whirling-motion, i.e. a turbulent component of motion, dominantly, whirling around imaginary sagittal axis 111. For the purposes of the present patent application, the term "sagittal axis" is applied to an axis co-directed with a prevalent direction of a flow headway motion. The mentioned term "streamlines", applied to imaginary contours 116.A and 116.B, has a widened sense, spread to the streamlines projections on a plane comprising imaginary sagittal axis 111, for instance, either sagittal or transversal, meaning that there is no essential mass exchange between: * air portions 115.A of space "Al"and air portions 115.C of space "C1", and " helically whirling jetstream 115.Bof space "B1" and air portions 115.D of space "D". The power, consumed by ordinary blowing ventilator 110 is expended for: " the complicated motion of air portions 115.A, which then are transformed into helically whirling jetstream 115.B; * the complicated motion of air portions 115.C, which then are transformed into moving air portions 115.D; * the overcoming of air viscous-resistance; and * the compensation of the inner resistance of the inherent engine.

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Wherein the part of the power consumption, expended for the overcoming of air viscous resistance and compensation of inner resistance of the inherent engine, dissipates in the acquired warmth of outflowing air portions 115.B and 115.D. Streamlines 116.A and 116.B constitute an imaginary convergent-divergent tunnel, where, in addition to the mentioned effect of flow complicated motion, powered by forcedly rotating blades 112, the Venturi effect, described above referring to Fig. 1b, occurring in an adiabatic process, is expected, thereby saving the power for the additionally acquired convective acceleration of jetstream 115.B. The velocity ofjetstream 115.B headway-motion is distributed on cross-section 118 non-uniformly. Shapes of forcedly rotating blades 112, on the one hand, define the shapes of imaginary contours 116.A and 116.B, and on the other hand, define the jetstream 115.B headway-motion velocity distribution on cross-section 118. The resulting functionality net efficiency of ordinary blowing ventilator 110 is defined by the ratio of the kinetic-power of launched jetstream 115.B headway-motion to the power, consumed by the inherent engine of ordinary blowing ventilator 110. Taking into the account the mentioned Venturi effect, the resulting net-efficiency of ordinary blowing ventilator 110 interrelates with the Venturi effect efficiency. The inventor points out and emphasizes that whereas the functionality net-efficiency of a blowing ventilator is provided, in particular, due to the Coanda-jet-effect, i.e. at the expense of ambient warmth, conditions, when the net-efficiency becomes higher than 100%, are not excluded. Looking ahead, in view of the description referring to Figs. 9g, 9h, 9j, 9k, 9L, and 9m of the invention, it will be evident to a person having studied the invention, that such conditions are specified.

The Phenomenon of Convective Self-Acceleration Fig. 1f is a prior art schematic drawing of a body 12.0 blown by an initially laminar airflow having portion 12.2 enveloping body 12.0. It is assumed that a velocity of the airflow motion is much lower than 0.5 Mach, for instance, 1r/sec. For simplicity and without loss of reasoning, consider a case when the body 12.0 corpus has at least partially airfoil shape providing for that ambient-adjoining sub-portions 12.5 and 12.6 of airflow portion 12.2 remain laminar at least upstream afore a frontal plane, crossing the body 12.0 corpus. Here, " such a frontal plane is marked with the dotted line having numeral 12.1; " dashed lines 12.3 and 12.4 are imaginary streamlines bordering airflow portion 12.2 as a whole and being sufficiently far from body 12.0 that allows to ignore the

Page 7 of 75 airflow streamlines minor curving when bordering ambient-adjoining sub-portions 12.5 and 12.6; and U arrow 12.7 symbolizes a portion of downstream airflow, not obligatorily laminar. When flowing around body 12.0, ambient-adjoining sub-portions 12.5 and 12.6 of airflow portion 12.2 become subjected to reshaping and can be considered as moving through an imaginary tunnel, which is characterized by varying cross-sectional area. According to the mass conservation law, called also the equation of continuity: Apu = Const, where p is the density of flux; u is the flux velocity, and A is the flux cross-sectional area, ambient-adjoining sub portions 12.5 and 12.6 move faster than yet to be reshaped airflow portion 12.2 because the air density changes are minor at low airflow velocities and the sub-portions have the cumulative cross-sectional area smaller than the cross-sectional area of yet to be reshaped airflow portion 12.2. Therefore, the cumulative kinetic energy of ambient-adjoining sub-portions 12.5 and 12.6 is higher than the kinetic energy of oncoming airflow portion 12.2 yet to be subjected to the reshaping. One of the key questions about the origin of flowing fluid portion acceleration is the following. At the expense of what kind of energy, the sub-portions became accelerated, if the case is adiabatic? The answer to the question is the self-acceleration occurs at the expense of the internal heat energy of the flowing fluid portion itself, wherein the initial velocity of the flowing fluid portion plays a role of a "trigger-catalyst" defining intensity of the self-acceleration, namely, a higher velocity results in a greater self-acceleration. The answer shows that the phenomenon of convective self-acceleration is inevitable for fluid flowing around a body with relatively low velocities in an adiabatic process, i.e. upon conditions usually provided in the actual practice. The inventor points out and emphasizes that a portion of the flowing fluid may play the role of a body subjected to blowing by another portion of the flowing fluid - this situation occurs, for instance, in acoustic waves.

Airfoil Wing (definition of attack angle)

Fig. Ig is a prior art schematic drawing of a classic airfoil profile of an airplane wing 10 oriented horizontally in a sagittal plane. The wing profile is recognizable by a rounded leading edge, a convex profile contour, having smoothly curved, elongated sides: more convex and lesserconvex, and a sharp trailing end. A horizontal oncoming airstream 12 runson the rounded leading edge and flows around wing 10, thereby being divided into two laminarly moving portions:

Page 8 of 75 upper air flux 14 and lower air flux 15, both going off from the sharp trailing end. The axis 11 of wing 10, codirectional with a so-called chord of wing, which (the chord of wing), sometimes, is defined relatively arbitrary based on a side-view profile the wing. Since a wing can have a twist, a chord line of the whole wing may not be definable, so an alternate reference line is simply defined. Often, the chord line of the so-called "root of the wing" is chosen as the reference line. Another choice is to use a horizontal line on the fuselage as the reference line (and also as the longitudinal axis) 11A. Some authors do not use an arbitrary chord line but use the so-called "zero lift axis" where, by definition, zero angle of attack corresponds to zero coefficient of lift. In contrast, for the purposes of the present patent application, taking into account the dual nature of lift-force: by impact and by the Coanda-effect, an "attack angle" or "angle of attack" should be understood as an angle between the horizontal direction and the longitudinal axis 11A, while the chord of wing is defined as separating the upper and lower fluxes. In other words, the attack angle is defined relative to the zero attack angle that, in turn, is specified by a manifestation such that the zero attack angle provides for minimized impact by the oncoming flow and for the lift force generation due to the Coanda-effect only or at least dominantly. Thereby, the shown profile of wing 10 oriented horizontally is defined as exposed to the oncoming wind at the zero attack angle. Axis 11 of wing 10 and the horizontal direction of oncoming air stream 12 constitute an angle of the wing asymmetry 13 when the angle of attack is zero. The more convex upper side provides a slippery surface, and the lesser convex lower side, exposed to oncoming air stream 12 with the attack angle (zero or non-zero positive) and so subjected to friction and impact by lower air flux 15, has thereby more frictional-dragging surface. The Coanda-effect is defined as a tendency of a fluid jetstream to be attracted to and aligned with a nearby airfoil surface. The well-known lift-effect of an airplane wing 10 arises due to the non-symmetrical profile of wing 10 when the upper side is more convex determining the angle of the wing asymmetry 13. Firstly, a lift-force is defined by the attack angle, which redirects the flowing wind. Secondly, when the attack angle is equal to zero, wing 10, having an ideally streamlined contour, provides that the sliding upper air flux 14 and the impacting lower air flux 15, both subjected to the Coanda-effect operation, meet behind wing 10. Sliding upper air flux 14 and impacting lower air flux 15, flowing around wing 10, incur changes in their cross-sectional areas and are accelerated convectively according to the mass conservation law. Considering relatively low velocities, the varying cross sectional areas result in that the sliding upper air flux 14 runs faster than the impacting lower flux 15. According to Bernoulli's principle, this results in less so-called static pressure on wing 10 from sliding upper flux 14 than the static pressure from the impacting lower flux 15. If upper flux 14 and lower flux 15 flow around wing 10 laminarly, the difference between the static pressures is

Page 9 of 75 defined as AP = Cdpu2 /2 , where AP is the static pressure difference defining the lift-force, in particular, when the attack angle is equal to zero, Cd is the coefficient, depending on wing 10's non-symmetrical profile, p is the density of the air; and u is the velocity of the ambient airflow relative to wing 10. A wing, having an elaborated airfoil profile, provides for a gradual variation of the airflow static pressure along the profile's smoothly curved contour and, when flying with a certain velocity, results in a linear change of the airflow static pressure along the profile's smoothly curved contour, thereby satisfying a condition preventing an origination of turbulences. In practice, there are also turbulence and vortices of the fluxes, which are not shown here. The prevalent flows, turbulence, and vortices result in spatial distribution of the air static pressure, particularly, in a local static pressure reduction and local extensions of the flowing air. Consider an air portion flowing around wing 10, referring to the Clapeyron-Mendeleev law concerning a so-called hypothetical ideal gas state: P = pROTI , where P is the gas static pressure, p is the gas density, T is the absolute temperature of the gas, y is the gas molar mass, and Ro is the universal gas constant. One could apply rough and more exact explanations for changes in the gas state parameters of the air portion flowing around wing 10. Roughly, for the sake of estimation of a relatively slow wind tendency only, considering the flowing air as substantially incompressible gas, Gay-Lussac's law for an isochoric process interrelates the static pressure P and absolute temperature T by the equation AP/P = ATIT, i.e. the reducing static pressure is accompanied by the decreasing absolute temperature. More exactly, for the wind at slow speeds as well as at higher speeds running, in general, at a non-zero attack angle, the air, being compressible-expandable as an ideal gas, flowing around wing 10, performs work W for the air portion volume extension, wherein the volume extension process is substantially adiabatic. The adiabatic extension results in a change of the portion of gas internal energy, accompanied by a static pressure reduction and temperature decrease. The work W performed by the wind portion of 1 mole flowing around wing 10 for the adiabatic process is defined as: W = CvATa, where Cy is the molar heat capacity for an isochoric process, and ATa is the adiabatic temperature decrease of the considered air portion. The value of the adiabatic temperature decrease ATa = T2 - T1 is bonded with static pressure reduction by the relation: T2/T1 = (P 2 /P 1 )(i 1)/i, where P, and P2 are the static pressures of the subject air portion before and after the adiabatic process correspondingly, and j is the adiabatic compressibility-constant, which is defined by the molecular structure of gas, wherein the value j = 7/5 is a good approximation for natural air as consisting dominantly of diatomic

Page 10 of 75 molecules. So, considering relatively low velocities, the Coanda-effect, occurring upon the convex side of wing 10, is accompanied by a kind of jet-effect, i.e. is accompanied by an observed acceleration of a wind portion and by the wind portion's static pressure and temperature decrease. Thus, the Coanda-effect and lift-effect are interrelated self-revealing-and-manifestations of the triggered jet-effect. The inventor emphasizes that, in other words, when the attack angle is zero, an aircraft consumes power for headway forwarding against the frictional-dragging only, and the lift-force working for the keeping a height of flight (i.e. for the upward motion against the gravity) is originated at the expense of the ambient warmth due to the Coanda-jet-effect. The use of this phenomenon is one of the primary features of claimed embodiments of the present divisional patent application. A well-known phenomenon of upper flux 14 adiabatic cooling at low-subsonic velocities is observed. Natural air is humid, and the local cooling, accompanied by the pressure reduction, acts, in particular, as a water condensation trigger. If the wind flows around a wing with an M velocity equal to or higher than the Mach number (i.e. the speed of sound), a well-known phenomenon of shock sound-wave emission takes place. This shock sound-wave is not caused by wing vibration, but arises when myriad of acoustic waves become in-phase superposed thereby forming the resonance resulting in the shock sound-wave; moreover, it becomes evident that the shock sound-wave is originated at the expense of the internal heat energy of air and so is accompanied by the air temperature shock decrease, provoking the process of vapor condensation into water-aerosols.

Fig. 1h is a prior art schematic drawing of considerable amounts of water-vapor condense into water-aerosols 16.1 and sublimate into micro-flakes-of-snow 16.2, which are observed behind the high-speed aircraft's 16 wings' nozzles. One could note that the effect occurs at flow speeds substantially lower than the Mach number, i.e. it is not triggered by the mentioned phenomenon of shock sound-wave emission. This phenomenon explanation cannot be derived from the classical equations of fluid motion, predicting the extra-decrease of static pressure and temperature at transonic and supersonic velocities only. On the other hand, air-fluxes, which flow nearby around a body, become warmer and extra-warmed, when the body flies in air environment with transonic, supersonic, and/or hypersonic velocities. Furthermore, when flying with transonic and supersonic velocities, the warmed and extra-warmed portion of flow moving above a wing, having the classic airfoil profile 10 oriented horizontally, results in a negative lift force and so a non-zero attack angle undesirably boosting a drag is required to fly horizontally.

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It is also found that, when flying with transonic and supersonic velocities, a wing, having the classic airfoil profile 10 oriented horizontally but knocked-over to have a convexity on the lower side of the wing, results in a positive lift-force. A correct prediction of thermodynamic effects that occurred in fluid flowing around a wing would provide an improved design of a wing shape to control and optimize the lift-effect. There is, therefore, a need in the art for a method and apparatus to provide a correct optimal design of the wing shape to reach the most efficient and controlled lift-effect.

Point of sail The term "point of sail" is used to describe a sailing boat orientation relative to a prevalent direction of the ambient wind.

Prior art Fig. 1i is a schematic illustration of points of sail. A sailboat exposed to ambient wind 18.0 in positions and orientations: 18.1, 18.3, 18.5, 18.6, 18.7, 18.9, 18.11, and 18.12 relative to the prevalent direction of ambient wind 18.0 is shown schematically. The positions and orientations of the sailboat, i.e. the points of sail, are classified by groups, indicated by symbols "A", "B", "C", "D", and "E". Group "A" is so-called "in irons" (into the wind) or "no-go zone", group "B" is so-called "close-hauled", group "C" is so-called "beam reach", group "D" is so-called "broad reach", and group "E" is so-called "running". The sailboat is a well-known example, showing that a passive sail, playing a role of a trivial nozzle, enables to move the sailboat at least partially in the upstream direction against ambient wind 18.0, for instance along a zigzag path. In other words, in fact, the passive sail exposed to ambient wind 18.0 produces "a netjet-thrust" against ambient wind 18.0. In simple words, in fact, the ambient wind 18.0 sucks the passive sail but not pushes it. Shaded sector 18.2 corresponds to the "no-go zone", where the single passive sail, being in position and orientation 18.12 belonging to point of sail group "A", does not provide a net jet-thrust in the upstream direction against ambient wind 18.0. Point of sail "B", called also "B"-point of sail, having the sailboat position and orientation 18.1, is shown also in enlarged view 18. Streamlines 18.13 show a windward wind flow aligned with the concave side of sail; streamlines 18.14 show a leeward wind flow subjected to the Coanda-effect and so moving along a curved trajectory adjoining the convex side of elastic sail, self-adapted to pressures of the wind flows; a multiplicity of arrows 18.15 indicate "lift-forces", in this case, directed horizontally, caused by the difference between static pressures at the concave and convex sides of sail; and arrow 18.16 indicates a portion of wind accelerated convectively,

Page 12 of 75 i.e. at the expense of the internal heat energy of wind. The convectively accelerated wind portion 18.16 acts on the sailboat by reactive force 18.17 according to Newton's Third Law. Reactive force 18.17 is vectored in the upstream direction. While lift-forces 18.15 become compensated dominantly by a stabilizing reaction of the sailboat's keel, which is not shown here, the reactive force 18.17 defines the sailboat headway motion primarily. The effect of net jet-thrust against ambient wind is a kind of jet-effect; i.e. it is the effect of convective acceleration of a wind portion flowing along a curved trajectory adjoining the convex side of passive sail in point of sail "B" due to the Coanda-jet-effect, and in turn, the accelerated wind portion causes the net jet-thrust, according to Newton's Third Law. To move against the wind, the sail, characterized by the point of sail "B" and orientation 18.1, must extract from the air the internal heat power, associated with the arisen reactive force 18.17, higher than the mechanical power of the oncoming wind 18.0 blowing the sail downstream away. In this case, one observes that the "drag-in-the-direct-sense", determined by the cumulative resistance of the sailboat to the oncoming airflow due to the sailboat non-zero frontal cross-sectional area and due to the effect of so-called skin-friction, is weaker than the seemingly "negative drag", determined by the jet-thrust. The inventor takes note that, when tracing after a wind portion relative to a system of coordinates linked with the wind portion yet to be accelerated due to the Coanda-jet-effect operation, one interprets the mentioned wind portion local acceleration as a peculiar shock-like wave propagating downstream, backward relative to the headway motion of the sailboat. For the purposes of the present invention, the introduced term "peculiar shock-like wave" or "peculiar wave" should be understood as a fluid reaction originated by a fluid portion local acceleration in a prevalent direction, in contrast to the term "forced wave" that should be understood as fluid oscillation originated and determined by an action of an external periodically alternating force. In view of the foregoing description referring to prior art Fig. 1i, it will be evident to a person skilled in the art that two sailboats, both being positioned in "B"-point of sail, wherein one of the sailboats has position and orientation 18.1 and the other sailboat has position and orientation 18.11, when connected and consolidated together and thereby aggregated as a whole, provide a condition for a resultant net jet-thrust applied to the aggregation, directed straight against ambient wind 18.0. In this case, the ambient wind 18.0 just sucks the passive pair of sailboats. The inventor points out and emphasizes that the phenomenon of netjet-thrust of sail in point of sail "B" occurs due to the self-acceleration of an airflow portion at the expense of the air

Page 13 of 75 portion's warmth. I.e., in other words, the net jet-thrust of sail in point of sail "B" occurs due to the Coanda-jet-effect. In spite of the fact that the effect of net jet-thrust against the ambient wind is widely used in cruising on the water, the effect remains unused in the world industry. There is, therefore, a need in the art for a method and apparatus to provide proper analysis and optimal design of a system, implementing the kind of jet-effect providing the net thrust in the upstream direction, for a controllable use in industry.

Flying Bird For the purposes of the present patent application, the inventor points out to a flying bird, to take note that the jet-effect is not so exotic, to emphasize the jet-effect potential efficiency, and to make clear that the Coanda-jet-effect is one of the primary and quintessential aspects of the present patent application. The inventor points out that a flying bird makes waving motions rather than rowing or pushing off motions by its wings. The waving can be interpreted as a booster of the Coanda-jet-effect as well as a source of forced elastic waves. The inventor points out to a flying bird, the wings waving of which is not so frequent but nevertheless is enviably efficient. In particular for a pigeon, while the wings waving velocity relative to the bird body is about 1 m/sec only, the bird flying-acceleration in a horizontal direction up to seemingly-paradoxical high velocities, higher than 10 m/sec (actually, higher than 30 m/sec and even 40 m/sec), becomes reachable; - it confirms that the primary mechanism of the flying-acceleration is at least not the pushing off in the direct sense. For comparison, a flying relatively large bird, for instance, a golden-eagle, and a running cheetah, both overcome the air drag and support the upward and downward mobility (wherein the cheetah's vertical mobility is defined by a ground relief and small jumps of the cheetah's center of mass only). For simplicity of the comparison, ignore the sidelong (leftward and rightward) mobility. The flying golden-eagle, "pushing off"gaseous air (take note, the "pushing off" is not intensively-frequent), overcomes the air drag and supports the upward and downward mobility much easier and moves in the horizontal direction much faster, than the running cheetah pushing off a solid surface, wherein pushing off substantially more intensive-frequently providing for a velocity of paws relative to cheetah's body being equal to the velocity of cheetah. At first glance, this fact looks like mystery and confusingly-paradoxical. However, it becomes easily-explainable, if not to ignore the triggered Coanda-jet-effect as for the lift-force as well as for the forward motion acceleration (analogously as the net jet-thrust in the aforementioned example with the sailboat in "B"-point of sail described with the reference to Fig. 1i). I.e. it

Page 14 of 75 becomes easily-explainable if the bird wing is interpreted as a sail oriented horizontally as "B" point of sail to provide an upward-and-forward jet-thrust as seemingly "negative drag". Furthermore, the wing of bird has a profile that makes the wing airfoil. As further examples, a flying a snowy owl is extremely noiseless, i.e. it has an actually-airfoil wing and body as a whole to provide for suppression of turbulences, and a bird-swift is capable of non-stop flying for a long time, measured in months and years, wherein the bird-swift, flying under its own power and wherein not-frequently waving, is capable of reaching a horizontal velocity of 47 m/sec (169 km/h). In spite of the fact, that the efficiency of net jet-thrust of the flying bird is attractively high, the phenomenon remains unused in the world industry.

Furthermore, the style of a flock of cranes flying is well-known. The style combines waving of wings, when the flying is accelerating, as well as wings gliding, when the flying is stabilized. This style prompts that: * on the one hand, there are no turbulent vortices behind the gliding wings of the flying cranes, i.e. the wings of crane are actually-airfoil, and so the previous gliding crane does not hinder but even helps to the next gliding crane in lift and in jet-thrust; and * on the other hand, there is an interference of omnidirectional waves generated by the waving wings of the cranes of flock, thus, it is self-suggested the assumption that the flying cranes use constructive interference thereby helping to each other in the waving-itself. In spite of the fact that the cranes apply the cascaded multi-stage repeating and thereby reinforcing the Coanda-jet-effect for originating both: the lift-force and the net jet-thrust during a long time, this technique remains unused in the world industry. There is, therefore, a need in the art for a method and apparatus to provide a proper analysis and optimal design of a system implementing the repeatedly reinforced Coanda-jet-effect of laminar moving fluid as well as the repeatedly reinforced constructive interference of waves in the fluid, both providing the scalable and controllable use of the acquired power in the industry.

Reference is now made to prior art Fig. 1k, a schematic illustration of a wind turbine 17.1 built-in into cylinder 17.2 having real sidewalls and open butt-ends. A widened description of Fig. 1k may be referred to the mentioned widened BACKGROUND OF THE INVENTION of AU03, which (the widened background) is not narrated herein for brevity. Instead, the inventor points out that the sub-portion 17.41 of the fluid stream enters cylinder 17.2 with a certain headway-motion velocity, indicated by U 4 1 , which is lower than the headway

Page 15 of 75 motion velocity of sub-portion 17.42, indicated by U 4 2 , which flows outside cylinder 17.2. The reason of the negative difference (U 4 1 - u 4 2 ) is explained by the drag of blades of wind turbine 17.1, namely, as the blades are subjected to impact of flow 17.41, the blades retard the flow 17.41 by the same drag according to the Newton's Third Law of motion. In such an application, the effect of flow retarding is undesired. There is, therefore, a need in the art for a method and apparatus to provide a design of an improved wind turbine where the undesired effect of flow retarding would be reduced and the desired effect of producing electric power would be boosted.

SUMMARY OF THE INVENTION

Unity and novelty of the invention

The unity and novelty of the invention are in a method providing for a use of a set of enhanced actually-airfoilwings to enforce the desired lift and jet-thrust forces originated due to flow convective self-acceleration boosted multi-stage repeatedly.

Primary basic features of the present invention

The invention is defined by the claims. One of the primary features of the present invention is a geometrical configuration of an actually-airfoilwing which is embodied as a biconvex wing comprising a convexity on each of the two opposite sides of the wing, wherein the geometrical configuration is such that, when the biconvex wing is exposed to an oncoming portion of fluid stream, a boundary layer originated adjacent to the wing surfaces has a varying cross-sectional area characterized by a cross-sectional area profile A(x) given by the equation of M-velocity expressed as: 1 y+1

A (x)- =A. y-1) (2+y(M(x))2(y-1) M( y y+1

where A,, is a constant, y is an adiabatic compressibility parameter of the portion of the fluid stream and M(x) is a gradual monotonic smooth function of x representing an M-velocity profile of the portion of the fluid stream moving within and through the boundary layer.

Principal objects

Page 16 of 75

Accordingly, it is a principal object of the present invention to overcome the limitations of existing method and apparatuses for efficient producing of useful-beneficial power from a fluid stream, wherein the useful-beneficial power is either: o power of lift-force, and/or o power of jet-thrust, and/or o electric power.

BRIEF DESCRIPTION OF THE DRAWINGS

To understand the invention and to see how it may be carried out in practice, a preferred embodiment will now be described, by way of a non-limiting example only, with reference to the accompanying drawings, in the drawings: Fig. 1b is a prior art schematic drawing of the convergent-divergent Venturi tube; Fig. 1c is a prior art schematic view of the convergent-divergent de Laval nozzle; Fig. 1d is a prior art schematic illustration graphics of gas velocity, static pressure, and temperature distributions within the de Laval convergent-divergent jet-nozzle; Fig. le is a schematic drawing of a prior art ordinary blowing ventilator; Fig. 1f is a prior art schematic drawing of a body blown by an airflow portion; Fig. 1g is a schematic drawing of a classical prior art profile of an airplane wing; Fig. 1h is a schematic drawing of considerable amounts of water-aerosols and micro-flakes-of snow, which are observed behind the high-speed aircraft's wings; Fig. 1i is a prior art schematic illustration of points of sail; Fig. 1k is a prior art schematic illustration of a wind turbine, built-in into a cylinder; Fig. 5e is a schematic illustration of a convex-concave corpus. Fig. 6a is a schematic illustration of an optimized convergent-divergent jet-nozzle, constructed according to the principles of the present invention; Fig. 6b is a graphical representation of air velocity, static pressure, and temperature distributions along an optimized convergent-divergent jet-nozzle, constructed according to the principles of the present invention; Fig. 6c is a schematic illustration of an exemplary profile of an optimized tunnel; Fig. 6d is a schematic illustration of an exemplary profile of an optimized tunnel; Fig. 6e is a schematic illustration of an exemplary profile of an optimized tunnel; Fig. 6f is a schematic illustration of an optimized inverse convergent-divergent jet-nozzle, constructed according to the principles of the present invention;

Page 17 of 75

Fig. 6g is a graphical representation of air velocity, static pressure, and temperature distributions along an optimized inverse convergent-divergent jet-nozzle, constructed according to the principles of the present invention; Fig. 6h is a schematic illustration of a two-stage convergent-divergent jet-nozzle, constructed according to the principles of the present invention; Fig. 7a shows comparative graphs of the dependencies of the nozzle extension ratio vs. the airflow M-velocity, calculated by the classical and suggested models; Fig. 7b is a schematic illustration of a compressor supplied by an optimized convergent divergent jet-nozzle, constructed according to the principles of the present invention; Fig. 7c is a schematic sectional view of a flying capsule, constructed according to the principles of the present invention; Fig. 7d is a schematic sectional view of a flying capsule, constructed according to the principles of the present invention;

Fig. 8a is a schematic illustration of an actually-airfoil wing blown by wind; Fig. 8b is a schematic illustration of a flying airfoil body; Fig. 8c is a schematic illustration of flying airfoil bodies; Fig. 8d is a schematic illustration of a two-humped airfoil profile; Fig. 9g is a schematic drawing of an improved wind-turbine, constructed according to the principles of the present invention; Fig. 9h is schematic side and front views of an improved wind-turbine; Fig. 9i is a schematic illustration of a jet-transformer; Fig. 9j is a schematic illustration of a jet-ventilator; Fig. 9k is a schematic illustration of a jet-propeller; Fig. 9L is a schematic illustration of a multi-module jet-ventilator; and Fig. 9m is a schematic illustration of cascaded multi-module jet-propellers.

All the above and other characteristics and advantages of the invention will be further understood through the following illustrative and non-limitative description of preferred embodiments thereof.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The principles and operation of a method and an apparatus according to the present invention may be better understood with reference to the drawings and the accompanying

Page 18 of 75 description, it being understood that these drawings are given for illustrative purposes only and are not meant to be limiting. A widened DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS of the invention and details of the embodiments may be referred to the mentioned AU03, which (the widened DETAILED

DESCRIPTION OF PREFERRED EMBODIMENTS) i not narrated herein completely for brevity. Instead, the inventor points out again that the jet-effect occurring in moving fluid, can be manifested as: " the Venturi effect and the de Laval jet-effect of either: o convective self-acceleration accompanied by self-cooling, or o self-retarding accompanying by self-warming, when the fluid is subjected to a headway motion; and * the Coanda-effect resulting in both: o lift-force acting on a profiled wing, and o thrust-force acting on a sail oriented as so-called "B-Point of Sail";

when a convexly-curved surface is tangentially blown by a headwind; wherein, again, these are manifestations of the jet-effect defined as an effect of transformation of the heat power into the kinetic power of fluid motion as a whole and, vice-versa, an effect of transformation of the kinetic power of fluid motion as a whole into the heat power. Hereinbelow, a set of sub-paragraphs of the widened EDDE SCRIPTION OF PREFERRED EMBODIMENTS of

AU03, which are related to the present divisional application directly, are repeated and amended as follows.

Jet-effect Embodiments

Fluid-Repellent Structured Surface Fig. 5e is a schematic illustration of a transparent-like body having convex-concave corpus 512. Convex-concave corpus 512 has a rounded airfoil outer convex side, and concave side 514, both contacting with ambient fluid 517. A multiplicity of holes [three shown] 513.1, 513.2, and 513.3 links together both: outside portions 517.1 of the ambient fluid 517 and the ambient fluid 517's portions 517.2 contacting with concave side 514. The concavity of side 514 has a parabolic profile with focal point 516. Focal point 516 comprises a heating element [not shown here], powered at the expense of either burned fuel or electricity. Thereby, hotter focal point 516 becomes omniphobic, repelling nearby ambient fluid portions 517.2 by omniphobic-repulsive van der Waals forces. The ambient fluid molecules, subjected to the omniphobic-repulsive van der Waals forces action, acquire a prevalent component of motion directed radially from the heating

Page 19 of 75 element at the focal point 516 toward concave parabolic side 514. When concave parabolic side 514 reflects the prevalent radial component of the molecular motion, the molecular prevalent motion component becomes collimated collinearly with sagittal axis 519, thereby forming outflowing jetstream 518. The headway motion of outflowing jetstream 518 provides for a jet thrust. Furthermore, preferably, concave side 514 has outer layer 515 contacting with ambient fluid 517.2. Layer 515 is either heated and/or implemented from a fluid-repellent material. The parabolic profile 514 of fluid-repellent outer layer 515, further acting on the fluid molecules by phobic-repulsive van der Waals forces, partially converts the Brownian random component of the fluid molecular motion into a motion of the molecules in a prevalent direction toward sagittal axis 519, thereby, focusing [i.e. converging] and more accelerating outflowing jetstream 518, in addition to the aforementioned motion collimation. In particular, it will be evident to a person skilled in the art that the body having convex concave corpus 512, supplied with a heating element arranged at focal point 516, when submerged in water 517, operates as a motionless hydrophobic-engine or hydrophobic jet-gear or heating-jet engine (having a heating compressor), providing a jet-thrust, wherein one can control the jet-thrust by the heating intensity. A net-efficiency of such a hydrophobic-engine, having a configured convex-concave corpus 512, is defined by the ratio of power consumed by the heating element to the useful kinetic power of outflowing jetstream 518 headway motion. The net-efficiency may come close to 100% if a dominant headway motion of outflowing jetstream 518 is obtained by convex-concave corpus 512 shape optimization. Moreover, water portions 517.2, yet to be accumulated into outflowing jetstream 518, are also subjected to a hydrophobic jet-effect, originated by parabolic fluid-repellent layer 515, resulting in an increase of the outflowing jetstream 518 headway motion kinetic power at the expense of the water warms and thereby, in principle, allowing for the net-efficiency to become even higher than 100%. Furthermore, outflowing jetstream 518 can be further subjected to convergence by a convergent funnel [not shown here], and thereby, become further accelerated and cooled. Thus, again, the net efficiency can exceed 100% at the expense of the water warmth.

Convergent-Divergent Jet-Nozzle Fig. 6a is a schematic illustration of a convergent-divergent jet-nozzle 610, pipe-section in a sagittal plane. Convergent-divergent jet-nozzle 610 is applied to accelerate a compressed and hot air stream, or more generally, a laminarly flowing compressed and hot compressible expandable fluid 611. Convergent-divergent jet-nozzle 610 has the inner tunnel opposite walls shaped, for simplicity, axis-symmetrically around an imaginary sagittal x-axis 615, as a

Page 20 of 75 convergent funnel 612 having open inlet, narrow throat 613 comprising point 618 of the narrowest cross-section, and divergent exhaust tailpipe 614 having open outlet, constructed according to an exemplary embodiment of the present invention providing the improved de Laval jet-effect. For simplicity, compressed and hot fluid stream 611 has a uniform front at the inlet. For the purposes of the present patent application, the de Laval effect should be understood in a wide sense as comprising both: the de Laval jet-effect, defined as an effect of flow extra acceleration, and the de Laval retarding-effect, defined as an effect of flow extra-slowing. Thus, the de Laval jet-effect is a particular case of the de Laval effect. The specifically shaped tunnel, comprising the three major successive constituents: convergent funnel 612 having an open inlet, narrow throat 613, and divergent exhaust tailpipe 614 having an open outlet, has no real separation features between the constituents. For the purpose of the present patent application, narrow throat 613 is specified as a fragment of the inner tunnel located between imaginary inlet 6131 and outlet 6132. For the purposes of the present patent application, the term "principal interval" of the x-axis is introduced as corresponding to the interval occupied by the specifically shaped tunnel, called an adapted convergent-divergent tunnel, i.e. at least comprising narrow throat 613. Fluid stream 611 is subjected to the Coanda-effect, observed as aligning of fluid stream 611 with the curvature of specifically shaped walls of the inner tunnel. The Coanda-effect is defined by a non-zero partial pressure-c Pc arising when the shape of a fluid portion is varying as the fluid portion moves along the shaped inner tunnel of convergent-divergent jet-nozzle 610. Looking ahead, point out that the specific shape of tunnel, constructed according to the principles of the present invention, prevents disturbances of the fluid motion. This stipulation corresponds to the case when the cumulative-inner-static-pressure P of streaming fluid 611 is varying gradually and the velocity of streaming fluid 611 is varying linearly as the fluid 611 moves within the shaped tunnel along imaginary sagittal x-axis 615. For simplicity, imaginary sagittal x-axis 615 is horizontal, i.e. moving fluid 611 does not change its effective height above the Earth's ocean surface level. Omitting algebraic manipulations described in the widened DETAILED DESCRIPTION OF

PREFERRED EMBODIMENTS of AU03, one formulates a differential equation interrelating a relative change in the flowing fluid cross-sectional area and a relative change in the flowing fluid headway velocity as follows:

= (- M2 _ Eq. (6.8), A \y-1 21u

Page 21 of 75 where A is the flowing fluid cross-sectional area, U is the flowing fluid headway velocity, and

M is the flowing fluid headway velocity measured in Mach numbers. Equation (6.8) comprises the term M 2y/(y - 1) characterizing the effect of the gas compressibility and expandability. In particular, equation (6.8) says that: if the horizontally moving

flow is relatively slow (i.e. M < (y- 1)/y), then the narrowing of the flow cross-section

(i.e. negative dA) corresponds to acceleration of the flow (i.e. positive du); and if the flow is

relatively fast (i.e. M > (y- 1)/y),then just the widening of the flow cross-section (i.e.

positive dA) corresponds to acceleration of the flow (i.e. positive du). This means, in particular, that at so-called "critical condition" point 680 defined for the narrowest throat of the de Laval nozzle, the flow specific M-velocity equals

M, = [(y- )/y Eq. (6.9). For the purposes of the present patent application, here and further, the lower index "" is applied to an M-velocity, geometrical and thermodynamic parameters in a critical condition point. For air as a diatomic molecular gas, the generalized adiabatic compressibility parameter y

equals y = 7/5 = 1.4, and M, = f (y- 1)/y ~~ 0.5345 Mach. For a gas composed

of multi-atomic molecules, the generalized adiabatic compressibility parameter y is closer to 1, and so the de Laval jet-effect is expected at lower M-velocities. In a particular case of an almost incompressible liquid, the generalized adiabatic compressibility parameter y is extremely great and equation (6.8) comes close to an approximated equation, for which M, = 1 Mach. In many actual and imaginary applications, the phenomenon of shock sound-wave emission, that arises at M-velocities near 1 Mach, is undesirable or unacceptable. Therefore, the conclusion of the resulting equation (6.8), that the de Laval jet-effect begins from the velocity being substantially lower than the speed of sound, becomes important to provide for utilization of this useful effect avoiding the phenomenon of shock sound-wave emission. Now consider the case where a compressed and/or heated gas, defined by the stagnation parameters: pressure PO, density po, and temperature To, is launching into a convergent divergent jet-nozzle. Let the stagnation pressure PO, temperature To, and density po be much

high to provide the specific M-velocity M, = (y - 1)/y at the narrowest cross-section of the throat. The gas characteristic heat portion per unit mass, expressed in terms of the gas temperature, is: Q = RT. Substitution of this expression into (6.1) gives:

Page 22 of 75

To = T+_=T (1 + M2 Y Eq. (6.10)

where To is the stagnation temperature; T is the gas portion current temperature; Usound=

yPv= RT, and M = U/Usound = u/yRT. Though the normalized value M

depends on temperature, one retains the form of equation (6.10) expressed via M, because the value of M = 1 Mach has the physical sense of the shock sound-wave emission condition. Taking into account relations between thermodynamic parameters in an adiabatic process, equation (6.10) can be rewritten as: y-1 - -- +YM2 Eq. (6.11) T P0 p- I 2

where P and p are the current static pressure and density correspondingly. It is important to introduce the ratio A/A, , where A, is the narrowest cross-sectional area of the nozzle throat, i.e. is the critical condition area corresponding to the critical condition point, and A is the current cross-sectional area. It follows from (6.2) that

A _P* Eq. (6.12) A* P u

Taking into account (6.11) and that the specific M-velocity equalsM= (y- 1)/y, the ratio A/A, can be expressed viaM-velocity: 1 y+1 A (Y-1 2+yM 2 2(y-1) Eq.(6.13) A* M y y+1

Equation (6.13) derived from the equation of continuity for an adiabatic process is the equation of M-velocity, bonding the generalized adiabatic compressibility parameter y, M velocity M, and ratio A/A, of the molecular fluid, fast and laminarly flowing through the de Laval nozzle, oriented horizontally. Equation (6.13), as one of the primary teachings of the present invention, says that to accelerate a warmed and compressed air portion up to 1 Mach, one must apply a convergent-divergent jet-nozzle and provide the nozzle inner tunnel divergent part expansion up to the ratio of A/A ~~ 1.5197. Considering an essentialM-velocity range, specified as an M-velocity range comprising M-velocities corresponding to the flow passing through the principal interval, equation (6.13) can be applied to make an ideal shape of the nozzle to provide for a laminar motion and thereby optimize the acceleration of the streaming fluid at least in the essential M -velocity range, i.e. at least within the specifically shaped tunnel. In

Page 23 of 75 contrast to the prior art concept of rapid expansion and acceleration of the gas, described hereinbefore with referenceto Figs.1cand 1d, that causes the arising of undesired Machwaves, the substantially gradual (or linear) increase of the M-velocity downstream along the gas motion accompanied by the interrelated gradual (or linear) change of fluid thermodynamic parameters, is a criterion of the nozzle inner tunnel shape optimization preventing turbulences and, in particular, providing suppression of the undesired Mach waves, according to an exemplary embodiment of the present invention. Further, for the purposes of the present patent application, the use of the equation of M velocity (6.13) assumes an inherent condition of a gradual change of the fluid thermodynamic parameters. So, axis-symmetrical convergent-divergent jet-nozzle 610, comprising specifically shaped convergent funnel 612 having an open inlet, narrow throat 613, and divergent exhaust tailpipe 614 having an open outlet, is designed according to equation (6.13), where the value M corresponds to x-coordinates along imaginary x-axis 615 as a smooth function M(x). In particular, a linearfunction M(x) was chosen as a desired for M(x), i.e.

M(x) = M(x) = M, -+a(x - x), where x is the x-coordinate atx-axis 615, and am is a positive constant defining a scale factor and having a sense of constant gradient of M

velocity spatial distribution, i.e. am = aM(x)/ax. Such a relationship enables a substantially smoothed increase of M-velocity as the fluid moves through the specifically shaped tunnel of convergent-divergent jet-nozzle 610. The linear increase of M-velocity prevents substantially the arising of streaming fluid 611 motion disturbances, accompanied by shock waves. In contrast to a jump-like sharp slope, the gradual change of the M-velocity and so of all the interrelated thermodynamic parameters is one of the primary features of the de Laval jet-effect improvement. For the purposes of the present patent application, the term "de Laval enhanced jet-effect" or briefly: "enhanced jet-effect" is introduced as relating to the modified de Laval jet-effect, occurring in a convergent-divergent tunnel having a specifically revised shape according to the principles of the present invention, such that the modified de Laval jet-effect becomes improved by smoothing of the fluid thermodynamic parameters spatial distribution, providing the following beneficial features: U smoothing of the flowing fluid M-velocity, providing suppression of the undesired flow disturbances accompanied by shock waves; 0 smoothing of the flowing fluid static pressure, providing suppression of the undesired Mach waves and, thereby, suppression of nearby body vibrations;

Page 24 of 75

" smoothing of the flowing fluid temperature, providing suppression of adjacent surface tensions; and " smoothing of the flowing fluid density, providing suppression of shock waves. Also, the term "de Laval-like jet-effect" should be understood in a wider, sense including a case when an enhanced jet-effect occurs in an open space imaginarily bordered by the flow streamlines, wherein the imaginary borders constitute a convergent-divergent shape, i.e. similar to a de Laval nozzle. If the exhaust tailpipe 614's outlet area is Ae, the ratio Ae/A, defines the nozzle expansion ratio that can be optimized in accordance with the estimations described hereinbelow with reference to Figs. 7a, 7b, 7c. Thereby, a convergent-divergentjet-nozzle, constructed applying equation (6.13) according to an exemplary embodiment of the present invention, allows a use of the de Laval enhanced jet effect to accelerate incoming compressed and hot airstream 611 moving with low M-velocities to obtain outflowing accelerated and cooled jetstream 616, reaching high M-velocities [i.e. M

velocities, higher than the specific M-velocityM= (y- 1)/y , in particular, high subsonic velocities.

Fig. 6b, in conjunction with Fig. 6a, is a schematic graphic illustration of the distribution of the flowing fluid 611's three parameters: velocity 620, static pressure 630, and temperature 640 along the length of nozzle 610, constructed according to the principles of a preferred embodiment of the present invention. The narrowest cross-section of the throat 613 (Fig. 6a) provides the "critical condition" point 618. Compressed and hot fluid 611 flows through throat 613, where the

velocity picks up 621 such that M-velocity reaches the specific M-velocity M, = (y- 1)/y 623 at the critical condition point 618. Ahead of the critical condition point 618, the pressure and temperature fall, correspondingly 631 and 641. Hot flowing fluid 611 crosses the critical condition point 618 and enters the widening stage of throat 613 and further divergent exhaust tailpipe 614 having an open outlet. Flowing fluid 611 expands there, and this expansion is optimized such that the extra-increase of M-velocity 622 is substantially smoothed; and the pressure and temperature extra-decrease, 632 and 642, correspondingly, are substantially smoothed as well, in contrast to that at the critical condition point 180 with reference to the classic prior art rocket nozzle 100 of Figs. 1c, 1d. The smoothed change of static pressure 630 provides suppression of unwanted Mach waves. In practice, the suppression of Mach waves provides suppression of undesired vibrations that, in particular, especially important for fast accelerating vehicles.

Page 25 of 75

In view of the foregoing description referring to Fig. 6a, it will be evident to a person skilled in the art that one can use different criteria of gradualness of M(x) for different preferred optimizations of the convergent-divergent shape of a tunnel. Namely, the conditions, providing laminarity of the airstream motion, are: U if suppression of Mach waves and of body vibrations are the most preferable, then M(x) should be given as the function M(x) =

2 t[Po/P(x)]_1 - 11 /y, where P(x) is a linear function of the static

pressure vs. x-coordinate: P(x) = P, + ap (x - x), P, is the static pressure

of the flowing fluid at the critical condition point x,, and ap = aP(x)/ax is a constant gradient of the static pressure distributed along the x-axis within a specially shaped tunnel; and Fig. 6c is a schematic illustration of an exemplary profile of an optimized specifically shaped tunnel providing a linear change of the flowing fluid static pressure corresponding to the essential M-velocity range comprising M velocities from 0.02 up to 2 Mach; U if the suppression of temperature jumps is the most preferable, then M(x) should

be given as the function M(x) = j2{[To/T(x)] - 1}/y , where T(x) is a

linear function of the fluid temperature vs. x-coordinate: T(x) = T, a(x - + x, T, is the temperature of the flowing fluid atthe critical condition point

x,, and aT = aT(x)/ax is a constant gradient of the fluid temperature distributed along the x-axis within a specially shaped tunnel; and Fig. 6d is a schematic illustration of an exemplary profile of an optimized specifically shaped tunnel providing a linear change of the flowing fluid temperature corresponding to the essential M-velocity range comprising M-velocities from 0.02 up to 2 Mach; and U if a trade-off between suppressions of Mach waves and temperature jumps is preferable, then M(x) should be given as the function M(x)=

2{[pO/p(x)](-- - 1}/y, where P(x) is a linear function of the fluid density vs. x-coordinate: P(x) = p, + ap (x - x,) , p, is the density of said

flowing fluid at the critical condition point x,, and ap = ap(x)/ax is a constant gradient of the fluid density distributed along the x-axis within a specially shaped tunnel; and Fig. 6e is a schematic illustration of an exemplary profile of an optimized

Page 26 of 75 specifically shaped tunnel providing a linear change of the flowing fluid density corresponding to the essential M-velocity range comprising M-velocities from 0.02 up to 2 Mach. Further, for the purposes of the present invention, the term "airfoil" or "actually-airfoil" should be understood as related to a wall shape and as specifying a convergent-divergent shape of a flow portion's streamlines aligned to the airfoil wall, wherein, in contrast to a seemingly-airfoil shape, the convergent-divergent shape calls for the differential equation of motion (6.8), equation of M-velocity (6.13), and at least one of the aforementioned conditions for the function M(x), thereby providing laminarity of the flow portion motion. Furthermore, it will be evident to a person skilled in the art that one can optimize the specifically shaped tunnel of convergent-divergent jet-nozzle 610 providing such a conformity of the cross-sectional area of the open inlet with the M-velocity of flowing fluid crossing the open inlet, that the flowing fluid M-velocity is substantially smooth at the entering the open inlet. Moreover, one can control the cross-sectional area of the open inlet, according to the equation of M-velocity, providing conformity of the open inlet cross-sectional area with the variable M velocity of the entering flowing fluid afore-and-nearby the open inlet. This may become important, for example, to suppress vibrations of a fast accelerating vehicle. Moreover, it will be evident to a person skilled in the art that, as soon as the de Laval effect occurs in an adiabatic process, the condition of fluid stream 611 motion through the narrowest cross-section of throat 613 at critical condition point 618 with the specific M-velocity M,=

(y- 1)/y 623, accompanied by thermodynamic parameters: static pressure P', temperature T,, and fluid density ps, interrelates with a condition of fluid stream 611 motion with an M-velocity and accompanied thermodynamic parameters static pressure P, temperature T, and fluid density p at any cross-section of convergent-divergent jet-nozzle 610's inner tunnel, wherein the conditions interrelation depends on the tunnel geometry only. In other words, if a hypothetical ideal propeller pushing a hypothetic inviscid fluid provides the inviscid fluid laminar

flow with the specific M-velocity M, = (y - 1)/y at the critical condition point of a de Laval nozzle, then the de Laval effect becomes triggered in the de Laval nozzle of a fanjet engine, wherein the thermodynamic parameters of the moving inviscid fluid portions are interrelated as in an adiabatic process. In this case, the hypothetical propeller triggering the de Laval effect expends power for the launching of accompanying shock and/or Mach waves only. In view of the foregoing description referring to Fig. 6a, it will be evident to a person skilled in the art that: Page 27 of 75

" in a more general case, when imaginary sagittal axis 615 is oriented at least partially in the vertical direction in the Earth's gravitational field, the equation of M-velocity should be corrected becoming different from equation (6.13) by a component depending on the gravitational acceleration g, namely: y+1

A M 1+ 2gAh 2-) - = -- Eq. (6.14), A, M 1+ M

where Ah is a change of the flow effective height with respect to the critical condition point. It will be further evident to a person skilled in the art that, when the considered temperatures and M-velocities are sufficiently high to provide for the conditions: gAhIRT « 1 and gAhIRT« yM2/2 to be satisfied, a use of the equation of M-velocity in the form of equation (6.13) becomes justified; * taking into account molecular interactions for flowing liquid or plasma, for which 6 changes of the partial deep-stagnation pressure-a Pa become at least noticeably

distributed in space, the generalized adiabatic compressibility parameter y in the equation of M-velocity (6.13) is not a constant, but varies with the changes of the partial deep-stagnation pressure-a 6 Pa, in conformance with equations (5.8b) and (5.8c); * if the flowing molecular fluid is an ionized gas, i.e. plasma, controlled by an external magnetic field, then the specifically shaped walls of the tunnel can be imaginary, formed by streamlines of the flowing plasma subjected to and controlled by an action of the magnetic field; and * according to the kinetic theory of matter, a substantial incompressible molecular fluid, characterized by almost not changeable thermodynamic parameters: density, temperature, and inner-static-pressure and characterized by the infinitely great generalized adiabatic compressibility parameter y - oo, cannot change its cross sectional area substantially, and so, according to equation of M-velocity (6.13), cannot flow laminarly through a horizontal tunnel having a varying cross-sectional area; and furthermore, strictly speaking, a hypothetical absolutely-incompressible molecular fluid cannot flow through a converging tunnel at all. This is a theoretically important teaching of the present invention.

Page 28 of 75

De Laval Retarding-Effect Fig. 6f is a schematic illustration of an inverse convergent-divergent jet-nozzle 650, pipe section in a sagittal plane. Convergent-divergent jet-nozzle 650, constructed according to the principles of a preferred embodiment of the present invention, as inverse de Laval nozzle, applied to retard a fast fluid-flow 651, streaming with a high M-velocity M 6 5 1 , higher than the specific

M-velocity M, = (y- 1)/y. Convergent-divergentjet-nozzle 650 has the sectional shape

mirror-symmetrically congruent to the sectional shape of convergent-divergent jet-nozzle 610, shown in Fig. 6a, and oriented to oncoming fluid-flow 651 in the back direction. Namely, the shape is axis-symmetrical around an imaginary sagittal axis 655; convergent funnel 652 having open inlet is as inverse divergent exhaust tailpipe 614; narrow throat 653 comprises point 658 of the narrowest cross-section; and divergent exhaust tailpipe 654 is as inverse convergent funnel 612. Convergent funnel 652, narrow throat 653, and divergent exhaust tailpipe 654 have not real separation features between them. For the purpose of the present patent application narrow throat 653 is specified as a fragment of the inner tunnel having imaginary inlet 6531 and outlet 6532, wherein the term "principal interval" of x-axis has a sense as corresponding to the interval occupied by the specifically shaped tunnel, i.e. at least comprising narrow throat 653.

Fig. 6g, in conjunction with Fig. 6f, is a schematic graphic illustration of the distribution of the fluid 651's three parameters: velocity 660, static pressure 670, and temperature 680 along the length of nozzle 650 calculated according to equations (6.11) and (6.13). The narrowest cross-section of the throat 653 (Fig. 6f) provides the "critical condition" point 658, triggering the inverse de Laval jet-effect, according to equation (6.13), that is observed as an effect of flow slowing, when the flow moves along convergent funnel 652, and further slowing, when the flow moves through the divergent stage of convergent-divergent jet-nozzle 650 downstream-behind the critical condition point 658. For the purposes of the present patent application, the term "de Laval retarding-effect" is introduced as relating to the inverse de Laval jet-effect. Fast fluid-flow 651 moves along convergent funnel 652, where, ahead of the critical condition point 658 of narrow throat 653, the velocity falls 661, and the pressure and temperature pick up, correspondingly 671 and 681. The velocity falls 661 such that M-velocity M 6 6 3 ,

corresponding to marker 663, reaches the specific M-velocity M, = (y- 1)/y at the

critical condition point 658. Fluid-flow 651 exits throat 653 and enters the widening divergent exhaust tailpipe 654, where fluid-flow 651 is subjected to increase of cross-sectional area, and this action is optimized such that the decrease of M-velocity 662 is accompanied by a

Page 29 of 75 substantially smoothed increase of the pressure and temperature, 672 and 682, correspondingly. Slow hot and compressed fluid at position 656 outflows from wide exhaust tailpipe 654. Again, the smoothed change of static pressure 670 provides suppression of unwanted Mach waves. In practice, the suppression of Mach waves provides suppression of undesired vibrations that, in particular, especially important for a fast decelerating flying vehicle. In view of the foregoing description referring to Figs. 6f and 6g, it will be evident to a person skilled in the art that, on the one hand, to trigger the de Laval retarding-effect the high M-velocity

M 6 5 1 must be low sufficient to reach the specific M-velocity M, while slowing in convergent funnel 652 and the convergent stage of throat 653. On the other hand, taking into account that, in practice, for the case wherein fluid-flow 651 is an airflow, the M-velocity is distributed in the direction normal to an adjacent surface such that decreases almost down to zero at the surfaces of convergent-divergent jet-nozzle 650's walls. Thus, a certain portion of fast fluid-flow 651 at the critical condition point 658 moves with the effective M-velocity equal to the specific M-velocity M, and is subjected to a convergent-divergent reshaping in throat 653, thereby, the conditions

for the de Laval retarding-effect triggering is satisfied for any high M-velocity M 6 5 1 , higher than

the specific M-velocity M,. In view of the foregoing description referring to Figs. 6a, 6b, 6f and 6g and derivation of equations (6.8) and (6.9), the de Laval jet-effect and the de Laval retarding-effect, both observed in the case of a converging flow, are specified as the following. The de Laval jet-effect is specified as an effect of a convergent flow portion convective acceleration, occurring, when the convergent flow portion moves with M-velocities lower than the specific M-velocity upstream-afore the critical condition point, reaches the specific M-velocity at the critical condition point, and moves with M velocities higher than the specific M-velocity downstream-behind the critical condition point; and the de Laval retarding-effect is specified as an effect of a convergent flow portion warming and slowing, occurring, when the convergent flow portion moves with M-velocities higher than the specific M-velocity upstream-afore the critical condition point, reaches the specific M-velocity at the critical condition point, and moves with M-velocities lower than the specific M-velocity downstream-behind the critical condition point. For the purposes of the present patent application, the terms "Venturi M-velocity", "de Laval M-velocity", "de Laval low M-velocity", and "de Laval high M-velocity" should be understood as the following:

Page 30 of 75

* a Venturi M-velocity is defined as an M-velocity, lower than the specific M-velocity M, and low sufficient to cross a narrow throat with said M-velocity, lower than the specific M velocity M,; " a de Laval low M-velocity is defined as an M-velocity lower than the specific M-velocity M, and high sufficient to reach the specific M-velocity M, at the critical condition point

x,;

* a de Laval high M-velocity is defined as an M-velocity higher than the specific M-velocity M, and low sufficient to reach the specific M-velocity M, at the critical condition point

x,; and U a de Laval M-velocity is at least one of the de Laval low M-velocity and the de Laval high M-velocity. In view of the foregoing description referring to Figs. 6f and 6g, it will be evident to a person skilled in the art that one can optimize the specifically shaped tunnel of convergent-divergent jet nozzle 650 providing such a conformity of the cross-sectional area of the open inlet with the de Laval high M-velocity of flowing fluid crossing the open inlet, that the flowing fluid M-velocity is substantially smooth at the entering the open inlet. Furthermore, one can control the cross sectional area of the open inlet, according to the equation of M-velocity, providing conformity of the open inlet cross-sectional area with the variable M-velocity of the entering flowing fluid. This may become important, for example, to suppress vibrations of a fast slowing vehicle.

Two-Stage Convergent-Divergent Jet-Nozzle Fig. 6h is a schematic illustration of a two-stage convergent-divergent jet-nozzle 690 exposed to an incoming fast fluid-flow 691, streaming with a high M-velocity M 6 9 1 , higher than

the specific M-velocity M, = (y- 1)/y, i.e. with a de Laval high M-velocity. Two-stage convergent-divergent jet-nozzle 690, constructed according to the principles of a preferred embodiment of the present invention, has an inner tunnel comprising the first and second convergent-divergent stages, separated by widened reservoir 694. The first convergent divergent stage performs the first-stage convergent inlet-funnel 692 gradually turning into the first-stage narrow convergent-divergent throat 693 having a local narrowest cross-section providing the first critical condition point 6981 and having an inverse-funnel shaped pipe leading to widened reservoir 694. The second convergent-divergent stage comprises the second-stage

Page 31 of 75 narrow throat 696, having a local narrowest cross-section providing the second critical condition point 6982, and the second-stage divergent exhaust tailpipe 697. Incoming fast fluid-flow 691 is gradually slowing down, becoming warmer and more thickened and compressed as moving along the first convergent-divergent stage to widened reservoir 694 as described hereinbefore with reference to Figs. 6f and 6g. Slow, hot and compressed fluid 695 further movies through the second convergent-divergent stage. The fluid flow is accelerating as moving through throat 696, where exceeds the specific M-velocity M,=

(y- 1)/y downstream-behind the second critical condition point 6982. Jetstream 699 outflowing through divergent exhaust tailpipe 697, is faster and colder than slow, hot and compressed fluid 695, yet to be entered into the second convergent-divergent stage, as described hereinbefore tracing after incoming compressed and hot airstream 611 with reference to Figs. 6a and 6b. Fast outflowing jetstream 699 has a cross-section wider than incoming fast fluid-flow 691 at the input of convergent inlet-funnel 692. So, the M-velocity M 6 9 9 of fast

outflowing jetstream 699 is higher than the M-velocity M 6 9 1 of fast fluid-flow 691, according to equation (6.13). Thereby, two-stage convergent-divergent jet-nozzle 690 operates as ajet-booster based on the de Laval enhanced jet-effect launching outflowing jetstream 699, which is faster than fast fluid-flow 691 incoming with the de Laval high M-velocity M 6 9 1 , i.e. higher than the specific M

velocityM= (y- 1)/y. This is one more teaching of the present invention.

Optimal Implementation of Convergent-Divergent Jet-Nozzle Fig. 7a shows comparative graphs 700 for the dependencies of the nozzle tunnel extension ratio vs. the airflow M-velocity, calculated by the classical and suggested models, namely, curves 703 and 704 correspondingly; wherein the vertical axis 701 is the ratio A/A, , and the horizontal axis 702 is the airflow M-velocity measured in temperature-dependent Mach numbers. The dashed curve 703 is the convergent-divergent cross-sectional area ratio A/A, profile vs. the airflow M-velocity, calculated using equation (1) derived from the Euler equations of fluid motion. The solid curve 704 is the convergent-divergent cross-sectional area ratio A/A, profile vs. the airflow M-velocity, calculated using the suggested equation (6.13) derived from the generalized equations of fluid motion. The critical condition point 708 corresponds to the specific M-velocity

M, = F(y- 1)/y ~ 0.5345. Comparative graphs 700 show that one needs in a

Page 32 of 75 substantially extra-widened nozzle tunnel 704 to reach the airflowM-velocities substantially higher than 1 Mach. Therefore, a convergent-divergent jet-nozzle, constructed according to an exemplary embodiment of the present invention, allows increased efficiency of the jet-effect for use at high subsonic, transonic, supersonic, and hypersonic velocities that can be applied to rocket nozzle design. Taking into account relation (6.11), one can derive equations bonding the exhaust-nozzle outlet M-velocity Me with the ratios PO/Pe and TO/Te, where Pe and Te are correspondingly the static pressure and temperature at the exhaust-nozzle tunnel outlet: y- 1 Me 2 (P -1 Eq. (7.1a)

Y P- 2 +yM l-1 Eq. (7.1b)

To (2+yMe'

P- (2Y Y1Eq. (7.1d)

Pe 2

In contrast to the classical theory, saying that both: the de Laval jet-effect and the velocity of sound are reachable when the ratio PO/Pe is of 1.893, equation (7.1b) shows that, on the one hand, to obtain the de Laval jet-effect [i.e. condition Me > M] for air using a nozzle tunnel having an optimal convergent-divergent shape, one must provide the ratio Po/P, at least of 1.893, and, on the other hand, to accelerate an air portion up to the velocity of sound [i.e. Me = 1], one must provide the ratio PO/Pe at least of 6.406. Equation (7.1c) says that, on the one hand, to obtain the de Laval jet-effect for air utilizing a nozzle tunnel having an optimal convergent-divergent shape, one must provide the ratio TO /T, at least of 1.2; and, on the other hand, to accelerate an air portion up to the velocity of sound, one must provide the ratio To/Te at least of 1.7. So, the principle condition either 1.893 < Po/Pe < 6.406 or/and 1.2 < To/Te < 1.7 may provide the de Laval jet-effect occurring without the phenomenon of shock sound-wave emission that is one of the primary principles of the present invention.

Page 33 of 75

Thus, a convergent-divergent jet-nozzle tunnel, constructed according to an exemplary embodiment of the present invention and exploited in accordance with the principle conditions, allows an optimal implementation and efficient use of an enhanced jet-effect at de Laval M velocities.

Wing as a Convergent-Divergent Jet-Nozzle Fig. 8a is a schematic visualization 800 of an oncoming wind portion 820, without loss of generality, moving horizontally and flowing around actually-airfoil biconvex wing 810. Oncoming wind portion 820 comprises airflow sub-portions 821, 822, 823, and 824 flowing around actually airfoil biconvex wing 810, having a side-view sectional profile, constructed according to the principles of the present invention. The side-view sectional profile determines a sagittal axis 820.0. The upper side of actually-airfoil biconvex wing 810 comprises: (a) a forward part meeting upper sub-portion 822 having imaginary cross-section 831; (b) a withers 810a defined as the highest point on the upper side of the airfoil profile convexity, where sliding sub-portion 822 has imaginary narrowed cross-section 832, and (c) a rearward part, attracting and, thereby, redirecting the mass-center of the upper sliding sub-portion 822 backward-downward, where sliding sub-portion 822 has imaginary widened cross-section 833. The lower side of the actually-airfoil biconvex wing 810 comprises a convexity 81Ob. The upper and lower sides of the actually-airfoil biconvex wing 810 join together forming a sharp trailing end 810c. When airflow sub-portions 821, 822, 823, and 824 are flowing around actually-airfoil wing 810, the streamlines [not shown here] of sub-portions 822 and 823, flowing near actually-airfoil biconvex wing 810, are curving in alignment with the airfoil-profile, the streamlines [not shown here] of portions 821 and 824, flowing farther from actually-airfoil biconvex wing 810, keep substantially straight trajectories aligned with imaginary horizontal lines 811 and 812 (collinear with the sagittal axis 820.0) correspondingly above and under actually-airfoil wing 810. Actually airfoil biconvex wing 810's surface material properties, porosity, and structure are elaborated according to the principles of the present invention such that air sub-portions 822 and 823 are subjected to the Coanda-effect, defined by the partial pressure-c 6Pc, rather than to the skin friction resistance, occurring in an imaginary boundary layer and being quantified by the difference (aw - a - aa).

Page 34 of 75

Imaginary lines 811 and 812 can be considered as imaginary walls, thereby, together with the airfoil-profile forming imaginary nozzles. The upper imaginary nozzle comprises imaginary cross-sections 831, 832, and 833, and the lower imaginary nozzle comprises imaginary cross sections 834 and 835. Cross-section 831 is wider than cross-section 832 and cross-section 832 is narrower than cross-section 833, thereby, the upper imaginary nozzle has a convergent divergent shape and sliding sub-portion 822 represents a convergent-divergent jetstream while flowing through cross-sections 831, 832, and 833. Cross-section 834 is wider than cross-section 835, so the lower imaginary nozzle has a converging shape. The orientation of the sharp trailing end 810c collinear with the sagittal axis 820.0 predetermines the direction of motion tendency of the outflowing sub-portions 822 and 823, which are going off from the sharp trailing end and joining downstream behind the cross-sections 833 and 835, correspondingly. For the purposes of the present invention, an angle between the sagittal axis 820.0 collinear with the direction of motion tendency of the lower outflowing sub portion 823 and the horizontal direction defines an angle of attack (called also an attack angle). The definition of the attack angle is in conformance with the definition of the attack angle specified hereinabove in the subparagraph "Airfoil Wing (definition of attack angle)" of the BACKGROUND OF THE INVENTION for a classic wing associated with a fuselage of airplane. Here is the zero attack angle in the shown schematic visualization 800. The zero attack angle provides for minimized impact by the oncoming flow and for a generation of the lift-force due to the Coanda effect only or at least dominantly. Consider a case, when actually-airfoil biconvex wing 810 flies with a de Laval low M-velocity

M 8 10 that is lower than the specific M-velocity M, = y- 1)/y ~~ 0.5345 Mach ~ 664 km/h, but such that sliding sub-portion 822, moving through the upper imaginary nozzle, reaches the specific M-velocity M, when passes through the narrowest cross-section 832. So, the de Laval-like jet-effect arising is expected above actually-airfoil wing 810, i.e. within the upper imaginary convergent-divergentjet-nozzle. This is accompanied by the static pressure decrease and extra-decrease, as described hereinabove with the reference to Fig. 6b, and thereby results in the lift-effect, becoming stronger. In frames of the aerodynamics, one estimates the narrowest cross-section 832 linear size, i.e. thickness of a so-called "boundary layer", normalized to a so called "characteristic size" of the considered wing, as proportional to so-called Reynolds Number. As well, the thickness of boundary layer can be specified experimentally for a kind of body corpuses. In view of the foregoing description referring to Fig. 6a and Fig. 8a, it will be evident to a person skilled in the art that, basing on the defined narrowest cross-section 832 linear size

Page 35 of 75 as the thickness of boundary layer, one can apply the equation of M-velocity (6.13) to design an improved profile of the wing. In view of the foregoing description referring to Fig. 8a, it will be evident to a person skilled in the art that the described de Laval-like jet-effect is similar to the classical de Laval jet-effect, but arising in an optimized convergent-divergent tunnel having imaginary walls formed by streamlines of a flow. Namely, the specifically shaped convergent-divergent tunnel comprises two opposite walls; wherein one of the two opposite walls is constructed from a solid material and another of the two opposite walls is imaginary and formed by streamlines of the flowing fluid subjected to the Coanda-effect operation. Further, it will be evident to a person skilled in the art that considering the case, when actually-airfoil biconvex wing 810 flying with a Venturi M-velocity M8 1 0

, which (the Venturi M-velocity M 8 1 0) is lower than the specific M-velocity M,=

(y-1)/y ~~ 0.5345 Mach ~~ 664 km/h and such that, when sliding sub portion 822 moves through the upper imaginary nozzle and passes through the narrowest cross-section 832, the maximally accelerated M-velocity remains lower than the specific M-velocity M,, the equation of M-velocity (6.13) allows to design an improved profile of the wing optimized to meet flow, oncoming with the Venturi M-velocity M 81 0 .While a gradual change in static pressure within boundary layers adjacent to the upper and lower surfaces of the actually-airfoil biconvex wing 810 is the primary condition for suppression of undesired turbulences nearby the wing surfaces, one of the primary criteria of the optimization is also to provide minimized differences between velocity-vectors and static pressures of the outflowing sub-portions 822 and 823, as the primary condition for suppression of undesired turbulences downstream behind the sharp trailing end 81Oc. While the curvatures of the upper and lower surfaces should provide gradual changes of the static pressures and M-velocities, the sharpness of the sharp trailing end 810c should provide the dominantly horizontal direction of motion tendency of both outflowing sub-portions 822 and 823. Thus, a method for a wing profile design, based on equation (6.13) according to an exemplary embodiment of the present invention, allows optimizing the wing airfoil shape to reach the best efficiency of the lift-effect as a result of the Coanda-jet-effect accompanied by enhanced at least one of the Venturi effect and de Laval jet-effect occurring above and under the wing. The inventor notes that the profile of the actually-airfoil biconvex wing 810 designed and optimized

Page 36 of 75 using the equation (6.13) has a shape similar to a shape of a birdwing rather than to the shape of the classic wing of airplane.

The Coanda-effect operation providing an imaginary convergent-divergent nozzle Fig. 8b is a schematic illustration of a flying airfoil body 840 having the shape of an elongated drop. For simplicity and without loss of reasoning, the shape is axis-symmetrical around the longitudinal axis 841. The airfoil body 840 comprises: " a forward part meeting oncoming flow portion 851; " a "withers", defined as the highest point on the upper side of the airfoil profile, where sliding sub-portion 853 has an imaginary narrowed cross-section 868, and " a rearward part. When an oncoming air portion 851, originally having a cross-sectional area 861, is running at the forward part of flying body 840, it is subjected to the Coanda-effect operation resulting in air portion 851 reshaping, and thereby forming an ambient-adjoining convergent-divergent jetstream, comprising sliding sub-portions: 852 being convergent, 853 being narrow and having imaginary narrowed cross-section 868 of the minimal cross-sectional area, 854 being divergent, and 855 becoming convergent due to the Coanda-effect attraction. Body 840's surface material properties, porosity, and structure are implemented according to the principles of the present invention, thereby providing that air portion 851 is subjected to the Coanda-effect, defined by the partial pressure-c 6Pc, rather than to the skin-friction resistance, occurring in an imaginary boundary layer and being quantified by the difference (aw - a - 6a). Furthermore, sliding sub-portions 855, join together, forming the resulting cumulative air portion 856. Oncoming air portion 851 and all the mentioned derivative sub-portions move within space "bordered" by imaginarywalls marked by dashed contours 842. The imaginarywalls 842 togetherwith the airfoil surface of body 840 constitute an imaginary tunnel. The tunnel's cross-section gradually constricts from the inlet cross-section 862 to the narrowest cross-section 868 and then gradually widens up to the outlet cross-section 863. I.e. sliding sub-portions 852 are shrinking while reaching the withers of airfoil body 840, where the cross-sections 868 of sub-portions 853 become minimal. Then, behind the withers, the cross-sections of sub-portions 854 and 855 are widening as moving. Sliding sub-portions 855, being under the subjection of the Coanda-effect operation, turn aside in alignment with the slippery surfaces of airfoil body 840's rearward part and join together, forming the resulting air portion 856. It results in a convergence of resulting air portion 856, i.e.

Page 37 of 75 in that, cross-section 864, located farther downstream, becomes narrower than cross-section 863 located immediately behind airfoil body 840, and opposite streamline-fragments 843 form an imaginary convergent funnel. Furthermore, opposite streamline-fragments 844, which are bordering flow portion 857, constitute an imaginary divergent stage of a tunnel downstream behind the narrowest cross-section 864. The converging opposite streamline-fragments 843 and divergent opposite streamline-fragments 844 together constitute the imaginary convergent divergent tunnel, and, correspondingly, portions 856 and 857 together constitute an outflowing convergent-divergent jetstream.

Jet-Booster based on the Venturi Effect First, consider a case, when airfoil body 840 flies with a Venturi M-velocity, i.e. with a low

M-velocity, lower than the specific M-velocity M, = y- 1)/y ~~ 0.5345 Mach, and low sufficient to provide that M-velocity M 8 6 8 of accelerated sliding sub-portions 853, passing cross-sections 868 over the withers, and M-velocity M8 6 4 of accelerated sub-portions 856, passing through the narrowest cross-section 864, both remain lower than the specific M-velocity M,, i.e. M 8 6 8 < M, and M8 6 4 < M. In this case, the narrowest cross-section 864 of outflowing air portion 856 is narrower than the original cross-section 861 of oncoming air portion 851, and the M-velocities M 8 6 1 , M 8 6 3 , M8 6 4 , M 8 6 5 , and M8 6 8 , where the indices correspond to markers of associated cross-sections, satisfy the following conditions:

* M 8 6 1 < M8 68 < M, U M 8 6 3 < M 8 6 8 < M,,

* M 8 6 3 < M8 64 < M, * M 8 6 1 < M8 64 < M, , and * M 8 6 5 < M8 64 < M* .

Thus, body 840 operates as a jet-booster basing on the Venturi effect occurring in the imaginary tunnel adjacent to body 840's surfaces. A practical application of the phenomenon that, under certain conditions, outflowing portion 856, moving through the narrowest cross-section 864, has a velocity higher than the velocity of oncoming portion 851 is one of the primary teachings of the present invention.

Jet-Boosters based on the de Laval-like Jet-Effect Secondly, consider a case, when airfoil body 840 flies relatively slowly, such that sliding sub-portions 853 pass cross-sectional areas 868 with an M-velocity that remains lower than the

Page 38 of 75 specific M-velocity, i.e. M 8 5 3 < M,, but high sufficient to provide that the increasedM-velocity of portion 856 is higher than M-velocity of sub-portions 853 and reaches the specificM-velocity

M, = (y- 1)/y at the critical condition point 864. In this case,M-velocity M 8 6 3 is the de Laval low velocity and the de Laval-like jet-effect is triggered, resulting in that theM-velocity of

the divergent flow portion 857 exceeds the specific M-velocity M, = [(y- )/y. In this case, the M-velocities M8 6 1 , M8 6 3 , M8 6 4 , M8 6 5 , and M8 6 8 satisfy the following conditions:

" M 8 6 1 < M8 6 8 < M, * M 8 6 3 < M8 6 8 < M, * M 8 6 3 < M8 6 4 = M, U M 8 6 1 < M8 64 = M*, and

" M 8 6 5 > M86 4 = M* .

So, body 840 operates as a jet-booster basing on the de Laval-like jet-effect occurring in the imaginary tunnel downstream-behind airfoil body 840. Thereby, the Coanda-jet-effect operation forcedly forms convergent-divergent laminar-like streamlines downstream-behind airfoil body 840, wherein the static pressure is distributed gradually along the convergent-divergent laminar-like streamlines that provides an optimized extension of air portion 857 resulting in the de Laval-like enhanced jet-effect accompanied by extra-cooling and extra-acceleration of air portion 857. This is one more teaching of the present invention. A practical application of the phenomenon that, under certain conditions, outflowing portion 857 has an M-velocity higher than the specific M-velocity is one of the primary teachings of the present invention. It will be evident to a person skilled in the art that the enhanced jet-effect results in an optimized reactive thrust-force applied to airfoil body 840. Thirdly, consider a case, when airfoil body 840's shape is optimized using the equation of M-velocity (6.13), basing on an estimated linear size of cross-section 868, and when airfoil body 840 flies with a de Laval lowM-velocity M 8 5 1 , i.e. lower than the specific M-velocity M=

(y- 1)/y ~~ 0.5345 Mach, but high sufficient to provide thatM-velocity of sliding sub portions 853 reaches the value of the specificM-velocity, i.e. M 8 6 8 = M, at the critical condition point 868. Thereby, the enhanced de Laval-like jet-effect occurs downstream-behind the withers, providing that M, < M8 5 4 < M8 5 5 , where the indexes correspond to associated sliding air sub-portions. In this case, according to equation (6.13), shrinking portion 856, moving with a de

Page 39 of 75

Laval high M-velocity, is slowing down, becoming warmer and more compressed, as moving on the way to the critical condition point associated with cross-section 864. The de Laval-like retarding-effect occurs downstream-behind cross-section 864 resulting in portion 857 expanding and further slowing down, warming, and compressing while reaching cross-section 865. The M velocities M 8 6 1 , M 8 6 3 , M8 6 4 , M8 6 5 , and M8 6 8 satisfy the following conditions:

" M 8 6 1 < M8 68 = M

, " M 8 6 3 > M8 6 8 M, * M 8 6 3 > M8 6 4 =M, " M 8 6 1 < M8 64 =M, and U M86 5 < M8 6 4 = M .

So, in the final analysis, body 840 operates as a jet-booster, triggering both the de Laval-like jet effect and the de Laval-like retarding-effect. Fourthly, consider a case, when airfoil body 840's shape is optimized using the equation of M-velocity (6.13), basing on an estimated linear size of cross-section 868, and when airfoil body 840 flies with a de Laval high M-velocity, i.e. higher than the specific M-velocity M=

(y - 1)/y ~~ 0.5345 Mach. According to equation (6.13), the de Laval-like retarding effect occurs in the imaginary convergent-divergent tunnel formed by streamlines 842. Namely, shrinking air portions 852 are slowing down, becoming warmer and more compressed, as moving on the way to withers such that theM-velocity of the narrowest sliding sub-portions 853 reaches the specific M-velocity, i.e. M 8 6 8 = M, at the critical condition point 868; and further, portions 854 continue to slow down while expanding downstream-behind the withers. Relatively slowly moving sliding sub-portions 855, now having a de Laval lowM-velocity, join downstream-behind cross-section 863, thereby, providing for resulting shrinking portion 856 acceleration, accompanied by a decrease of temperature and static pressure, while reaching again the specific M-velocity M, at the narrowest cross-section 864. The de Laval-like jet-effect occurs downstream-behind cross-section 864 resulting in expanding portion 857 further acceleration accompanied by a deeper decrease of temperature and static pressure on the way to cross section 865. So, theM-velocities M8 6 1 , M 8 6 3 , M8 6 4 , M8 6 5 , and M8 6 8 satisfy the following conditions: U M 8 6 1 > M 8 6 8 = M,,

* M 8 6 3 < M 8 68 = M, * M 8 6 3 < M8 64 = M,

Page 40 of 75

* M 8 6 1 > M8 64 = M,, and * M 8 6 5 > M8 6 4 = M*

. Again, in the final analysis, body 840 operates as a jet-booster, triggering both the de Laval-like retarding-effect and the de Laval-like jet-effect. In view of the foregoing description referring to Figs 6a, 7a, 7b, 7c, 8a, and 8b, it will be evident to a person skilled in the art that: * a method for an airfoil body shape design, based on equation (6.13) according to an exemplary embodiment of the present invention, allows, modifying the overall geometry of the body, to optimize the efficiency of the enhanced jet-effect occurring outside of the body; " the described convergent-divergentjet-nozzles can be applicable to many apparatuses using mechanical and heat energy provided by either a flowing gas or liquid; " triggering and controlling the desired de Laval-like jet-effect can be provided by manipulating by the oncoming wind de Laval M-velocity. As the M-velocity is temperature-dependent, one can heat or cool air portions flowing within a specifically shaped tunnel, in particular, in an imaginary tunnel around a flying body; * reaching and controlling the desired de Laval-like jet-effect can be provided by manipulating by the value of specific M-velocity, depending on the generalized adiabatic compressibility parameter y. For example, one can inject a gas composed of multi atomic particles into a tunnel, in particular, into an imaginary tunnel around a flying body. As well, it will be evident to a person skilled in the art that, for example, micro-flakes-of snow could play the role of such multi-atomic particles. Another technique to change the generalized adiabatic compressibility parameter y and thereby to control the specific M-velocity is to ionize the flow, moving through the tunnel; and U the described convergent-divergentjet-nozzles can be applicable to many apparatuses using mechanical and heat energy, provided by flowing gas or liquid.

Two-stage operation of the Coanda-let-effect Fig. 8c is divided between two parts: Case (A) and Case (B). Fig. 8c Case (A) is a schematic illustration of flying airfoil bodies 850 and 860, arranged such that the withers of airfoil bodies 860 follow downstream-behind the withers of body 850. For simplicity and without loss of reasoning, each airfoil body 850 and 860 has the shape of an elongated drop 840 described above with reference to Fig. 8b. All reference numerals 841, 861, 851, 862, 852, 868, 853, 842, and 854 are the same as described referring to Fig. 8b. Page 41 of 75

Consider a case, when flying airfoil bodies 850 and 860 meet oncoming portion 851 with a

de Laval high M-velocity M 8 51 , higher than the specific M-velocity M, = (y- 1)/y 0.5345 Mach. According to equation (6.13), sub-portions 852 of flowing fluid (for instance and without loss of generality, the flowing fluid is airflow) are slowing down as constricting on the way to the withers of body 850, such thatM-velocity of the narrowest sliding sub-portions 853 reach the specific M-velocity, i.e. Ms5 3 = M, at the critical condition point 868. The de Laval-like retarding-effect occurs downstream-behind the withers. It provides the condition M, > M8 5 4

, where index "854" corresponds to air sub-portions 854. So, airfoil bodies 860 meet oncoming

sub-portions 854 flowing slower than with the specific M-velocity M, = 1T(y- 1)/y, but high sufficient to provide the critical condition near their [bodies 860's] withers. Again, according to equation (6.13), air sub-portions 859 have anM-velocity M859 higherthan the specificM-velocity M,. Thus, flying airfoil bodies 850 and 860 meet the upstream air portions, and leave the

downstream air portions, flowing faster than with the specific M-velocity M, = (y- 1)/y. Furthermore, a cumulative cross-section of air sub-portions 859, wider than cross-section 861 of oncoming portion 851, means that theM-velocity M 8 5 9 is higher than the highM-velocity M8 5 1

of oncoming portion 851. In this case, the Coanda-jet-effect two-stage operation accelerates a portion of ambient airflow that originally moves faster than with the specificM-velocity M,. Thus, in contrast to the case when a body, having not-optimized shape, flies in air-environment with transonic, and/or supersonic, and/or hypersonic velocities, flying airfoil body 850, operating in tandem with each flying airfoil body 860, moving downstream behind the withers of airfoil body 850, results in a specific effect of acceleration and cooling air portion 851, oncoming faster than with the specific M-velocity M,. This is one other primary teaching of the present invention.

Fig. 8c Case (B) is a schematic illustration of a sectional cut of flying actually-airfoil wings 850.B and 860.B in a sagittal plane. The flying actually-airfoil wings 850.B and 860.B are arranged to meet and act on an oncoming portion 851.B of flowing fluid sequentially (for instance and without loss of generality, the flowing fluid is airflow). In view of the foregoing description referring to Fig. 8c Case (A), it becomes evident that, in particular, considering a tandem 880.B of two airfoil bodies consolidated as a whole embodied in the form of actually-airfoil wings 850.B and 860.B (for instance, each of which similar to that described hereinabove referring to Fig. 8a) will provide the described specific effect of acceleration and cooling of the airflow portion 851.B originally oncoming faster than with the

Page 42 of 75 specific M-velocity M,. The tandem 880.B comprises all the features of the flying airfoil bodies 850 and 860 of Case (A), and, in contrast to Case (A), the two airfoil bodies, namely, the two actually-airfoil wings 850.Band 860.B, have an asymmetry relative to the horizontal plane 841.B. The reference numerals are as follows: U 851.B is an oncoming flow portion yet to be subjected to an action of the tandem 880.B of two actually-airfoil wings 850.B and 860.B consolidated as a whole; * 852.B1 and 852.B2 are sub-portions of the oncoming flow portion 851.B in positions where, when running on the first met local convexity 869.B1 and 869.B2, correspondingly, subjected to convergence above and under the tandem 880.B; U 868.B1 and 868.B2 are narrowed cross-sections of the locally-minimal cross-sectional areas, correspondingly, above and under the first met local convexity: 869.B1 and 869.B2, of the tandem 880.B; * 853.B1 and 853.B2 are sub-portions of the oncoming flow portion 851.B in positions where, when flowing adjacent to the first met local convexity: 869.B1 and 869.B2, correspondingly, subjected to narrowing to have narrowed cross-sections 868.B1 and 868.B2 of the locally-minimal cross-sectional areas, correspondingly, above and under the first met local convexity: 869.B1 and 869.B2, of the tandem 880.B; * 854.B1 and 854.B2 are sub-portions of the oncoming flow portion 851.B in positions where, when passing the first met local convexity: 869.B1 and 869.B2, correspondingly, subjected to divergence above and under the tandem 880.B; * 852.B3 and 852.B4 are sub-portions of the oncoming flow portion 851.B in positions where, when running on the second met local convexity: 869.B3 and 869.B4, correspondingly, subjected to convergence above and under the tandem 880.B; * 868.B3 and 868.B4 are narrowed cross-sections of the locally-minimal cross-sectional areas, correspondingly, above and under the second met local convexity: 869.B3 and 869.B4, of the tandem 880.B; and * 854.B3 and 854.B4 are sub-portions of the oncoming flow portion 851.B in positions where, when passing the second met local convexity: 869.B3 and 869.B4, correspondingly, subjected to divergence above and under the tandem 880.B.

The profiles of the two actually-airfoil wings 850.B and 860.B are elaborated to meet the oncoming flow portion 851.B originally oncoming faster than with the specific M-velocity M, such that the two boundary layers composed of the sub-portions, flowing above and under the tandem 880.B, correspondingly, both, when subjected to action by the tandem 880.B, become subjected

Page 43 of 75 to a two-stage convergence-divergence accompanying first, by the triggered de Laval retarding effect and then by the triggered de Laval jet-effect. Borders of the two boundary layers are schematically marked by double-dot dashed lines 842.B1 and 842.B2 symbolizing imaginary, in general, curved surfaces formed by streamlines bordering the portion 581.B above and under the tandem 880.B, correspondingly; without loss of generality, the surfaces are indicated as being almost plane and separating, on the one hand, thetwo two-stage convergent-divergent boundary layers composed of sub-portions of the portion 581.B, which are substantially deforming as moving along the tandem 880.B, and, on the other hand, portions of the ambient flowing fluid which remain relatively weakly deformed. The triggering of the de Laval retarding effects occurs when the retarding of sub-portions 852.B1 and 852.B2 are such that the sub portions 853.B1 and 853.B2 cross the narrowed cross-sections 868.B1 and 868.B2 of the locally minimal cross-sectional areas, correspondingly, with the specific M-velocity M"; and the triggering of the de Laval jet-effects occurs when the acceleration of sub-portions 852.B3 and 852.B4 are such that the sub-portions 853.B3 and 853.B4 cross the narrowed cross-sections 868.B3 and 868.B4 of the locally-minimal cross-sectional areas, correspondingly, again, with the specific M-velocity M,.

The asymmetry of the tandem 880.B relative to the horizontal plane 841.B causes that: * on the one hand, as soon as the upper outlet sub-portion 854.B3 is wider than the upper inlet sub-portion 852.B1, integrally, the upper sub-portion becomes accelerated, as it is described hereinabove in the sub-paragraph "Two-Stage Convergent-Divergent Jet Nozzle" referring to Fig. 6h; and * on the other hand, since the lower outlet sub-portion 854.B4 is narrower than the lower inlet sub-portion 852.B2, integrally, the lower sub-portion remains retarded. Such an action of the tandem 880.B on the sub-portions of the relatively fast oncoming flow portion 851.B, which (the action) is imbalanced relative to the horizontal plane 841.B, originates a resulting upwardly-vectored lift-force cumulatively acting on the tandem 880.B, that is also one of the primary teachings of the present invention.

Fig. 8d is a schematic drawing of a flying wing 870 having a side-view sectional two-humped airfoil profile 871, constructed according to the principles of the present invention. The side-view sectional two-humped airfoil profile 871 determines a sagittal axis 871.0. The flying wing 870 comprises two withers: forward 872 and rear 873, separated by concavity 874. The flying M

velocity is higher than the specific M-velocity M, = y- 1)/y ~~ 0.5345 Mach.

Page 44 of 75

An oncoming flow portion 875 runs at the two-humped airfoil wing 870, becomes a boundary layer moving adjacent to the upper surface of the two-humped airfoil wing 870 under an imaginary surface, which, in a sagittal sectional plane, is indicated by a double-dot dashed line 871.1 symbolizing an imaginary, in general, curved surface formed by streamlines bordering the portion 875 above the two-humped airfoil wing 870, and passes positions: 801, 802, 803, 804, 805, 806, 807, 808, and 809 sequentially with associated M-velocities: M8 0 1 , M8 0 2 , M8 0 3 , M8 0 4 , M8 0 5

, M 8 0 6 , M8 0 7 , M8 0 8 , and M8 0 9 , correspondingly. The two-humped airfoil profile 871 provides for the Coanda-jet-effect two-stage operation: upstream-afore and downstream-after concavity 874. At position 801, flow portion 875, having the de Laval high M-velocity M 8 0 1 , is yet to be subjected to the Coanda-jet-effect operation over wing 870's profiled surfaces. The two-humped airfoil profile 871 causes that the cross-sectional area of portion 875 is varying as portion 875 moves over wing 870 as the boundary layer under the imaginary surface 871.1. So, portion 875 shrinks at position 802 while upping over the forward part, has the first local minimum of cross section area at position 803 above the forward withers 872, expands at position 804 while downing into concavity 874, reaches the local maximum of cross-section area at position 805 when passing concavity 874, shrinks again at position 806 on the way to the rear withers 873, gets the second local minimal value of cross-section area at position 807 above the rear withers, and expands at positions 808 and 809. Thus, there are two convergent-divergent portions of the boundary layer moving adjacent to the upper surface of the two-humped airfoil wing 870: U first, upstream relative to concavity 874, comprising positions 802, 803, 804, and 805 when flowing over the forward withers 872, and * second, downstream relative to concavity 874, comprising positions 805, 806, 807, 808, and 809 when flowing over the rear withers 873. Each of the two convergent-divergent portions of the boundary layer is elaborated according to the equation of M-velocity (6.13) providing for gradually smooth changes of M-velocity to suppress undesired turbulences. According to the equation of M-velocity (6.13), portion 875, as the boundary layer moving under the imaginary surface 871.1, is subjected to the de Laval-like jet-effect and the de Laval like retarding-effect such that: U at position 802, the flow convergence is accompanied by the de Laval-like retarding effect resulting in compressing and warming of flow portion 875 and a decrease of M velocity, i.e. M 8 0 1 > M8 0 2 ;

Page 45 of 75

" at position 803, the first critical condition point, where the varying value of flow portion 875's cross-sectional area has the first local minimum, provides for that the M-velocity of flow portion 875 reaches the specific M-velocity M,, so, M 8 0 1 > M 8 0 2 >

M8 0 3 = M,, i.e. the critical condition of the de Laval-like retarding-effect triggering is satisfied; * at position 804, the flow divergence is accompanied by further compressing and warming of flow portion 875 and a decrease of M-velocity lower than the specific M velocity M,, i.e. M, > M8 0 4 ; * at position 805 above concavity 874, the M-velocity M8 0 5 is minimal, thereby, providing the condition: M 8 0 1> M 8 02 > M 8 0 3 = M, > M8 0 4 > M8 0 5 ; * at position 806, the flow convergence is accompanied by cooling of flow portion 875, a decrease of static pressure, and an increase of M-velocity, i.e. M 8 0 5 < M8 0 6 ; " at position 807, the second critical condition point, where the varying value of the flow portion 875's cross-sectional area has the second local minimum, is designed to provide for that the M-velocity of flow portion 875 reaches the specific M-velocity M, i.e. the condition M 8 0 5< M 8 0 6 < M8 0 7 = M, triggering the de Laval-like jet effect is satisfied; and so, * at positions 808 and 809, the flow divergence is accompanied by further cooling of flow portion 875, a decrease of static pressure, and an increase of M-velocity, i.e. M 8 0 5 < M 8 0 6 < M8 0 7 = M, < M8 08 < M8 0 9 .

Depending on profile 871, the M-velocity M 8 0 9 of flow portion 875 at downstream position 809, may exceed the high M-velocity M 8 0 1 of flow portion 875 at upstream position 801, so, wing 870 may be used as a jet-booster based on the de Laval-like jet-effect, operating at high velocities. In general, the use of a two-humped airfoil profile of a wing flying with the de Laval high M velocities, in order to provide for the desired jet-effect, is yet one of the teachings of the present invention. In view of the foregoing description referring to Fig. 8d, it will be evident to a person skilled in the art that the effect of high M-velocity acceleration by the Coanda-jet-effect two-stage operation is applicable, for example, to high-speed aircraft design. One of the primary advantages of a two-humped airfoil wing is that, in contrast to a classic wing, the two-humped airfoil wing 870 being stationary (not-variably) configured-and-oriented has a positive lift force as for low M-velocities and for high M-velocities.

Page 46 of 75

In view of the foregoing descriptions referring to Figs. 8a, 8c, and 8d, it will be also evident to a person skilled in the art that a pair of actually-airfoil wings (i.e. having sharp trailing ends adapted to provide laminarity of air sub-portions outflowing downstream behind the sharp trailing ends), being arranged in-line along a sagittal axis one downstream behind the other and combined as a whole being stationary (not-variably) configured-and-oriented, can function similar to a two-humped airfoil wing to provide a positive lift force as for low M-velocities as well as for high M-velocities. Thus, the tandem 880.B of two airfoil bodies embodied in the form of actually airfoil wings 850.Band 860.B consolidated as a whole (Fig. 8c Case (B)) can be interpreted as a broken two-humped airfoil wing. In view of the foregoing descriptions referring to Figs. 6h, 7d, 8c, and 8d, it will be evident to a person skilled in the art that, considering a body, flying in air-environment with transonic, and/or supersonic, and/or hypersonic velocities, i.e. with high M-velocities higher than the

specific M-velocity M, = (y-1)y " incontrast to a case, wherein a body having an arbitrary shape is decelerating when air-fluxes, which flow nearby around the body, become warmer and extra-warmed, * a specifically-shaped body, having a two-humped airfoil profile providing for the two stage operation of the Coanda-jet-effect, is accelerating, and air-fluxes, which flow nearby around the accelerating specifically-shaped body, become cooled and extra cooled.

Cascaded Jet-Boosters Fig. 9a is a schematic illustration of a sequential cascade of in-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016, each in the shape of an elongated drop, exposed to oncoming wind 900 having the ambient M-velocity substantially lower than the specific M-velocity M,=

(y- 1)/y. The shape of the elongated drops is optimized using the equation of M-velocity (6.13), basing on a specified thickness of a boundary layer over convex withers, as described hereinabove referring to Figs. 8a and 8b. Points 9012 symbolize that the sequence of airfoil bodies may be much longer than shown. For simplicity, oncoming wind 900 is laminar. Trace a moving-small-portion 910 of ambient oncoming wind 900 passing positions 911, 9110, 912, 913, 9130, 914, 9140, 915, 9150, 916, 9160, and 917, considering a case when moving-small-portion 910 is subjected to the Coanda-jet-effect in an adiabatic process, defined by the partial pressure c 6Pc, rather than affected by the skin-friction resistance, quantified by the difference (a, - a - aa). Moving-small-portion 910 at position 911 is yet to be subjected to the

Page 47 of 75

Coanda-jet-effect operation. I.e. at least the forward airfoil body 9011 meets moving-small

portion 910 with M-velocity, lower than the specific M-velocity M, = (y- )/y, and so body 9011 operates as a jet-booster based on the Venturi effect occurring in the adiabatic process in an imaginary tunnel adjacent to body 9011, as described above with reference to Fig. 8b. Further, moving-small-portion 910 is subjected to a cascaded operation of the Coanda-jet effect in the adiabatic process by in-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016, each of which operates as an elemental jet-booster, while meeting moving-small-portion

910 with M-velocity, lower than the specific M-velocity M, = (y- )/y.The cascaded operation of the Coanda-jet-effect results in aligning of the Brownian random motion of moving small-portion 910's molecules with the surfaces of in-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016, that is observed as an increase of the effective velocity of moving-small portion 910, accompanied by moving-small-portion 910 temperature decrease, as moving-small portion 910 sequentially passes positions 9110, 9130, 9140, 9150, and 9160, where flowing as ambient-adjoining convergent-divergent jetstreams. Thus, this results in an increase of moving small-portion 910's kinetic energy at the expense of moving-small-portion 910's internal heat energy. Consider certain identical cross-sectional areas at positions 911, 912, 913, 914, 915, 916, and 917, marked by dashed ellipses, such that the Coanda-jet-effect operation influence is still perceptible within the marked areas. Considering flow velocities much lower than the specific

M-velocity M, = (y- )/y,the effective velocity of flow crossing the marked areas at positions 911, 912, 913, 914, 915, 916, and 917 increases exponentially as the flow moves along the sequential cascade of in-line arranged airfoil bodies 9011 -9016. For example, if the Coanda jet-effect operation of each of airfoil bodies 9011 - 9016 in the adiabatic process provides an increase of the effective velocity of a flow portion, crossing the associated marked area, on 2%, then after 35 airfoil bodies 9011 - 9016 the effective velocity of the wind portion, crossing the marked area, is twice as high as the velocity of oncoming wind 900 yet to be subjected to the Coanda-jet-effect multi-stage cascaded operation. Consider a case, when the M-velocity M 9 1 3 0 of moving-small-portion 910, flowing as an ambient-adjoining convergent-divergent jetstream

nearby the withers of airfoil body 9013, reaches the specific M-velocityM,= (y- 1)/y at position 9130. Triggering of the de Laval-like jet-effect causes the M-velocity M9 1 4 at position 914 to become higher than the specific M-velocity M,. The moving-small-portion 910 becomes cooled between positions 913 and 9130 and becomes extra-cooled between positions 9130 and 914. Running at airfoil body 9014, moving-small-portion 910 is subjected to the de Laval-like

Page 48 of 75 retarding-effect, such that the portion's M-velocity decreases down to the specific M-velocity

M,= (y- 1)/y at position 9140 nearby the withers of airfoil body 9014, and becomes lower than the specific M-velocity M, at position 915. The moving-small-portion 910 becomes warmer between positions 914 and 9140 and becomes extra-warmed between positions 9140 and 915. Then moving-small-portion 910 is subjected to the de Laval-like jet-effect and the M velocity increases again. Thus, when the sequence of airfoil bodies 9011 - 9016 is sufficiently long, the effective M-velocity of moving-small-portion 910 reaches the value of the specific M

velocity M, = (y - 1)/y nearby the withers of airfoil bodies and varies around the value between the airfoil bodies. This is yet one more of the teachings of the present invention. In view of the foregoing description referring to Fig. 9a, it will be evident to a person skilled in the art that: * in a more general case, when oncoming wind 900 is turbulent, such that moving-small portion 910 comprises whirling groups of molecules, the Coanda-jet-effect multi-stage cascaded operation results in aligning also of the turbulent motion of the whirling groups of molecules with the surfaces of in-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016, that is observed as an increase of the effective velocity of moving-small portion 910, accompanied by moving-small-portion 910's inner turbulence decrease, as moving-small-portion 910, flowing as ambient-adjoining convergent-divergent jetstreams nearby around the withers of airfoil bodies 9011, 9013, 9014, 9015, and 9016, sequentially passes positions 9110, 9130, 9140, 9150, and 9160, correspondingly. Thus, this results in an increase of moving-small-portion 910's kinetic energy also at the expense of moving-small-portion 910's inner turbulent energy; * the effect of M-velocity acceleration and stabilization by a multi-stage cascaded operation of the Coanda-jet-effect thereby reinforced multi-repeatedly is applicable, for example, to a high-speed long-train design; " the effect of M-velocity stabilization is applicable, for example, to a flying train-like object, in particular, supplied with wings, which are not shown here, providing for a lift force; * an arrangement of airfoil bodies 9011, 9013, 9014, 9015, and 9016 along a smoothly curved locus, instead of the in-line arrangement, can be implemented; and * the stabilized temperature difference between the extra-cooled airflow portions subjected to the triggered de Laval-like jet-effect and the extra-warmed airflow portions

Page 49 of 75 subjected to the triggered de Laval-like retarding-effect may be used to power a Peltier element operating as a thermoelectric generator producing electricity.

Reference is now made again to Fig. 9a, wherein now, all the in-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016 are made from a conductive material, for simplicity, from a hypothetic super-conductor, wherein the sequence is exposed to electric flux 900. In view of the foregoing description referring to prior art Fig. 1f, the inventor points out that the effective electric flux crossing the marked areas at positions 911, 912, 913, 914, 915, 916, and 917 is self increasing exponentially as flowing along the sequential cascade of in-line arranged airfoil conductive bodies 9011 to 9016 due to the electromagnetic jet-effect.

Fig. 9b is a schematic illustration of a sequential multi-stage cascade of outer and nested airfoil rings 920, exposed to oncoming wind 921. Outer and nested airfoil rings 920 are formed by coiled-up walls having an actually-airfoil wing profile, similar, for example, to the profile of actually-airfoilwing 810, shown schematically in Fig. 8a. Thereby, outer and nested airfoil rings 920 have shapes of streamlined converging nozzles. The actually-airfoil wing profiles are optimized using the equation of M-velocity (6.13), basing on the specified thickness of a boundary layer over convex withers, as described hereinabove with the references to Fig. 8a. Points 929 symbolize that the sequence of outer and nested airfoil rings 920 may be much longer than shown. Airflow portions 922, flowing as ambient-adjoining convergent-divergent jetstreams, sliding outside of the sequential multi-stage cascade of outer rings 920, as well as wind portions 923, flowing and impacting inside of outer and nested airfoil rings 920, are subjected to the Coanda-jet-effect operation. Again, consider a case when airflow portions 922 and 923 are subjected to the Coanda-effect operation rather than to skin-friction resistance, thereby providing that each pair of outer and nested airfoil rings 920 operates as an elemental jet-booster. Airflow portions 922 and 923 join a cumulative outflow 924, wherein the Coanda-effect provides streamlines 925 forming an imaginary convergent-divergent nozzle downstream-behind the sequential multi-stage cascade of outer and nested airfoil rings 920. A sufficiently long multi stage cascade of outer and nested airfoil rings 920 provides that the M-velocity of resulting

cumulative outflow 924 reaches the specific M-velocity M, = y- )/y at the minimal cross-section 926 of the imaginary convergent-divergent nozzle and the de Laval-like jet-effect is triggered downstream-behind the minimal cross-section 926. Airflow portion 927 is expanded adiabatically; therefore, it is extra-cooled and extra-accelerated.

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A prolonged multi-stage cascade of outer and nested airfoil rings 920 may enable the M velocity of airflow portions 922 to reach the specific M-velocity M, nearby the withers of airfoil outer rings 920. In this case, airflow portions 922 become subjected to the de Laval-like jet-effect, such that the effective M-velocity of airflow portions 922 is stabilized, as described hereinbefore with reference to Fig. 9a, considering a sequential multi-stage cascade of in-line arranged airfoil bodies, each having the shape of an elongated drop.

Fig. 9c is a schematic illustration of a modified sequential multi-stage cascade of the outer and nested airfoil rings 920 of Fig. 9b into a pair of unbroken spirals shaped as the Archimedean screws 931 and 932 by helical coiling-up walls having airfoil profile 937, for example, similar to described above with reference to Fig. 8a. Airfoil profile 937, also shown separately above and to the left in an enlarged scale, is optimized using the equation of M-velocity (6.13), basing on the specified thickness of a boundary layer over convex withers, as described hereinabove with the reference to Fig. 8a, and taking into account an M-velocity range actually used for the spirals 931 and 932. Oncoming airflow portion 933 is yet to be subjected to the Coanda-jet-effect operation. Both: the sliding outside air sub-portions 934 flowing around and the inside impacting air sub-portions 935 flowing through the pair of spirals 931 and 932, are subjected to the Coanda jet-effect operation, resulting in a converging flow when convergent flow sub-portions 934 and 935 laminarly join a resulting cumulative outflow 936. I.e. a fragment [for instance, one coil] of the pair of spirals 931 and 932 operates as an elemental jet-booster, and a longer fragment of converging spirals 931 and 932 provides higher acceleration of the airflow. Again, the Coanda jet-effect provides streamlines 930 forming an imaginary convergent-divergent jet-nozzle downstream-behind the airfoil construction. Moreover, the two spirals 931 and 932 have opposite helical screwing rotations, namely: clockwise and inverse-clockwise, thereby providing a spatially varying cross-sectional area of gaps between the walls of the two spirals 931 and 932. The spatially varying cross-sectional area of the gaps provides a Venturi effect for velocities lower than the specific M-velocity M, =

(y- )/y and the de Laval-like jet-effect for velocities providing for reaching the specific M velocity M, = [(y- )/y at the critical condition point where the variable cross-sectional area of gaps becomes minimal. Sufficiently long converging spirals 931 and 932 provide acceleration of the airflow and stabilization of the effective velocity at the value of the specific M

velocity M, = (y- 1)/y analogous to the cases described above with references to Figs. 9a and 9b.

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In view of the foregoing description of Figs. 9a, 9b, and 9c, it will be evident to a person skilled in the art that: " One can implement many alterations, re-combinations and modifications of elemental jet boosters, taught herein, without departing from the spirit of the disclosure that can be generalized as the following. A sufficiently long aggregation of elemental jet-boosters provides acceleration of an airflow portion, reaching the specific M-velocity M, =

(y- )/y, thereby triggering alternating the de Laval-like jet-effect and the de Laval like retarding-effect, resulting in a stable alternation of the airflow portion effective M-velocity

above and below the specific M-velocity M, = (y- 1)/y between the elemental jet boosters; and " The cumulative useful kinetic-power, including both: the originally brought kinetic-power and the acquired kinetic-power, provided by a multiplicity of elemental jet-boosters, aggregated into an adiabatic converging system, depends on quality and quantity of the elemental jet boosters and how the elemental jet-boosters are arranged and exploited. Moreover, it will be evident to a person skilled in the art that a sequential in-line multi-stage cascading of the elemental jet-boosters has an especial sense. For example, consider an aggregation comprising N elemental jet-boosters exposed to an ambient flow and oriented such that each elemental jet-booster provides an increase of the effective velocity of the flow portion moving through a certain effective cross-sectional area, by a factor F, wherein F > 1, and for simplicity and without loss of the explanation generality, consider a case of sufficiently low velocity of the ambient flow and assume that it is the same factor, independently of the elemental jet-boosters arrangement and exploitation. As well, for simplicity, consider the case, when the M-velocities of accelerated flow remain lower than the

specific M-velocity M, = (y- 1)/y, thereby, justifying neglecting the flow density change in further approximate estimations. As the kinetic-power of a flow portion moving through a certain cross-sectional area is directly-proportional to the cross-sectional area and proportional to the third power of the flow portion velocity, each elemental jet-booster, when operating separately, launches a jetstream having the solitary useful kinetic-power, indicated by W1,

proportional to the third power of the factor F, expressed by W 1 = Wo x F3 , where Wo is the originally brought ambient useful kinetic-power associated with the effective cross-sectional area of one elemental jet-booster.

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The solitary acquired kinetic-power AW 1 is defined by the difference between the solitary

useful kinetic-power W1 and the originally brought ambient useful kinetic-power Wo, namely,

AW 1 = Wo x (F3 - 1); and so the aggregation, comprising N such elemental jet

boosters and thereby accelerating the flow portions, moving through N effective cross-sectional areas, results in the cumulative useful kinetic-power: * indicated by Wparaie, equal to Wparalle = N x W 1 = N x Wo x F3

wherein the cumulatively acquired kinetic-power AWparaiei is defined as:

AWparaiie = N x AW 1 = N x Wo x (F3 - 1),

in the case, when the elemental jet-boosters operate independently, that occurs, 0 if the elemental jet-boosters are arranged in parallel, or • if the elemental jet-boosters are arranged sequentially, but operating in a not adiabatic process, allowing for the solitary useful kinetic-power W 1 to be consumed in parallel within or behind each elemental jet-booster and restored afore each next elemental jet-booster; or, alternatively, * indicated by Wsequentia, equal to Wsequential = Wo x (F 3 )N, wherein the

cumulatively acquired kinetic-power AWsequential is defined as:

AWsequential = Wo x [(F 3 )N - N], in the case, when the elemental jet-boosters are arranged sequentially operating in the adiabatic process, and the consumption of the cumulative useful kinetic-power is allowed behind the downstream-end of the last elemental jet-booster only. In an exemplary practical case, the effective velocity increase factor equals F = 1.097.Then the following conditions become satisfied: * the condition Wsequentia< Wparaie is satisfied for N 8;

U the condition Wsequentia> Wparalel is satisfied for N 9;

* the condition Wsequential > 2Wparalel is satisfied for N 13;

* the condition Wsequential > 3Wparalel is satisfied for N 15; and

* the condition Wsequential > 4Wparalel is satisfied for N 16.

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In view of the foregoing description of Figs. 9a, 9b, and 9c, one of the primary teachings is that an artificial wind can be used for profitable harvesting of electricity. For example, one can: 0 use a big-front ventilator [or group of ventilators], having 50%-net-efficiency, i.e. consuming electric-power Wconsumed and creating an originally incoming artificial airflow, bringing kinetic

power Wincome = 0.5 X Wconsumed, wherein the originally incoming artificial airflow has the front area Aincome of 4 times bigger than the effective cross-sectional area of an elemental

jet-booster and has the effective velocity Uincome;

0 implement a sequential multi-stage cascade, comprising N = 15 elemental jet-boosters,

each of which is characterized by the effective velocity increase factor F = 1.097, such that

altogether making an outflowing artificial jetstream, having the velocity Uetsrteam =

Income x FN [FN= 1.09715 4] and having the resulting effective frontal cross sectional area Ajetsrteam, decreased approximately 4 times relative to the area Aincome of

originally incomingairflow[Aincome/Ajetsrteam= FN ~ 4]. Thus, the outflowing

artificial jetstream brings the resulting useful kinetic-power WIetsrteam' estimated as:

Wjetsrteam = (ujetsrteam/uincome)3 X (Ajetsrteam/Aincome) XWincome, i.e.

Wetsrteam = [43/4] X Wincome = [16] X 0.5 X Wconsumed = 8 X Wconsumed; and * use a wind-turbine, producing electricity with 50%-net-efficiency, thereby, harvesting the useful electric-power Wuseful of 4 times higher than the consumed electric-power Wconsumed,

namely, Wuseful = 0.5 X Wjetstream = 0.5 x (8X Wconsumed) = 4 x Wconsumed

Wherein, the profit becomes greater than estimated, when the de Laval-like jet-effect is triggered. Thereby, in view of the foregoing description referring to Figs. 9a, 9b, and 9c, it will be evident to a person skilled in the art that a profitable harvesting of electricity, using a jet-effect created by a multi-stage cascaded operation of the Coanda-jet-effect thereby reinforced multi-repeatedly, is feasible, for example, attaching sequentially arranged elemental jet-boosters to a sufficiently long moving vehicle and using a wind-turbine, arranged behind the downstream-end of the last elemental jet-booster.

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In view of the foregoing description referring to Figs. 9a, 9b, and 9c, the inventor points out that, when reaching the stabilized effective velocity equal to the value of the specific M-velocity

M = (y- 1)/y, the periodical local extra-acceleration and extra-retarding generate a forced extra-intensive elemental acoustic wave, wherein the distance between each two neighbor withers equals half of the wavelength of the forced extra-intensive elemental acoustic wave. Furthermore, the forced extra-intensive elemental acoustic waves are superposed in-phase thereby constituting the resulting extra-intensive acoustic wave as constructive interference. It will be evident to a person skilled in the art that the arrangement of airfoil bodies, either: * 9011, 9013, 9014, 9015, and 9016 as shown in Fig. 9a; or U a sequential multi-stage cascade of outer and nested airfoil rings 920 as shown in Fig. 9b; or * a pair of unbroken spirals shaped as the Archimedean screws 931 and 932 by helical coiling-up walls having airfoil profile 937, as shown in Fig. 9c, subjected to the generalized jet-effect (namely, the Coanda-jet-effect, the de Laval-like jet-effect, the de Laval-like retarding effect, and the enhanced waving jet-effect) and supplied by an acoustic detector capable of detection of the resulting extra-intensive acoustic wave power, can play a role of an electricity generator that, in the final analysis, produces the electric power at the expense of the warmth of the air.

Jet-Turbine as Improved Wind-Turbine Fig. 9g is a schematic drawing of a jet-rotor of modified improved wind-turbine, called also ajet-turbine, 9.0, constructed according to the principles of the present invention to operate under relatively fast airflow 9.1 for producing the electric power at the expense of the warmth of relatively fast airflow 9.1. Modified improved wind-turbine or jet-turbine 9.0 comprises: U axle 9.2 oriented along sagittal axis 9.21 codirected with fast airflow 9.1, " identical asymmetrical biconvex actually-airfoilblades 9.3, attached to axle 9.2; and * an engine, which is not shown here, having a stator and rotatable shaft; the engine is capable of transforming the power of the forced mechanic rotational motion 9.4 of axle 9.2 into the electric power. The primary feature, making the jet-turbine 9.0 practically implementable and extremely efficient, is the specifically configured and so specifically functioning biconvex actually-airfoil blades 9.3. Namely, in contrast to standard wind-turbines having standardly shaped blades configured to be subjected to impacting by an incoming airflow that, in particular, results in the

Page 55 of 75 airflow turbulence, retarding, and warming, the jet-turbine 9.0 has asymmetrical biconvex wing like actually-airfoil blades 9.3: * having opposite convex sides 9.31 and 9.32 with withers differing in convexity, and * being oriented along and so adapted to the incoming fast airflow jetstream 9.11 headway motion. Thereby configured and oriented blades provide the zero attack angle: * to exclude or at least to minimize the impact by the incoming fast airflow jetstream 9.11, but * to provide an interaction with the fast airflow jetstream 9.11 by the Coanda-jet-effect only, thereby resulting in an acceleration and cooling of outflowing jetstream 9.6 and resulting in lift-forces, acting on identical biconvex actually-airfoil blades 9.3 and being disbalanced because of the aligned asymmetry of the identical biconvex airfoil blades. In this case, the axle 9.2 rotational motion, shown by the curved arrow having numeral 9.4, is caused by the cumulative resulting lift-force. Take note again, that the Coanda-jet-effect is triggered by the airflow kinetic-power and is actually powered at the expense of the airflow warmth but not at the expense of the incoming fast airflow jetstream 9.11 kinetic-power; contrariwise, the kinetic-power of outflowing jetstream 9.6 is increased or at least not decreased with respect to the oncoming fast airflow 9.1. Thus, in contrast to the standard wind-turbines, the proposed improved wind-turbine 9.0 is specifically characterized: 0 by the mechanism of operation, that is the Coanda-jet-effect but not the impact; and U by the power source of operation, that is the warmth but not the kinetic power of airflow. Also, in contrast to a kind of the standard wind-turbines having wing-like blades moving around a vertical axis, the proposed jet-turbine 9.0 is specifically characterized by the excluding of varying poorly-streamlined positions of the wing-like blades. As well, in contrast to the standard wind-turbines, a productivity of the proposed jet-turbine 9.0 is defined by the area of the biconvex airfoil blades rather than by a so-called "swept area", namely, the produced electric power due to the Coanda-effect is specified as proportional to the biconvex airfoil blades area, i.e. the productivity can be increased substantially for a given swept area. In view of the foregoing description referring to Fig. 9g, it will be evident to a person skilled in the art that jet-turbine 9.0 comprising: * the biconvex airfoil blades, having a wing-like sectional contour with a longer so-called chord of wing, and/or

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* an increased quantity of the biconvex airfoil blades, both circumstances provide for enforcing of the desired Coanda-jet-effect. As well, it is self suggested a sequential in-line arrangement of a multiplicity of jet-turbines 9.0 one downstream after another (optionally, alternatingly differing in asymmetry to become forcedly rotated alternatingly clockwise and inverse-clockwise, correspondingly), each separately and all together efficiently operating within the given swept area. Moreover, at least one of the profiles 9.31 and 9.32 is implemented to provide the de Laval enhanced jet-effect, when the incoming fast airflow jetstream 9.11 is flowing with a de Laval M velocity and so a portion of jetstream 9.11 is reaching the specific M-velocity nearby the withers of the asymmetrical biconvex actually-airfoilblades 9.3. In this case, the extra-efficiency of the modified improved wind-turbine is expected. Furthermore, optionally, sides 9.31 and 9.32 differ in shape such that one of the sides has one convex withers and the opposite side has a two-humped airfoil profile providing for the two stage operation of the Coanda-jet-effect as described hereinabove with the reference to Fig. 8d. Such asymmetrical blades, when exposed to oncoming fast airflow 9.1 moving with a high M velocity, higher than the specific M-velocity, become subjected, on the one hand, to the de Laval retarding effect, and on the other hand, to the de Laval enhanced jet-effect. This provides for extra-increased lift-forces acting in unison and in the same direction of rotation and so rotating axle 9.2. In this case, the extra-efficiency of the modified improved wind-turbine is expected in a wide range of velocities.

Fig. 9h is a schematic drawing comprising the side-view and front view of a jet-rotor of jet turbine 9.7, constructed according to the principles of the present invention to operate under relatively fast airflow 9.70 for producing the electric power at the expense of the warmth of relatively fast airflow 9.70. An engine of the jet-turbine, which (the engine) having a stator and rotatable shaft, is not shown here. Axle 9.73, collinear with sagittal axis 9.74, is oriented to be codirected with the headway motion of the relatively fast airflow 9.70. In relation to all the principal features, the jet-turbine 9.7 is similar to the jet-turbine 9.0, described hereinabove referring to Fig. 9g, but now, referring to the aforementioned optional diversity of the principal features implementation, the biconvex actually-airfoil blades, which having opposite at least partially convex sides 9.71 and 9.72 with withers differing in convexity, are further curved and screwed to optimize a suppression of turbulence as well as are cascaded one downstream after another to provide a multi-stage repeated operation of the Coanda-jet-effect thereby contributing to the desired cumulative lift-force to rotate axle 9.73.

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In view of the foregoing description referring to Figs. 9g and 9h, it will be evident to a person skilled in the art thatjet-turbine 9.0 or 9.7, when attached to a flying aircraft, is capable of efficient harvesting of the electric power from the ambient air warmth. Furthermore, in view of the description expound hereinabove with references to Figs. Si, 5j, 5k, 9a, 9b, 9c, 9d, 9e, and 9f, the inventor points out that the mentioned multiplicity of jet-turbines 9.0 or 9.7, arranged sequentially one downstream after another [not shown here], results in generation of acoustic waves accompanied by extraction of the internal heat energy of ambient air in favor for the wave power due to the enhanced waving jet-effect. Thus, a system, comprising the arrangement and a detector of the acquired wave power, has an additional degree of freedom to increase the efficacy of the production of electricity. In view of the foregoing description referring to Figs. 9g and 9h in combination with the foregoing description of subparagraphs "Point of Sail" and "Flying Bird", both with the reference to prior art Fig. 1i, it will be evident to a person skilled in the art that the construction of jet-turbine 9.7, when having a controllable speed of the axle 9.73 rotation adapted to the velocity of oncoming airflow 9.70 to keep the airflow remaining laminar, provides a controllable net jet-thrust against the oncoming airflow 9.70 and so becomes applicable as a kind of jet-engine for a controllable and substantially noiseless flying. Furthermore, in view of the foregoing description referring to Figs.9g and 9h, it will be evident to a person skilled in the art that jet-rotor 9.7 having relatively massive actually-airfoil wings, when being attached to a body moving in a fluid and being capable of free rotation around the sagittal axis 9.74 due to the self-originated lift-forces acting on all the massive wings in unison and in the same direction of rotation, creates the gyroscopic effect that is defined as a tendency of the moving body to maintain a steady direction collinear with the sagittal axis 9.74 being the axis of the massive wings rotation and is manifested as a resistance to gusty fluctuations of motion of the ambient fluid, wherein the energy to generate the desired gyroscopic effect improving ballistic properties of the moving body is harvested from the ambient fluid warmth due to the Coanda-jet-effect.

A Jet-Transformer Fig. 9i is a schematic illustration of a concept to transform the ambient warmth into electricity. The concept is embodied as a jet-transformer 9.80 comprising: Sa vertically oriented specifically shaped pipe 9.81 having the optimized convergent divergent inner tunnel, described hereinabove in sub-paragraph "Convergent Divergent Jet-Nozzle" with reference to Fig. 6a,

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* at least one laminar flow maker 9.82, conceptually, having a geometry of convex concave corpus 9.821 supplied by a heater 9.822, i.e. being designed as the convex concave corpus 512 described hereinabove with reference to Fig. Se, and • at least one jet-turbine 9.83, designed as the jet-turbine 9.7 described hereinabove referring to Fig. 9h, all, constructed according to the principles of the present invention. The specifically shaped pipe 9.81 is elevated above the ground to allow for the ambient air 9.841 entering the optimized convergent-divergent inner tunnel from below. The heater 9.822 supplies the heat energy to a fluid portion adjacent the focus of the parabolically-concave surface 9.823 of the convex-concave corpus 9.821, thereby, on the one hand, to trigger the Archimedes upward-vectored buoyant force lifting the heated fluid portion and, on the other hand, to align the airflow 9.842 upward along the vertical axis 9.851 which is a sagittal axis, for the case. The upward airflow 9.842 is relatively slow and substantially-laminar. The optimized convergent divergent inner tunnel is designed according to the equation of M-velocity (6.13) to provide for substantial suppression of jumps of the air thermodynamic parameters and, thereby, to provide for the substantial acceleration of the airflow 9.842, laminarly and so noseless streaming upward. So, the heating triggers the upward motion of air, and, in turn, the fluid motion itself triggers the convective acceleration as the airflow moves through the narrowing cross-section of the optimized convergent-divergent inner tunnel. Considering: • the ambient temperature above the exhaust 9.854 equal Te, * the temperature near the level 9.852 equal To, and * the temperature near the narrow throat 9.853 equal T,, equation (7.1c), described hereinabove referring to Fig. 7a, says that: • on the one hand, to obtain the de Laval jet-effect for air utilizing the optimized convergent-divergent inner, one must provide the ratio TO/T, at least of 1.2; and • on the other hand, to accelerate an air portion up to the velocity of sound, one must provide the ratio To/Te at least of 1.7. Hence, providing the heating of air near the level 9.852 up to about the temperature 2340C only, the condition of the enhanced de Laval jet-effect becomes satisfied, in turn, providing that the relatively low heat power, supplied by heaters 9.822, triggers the enhanced de Laval jet-effect transforming the warmth of the moving airflow into the acquired kinetic power of the airflow. The energy E0 , necessary for warming 1 cube meter of air from the temperature 25 0 C up to the temperature 234 0C, is estimated as EO = pVCv (To - Te), where V is the volume of

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1 cube meter, p is the air density, p ; 1.2 kg/m 3 , Cv is the air heat capacity, Cy 0.72 kJ/(kg - K), thereby, EO 1.2 x 1 x 0.72 x (234 - 25) ; 180 kJ. As the mentioned assumed condition allows to accelerate the airflow portion 9.854 up to the

specific M-velocity M, = (y- 1)/y near the narrow throat 9.853 and to accelerate the airflow portion 9.854 up to almost the speed of sound (i.e. the exhaust M-velocity is of Me z 1), then: • the acquired kinetic energy, Ke, of the outflowing airflow portion 9.854, which (the acquired kinetic energy Ke) is specified as the difference between bringing heat energies, equalsKe n x (To - Te) x R, where n is number of moles in the considered 1 cube meter of air, n 44.64, and R is the specific gas constant, approximated for the air by R = 287J/(kg - K), i.e. K, z 44.64 X 209 X 287 ; 2,677 kJ, that, in turn, says that the acquired kinetic energy Ke may exceed the consumed energy EO at least at subsonic velocities by the factor of 15; and • the acquired kinetic energy, K,, of the airflow portion 9.854, when crossing the narrow

throat, equals K, n x (To - T,) x R z 764 kJ, thereby showing that the acquired kinetic energy K, may exceed the consumed energy EO by the factor of 4.24. It will be evident to a commonly educated person that, if not to use the optimized convergent divergent inner tunnel, designed according to the equation of M-velocity (6.13), the mentioned effective conversion of the airflow heat energy into the airflow kinetic energy is impossible because of originated turbulences and Mach waves, both accompanied by noise and energy dissipation back to the air warmth. The jet-turbine 9.83 meets the upping laminar airflow and provides for the production of electricity neither retarding the upward airflow and nor distorting the upward airflow laminarity as described hereinabove referring to Figs. 9g and 9h. The inventor points out again that the improved wind-turbine 9.83 harvests electric power at the expense of the airflow warmth but not from the airflow kinetic power, wherein the increased kinetic power of the airflow plays the role of an enforced trigger of the lift-force rotating the improved wind-turbine. Moreover, optionally, in-line arranged several jet-turbines 9.83 provide for a multi-stage repeatedly harvesting of electricity from the same airflow portion.

Jet-Ventilator and Jet-Propeller

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Fig. 9j is a schematic drawing of a modified improved ventilator, called also a jet-ventilator, 9J.0, constructed according to the principles of the present invention to create a headway laminarly moving flow. The jet-ventilator 9J.0 comprises a jet-rotor, which also is marked by numeral 9J.,and a motor, which is not shown here, having a stator and rotatable shaft. The motor, being powered by either a burned fuel or electrical power, forcedly rotates the rotatable shaft and, thereby, the jet-rotor 9J.0. One of specifics of the jet-ventilator 9J.0 is that blades 9J.1, having a profile 9J.2 similar to the profile of actually-airfoil biconvex wing 810 described hereinabove referring to Fig. 8a, are configured to be actually-airfoil and, when rotating, oriented to run over air portions 9J.6 (yet to be subjected to a motion) under the zero attack angle and to act on the air portions 9J.6 due to the Coanda-effect only. As the air portions 9J.6, when subjected to the Coanda-effect, originate lift-force 9J.3 acting on the blades 9J.1, the blades 9J.1 push off the air portions 9J.6 in the opposite direction collinear to sagittal axis 9J.7 according to the Newton's Third Law. Thereby, headway-forwarding air portions become a headway-forwarding laminar no-whirling outflow 9J.5 created by the jet-ventilator 9J.0. As the used blades 9J.1 are actually-airfoil, relatively low power consumption can provide a relatively fast rotation 9J.9 of the blades 9J.1, wherein the velocity of the fast rotation 9J.9 is in conformance with an optimal configuration 9J.2 of the actually-airfoil blades 9J.1. Since the desired acceleration of the outflow occurs due to the Coanda-effect only, the method of accelerating the outflow allows for significantly reducing energy consumption compared with the classical technique based on the impact of the blades. It will be evident for a commonly educated person, that the concept of jet-ventilator 9J.0 is applicable to any fluid either gas or liquid. A disadvantage of the technique to create the laminar no-whirling flow 9J.5 is that the relatively fast rotation 9J.9 of the blades 9J.1 produces relatively slow laminar no-whirling flow 9J.5.

Fig. 9k is a schematic drawing of jet-propeller 9K.0, constructed according to the principles of the present invention. The jet-propeller 9K.0 comprises a jet-rotor, which also is marked by numeral 9K.0, and a motor, which is not shown here, having a stator and rotatable shaft. The motor, being powered by either a burned fuel or electrical power, forcedly rotates the rotatable shaft and, thereby, the jet-rotor 9K.0. As the function difference between jet-propeller 9K.0 and jet-ventilator 9J.0 is that, while the jet-rotor of jet-ventilator 9J.0 acts to initially motionless air portions 9J.6, the jet-rotor of jet-propeller 9K.0 acts to airflow 9K.6 oncoming to blades with a certain velocity; so, the primary constructive difference between jet-propeller 9K.0 and jet ventilator 9J.0 is in orientation of blades. Namely, blades 9K.1 of jet-propeller 9K.0 are turned

Page 61 of 75 on a certain angle 9K.8, called also pitch, such that, when rotating with a certain rate 9K.9, to run over oncoming airflow 9K.6 under the zero attack angle and to act on oncoming airflow 9K.6 due to the Coanda-effect only. As the lift force 9K.3 acting on wings 9K.1 has a component directed collinearly to sagittal axis 9K.7 against the direction of the oncoming airflow 9K.6, the oncoming airflow 9K.6 becomes subjected to acceleration according to Newton's Third Law, thereby forming, resulting headway-forwarding outflow 9K.5. As the certain velocity of oncoming airflow 9K.6,the certain rate of blades 9K.1 rotation 9K.9, and the certain angle 9K.8 of blades 9K.1 orientation, all are interrelated, one can adapt the blades 9K.1 rotation rate 9K.9 and angle of orientation 9K.8 to the oncoming flow velocity 9K.6 to provide the zero attack angle to act on oncoming airflow 9K.6 due to the Coanda-effect only. When all the parameters are matched, the resulting headway-forwarding outflow 9K.5 accelerated by jet-propeller 9K.0 is laminar and no whirling. In view of the foregoing description referring to Figs. 9j and 9k, it becomes evident, that: * jet-propeller 9K.0 can comprise a variable pitch being capable of being adapted to the velocity of oncoming flow and rotation rate; * jet-ventilator 9J.0 can be interpreted as a particular case of jet-propeller 9K.0, the pitch of which is adapted to initially stationary fluid; * jet-ventilator 9J.0, pitch 9J.8 of which providing the zero attack angle of meeting stationary portions of air, and jet-propeller 9K.0, pitch 9K.8 of which being adapted to velocity of airflow 9J.5 created by jet-ventilator 9J.0, can be arranged in-line: the jet propeller after the jet-ventilator, thereby forming a system that as a whole performs an improved jet-ventilator providing for boosted outflow; and * since the blades of jet-propeller 9K.0, when moving, meet the ambient fluid at the zero attack angle and so, on the one hand, consume power to overcome a minimized drag and, on the other hand, produce the useful-beneficial power of accelerated outflow at the expense of ambient warmth due to the Coanda-jet-effect, a net-efficiency higher than 100% becomes reachable.

Reference is now made to Fig. 9L. Fig. 9L is a schematic illustration of a multi-module jet ventilator 9L.0, constructed according to the principles of the present invention to create a boosted headway-forwarding laminar no-whirling 9L.5. The multi-module jet-ventilator 9L.0 is composed of modules 9L.01 to 9L.07 attached to a common shaft. Each of the modules 9L.01 to 9L.07 is characterized by an individual pitch, wherein:

Page 62 of 75

0 The "zero" pitch of the first module 9L.01 provides for that, when the rotating blades of the first module 9L.01 run over the originally stationary portion of air 9L.6 at the zero attack angle, i.e. the first module 9L.01 functions as jet-ventilator 9J.0 described hereinabove referring to Fig. 9j; U A relatively small pitch of the second module 9L.02 provides for that, when the rotating blades of the first module 9L.02 run over portions of a relatively slow flow originated by the first module 9L.01 at the zero attack angle, i.e. the second module 9L.02 functions as jet-ventilator 9K.0 adapted to a certain oncoming flow as described hereinabove referring to Fig. 9k; U The individual pitch of each next module: 9L.03 to 9L.07, provides for that, when the rotating blades of the next module: 9L.03 to 9L.07 run over portions of a flow originated the previous module: 9L.02 to 9L.06, correspondingly, at the zero attack angle, i.e. all each of the modules 9L.03 to 9L.07 functions as jet-ventilator 9K.0 adapted to an associated oncoming flow as described hereinabove referring to Fig. 9k. As a result of all the modules 9L.01 to 9L.07 operation as a whole, the resulting headway forwarding laminar no-whirling outflow 9L.5 becomes accelerated reaching a relatively high velocity vectored collinearly to sagittal axis 9L.7.

Reference is now made to Fig. 9m. Fig. 9m is a schematic illustration of a cascade 9M.0 of multi-module jet-ventilator 9M.01 and two multi-module propellers 9M.02 and 9M.03 aggregated along the common sagittal axis 9M.7. The cascade 9M.0 is constructed according to the principles of the present invention. The multi-module jet-ventilator 9M.01 acts on an initially stationary portion of fluid 9M.6 and creates outflow 9M.51, which, in turn, becomes oncoming flow 9M.51 blowing the multi-module jet-propeller 9M.02. The multi-module jet-propeller 9M.02 acts on the oncoming flow 9M.51 and creates outflow 9M.52, which, in turn, becomes oncoming flow 9M.52 blowing the multi-module jet-propeller 9M.03. The multi-module jet-propeller 9M.03 acts on the oncoming flow 9M.52 and creates the resulting outflow 9M.53. The multi-module jet-ventilator 9M.01 is composed of three modules attached to a common shaft. As well, each of jet-propellers 9M.02 and 9M.03 is composed of three modules attached to a common shaft. Each of the mentioned modules comprises three sets of blades, wherein each of the sets is characterized by an individual pitch. The pitches of modules and rates of rotations 9M.91, 9M.92, and 9M.93 are chosen such that all the blades run over portions of oncoming flow at the zero attack angle. Optionally, blades of jet-propeller 9M.02 are configured

Page 63 of 75 for rotations 9M.91 and 9M.92 in mutually-opposite directions: clockwise and contrary-clockwise, correspondingly. The alternating directions of the rotations of in-line arranged jet-rotors are preferred to compensate for the unwanted whirling of flow. Although the unwanted whirling is purposely suppressed by excluding or at least minimizing the impact by blades, it (the unwanted whirling) can be originated due to other effects such as skin-friction between the flow and blades as well as jet-thrust described hereinabove in subparagraphs "Point of Sail" and "Flying Bird", both with the reference to prior art Fig. ii.

In the claims, reference signs are used to refer to examples in the drawings for the purpose of easier understanding and are not intended to be limiting on the monopoly claimed.

Page 64 of 75

Claims (1)

1. An airfoil wing [810] exposed to fluid flow; the airfoil wing is embodied as a biconvex wing having a sectional elongated profile, comprising two opposite curved sides: upperand lower, and two opposite butt-ends: forward being rounded and rearward being sharp, wherein the upper side comprising: " a forward part meeting an upper sub-portion of said fluid flow; " an upper convexity [810a], where the upper sub-portion [822], when sliding upon the upper convexity, has imaginary narrowed cross-section [832], and " a rearward part, attracting and, thereby, redirecting mass-center of the sliding upper sub-portion [822] backward-downward, where the sliding upper sub-portion [822] has imaginary widened cross-section [833], and wherein the lower side is curved to form a lower convexity [810a] at the rearward part; said lower side meeting a lower sub-portion of said fluid flow, wherein: * a sagittal axis is defined as an axis codirected with a motion of an oncoming portion of the fluid flow yet to subjected to an action of the airfoil wing; * an attack angle is defined as an angle between a sagittal axis and a direction of motion tendency of said lower sub-portion of said fluid flow when the lower sub-portion of the fluid flow outflowing nearby and stalling from the sharp rearward butt-end of the biconvex wing, and * a zero attack angle is specified as said attack angle equal to zero; wherein a geometrical configuration of the biconvex wing is such that, when the biconvex wing is exposed to an oncoming portion of the fluid flow at the zero attack angle, each boundary layer originated adjacent to each of the upper side and lower side of the biconvex wing has a varying cross-sectional area characterized by a cross-sectional area profile function A (x) given by an equation of M-velocity expressed as: 1 y+1

2+y(M(x))I 2(y-13 A (x) = *. (y-1) M(x) y y+1

where A, is a constant, y is an adiabatic compressibility parameter of the oncoming portion

of the fluid flow and M(x) is a gradual monotonic smooth function of x representing an M-velocity profile of the oncoming portion of the fluid flow moving through the boundary layer;

Page 65 of 73 wherein the sectional elongated profile of the biconvex wing is either mirror-symmetrical or asymmetrical relative to a sagittal axis.

2. A tandem of two airfoil bodies consolidated as a whole [880.B]; the tandem is exposed to an oncoming portion of fluid flow; each of the two bodies [850.B and 860.B] is the airfoil wing of claim 1; the two airfoil wings: first and second, are arranged to meet the oncoming portion [851.B] of the fluid flow, divide the oncoming portion of the fluid flow into two sub-portions of the fluid flow: upper [852.B1, 853.B1, 854.B1, 852.B3, 853.B3, 854.B3] and lower [852.B2, 853.B2, 854.B2, 852.B4, 853.B4, 854.B4], and act on each of the sub-portions of the fluid flow: upper and lower, sequentially in two stages: first and second, namely: 0 at the first stage, the first airfoil wing, meeting the oncoming portion of the fluid flow yet to be subjected to the Coanda-effect and acting on the oncoming portion of the fluid flow by the Coanda-effect, and 0 at the second stage, the second airfoil wing, meeting the oncoming portion of the fluid flow already subjected to the action by the first airfoil wing at the first stage; wherein: U a first convexity is defined as the upper or lower convexity [869.B1 or 869.B2] of the first airfoil wing; and * a second convexity is defined as the upper or lower convexity [869.B3 or 869.B4] of the second airfoil wing; such that a boundary layer, originated adjacent to the upper or lower side of the biconvex wing, is composed of two parts: first, flowing nearby the first convexity, and second, flowing nearby the second convexity; the boundary layer is subjected to at least one of: * the Venturi effect, when an M-velocity of the upper sub-portion of the fluid flow remains lower than the specific M-velocity; * the de Laval effect of flow acceleration nearby the first convexity and to de Laval effect of flow retarding nearby the second convexity, when an M-velocity of the oncoming portion of fluid flow [851.B] is lower than the specific M-velocity and sufficiently high to reach the specific M-velocity nearby the first convexity; or

Page 66 of 73

* the de Laval effect of flow retarding nearby the first convexity and to de Laval effect of flow acceleration nearby the second convexity, when an M-velocity of the oncoming portion of fluid flow [851.B] is higher than the specific M-velocity.

3. A jet-rotor [9.7] comprising an axle [9.73] oriented along a sagittal axis and supplied with a set of blades, wherein the set of blades is a set of at least one of: o the airfoil wings of claim 1; and o the tandems of two airfoil bodies consolidated as a whole of claim 2; the blades are assembled to: * be exposed to oncoming fluid flow at the zero attack angle and thereby subjected to an action of lift-forces originated due to the Coanda-effect dominantly, wherein the Coanda-effect is accompanied by at least one of: o the Venturi effect; and o the de Laval jet-effect; and * vector the originated lift-forces in a frontal plane perpendicular to the sagittal axis to rotate the axle around the sagittal axis

4. A jet-turbine [9.7] comprising: * an engine, having a stator and rotatable shaft, and * the jet-rotor of claim 3; wherein the axle [9.73] is attached to the rotatable shaft to provide for the rotatable shaft to be rotated in unison with the axle rotation around the sagittal axis,

5. A set of the jet-turbines of claim 4, wherein the jet-turbines are arranged in-line along the sagittal axis one downstream behind another.

6. A jet-ventilator [9J.0] comprising: * a motor, having a stator and rotatable shaft, and * a jet-rotor [9J.0] supplied with a set of blades [9J.1], wherein each of the blades is the airfoil wing of claim 1;

Page 67 of 73 the airfoil wings are assembled to be oriented perpendicularly to a sagittal axis such that, when being submerged in stationary fluid [9J.6] and forcedly rotated due to operation of the motor, to run over portions of the ambient stationary fluid at the zero attack angle and, thereby, to be subjected to an action of lift-force [9J.3] originated due to the Coanda-effect dominantly and vectored collinearly to the sagittal axis; thereby, to act on the portions of the stationary ambient fluid by a pushing force vectored against the lift-force according to Newton's third law and so to accelerate the portion of the stationary ambient fluid in conformance with the vectored pushing force.

7. Ajet-propeller[9K.0] comprising: * a motor, having a stator and rotatable shaft, and * a jet-rotor [9K.0] supplied with a set of blades [9K.1], wherein the set of blades is at least one of: o the airfoil wings of claim 1; and o the tandem of two airfoil bodies consolidated as a whole of claim 2; wherein: 0 a pitch is defined for a stationary jet-rotor as an angle between a sagittal axis and an attack angle defined for an airfoil wing of the stationary jet-rotor; each of the blades is assembled to be oriented such that, when being submerged in fluid flow, to provide a pitch adapted to rate of the forced rotation of the rotatable shaft and thereby the jet-rotor such that each of the blades runs over portions of the fluid flow [9K.6] at the zero attack angle and, thereby, is: o subjected to an action of lift-force [9K.3] originated due to the Coanda-effect dominantly, wherein the Coanda-effect is accompanied by at least one of: * the Venturi effect; and • the de Laval jet-effect; and a vectored to have a component collinear to the sagittal axis; thereby, due to the Coanda-effect dominantly, each of the blades acts on the portions of the fluid flow by a pushing force vectored against the component of lift-force according to Newton's third law and so to accelerate the portions of the fluid flow in conformance with the vectored pushing force.

Page 68 of 73

8. An enhanced jet-ventilator comprising the jet-ventilator of claim 6 and at least one of the jet propellers of claim 7, wherein the jet-ventilator and said at least one of the jet-propellers are arranged in-line along a sagittal axis [9L.7 or 9M.7] one downstream behind another.

9. A set of the jet-propellers of claim 7, wherein the jet-propellers [9M.02 and 9M.03] are arranged in-line along a sagittal axis [9M.7] one downstream behind another.

10. A jet-transformer [9.80] comprising: * a nozzle having a convergent-divergent tunnel [9.81] oriented along a sagittal axis [9.851]; * a heater capable of heating a portion of ambient fluid to trigger the Archimedes upward-vectored buoyant force lifting the heated fluid portion and thereby to create upward-moving laminarly headway-forwarding fluid flow such that the sagittal axis is directed vertically; and " a jet-turbine [9.83] of claim 4 capable of transforming the kinetic power of the jet rotor rotation into electric power; wherein: * said convergent-divergent tunnel [9.81] comprising sequentially joint a converging funnel having an open inlet, a narrow throat, and a divergent horn having an open outlet, such that a cross-sectional area profile function A (x) is given by equation of M-velocity expressed as: 1 1y+1 A. y-1L- (2+y(M(x))2 2(y-1) (x) = M(X) yYy+1 where A, is a constant, y is an adiabatic compressibility parameter of the portion of

the fluid stream, x is coordinate along the sagittal axis, and M(x) is a monotonic

gradually-smooth function of x representing an M-velocity profile of the portion of the

fluid stream moving through the tunnel; wherein the constant A, is equal to a cross sectional area of the narrow throat; * said heater is capable to increase an absolute temperature of the portion of ambient fluid entering the convergent-divergent tunnel up to a value To being higher than the absolute temperature Te of ambient fluid outside the convergent-divergent tunnel

Page 69 of 73 beyond the open outlet of the convergent-divergent tunnel such that ratio To/Te is at least 1.2 to provide a condition that when the upward-moving laminarly headway forwarding fluid flow moves within the converging funnel and becomes subjected to the Venturi effect, the upward-moving laminarly headway-forwarding fluid flow reaches the specific M-velocity within the narrow throat and so triggering the de Laval jet-effect; and * the jet-rotor of the jet-turbine is arranged either: * within the convergent-divergent tunnel near or downstream behind the narrow throat, where the M-velocity is determined by the specific M-velocity, or 0 immediately beyond the open outlet, where the M-velocity is determined by a cross-sectional area of the open outlet according to the equation of M-velocity; thejet-rotorof thejet-turbine is arranged to be exposed to said upward-moving laminarly headway-forwarding fluid flow moving through and outflowing from the convergent divergent tunnel such that all the blades of the jet-rotor are oriented to meet portions of said laminarly headway-forwarding fluid flow at the zero attack angle; wherein an overall shape of the blades is adapted to the M-velocity dependent on the x coordinate along the sagittal axis to satisfy conditions of said upward-moving laminarly headway forwarding fluid flow.

11. A jet-transformer comprising: U a nozzle having a convergent-divergent tunnel oriented along a sagittal axis; * a jet-ventilator [9J.0 or 9L. or 9M.0] comprising at least one of the jet-ventilator of claim 6 and the enhanced jet-ventilator of claim 8, said jet-ventilator capable of creating laminarly headway-forwarding fluid flow directed along the sagittal axis; and * a jet-turbine of claim 4 capable of transforming the kinetic power of the jet-rotor rotation into electric power; wherein:

Page 70 of 73

" said convergent-divergent tunnel [9.81] comprising sequentially joint a converging funnel having an open inlet, a narrow throat, and a divergent horn having an open outlet, such that a cross-sectional area profile function A (x) is given by equation of M-velocity expressed as: 1 1y+1 2+y(M(x))z 2(y-1) A(x) = A. y-l( M(x) y y+1

where A, is a constant, y is an adiabatic compressibility parameter of the portion of

the fluid stream, x is coordinate along the sagittal axis, and M(x) is a monotonic

gradually-smooth function of x representing an M-velocity profile of the portion of the

fluid stream moving through the tunnel; wherein the constant A, is equal to cross

sectional area of the narrow throat, and the open inlet is located at the coordinate xo

on the sagittal axis and has an inlet cross-sectional area indicated by A (xo); " said jet-ventilator providing for that the laminarly headway-forwarding fluid flow, when entering the open inlet, has an M-velocity equal to M(xo) estimated according the equation of M-velocity such that the laminarly headway-forwarding fluid flow, when moving along the converging funnel and becoming subjected to the Venturi effect, reaches the specific M-velocity within the narrow throat and so triggering the de Laval jet-effect wherein distribution of M-velocities along the sagittal axis is determined by the value M(xo) of the M-velocity at the open inlet having the cross-sectional area

A (xo); and * the jet-rotor of the jet-turbine is arranged either: * within the convergent-divergent tunnel near or downstream behind the narrow throat, where the M-velocity is determined by the specific M-velocity, or • immediately beyond the open outlet, where the M-velocity is determined by a cross-sectional area of the open outlet according to the equation of M-velocity; the jet-rotor of the jet-turbine is arranged to be exposed to said laminarly headway forwarding fluid flow moving through and outflowing from the convergent-divergent tunnel such that all the blades of the jet-rotor are oriented to meet portions of said laminarly headway-forwarding fluid flow at the zero attack angle; wherein an overall

Page 71 of 73 shape of the blades is adapted to the M-velocity dependent on the x coordinate along the sagittal axis to satisfy conditions of said laminarly headway-forwarding fluid flow.

12. A jet-transformer comprising: " a nozzle having a convergent-divergent tunnel oriented along a sagittal axis; " a jet-ventilator [9J.0 or 9L. or 9M.0] comprising at least one of the jet-ventilator of claim 6 and the enhanced jet-ventilator of claim 8, said jet-ventilator capable of creating laminarly headway-forwarding fluid flow directed along the sagittal axis; and " a jet-turbine of claim 5 capable of transforming the kinetic power of the jet-rotor rotation into electric power; wherein: * said convergent-divergent tunnel [9.81] comprising sequentially joint a converging funnel having an open inlet, a narrow throat, and a divergent horn having an open outlet, such that cross-sectional area profile functions A 1(x) and A2 (x) of said converging funnel and said divergent horn are given by equations of M-velocity expressed as: 1 y+1 m A 1 (x)= 2+y(M(x)) 2)(y-1) , and M1(x) yy+1

2 )2(y-1) * A 2 (x) = A* (y1)( 2(2+(M2(X)) M2(x Yy+1' y

correspondingly, where A* is a constant, y is an adiabatic compressibility parameter

of the portion of the fluid stream, x is coordinate along the sagittal axis, and M1 (x)

and M2 (x) are a monotonic gradually-smooth functions of x representing an M velocity profiles of the portion of the fluid stream moving through said converging funnel and said divergent horn, correspondingly; wherein the values of the functions M, (x)

and M2 (x) within said converging funnel and said divergent horn, correspondingly, remain lower than the specific M-velocity, and wherein the open inlet is located at the

Page 72 of 73 coordinate xo on the sagittal axis and has an inlet cross-sectional area indicated by

A (xo); " said jet-ventilator providing for that the laminarly headway-forwarding fluid flow, when entering the open inlet, has an M-velocity equal to M(xo) estimated according the equation of M-velocity such that the laminarly headway-forwarding fluid flow, when moving along the converging funnel and becoming subjected to the Venturi effect, remains lower than the specific M-velocity within the narrow throat and further when moving along the divergent horn, wherein distribution of M-velocities along the sagittal axis is determined by the value M(xo) of the M-velocity at the open inlet having the

cross-sectional area A(xo); and * the jet-rotor of the jet-turbine is arranged either: * within the convergent-divergent tunnel near or downstream behind the narrow throat, or • immediately beyond the open outlet; the jet-rotor of the jet-turbine is arranged to be exposed to said laminarly headway forwarding fluid flow moving through and outflowing from the convergent-divergent tunnel such that all the blades of the jet-rotor are oriented to meet portions of said laminarly headway-forwarding fluid flow at the zero attack angle; wherein an overall shape of the blades is adapted to the M-velocity dependent on the x coordinate along the sagittal axis to satisfy conditions of said laminarly headway-forwarding fluid flow subjected to the Venturi effect.

Page 73 of 73

1 / 17 03 Mar 2020

102 1071 1081 1072 1082 1073 1083

106

Prior Art Fig. 1b 2020201562

103 104 105

100 140 180 141 142

Prior Art Fig. 1c 101

170 171

160 161 152

Prior Art Fig. 1d 162 172

150 151

2 / 17 03 Mar 2020

115.C “C1” 116.A 110 “D1” 115.D 116.B 115.A 118 115.B “A1” 112 “B1” 111

114 2020201562

116.B 115.D “D1” 116.A 119 Prior Art Fig. 1e “C1” 115.C

12.0 12.5 12.1 12.3 12.7 Prior Art Fig. 1f 12.2

12.4 12.6

10 14 11 12

13 ` Prior Art Fig. 1g 11A 15

16 16.1, 16.2

Prior Art Fig. 1h

3 / 17 03 Mar 2020

18.0 18.2 18.0 18.12 18.17 18 18.13 18.1 B 18.14 2020201562

A 18.11 B 18.15 C 18.3 18.1 18.9 D E 18.16 18.5 18.7 18.6 Prior Art Fig. 1i

17.40 17.2 17.50 17.6 17.3 17.1 17.42 17.52

17.41 17.51

17.42 17.52 Prior Art Fig. 1k

4 / 17 03 Mar 2020

512 517 516 518 517.1 2020201562

513.1 519

514, 513.2 515

513.3 517.2 Fig. 5e

5 / 17 03 Mar 2020

610 618

611

612 614 2020201562

616 613

615

6131 6132

Fig. 6a

641 640

642 631 630 622

623 632 Fig. 6b 620 621

6 / 17 03 Mar 2020

Pressure is linear 2020201562

Fig. 6c

Temperature is linear

Fig. 6d

Density is linear

Fig. 6e

7 / 17 03 Mar 2020

658 650 656 652 654 651 653 2020201562

655

6532 6531 Fig. 6f

660 661 682

663

672

681 662

680 670 671 Fig. 6g

8 / 17 03 Mar 2020

690 694

692 6981 6982 697 691 699 693 696 2020201562

695

Fig. 6h

700 708

8

6 704 701 4 703 2

702 0.5 1 1.5 2 Fig. 7a

9 / 17 03 Mar 2020

800 820 811 810a 821 832 833 810 822 820.0 810c 2020201562

831

823 835 810b 834 824

812

Fig. 8a

865 57 86 4 8

856 863 854 844 840 842 843 868 852 862 855

851 868 Fig. 8b

853 861

10 / 17 03 Mar 2020

860 850 859 854 842 868 853 862 852 851 2020201562

861

841 868 Case (A)

880.B

852.B1 852.B3 853.B1 854.B1 853.B3 869.B1 860.B 86 868.B1 868.B3 842.B1 851.B 850.B

854.B3 841.B

869.B3 869.B1 869.B2 853.B2 853.B4 842.B2 852.B2 869.B2 852.B4 868.B4 854.B4 868.B2 854.B2 869.B4

Case (B)

Fig. 8c

11 / 17 03 Mar 2020

870 , 871 871.1 801 802 803 804 805 806 807 808 809

875

871.0 872 874 873 2020201562

Fig. 8d

9016 9015 9014 917 9013 9160 9012 916 910 9150 9011 915 900 9140 914 9130 913 912 9110 911 Fig. 9a

12 / 17 03 Mar 2020

927 926

922 924

920 929 2020201562

925

921

923

Fig. 9b

930 937 934 936

933 931

Fig. 9c 932 934

13 / 17 03 Mar 2020

9.0 9.6 2020201562

9.31 9.3 9.11 9.1

9.32

9.21 9.3

9.2 9.4 Fig. 9g

14 / 17 03 Mar 2020

9.70 9.7 Side View 2020201562

9.73

9.71 9.72 9.7 Front View

Fig. 9h

15 / 17 03 Mar 2020

9.80 9.851

9.844

9.854 2020201562

9.843 9.81

9.853

9.83

9.842 9.852 9.822 9.823

9.841 9.841 9.821 9.82

Fig. 9i

16 / 17 03 Mar 2020

9J.0 9J.1 9J.5 9J.1 9J.3 9J.9

9J.2 2020201562

9J.7 9J.6

9J.3 9J.9

Front View Side View Fig. 9j

9K.0 9K.1 9K.5 9K.1 9K.3 9K.9

9K.2

9K.7

9K.6 9K.8 9K.9

9K.3 Front View Side View Fig. 9k

17 / 17 03 Mar 2020

9L.01 9L.03 9L.05 9L.07 9L.0 9L.6 9L.02 9L.04 9L.06 9L.5 2020201562

9L.7

Fig. 9L

9M.0 9M.6 9M.01 9M.51 9M.02 9M.52 9M.53 9M.03

9M.7

9M.91

9M.92 9M.93

Fig. 9m