RU2588409C2 - Natural laminar wing for supersonic aircraft - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: natural laminar wing for supersonic aircraft, in which shape of cross section of wing along wing chord at each point along wing span is selected so that curvature near leading edge has a predetermined value 1/3 or less in comparison with normal cross-section in area of linear element 0.1 % of length of wing chord. Curvature in area of linear element 0.2 % of wing chord length from linear element to wing trailing edge is additionally decreased to 1/10. Required pressure distribution for top and bottom surfaces of wing is selected on basis of obtained pressure distribution.

EFFECT: invention is aimed at maximum displacement backwards downstream of turbulisation point.

6 cl, 12 dwg

Description

FIELD OF THE INVENTION

The present invention relates to a method for designing a wing with natural laminar flow around a real supersonic aircraft (LA), in particular, to a method for designing a wing with natural laminar flow around, which, in addition to reducing pressure resistance, which was a problem in the design of supersonic aircraft in the past, reduces friction resistance by delaying the turbulization of the boundary layer on the wing surface under flight conditions similar to those observed on real aircraft (at high numbers eynoldsa), and provides a significant increase in aerodynamic efficiency.

State of the art

In addition to the usual inductive and friction drags, a supersonic aircraft differs from a subsonic aircraft in that it also adds wave resistance due to the action of compaction shocks due to air compressibility (see Fig. 8), resulting in a decrease in aerodynamic quality (lift ratio strength to resistance), which is an indicator of economic efficiency. Concord aircraft, which was the only supersonic transport aircraft, had to deal with problems of economic efficiency and environmental impact due to increased engine noise and sonic boom. Comparing the Boeing 747, which is a subsonic aircraft, and Concord, we see that their aerodynamic quality values are 14 and 7, respectively, and when developing the next generation supersonic transport aircraft, designers will seek to further increase the aerodynamic quality compared to 7 to improve economic efficiency (K. Yoshida, "On fundamental research regarding aerodynamic shape of supersonic transports: an example of in-house research results", Journal of The Japan Society For Aeronautical and Space Sciences, Vol. 42, N486 (1994) , pp. I-13, and K. Yoshida, K. Suzuki, T. Iwamiya and F. Kuroda, "Reconsideration on Aerodynamic Des ign Concepts of the Scaled Supersonic Experimental Airplane - Comparison of the lst Generation SST - ", 3 lst Annual Conference of the Japan Society for Aeronautical and Space Sciences, 2000).

In the optimal aerodynamic design methods using the design gas dynamics method developed in recent years, attempts have been made to create a structure aimed at reducing the pressure resistance, an indicator of which is the aforementioned wave resistance, and significant progress has been made in comparison with the Concord development era (K. Yoshida, "Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA," Progress in Aerospace Sciences, Vol. 45, N4-5, pp. 124-146 (2009)). It was assumed that the combination of the computational gas dynamics method with the design method using numerically optimized algorithms is at a stage in which it can provide practically optimal solutions within various constraints on the performance of the computing system and design (i.e., the constraints imposed by strength calculation, equipment design, flight characteristics, etc.). Therefore, when designers strive for further improvement, and not only to reduce the pressure resistance, it is considered important to try to reduce the friction resistance, which until now has not been taken into account when designing real supersonic aircraft. We also note that this invention is directed to reducing friction resistance.

In general, friction resistance is based on the following physical mechanism. Firstly, due to the viscosity of the air, the speed of the air flow in the immediate vicinity of the aerodynamic surface is practically equal to the speed of the flow on the surface itself, but in the direction perpendicular to the aerodynamic surface, the flow velocity increases sharply from zero to a speed that is approximately equal to the speed of the steady flow, and therefore, the velocity gradient in the perpendicular direction in the immediate vicinity of the aerodynamic surface is extremely high. According to the laws of aerodynamics, the friction force created by air on an aerodynamic surface is equal to the product of the mentioned velocity gradient by the coefficient of viscosity of air. Thus, the goal (the main design task) of reducing the friction force acting on the aerodynamic surface is to reduce the aforementioned viscosity coefficient or velocity gradient. The first of these parameters is an aerodynamic physical constant, and therefore artificial regulation is difficult. Therefore, the fundamental task of designing is to reduce the second parameter, that is, the velocity gradient, in order to reduce the friction resistance.

Further, from the general properties of the boundary layer, it is known that a relatively stable laminar flow is retained on the front of the aerodynamic surface (it is called the laminar boundary layer), and that on the rear of the surface this laminar flow is destroyed and a turbulent flow changes around in time and space (turbulent boundary layer). This change is called border layer turbulization. The phenomenon of turbulization of the boundary layer is that extremely small perturbations of the air flow within the boundaries of the laminar boundary layer are amplified and propagate above the physical body, causing unsteady and spatially irregular perturbations in the boundary layer (see Fig. 9). This is a gain property. and attenuation of disturbances in the laminar boundary layer is called instability of the boundary layer; it is known that in general there are two mechanisms of instability (see Figure 10). One of them is an unstable wave, arising as a result of an unsteady distribution, with an axis perpendicular to the direction of flow that occurs on the wing in a two-dimensional flow. Usually it is called the Tolmin-Schlichting wave in honor of the theoretical discoverers. Thus, this type of instability is called the Tolmin-Schlichting instability (T-S).

The second type of instability is instability arising from velocity components in the boundary layer induced by a pressure gradient in a direction perpendicular to the direction of flow on the three-dimensional swept wing. It is believed that it corresponds to an unsteady distribution with an axis in the direction of flow. This flow is commonly referred to as "transverse flow", so this type of instability is called transverse flow instability (C-F).

It is known that in a turbulent boundary layer resulting from turbulence, under the influence of unstable and spatially irregular turbulence, the flow velocity in places located only at a small distance from the surface, where the velocity is zero, is much higher, and the velocity gradient is much larger than in laminar boundary layer, as a result of which the friction coefficient is about 7 times higher than for the laminar boundary layer, which leads to a sharp increase in friction resistance. Thus, probable ways to reduce friction resistance should include changing the shape of the object (wing) so that the aforementioned turbulence of the boundary layer occurs as far downstream as possible (closer to the trailing edge of the wing), or so that flow can be artificially controlled. The first method uses an improvement in wing design; since natural laminar flow is achieved through the distribution of ambient pressure, it is called natural laminarization; in the second method, active control of the boundary layer is applied by means of suction and discharge, and therefore it is called artificial laminarization of the flow

The main objective of the invention described below is the effective natural flow laminarization, most. efficient and beneficial in the use of energy; This invention relates to a new design method, which, being used for conventional supersonic aircraft to reduce pressure resistance, provides a natural laminar flow around the main wing in order to provide an additional reduction in friction resistance. Until 1998, no such attempts were made anywhere in the world, and the Japan Aerospace Research Agency (hereinafter JAXA) was the first to make such an attempt in its project to create a national experimental supersonic transport aircraft (NEXST). During this project, an experimental supersonic unmanned aircraft with a subsonic leading edge of the swept wing located inside the Mach cone was designed and developed on a reduced scale; first, a theoretical pressure distribution was created on the upper surface of the main wing, causing a significant shift of the turbulence zone of the boundary layer near the front edge of the wing back to the trailing edge of the wing; then a new wing design method was developed to provide such a pressure distribution (K. Yoshida, "Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA", Progress in Aerospace Sciences, Vol. 45, N4-5, pp. 124 -146 (2009); K. Yoshida, "Overview of NAL's Program Including the Aerodynamic Design of the Scaled Supersonic Experimental Airplane", Fluid Dynamics Research on Supersonic Aircraft of VKI, RTO Educational Notes 4, 1998; K. Yoshida and Y. Makino , "Aerodynamic Design of Unmanned and Scaled Supersonic Experimental Airplane in Japan", ECCOMAS 2004; and K. Yoshida, "Flight Test Results of Supersonic Experimental Airplane (NEXST-1)", Nagare, Journal of Japan Society of Fluid Mechanics, Vol. 25, pp. 321-328 (2006)).

11 is a structural diagram illustrating a method for designing a wing with natural laminar flow used in the NEXST project.

This method of designing the wing is the opposite of the conventional method, in which the distribution of pressure is determined in a given shape; here, on the contrary, the shape of the wing is determined for a given pressure distribution. According to the aforementioned method of designing the main wing, the initial configuration of a natural-scale aircraft is first selected to subsequently reduce the pressure resistance; then, using the calculated gas dynamics method and the method for predicting the boundary layer turbulization point (method e ^N, see Fig. 9), the required distribution of the pressure coefficient on the upper wing surface (Ср, required-upper) is determined, and the distribution Ср on the lower wing surface (Ср , required-lower) is obtained by calculating the difference between the distributions of the pressure coefficients on the lower and upper surfaces of the wing (ΔСр, required) and the design method of a swirling wing of the Carlson type in combination with a design concept that concludes Xia to reduce the inductive resistance, which is one type of pressure resistance, a desired distribution Cp on the upper surface of the wing (Cp treb.-top.). After that, the calculated gas dynamics method is applied to the wing cross section of the aircraft's initial configuration, a new pressure distribution is determined in the region of this cross section, and then the difference between the given pressure distribution and the above required distribution of Cp (Cp, req.) Is determined; repeating the process of correcting the shape of the main wing and analyzing using the design gas dynamics method until this calculated difference becomes less than a predetermined value (limit value), determine the cross-sectional shape of the main wing (hereinafter, this method for determining the shape of the wing is called based on the design gas dynamics by reverse engineering). Here, the calculated gasdynamics method is a flow calculation method based on the numerical dynamics of the liquid, and the conventional analysis method using the calculated gasdynamics for a given shape uses the calculated gasdynamics to determine the physical value of the flow field in the immediate vicinity of the surface; A reverse-engineering method based on computational gasdynamics for a given pressure distribution characterizing the flow field serves to determine the shape by realizing the aforementioned distribution by combining conventional analysis using the design dynamics method and the method of sequential shape correction. Thus, when designing the cross-sectional shape of the main wing based on the aforementioned wing design method, in addition to the required distributions of Ср on the upper and lower profile surfaces (Ср, req.), It is important to establish (set) the required distribution of Ср on the upper surface of the main wing (Wed, req.). As already explained above, in flight conditions (with large Reynolds numbers) of a large-sized commercial supersonic transport aircraft (STS) there is no previous example to a large-sized STS with a wing with a natural laminar flow around with a decrease in the friction resistance on the upper surface, and currently there are no publicly available data on the pressure distribution on the upper surface of the main wing, which provides a natural laminarization of the flow around the upper surface of the wing at high Reynolds numbers (Re). In addition, the creation of the required distribution of Cp (Cp, demand-top.) On this upper surface of the main wing requires considerable effort, since this pressure distribution must be set for the entire surface of the main wing in the chord direction from the front to the rear edge of the wing at all points wing span.

The above distribution of Cp (i.e., the distribution of the pressure coefficient) makes the pressure distribution more accurate, and the concept of the distribution of Cp is expressed in the same way as one of the pressure distributions. Here the principle stated above is changed.

The Japanese aerospace research agency, on the assumption that in the NEXST project the problem of pressure resistance at a supersonic leading edge during supersonic flight, is the main one, and that when using its results for the leading edge when flying at subsonic speeds, even higher characteristics will be obtained, first applied both described above the concept of reducing pressure resistance when designing using a linear theoretical technique (principles 1, 2, 3 of reducing pressure resistance in FIG. 12 BUT). Then an attempt was made to develop a method for designing a wing structure with natural laminar flow, limited by the upper surface of the main wing, using the reverse design method based on the calculated gas dynamics. In this method of designing a wing with natural laminar flow, first a shape with a theoretical pressure distribution is found to slow down the turbulence of the boundary layer on the upper surface of the main wing (Fig. 112B), then this theoretical pressure distribution is taken as required using the resistance reduction method described above pressure, the projected form of the airframe is selected as the initial one, based on this form of the wing cross section, the analysis using the method of calculated gasdynamics is used ki for estimating the pressure distributions on the upper and lower surfaces of the main wing, and then the analysis by the method of calculated gas dynamics is repeated, making small corrections in the shape of the wing, until the difference between the estimated and the required pressure distributions becomes less than a certain specified value. Using the method of designing a wing with natural laminar flow based on the reverse-design method based on computational gasdynamics, by repeating this usual method of computational gasdynamics and correcting the shape, a certain transverse shape of the wing is developed (Fig. 12C). As a method of easy shape correction based on the formulation of a supersonic linear theory (theory of a bearing surface), and using the fact that the pressure and curvature and thickness of the aerodynamic profile are in one-to-one correspondence, a numerical solution of the integral equation that determines this correspondence was used.

A qualitative assessment of the effect of a natural laminar flow wing designed in this way was first made through a wind tunnel test (see Fig. 12D). The term “quality” here means that since disturbances inevitably arise in the design of a wind tunnel creating a supersonic flow, the incoming air stream already contains a significant amount of small turbulences, and they are combined with the instability of the boundary layer, that is, there is a physical mechanism contributing to turbulization, and as much as in the general case it was difficult to eliminate this influence (in rare cases, under specific blowing conditions, a significant but to suppress the turbulence of the air flow in the wind tunnel, but could not be completely eliminated), it is believed that the turbulence of the air flow in the wind tunnel affects the turbulence of the boundary layer. That is why the Japanese Agency for Aerospace Research created a reduced-scale experimental supersonic aircraft and evaluated the design of the wing with natural laminar flow under real flight conditions without turbulence of air flow. The total glider length of the experimental aircraft was 11.5 m, and it was completed on a scale of 11% of the estimated dimensions of the real STS in full size. The results of the analysis of the boundary layer turbulization data obtained during flight tests confirmed that the turbulization point shifted approximately 40% down the chord of the wing, and the effect of the design principle of a wing with natural laminar flow was evaluated on the experimental NEXST-1 aircraft (see. 12D and K. Yoshida, "Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA," Progress in Aerospace Sciences, Vol. 45, N4-5, pp. 124-146 (2009)).

However, since these experiments used a scaled-down aircraft with a total length of 11.5 m, the Reynolds number was also 11% of the estimated large-scale STS, and the aforementioned method of designing a wing with natural laminar flow around developed in the NEXST project had problems regarding the development of a method for applying in the design of a real aircraft; it became clear that significant improvement was required in the required pressure distribution obtained for the NEXST-1 aircraft design (R. Ueda and K. Yoshida, "Numerical Study on Optimum Pressure Distribution for Supersonic Natural Laminar Flow Wing Design", Proc. 32 nd Fluid Dynamics Conference , 2000).

This is equivalent to an increase in the Reynolds number, causing a significant increase in instability in the boundary layer, so that the creation of the required pressure distribution on the upper surface of the main wing should fully take into account the dependence on the Reynolds number. In particular, at high Reynolds numbers corresponding to a real aircraft, extremely high transverse instability (CF) is observed, and with the required pressure distribution on the upper surface of the main wing obtained for the construction of a real aircraft in the NEXST-1 project, it was subsequently discovered that an adequate effect not reflected. Therefore, the Japanese Agency for Aerospace Research conducted a study of the effect of improving pressure distribution in order to obtain a similar natural laminarization even for high Reynolds numbers, corresponding to those observed in large-sized aircraft, such as STS. As a result, as one of the results, it was found that if the acceleration gradient near the leading edge was increased by 3 or more times than during the design of the experimental NEXST-1 aircraft, then the effect took place (R. Ueda and K. Yoshida, " Numerical Study on Optimum Pressure Distribution for Supersonic Natural Laminar Flow Wing Design ", Proc. 32 nd Fluid Dynamics Conference, 2000), but with the subsequent detailed analysis it became clear that although the basic approach to obtaining this result was qualitatively rational, in quantitative terms it not as expected, and extensive refinement was needed ka. The main reason for this was the error due to the lack of accuracy of the model in the method of turbulization analysis applied this time. In addition, a universal method for designing a wing with natural laminar flow, applicable not only to the main wing, but also to other bearing surfaces of the experimental NEXST-1 aircraft, was not created. The present invention addresses these problems.

And finally, in the USA, independent studies of natural laminarization at supersonic speeds were carried out almost at the same time period as the aforementioned NEXST project (I. Kroo, P. Sturdza, R. Tracy and J. Chase, "Natural Laminar Flow for Quiet and Efficient Supersonic Aircraft ". AIAA-2002-0146, 2002). These studies used the concept of designing a wing with laminar flow around, different from the concept of designing a wing with natural laminar flow used in the design of NEXST-1; as mentioned above, while the NEXST-1 design used a method for suppressing transverse flow instability (CF), the principle of creating the design in the aforementioned US studies was to suppress Tolmin-Schlichting instability, and unlike a conventional wing with a large sweep angle of about 45 ° or more, chosen to reduce pressure resistance, a U.S. project examined a wing with a small sweep angle of about 10 ° to 20 °, with a supersonic leading edge. Since the leading edge of this wing has a characteristic cross-sectional shape with an acute fine distribution, the pressure gradient in the direction of flow reliably decreases monotonously, and here there is an advantage in the acceleration gradient, which has a decisive influence in suppressing Tolmin-Schlichting instability; but since with a small elongation, the wing sweep angle is small, in the above range from about 10 ° to 20 °, the inductive resistance increases, and it is believed that a simultaneous decrease in the friction resistance and pressure resistance is difficult. The effect of turbulence point displacement using this method was visually confirmed by flight tests with the wing of the shape described above attached perpendicular to the fuselage of the F-15 fighter (however, the wing itself was made on a scaled-down model); as for the confirmation of natural laminarization on the glider of a real aircraft, the advanced technical level is obvious here, but if we take into account that the scale model was used (the Re number did not correspond to the Re number of the real plane here), and that no attempt was made to simultaneously reduce the pressure resistance, this the study is regarded as completely unfinished in terms of its use in the construction of a real aircraft. In addition, since no research and development on natural laminarization is currently underway in Europe, the usefulness of the invention is obvious.

Disclosure of invention

This invention was developed as a result of the analysis of the problems of the prior art described above, and its purpose is to provide a method for designing a wing with natural laminar flow around a large-scale commercial supersonic aircraft, which, in addition to reducing the pressure resistance, which is usually a task when designing supersonic aircraft, provides displacement points of turbulization of the transition layer on the wing surface at high Re numbers corresponding to those arising on real aircraft, as well as ensuring There is a significant improvement in aerodynamic quality.

To achieve the aforementioned goal, a method for designing a wing with a natural laminar flow around p. 1 according to claim 1 is proposed, including: a process for determining an initial shape of a wing cross section; the analysis process by the method of design gas dynamics to determine the pressure distribution of the flow field near the wing surface of the obtained cross-sectional shape; the turbulization analysis process with the aim of approximating the position of the boundary layer turbulization point on the wing surface; the process of establishing the required pressure distributions for the upper and lower wing surfaces, based on the obtained pressure distribution; and a reverse engineering process based on computational gasdynamics, including an analysis process using the computational gasdynamics method and a shape adjustment process that corrects the wing cross-sectional shape so that the pressure distribution obtained during the computational gasdynamics analysis converges at the required pressure distribution, characterized in that From the required pressure distributions, the pressure distribution on the upper surface of the wing determines the “direction along the chord of the wing from the front to the back to fittin g "as a field in each point of the wing span, and moreover, which is assigned to the function type with parameters depending on the position along the span as coefficients; then the turbulization sensitivity of the boundary layer on the upper surface of the wing due to a change in the magnitude of each of the above parameters is analyzed by the turbulization analysis process; and through the search, the optimal combination of parameter values is determined, which maximally shifts to the trailing edge of the wing the point of turbulence of the boundary layer on the upper surface of the wing for a given Reynolds number.

The aforementioned method of designing a wing with natural laminar flow around uses a new process that facilitates the creation of the required pressure distribution corresponding to a wing with natural laminar flow, effectively shifting back the point of turbulence of the boundary layer on the upper surface of the wing even at high Reynolds numbers occurring on large STS, which is part of the design method for a wing with natural laminar flow developed in the NEXST project, and the appropriateness of applying This was confirmed by wind tunnel tests and flight tests of the NEXST-1 aircraft, i.e., a reverse engineering process based on computational gasdynamics, containing operations to obtain the required pressure distribution, conducting a conventional analysis using the design gasdynamics to obtain this distribution, and making shape adjustments. In other words, for the required pressure distribution on the upper surface of the wing, corresponding to natural laminarization, the parameters depending on each of the points along the wing span are determined by the types of functions with coefficients, and separate analyzes of the sensitivity of the fluctuations of the points of turbulence of the boundary layer to the change in the value of each of the parameters with using a turbulization analysis method called a “method e ^N ”; By searching for the optimal combination of each of the parameter values that provide the maximum displacement of the point of turbulence of the boundary layer to the trailing edge of the wing, it is easy to obtain the required pressure distribution, which ensures the displacement of the point of turbulence of the boundary layer on the upper surface of the wing even at high Reynolds numbers occurring on large-scale STS.

In the method for designing a wing with a natural laminar flow around claim 2, among the required pressure distributions, the required pressure distribution on the lower surface of the wing is determined based on the required pressure distribution on the upper surface of the wing, as well as the distribution of the pressure difference between the upper and lower surfaces, which ensures optimal a combination of the distribution of the angle of aerodynamic twist and the curvature of the wing at points along the wing span.

In the aforementioned method of designing a wing with a natural laminar flow, it is possible to easily obtain the desired pressure distribution on the lower surface of the wing by sharing the desired pressure distribution on the upper surface of the wing, obtained using the sensitivity analysis using the turbulization analysis method described above, and the distribution of the pressure difference between the upper and the lower surfaces obtained by the design method, in order to obtain the optimal combination of distribution la aerodynamic wing twist and curvature along the wing span, such as a method of designing the angle of twist of the wing. Thus, using the pressure distribution obtained using the required pressure distributions on the upper and lower surfaces as the required pressure distribution in the reverse-engineering process based on the calculated gas dynamics, the pressure resistance and the friction drag of the wing are reduced, and a wing with a natural laminar shape can be designed flow around the STS, providing a significant improvement in aerodynamic quality.

In the method for designing a wing with a natural laminar flow around claim 3, when the direction of the wing chord is along the X axis, the direction of the wing span is along the Y axis, and the length of the wing chord (= c (y)) is used to create a point in the direction of the chord (X ) from the leading edge of the wing, in each position by the span (Y = y) dimensionless (ξ≡х / s (y)), the shape of the required pressure distribution on the upper surface of the wing in each position along the wing span is created in such a way that it is extremely narrow the area from the leading edge of the wing in which Δξ <0.01 is set, the gradient the rapid increase in pressure and the gradient of rapid decrease are continuous, and in the next wide region in which Δξ≤ξ≤1 is established, the pressure gradually increases, and at the same time, the acceleration decreases, and the gradually accelerating gradient, asymptotically approaching the specified value, is continuous.

In the aforementioned method of designing a wing with a natural laminar flow, the main wing of a large-scale STS with a large sweep angle is considered. Thus, the main task is to suppress transverse flow instability (C-F), which is the main type of instability near the leading edge of the wing with a large sweep angle (45 ° or more); further, an attempt was made to further suppress the Tolmin-Schlichting instability (T-S), which is dominant at a distance from the leading edge. In particular, since transverse flow instability (C-F) is the main reason for the appearance of a pressure gradient in the transverse direction, from the very beginning the design principle was to reduce pressure gradients in all directions. However, taking into account the influence of wing thickness, wingtips and the phenomenon of lift, it becomes clear that it is impossible to maintain a small pressure gradient.

Thus, for starters, such a distribution form was chosen as the pressure gradient in the direction of the oncoming flow that the region in which a large change was observed was limited to the initial section near the leading edge of the wing, for about 1% of the length of the wing chord, and after that, as they developed in the direction of the wing span, the pressure gradient remained almost unchanged, and the pressure level remained almost constant, so that large pressure gradients did not arise. We believe that this corresponds to the ideal form of pressure distribution for natural laminarization, which is most appropriate for the main wing with a large sweep angle; The sensitivity of the parameters characterizing the shape of the pressure distribution to the turbulization characteristics was studied in detail, and for each Reynolds number, specific distribution forms were selected that corresponded to the scale of the main wing for application. Considering this form of distribution in the direction of flow, we see that there is a very sharp acceleration in the area near the leading edge at a distance of about 0.5% of the length of the wing chord, and after reaching the minimum pressure point, there is a sharp decrease in approximately the same small area and then there is a tendency to smooth acceleration up to the trailing edge of the wing. A sharp initial acceleration is intended to reduce the aforementioned deceleration portion, and a second rapid deceleration is provided to suppress the lateral flow arising in the initial deceleration portion by creating a pressure gradient in the opposite direction. The higher the Reynolds number, the greater the need for the systematic use of this phenomenon; this characteristic form of pressure distribution is almost everywhere described by a step function.

In the method for designing a wing with a natural laminar flow around claim 4, in addition to the required pressure distribution on the upper surface of the wing described above, for the point of maximum pressure attainment (minimum pressure value) of the rapid deceleration of the gradient in each position along the wing span and the given value of the smooth gradient acceleration, based on the set values, so as to be equal to the average values of the pressure distributions, on predetermined sections along the length of the wing chord in the same position on the span the initial pressure distribution obtained by analyzing the calculated gas dynamics of the initial distribution, conducting the process of turbulization analysis and adjusting both values, again selects the combination that provides the maximum displacement of the turbulization point back.

In the above-described method for designing a wing with a natural laminar flow, considering that the development of the pressure distribution over the wing span is directly related to the instability of the transverse flow (CF), the average pressure levels are in a constant range, for example, in the range from 20% to 80% along the chord length the wings in each position according to the wing span of the initial pressure distribution, obtained by applying the usual analysis by the method of calculated gas dynamics to the initial shape, are selected as characteristic distribution values pressure in the chord direction for each position along the wing span, and the required pressure distribution on the upper surface of the wing is created in each position along the wing span, so that the points of maximum pressure (minimum pressure values) near the leading edge in each position along the wing span almost equal to the aforementioned characteristic values, and also so that the asymptotic values at the trailing edge of the wing are practically equal to these characteristic values. Finding a combination of values at which the point of turbulization of the boundary layer is maximally shifted backward, while simultaneously analyzing the turbulization and independently adjusting the characteristic values, it is possible to suppress the instability of the transverse flow.

In the method for designing a wing with a natural laminar flow around claim 5, in addition to the required pressure distribution on the upper surface of the wing, in each position along the wing span, as a basic principle, the pressure value at the leading edge of the wing obtained by multiplying the pressure at the critical point is set, determined by the number M of the unperturbed flow and the sweep angle of the leading edge, by a predetermined value.

With a positive lift, since, in the general case, the critical point is near the lower surface of the wing near the leading edge, the required pressure distribution on the upper surface of the wing at the leading edge of the wing should be set slightly less than required. With this determination, the Cp value at the leading edge is calculated based on the results of the analysis of the initial form by the method of calculated gas dynamics, and the adoption of this value provides the highest accuracy. Therefore, this value can be used. However, the author of this application experimentally found that, in addition to determining from the results of analysis by the method of calculated gas dynamics, the value obtained by multiplying the pressure at the critical point (Crit.), Determined by the number M of undisturbed flow (M _∞ ) and the sweep angle of the leading edge (Λ _LE ), by a constant value, for example, 0.86, gives a result that corresponds quite accurately to the results of analysis by the method of calculated gas dynamics for the initial form, and when using this value, the design process of the plant It is more effective; Thus, as a basic principle, we select this value.

In the method for designing a wing with a natural laminar flow around claim 6, when each position according to the wing span (Y = y) is defined as the dimensionless (η≡y / s) no half-span, the required pressure distribution on the upper surface of the wing (Сp (ξ, η )) is described by the following exponential function, having as parameters the parameters {A ₀ (η), A ₁ (η), A ₂ (η), A ₃ (η), A ₄ (η), B ₁ (η), B ₂ (η), B ₃ (η)}, which depend on each position in terms of the wingspan, and parameters {P ₁ , P ₂ }, which do not depend on the positions in terms of wingspan,

Equation 1

$$$$

, $$\begin{array}{l}Cp\left(\xi ,\eta \right)=A_0\left(\eta \right)\cdot \mathrm{one}+A_{\mathrm{one}}\left(\eta \right)\cdot \left[\exp \left(B_{\mathrm{one}}\left(\eta \right)\xi \right)-\mathrm{one}\right]+A_2\left(\eta \right)\cdot \left[\exp \left(B_2\left(\eta \right)\xi \right)-\mathrm{one}\right]+\\ A_3\left(\eta \right)\cdot \left[\exp \left(B_3\left(\eta \right){\xi }^{P\mathrm{one}}\right)-\mathrm{one}\right]+A_{\mathrm{four}}\left(\eta \right)\cdot {\mathrm{<figure-callout\; id="2"\; label="\xi \; P"\; filenames="00000010.png"\; state="\{\{state\}\}">\xi \; </figure-callout>}}^P\end{array}$$

$$$$

,

using the turbulization analysis process, we study the dependence of the boundary layer turbulization on the upper surface of the wing on the change in the values of each parameter, and search for the optimal combination of parameter values that "ensures the maximum backward shift of the boundary layer turbulization point on the upper surface of the wing for the Reynolds number under consideration."

The author of this application found that the above type of function quite accurately reflects the required pressure distribution corresponding to natural laminarization, which, for a given Reynolds number, provides a backward displacement of the boundary layer turbulization points on the upper surface of the wing, i.e. a pressure distribution at which the gradient accelerates rapidly in an extremely narrow in the range of about 1% along the length of the wing chord at the leading edge of the wing and the rapid deceleration of the gradient are continuous, and the gradual acceleration of the gra ienta continues on a long section thereafter. When determining each of these parameters, based on the already determined parameter values (measured values), a turbulization analysis method is used to carry out sensitivity analysis (parametric studies) in order to determine the parameters. Thus, the required pressure distribution corresponding to natural laminarization is determined using the type of function having as parameters coefficients determined by sensitivity analysis by means of a turbulization analysis method, and by searching for the optimal combination of parameter values for maximum backward displacement of the boundary layer turbulization point, the required pressure distribution, which even with high Reynolds numbers occurring on large-scale STS, is espechivaet maximum rearward displacement of the point of turbulence of the boundary layer on the upper surface of the wing.

On supersonic aircraft built using the method of designing a wing with natural laminar flow according to any one of the preceding paragraphs 1-6, the shape of the wing cross section in the direction along the wing chord in each position along the wing span differs in that it has a curvature near the leading edge ( critical point), which is a constant value and 1/3 or less of the curvature of the normal shape of the wing cross section (the shape of the wing cross section of the Concord aircraft, which is practically used as a commercial supersonic aircraft) in the contour element of at least 0.1% along the length of the wing chord, including the leading edge, and the fact that its curvature further rapidly decreases to 1/10 or less of this constant value in the contour element 0.2% along the wing chord from of the aforementioned contour element to towards the trailing edge of the wing.

The aforementioned wing of a supersonic aircraft, in addition to reducing pressure resistance, can also reduce the friction resistance on the wing surface, and provides a significant improvement in aerodynamic quality.

Using the method of designing a wing with natural laminar flow, proposed by the present invention, for the original form of a natural-scale aircraft, optimized in such a way as to reduce the pressure resistance of a supersonic aircraft, it is possible to further reduce the friction resistance on the upper surface of the wing, avoiding the negative impact on its inductive resistance. In particular, at the moment there are no technical reports on the main wing in the plan (for an airplane) with a subsonic leading edge for large-scale STS (with high Reynolds numbers), the purpose of which would be the so-called natural laminarization of the flow around the upper surface of the wing with the purpose of expanding the area of laminar flow and reducing friction due to rearward displacement of the point of turbulence of the boundary layer on the upper surface of the wing, and, thus, the proposed design method has not yet been set; but using the method of designing a wing with natural laminar flow proposed by the present invention, it is possible to simultaneously reduce the inductive resistance (pressure resistance) of the wing and fuselage, and the friction resistance on the upper surface of the main wing of a large-scale STS.

Brief Description of the Drawings

Figure 1 is a flowchart illustrating a method of designing a wing with natural laminar flow around, proposed by this invention;

FIG. 2 is an explanatory diagram showing typical plan views of an STS wing considered by the present invention; FIG.

Figure 3 is an explanatory diagram showing the pressure distributions on the upper surface of the wing, obtained by conventional analysis using the design gas dynamics method for the initial form of a natural-scale aircraft (for a triangular wing in plan);

Fig. 4A is an explanatory diagram showing the shape characteristics of the desired Cp distribution on the upper surface of the wing, corresponding to the natural laminarization necessary to reverse the point of turbulence of the boundary layer at high Reynolds numbers;

Fig. 4B is an explanatory diagram showing an example of a type of function determining the desired distribution of Cp on the upper surface of the wing, corresponding to the natural laminarization necessary to shift back the point of turbulence of the boundary layer at high Reynolds numbers observed on large-scale STS;

Fig. 5A is an explanatory diagram showing an example of parameters of the desired distribution of Cp on the upper surface of the wing, corresponding to the natural laminarization necessary to shift backward the points of turbulence of the boundary layer at high Reynolds numbers observed on large-scale STS;

Figv - the desired distribution of Cp for the parameters of Fig.5A;

FIG. 6 is an explanatory diagram showing the results of a turbulization analysis conducted for the shape of the desired Cp distribution shown in FIG. 5B;

Fig. 7A is an explanatory diagram for comparing wing cross-sectional shapes as examples of a natural laminar flow wing structure for large-scale STS at high Reynolds numbers;

Fig. 7B is an explanatory diagram for comparing (by superimposing) wing cross-sectional shapes as examples of a natural laminar flow wing structure for large-scale STS at high Reynolds numbers;

Fig. 7C is an explanatory diagram for comparing (by overlaying) the distribution of curvature near the leading edge for wing cross-sectional shapes as examples of a natural laminar flow around wing structure for large-scale STS at high Reynolds numbers;

Fig. 8 is an explanatory diagram showing the distribution of drag of a supersonic aircraft as the basis of the present invention;

Fig.9 is an explanatory diagram showing the main results of calculating the point of turbulence of the boundary layer as a base of the present invention;

Figure 10 is an explanatory diagram showing the physical principle of the phenomenon of turbulization of the boundary layer as the basis of this invention;

11 is a structural diagram illustrating a method of designing a wing with natural laminar flow around used in the NEXST project;

12A is an explanatory diagram showing the principle of aerodynamic design of a pilot scaled-down supersonic aircraft of the Japan Aerospace Research Agency;

Figv is an explanatory diagram showing the main results of the required distribution of Cp for the experimental performed on a reduced scale supersonic aircraft of the Japanese Agency for Aerospace Research;

Fig. 12C is an explanatory diagram showing the main results of a design-based gas dynamics method for reverse engineering an experimental, scaled-down supersonic aircraft of the Japanese Aerospace Research Agency; and

12D is an explanatory diagram showing the main results of an experimental evaluation of a wing structure with natural laminar flow around an experimental scaled-down supersonic aircraft of the Japan Aerospace Exploration Agency.

The implementation of the invention

The following is a more detailed description of the present invention using the designs presented in the drawings.

Figure 1 is a flow diagram illustrating a method for designing a wing with natural laminar flow around this invention.

The proposed design method, along with the fact that it includes an inverse design method based on computational gasdynamics for determining the shape of the wing providing a desired pressure distribution, is a conventional analysis by the design of gas dynamics to determine the pressure distribution near the wing of a given shape, which is typical of the design method natural laminar flow wings (hereinafter referred to as the "existing method for designing a natural laminar wing "), developed in the NEXST project and presented in FIG. 11, and a method for adjusting the wing shape so that the pressure distribution near the wing shape converges to the desired pressure distribution, provides an easy way to create the desired pressure distribution (the required distribution of Cp) needed for designing a wing with natural laminar flow, which reduces the friction resistance on the upper wing surface (shifting back the point of turbulence of the boundary layer) in flight conditions, ha typical for large-scale STS (at high Reynolds numbers), which was difficult when using the existing method of designing a wing with natural laminar flow. Details are explained below with reference to FIGS. 3 and 4, but under flight conditions characteristic of large-scale STS flight, the required distribution of Cp on the upper surface of the wing, providing a natural laminar flow around the wing, is quantified by the type of function in which the direction along the chord of the wing from the front edges to the trailing edge in each position according to the wing span (η) is considered as a region (ξ), and having as a coefficient a number of parameters (in the present version {A ₀ , A ₁ , A ₂ , A ₃ , A ₄ , B ₁ , B ₂ , B ₃ }, depending on the position in terms of wing span .. The basic type of function remains unchanged, but for analyzing sensitivity and changing parameters (parametric studies), a turbulization analysis method (method e ^N ) is used to simplify obtaining the required distribution of Cp, which positively affects the wing with natural laminar flow with satisfactory characteristics boundary layer turbulization in flight conditions typical of large-scale STS (at large Reynolds numbers), i.e., providing a backward shift of the turbulization point uu boundary layer on the wing surface.

Thus, in addition to the conventional method for designing a wing with natural laminar flow, the flowchart in FIG. 1 introduces the process of analyzing the initial characteristics of the Cp distribution on the upper surface of the wing obtained using conventional analysis using the design gas dynamics method for the initial configuration of the aircraft (step S4 ), and by adjusting the distribution parameters of Cp on the upper surface of the wing by means of sensitivity analysis using method e ^N (steps S5 and S6). In other words, at the first stage, the initial configuration of a natural-scale aircraft is developed in order to reduce pressure resistance (steps S1 and S2); then, for this initial configuration of a natural-scale aircraft, the usual analysis is performed by the method of calculated gas dynamics and the characteristics of the pressure distribution on the upper surface of the wing are analyzed (steps S3 and S4). After that, based on the results of this analysis, the parameters of the type of function are corrected for the required distribution of Cp (on the upper surface of the wing) (steps S5 and S6). Then, based on the distribution of the pressure difference between the upper and lower surfaces of the wing obtained during the design of the swirling wing (Carlson type), the pressure distribution form on the lower surface of the wing is calculated and the required distribution Cp of the main wing is established, which is necessary for the reverse design method based on the calculated gas dynamics (step S7). The analysis using the design gas dynamics method is applied to the wing cross-sectional shape of the initial configuration of a natural-scale aircraft, the shape is corrected to eliminate the difference between the Cp distribution obtained by analyzing the calculated gas dynamics method and the required C distribution on the main wing described above, and this process is repeated until until convergence occurs and the difference becomes zero (step S8). Typically, an equation based on a supersonic linear theory is used as the aforementioned form correction method; but even if the linear approximation error becomes too large with increasing wing thickness and approaching the leading edge, it is believed that as long as the non-linearity analysis is cyclically used by the method of calculated gas dynamics, this method will be most effective.

Below is an explanation of each of the above steps.

First, in step S1, settlement points are set. As calculation points, for example, the cruising number M, the lift coefficient when flying in the cruise mode C _L , the angle of attack α, the Reynolds number for the average aerodynamic chord R _{e, MAC} , the flight height in the cruise mode N, and the aircraft length L can be selected , MAC average aerodynamic chord (SAX) and wing sweep angle Λ _LE .

As for the ranges of the above parameters, for the number M, for example, we choose the range 1.4≤M≤3.0. As a range of Reynolds number for SAX, we choose, for example, 14 * 10 ⁶ ≤R _{e, MAC} ≤180 · 10 ⁶ . The height of the cruise flight, for example, let it be in the range of 16 km (M = 1.4) ≤H≤20 km (M = 3.0). The full length of the aircraft, for example, let it vary in the range of 48 m (small-sized STS) ≤L≤105 m (large-sized STS). The average aerodynamic chord, for example, let it vary in the range of 13 m ≤ MAC ≤ 48 m. And, the range of the angle of sweep of the wing), for example, let it be as follows: 45 ° (M = 1.4) ≤ Λ _LE ≤ 80 ° (M = 3.0 )

As one example for this design, select the following design points:

(1) M = 2.0, C _L = 0.1, α = 2 °

(2) N = 18.3 km, R _{e, MAC} = 120 · 10 ⁶

(3) L = 91.4 m, MAC = 25 m

Then, in step S2, we determine the initial configuration of the natural-scale aircraft. First, we determine the initial configuration of a natural-scale aircraft, bearing in mind the task of reducing pressure resistance. The main components of pressure resistance are volume-dependent wave resistance and inductive resistance; as a design principle to reduce the volume-dependent impedance, we choose, for example, a fuselage with contours according to the "area rule", and as a design principle in order to reduce inductance we choose, for example, a swept wing in plan and a wing with a Carlson twist (optimal combination of wing curvature and aerodynamic twist distributions).

FIG. 2 is an explanatory diagram showing typical plan views of an STS wing considered by the present invention; In this invention, if the wing shape in plan (with a subsonic leading edge) is located with the leading edge inside the Mach cone created by each part of the aircraft, as shown in Figure 2, the application of this invention is in principle possible, regardless of the shape of the wing in consideration in plan. Application is possible for numbers M from about 1.4 to 3.0, and as a result for wing shapes in plan with a sweep angle along the leading edge of about 45 ° to 80 °. As a scaled-down model of a natural airplane, we consider aircraft that have already been approved by the Japan Aerospace Research Agency (experimental scaled NEXST-1 with a total length of 11.5 m); we assume that the study involved aircraft from small-sized STS with a passenger capacity of 35 to 50 people (total length of about 48 m), including medium-sized STS of the Concord type with a passenger capacity of 100 people (total length 62 m), and to large-sized STS with a passenger capacity of 300 passengers (total length 91 m); at the same time, Reynolds numbers for the MAR are covered in the range from 14 · 10 ^-6 to 180 · 10 ^-6 . Of course, even for lower Reynolds numbers of 14 · 10 ^-6 and lower, considering the aerodynamic characteristics, we will see that the instability of the boundary layer on the upper surface of the wing decreases, and therefore, this invention can be applied without modification.

In the next step (S3), the analysis by the method of computational gas dynamics is applied to the original form of a natural-scale aircraft. The analysis results (evaluation results) are used to determine the parameters {A ₀ , A ₁ } from among the above parameters related to the type of the required distribution function Ср, the receipt of which is the purpose of the method for designing a wing with natural laminar flow around the invention.

Then, in step S4, the initial distribution of Cp on the upper surface of the wing is analyzed.

Figure 3 presents an explanatory diagram showing the pressure distribution on the upper surface of the wing, obtained by conventional analysis by the method of calculated gasdynamics for the original form of a natural-scale aircraft (for a triangular wing in plan). The vertical axis represents the pressure coefficient Cp obtained by converting the difference with the static pressure of the steady flow into a dimensionless quantity using dynamic pressure. Usually negative values are laid up, and the upward trend observed in the Cp distribution indicates the direction of acceleration in flow rate.

In this distribution of Cp, in order to make analysis possible, the position along the chord (X) in each position according to the wing span (Y = y) is defined as the new variable ξ (≡X / s (y)), translated into a dimensionless quantity (= X / s (y)) using the length along the wing chord (= c (y)) with the origin from the leading edge of the wing. Thus, by transforming to obtain the dimensionless abscissa, the distribution region of Ср in the direction along the chord of the wing at each position in the wing span is completely located between the values 0 and 1, regardless of the position in the wing span, and the set of distributions Ср in different positions along the wing span can be displayed simultaneously in the same coordinate plane. Figure 3 shows the distribution of Cp at six characteristic points along the wingspan (y / s = 0.2; 0.3; 0.5; 0.7 and 0.9).

Similarly, the coordinate in the direction of the wing span (y) is converted to a dimensionless quantity (= y / s) by dividing by the half-span (= s), and is denoted as the new variable η (= y / s).

As can be seen from the drawing, in general, the average value of the pressure level in the rear part from the center of the wing over the distribution of Cp tends to shift from the inner region of the wing to the outer (with increasing η). Therefore, the parameter A ₁ is determined so as to follow this trend. The simplest way of tuning is to use the average values (C _{p, av (η)} ) of the pressure levels near the wing chord length from 20 to 80% (0.2≤ξ≤0.8) as A ₁ (0.2), A ₁ (0, 3), A ₁ (0.5), A ₁ (0.7) and A ₁ (0.9) in each of the aforementioned wing spans.

Further, A ₀ is the value of the required distribution of Cp at the leading edge (ξ = 0), but with a positive lifting force, in general, the critical point is near the lower surface of the wing near the leading edge, and therefore, the pressure should be set slightly less. than pressure at a critical point. This is most accurately determined by calculating the Cp value at the leading edge (each Cp value in Fig. 3, for which ξ = 0) according to the results of a conventional analysis using the calculated gas dynamics method; but when using the simplified method of determination, as shown in equations 2 and 3 below, it is recommended to take a value equal to a coefficient of 0.86 times the value of Cp at the critical point (Crit. Crit.), determined by the number M of the steady stream (M _∞ ) and leading edge sweep angle (Λ _LE ) according to the isentropy equation.

The equation

$$Cp\mathrm{to}R\mathrm{and}t.=\left[{\left\{\mathrm{one}+0.2M_{\infty }^2\left(\mathrm{one}-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="00000010.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2{\Lambda }_{LE}\right)\right\}}^{3.5}-\mathrm{one}\right]\times {\left(0.7M_{\infty }^2\right)}^{-\mathrm{one}}$$

Equation 3

. $$A_0=0.86\times Cp\mathrm{to}R\mathrm{and}t$$

.

Then, in step S5, the parameters of the required Cp distribution on the upper surface of the main wing are corrected.

Fig. 4A is an explanatory diagram showing the shape characteristics of the desired Cp distribution on the upper surface of the wing, corresponding to the natural laminarization necessary to shift back the point of turbulence of the boundary layer at high Reynolds numbers.

Distinctive features of this desired distribution of Cp on the upper surface of the wing are the rapid acceleration of the gradient (parameter A ₁ ) in an extremely narrow region near the leading edge of the wing (for example, Δξ <0.01) followed by a fast deceleration gradient (parameter A ₂ ), after which a slow acceleration, the speed of which gradually decreases, and the gradient of slow acceleration continues at the trailing edge.

Such fast acceleration near the leading edge of the wing, similar to the design principle of the experimental NEXST-1 aircraft, is based on the principle of suppressing the appearance of transverse flow around the leading edge, where it is most powerful when the acceleration region narrows in the direction along the wing chord, which is its main reason. However, in contrast to the flight conditions of the experimental NEXST-1 aircraft, the Reynolds number for this large-sized STS to which the invention in question relates is 10 times or more, and the acceleration value must be significantly increased.

Further, with regard to deceleration from parameter A ₁ to parameter A ₂ , the task is to create a transverse flow growth that cannot suppress transverse flow instability (CF) by creating an inverse pressure distribution over the wing chord in each position along the wing span. by narrowing the region of acceleration in the direction along the wing chord to 0.5% or less of the length of the wing chord by means of rapid acceleration. After this, the slow acceleration is mainly intended to suppress the Tolmin-Schlichting instability, but the change in the acceleration from the parameters A ₂ to A _{3 is} also chosen so that it is possible to suppress the cross-flow.

The following is a brief explanation for the parameters {A ₀ , A ₁ , A ₂ , A ₃ , A ₄ , B ₁ , B ₂ , B ₃ , P ₁ , P ₂ } .

Parameter A ₀ characterizes the pressure at the leading edge of the wing (ξ = 0). As a specific value, either the calculated values of the initial distribution of Cp on the upper surface of the wing (Figure 3) are used, obtained by applying the analysis by the method of calculated gas dynamics to the initial configuration of the aircraft in step S3 of Figure 1, or the value obtained by multiplying the coefficient 0.86 by the value of Cp at the critical point (Crit.) obtained by the number M of the unperturbed flow (M _∞ ) and the sweep angle along the leading edge (Λ _LE ) in accordance with the isoentropy equation.

Parameter A ₁ characterizes the minimum pressure point (minimum acceleration point). As a specific value, we take the calculated value of the distribution of Ср on the upper wing surface (Ср, av (η) in Fig. 3), obtained by analyzing the initial configuration of the natural-scale aircraft in step S3 (Fig.) 1, or the approximate value, by the gasdynamic calculation method.

Parameter A ₂ characterizes the point of maximum pressure (point of minimum acceleration). As a specific value, select a negative value.

Parameter A ₃ characterizes the constant to which the pressure distribution at the trailing edge of the wing asymptotically approaches (ξ = 1). As a specific value, we select a positive value proportional to the wing sweep angle Λ _LE .

Parameter A ₄ characterizes the shift from a constant value at the trailing edge of the wing (ξ = 1). As a specific value, choose a negative value, the absolute value of which is proportional to the angle of sweep of the wing Λ _LE .

Parameter B ₁ characterizes the gradient of fast acceleration. As a specific value, choose a negative value, the absolute value of which is a large value of the order of 10 ⁴ .

Parameter B2 characterizes the gradient of fast deceleration. As a specific value, choose a negative value, the absolute value of which is proportional to the angle of sweep of the wing Λ _LE .

Parameter B3 characterizes the gradient of slow acceleration. As a specific value, choose a negative value, the absolute value of which is proportional to the angle of sweep of the wing Λ _LE .

The default P ₁ value is 2.0, and the default P ₂ value is 1.0.

Fig. 4B is an explanatory diagram showing an example of a type of function determining the desired distribution of Cp on the upper surface of the wing, corresponding to the natural laminarization necessary to shift back the point of turbulence of the boundary layer at high Reynolds numbers observed on large-scale STS.

This type of function can determine the required distribution of Cp corresponding to natural laminarization (shifting the point of turbulence of the boundary layer backward at high Re numbers), in which, in an extremely narrow region near the leading edge, the gradient of fast acceleration and the gradient of fast deceleration are constant, after which there is a slow acceleration whose speed is gradually reduced, and the gradient of slow acceleration continues at the trailing edge.

This type of function can be expressed as the sum of a linear combination of basic functions, including f ₀ = 1, f ₁ = exp (B ₁ (η) ξ) -1, f ₂ = exp (B ₂ (η) ξ) -1, f ₃ = exp (B ₃ (η) ξ ^P1 ) -1, f ₄ = ξ ^P2 , having the parameters {B ₁ (η), B ₂ (η), B ₃ (η)} as internal parameters, depending on the position in terms of wing span, (η) and parameters {P ₁ , P ² }, which are independent of the position in wing span (η), as well as parameters {A ₀ (η), A ₁ (η), A ₂ (η), A ₃ (η), A ₄ (η)}, depending on the position of the wing span (η). In other words, the required distribution of Cp corresponding to natural laminarization can be determined in advance, in the form of a dependence not only on the position along the wing chord (ξ), but also on the position on the wing span (η).

Equation 4

$$\begin{array}{l}Cp\left(\xi ,\eta \right)=A_0\left(\eta \right)\cdot \mathrm{one}+A_{\mathrm{one}}\left(\eta \right)\cdot \left[\exp \left(B_{\mathrm{one}}\left(\eta \right)\xi \right)-\mathrm{one}\right]+A_2\left(\eta \right)\cdot \left[\exp \left(B_2\left(\eta \right)\xi \right)-\mathrm{one}\right]+\\ A_3\left(\eta \right)\cdot \left[\exp \left(B_3\left(\eta \right){\xi }^{P\mathrm{one}}\right)-\mathrm{one}\right]+A_{\mathrm{four}}\left(\eta \right)\cdot {\mathrm{<figure-callout\; id="2"\; label="\xi \; P"\; filenames="00000010.png"\; state="\{\{state\}\}">\xi \; </figure-callout>}}^P\end{array}$$

Thus, using the type of function with parameters as coefficients for determining the corresponding natural laminarization of the required Cp distribution on the upper wing surface at which the point of boundary layer turbulization shifts backward at high Re numbers, even for the large-scale STS described below in Fig. 5, by determining the parameters, the desired Cp distribution on the upper surface of the wing can be determined. As for the determination of the parameters, repeating several times (two or three times) for each parameter the so-called sensitivity analysis (parametric study) to estimate the fluctuations of the turbulence point of the boundary layer when changing the value of each of the parameters using the method e ^N , based on the measured values for of each parameter (specific parameter values), it is easy to find the optimal combination of parameter values, providing a backward shift of the boundary layer turbulization point.

Thus, having the distribution of Cp determined by the type of function, it is possible to analyze the characteristics of turbulization using the method e ^N using only simple calculations, and such a parametric study is not a particularly difficult task.

Therefore, the present invention, by determining in advance the corresponding natural laminarization of the required Cp distribution, using the type of function with parameters as coefficients, and analyzing the sensitivity of the parameters in the ranges corresponding to the measured values (corresponding to natural laminarization), makes it possible to always find the desired Cp distribution satisfactory turbulence characteristics of the boundary layer even at high Re numbers for large C S. This feature of the present invention is a hallmark not found in the previously proposed methods for designing a wing with a laminar flow

Fig. 5A is an explanatory diagram showing an example of parameters of the required Cp distribution on the upper surface of the wing, corresponding to the natural laminarization necessary to shift backward the point of turbulence of the boundary layer at high Reynolds numbers observed on large-scale STS.

This drawing shows the values of the parameters of the required Cp distribution with turbulization characteristics with a turbulization point offset of 20% on the center wing almost to the trailing edge on the detachable part of the wing (BV), obtained for the shape of the main wing in terms of a reduced-scale supersonic experimental aircraft NEXST-1 in the process of searching for the required Cp distribution for the Re numbers characteristic of the expansion observed on large-scale STS using similar calculation points.

The shape of the main wing in terms of this aircraft is a wing with a kink in the leading and trailing edges (center wing sweep angle is 66 °, sweep angle is 61.2 °), and the leading edge kink is located at the point y / s = 0.5 in span. The sweep angles of the inner part of the wing and the VLF are different, and therefore their pressures at the critical point (Crit.) Are also different, and as a result we see a characteristic at which the shape of the distribution of Cp near the leading edge is widely divided into two types. Thus, there are two types of parameters corresponding to each of them. In the present invention, the pressure obtained by multiplying the coefficient 0.86 by the value of Cp at the critical point (Crit.), Determined by the number M of undisturbed flow (M _∞ ) and the sweep angle, was taken as the pressure at the leading edge of the wing (A ₀ ). leading edge (Λ _LE ) according to the isentropy equation.

The parameter A ₀ for the center section is equal to A ₀ = 0.167393842079683, and for the OFP parameter A ₀ is equal to A ₀ = 0.250316114631497.

The parameter A ₁ for the center section was determined on the basis of the calculated values of the Cp distribution obtained by applying the analysis by the method of calculated gas dynamics to the initial form of a natural-scale aircraft, analyzing the trends of the average pressure (Cp, av (η) in Figure 3) in the direction of the wing span ( η) in the range from 20 to 80% in the direction along the wing chord in each position according to the wing span, using a function depending on the point on the wing span (η) (for this version, this is a fourth-order polynomial).

The parameter A ₁ for the center section is equal to:

Equation 5

. $$A_{\mathrm{one}}=2.0{\eta }^{\mathrm{four}}-1.8{\mathrm{<figure-callout\; id="3"\; label="\eta "\; filenames="00000011.png,00000014.png"\; state="\{\{state\}\}">\eta </figure-callout>}}^3+0.495{\eta }^2+0.0695\eta +0.2085$$

.

The parameter A ₁ for OCHK is:

Equation 6

. $$A_{\mathrm{one}}=0.9116{\eta }^{\mathrm{four}}-\mathrm{2,4014}{\mathrm{<figure-callout\; id="3"\; label="\eta "\; filenames="00000011.png,00000014.png"\; state="\{\{state\}\}">\eta </figure-callout>}}^3+2.2538{\eta }^2+0.8274\eta -0.4427$$

.

The parameters for the center section and OCHK (A ₂ , A ₃ , A ₄ , B ₁ , B ₂ , B ₃ , P ₁ , P ₂ ) were chosen respectively as follows: (00.0, -1500.0, -20.0, 2.0, 1.0) and (-0.015, 0.01, 0.0, -90000.0, -500.0, -10.0,2.0, 1.0).

FIG. 5B shows the desired distribution of Cp for the parameters shown in FIG. 5A in the wing width direction (η). As indicated above, a distinctive feature of the required Cp distributions of the present invention is that the distribution characteristics have a gradient of rapid pressure growth in an extremely narrow region near the leading edge of the wing, and a decrease gradient, therefore, the pressure distribution near the leading edge of the wing (parts A and B) is presented separately, enlarged in the direction of the wing chord.

The shape of the wing in terms of this aircraft is a wing with a break in the front and rear edges, a break in the front edge is located at the point y / s = 0.5 in span;

since the sweep angles on different sides of the kink are different, the values of Cr crit are different, and as a result, we see that the shape of the distribution of Cr near the leading edge is divided into two types. That is why, as the aforementioned method of selecting the parameter A ₀ , a simple method of multiplying Wed crit is used. at 0.86.

In addition, we see the need for a fairly rapid deceleration from the point of minimum pressure near the leading edge. This is because, at a large wing sweep angle of about 60 ° or more, the average value of the minimum pressure level on the distribution graph Ср increases uniformly when moving to the wing tip, and therefore, no matter how fast the pressure increase near the leading edge, in this areas near the leading edge there is a transverse flow due to the pressure gradient, which is always present in the direction of the wingspan. In other words, the complete suppression of the increase in transverse flow is difficult, so that the narrowing of the aforementioned area of rapid decline has an effect equivalent to the influence of an external force aimed at changing the direction of the gradient along the wing span. (In fact, due to the inertia of the flow, the direction of the transverse flow velocity does not change instantly, but the tendency to increase the flow velocity in one direction is clearly suppressed). Thus, a forced change in the direction of the transverse flow is used to slow the increase due to acceleration near the leading edge. This is the main principle of this invention.

FIG. 6 is an explanatory diagram showing the results of a turbulization analysis conducted for the shape of the desired Cp distribution shown in FIG. 5 B.

Here, the turbulization analysis method is a method in which the place in which small perturbations existing in the flow develop in time and space together with the flow, until their amplitude (A ₀ ) reaches a certain value (A = A ₀ e ^N , is estimated the position of the transition from laminar to turbulent flow. in other words, the method is used e ^N (see. Figure 10), which examines the relative instability of the laminar boundary small perturbations, the combination occurs in the flow disturbances, and on the basis of index Called the value N, is determined by the position of the point of turbulence.

The only uncertain factor in this method of analysis is the fact that the value of N corresponding to the criterion for determining the point of turbulence in flight conditions cannot be determined theoretically. Therefore, on a plane with a supersonic flight speed, a simple profile is established, the location of the boundary layer turbulization point is measured, and an assessment is made by comparing it with the results of the analysis. In the case of a complex shape, the production of such a real aircraft is difficult, therefore, tests to determine the location of the turbulization point are carried out in one of several special wind tunnels available in the world (wind tunnels in which the disturbance of the air flow decreases to approximately the level corresponding to the flight conditions), and by comparison with the results of the analysis, a database is created to determine the point of turbulization.

In the analysis presented in FIG. 6, the result obtained by NASA (N = 14) was used as an example of such a database. An independent evaluation criterion (N = 12.5) was obtained at the Japan Aerospace Research Agency by comparing flight test data of a scaled-down experimental supersonic aircraft with the analysis results. Analysis results using this value are also shown.

When considering the analysis results, it becomes clear that if N = 14 is taken as an independent criterion for turbulization, the local wing chord length increases for the center section, which (in terms of turbulization characteristics) means that a significant backward shift of the turbulization point is difficult, and for this distribution of CP turbulence of the boundary layer will occur approximately in the region of 15% of the wing chord length; on the other hand, for the BVP, the local number Re decreases, so that the turbulization characteristics are good, and the turbulization point shifts almost to the trailing edge of the wing. As a result, it is estimated that flow laminarization is on average 26% possible. Thus, according to the estimate, the gain in aerodynamic quality is approximately 0.4 (that is, a decrease in impedance of 5% is achieved).

Finally, FIG. 7 shows an example of the development of a natural laminar flow wing design using the natural laminar flow wing design method of the present invention. Fig. 7A compares the cross-sectional shape of a wing of the Concord type aircraft (a design form independently developed by the Japan Aerospace Research Agency) that considers only the reduction in pressure resistance for large-scale STS; the shape of the wing with natural laminar flow around the NEXST-1 aircraft corresponds to the number Re = 14 · 10 ⁶ ; and as an object of application of the present invention, a large-scale STS is adopted (the total length of the aircraft is 91.4 m, the conditional number Re along the length of the wing chord is approximately 120 · 10 ⁶ ). FIG. 7B shows three types of wing cross-sectional shapes at a 40% half-span point, and FIG. 7C shows the curvature distributions of the wing near the leading edge (at the critical point region) of these cross-sectional shapes in an overlaid form. It can be seen from the drawings that, despite the fact that for higher Re numbers, the wing curvature is less, at the wing chord length of 0.1% (0.1% s) or more, including the critical point (s / 2c = 0.0), the curvature is constant, which is 1/3 or less of the Concord wing shape, and in the region of the linear element from this region of the linear element (0.1% s or more) towards the trailing edge more than 0.2% of the wing chord length (0.2% s), there is a tendency to a further rapid decrease in curvature to 1/10 and below. It is believed that this is highly dependent on the shape of the pressure distribution near the leading edge of FIG. 5A. The term "linear element" here means the distance from a certain reference point on the outer surface of the outer profile of the wing cross section along the outer periphery in a constant direction. In Fig. 7C, this reference point is defined as a critical point, the direction along the upper surface of the wing is considered positive, the direction along the lower surface of the wing is considered negative.

The method of designing a wing with natural laminar flow proposed by the present invention can be applied in the development of wing designs with natural laminar flow when changing the Reynolds number in the range from 14 × 10 ⁶ (for small-sized STS) to 180 × 10 ⁶ (for large-sized STS)

Claims (6)

1. A wing with natural laminar flow around a supersonic aircraft, in which the shape of the cross section of the wing in the direction along the chord of the wing at each point along the wing span is selected so that the curvature near the leading edge has a predetermined value of 1/3 or less compared to the normal cross-sectional shape in the region of the linear element is 0.1% of the wing chord length or more, including the leading edge, and so that the curvature in the region of the linear element is 0.2% of the wing chord length from the region of the linear element nta to the trailing edge of the wing is additionally reduced to 1/10 or less from a predetermined value, while to select the shape of the wing cross section,
the choice of the original shape of the wing cross section;
analysis by the method of design gas dynamics in order to determine the resulting pressure distribution of the flow field near a given wing cross-sectional shape;
turbulization analysis to assess the location of the transition point turbulization point on the wing surface;
select the desired pressure distributions for the upper and lower wing surfaces based on the obtained pressure distribution; and a reverse-engineering process based on computational gasdynamics is performed, including an analysis process using the computational gasdynamics method and a shape correction process that corrects the wing cross-sectional shape so that the pressure distribution obtained as a result of the computational gasdynamic analysis approaches the desired pressure distribution, among those required pressure distributions, the required pressure distribution on the upper surface of the wing determines the "distance along the chord of the wing from the leading edge and the wing to the trailing edge of the wing "as an area in each position according to the wing span, and, in addition, is determined by the type of function with parameters depending on the position on the wing span, as coefficients;
subsequent analysis of the sensitivity of the position of the point of turbulization of the boundary layer on the upper surface of the wing to changes in the values of each of the above parameters using the turbulization analysis process; and
determining by searching the optimal combination of parameter values that ensures the maximum backward shift of the point of turbulence of the boundary layer on the upper surface of the wing for a given Reynolds number. 2. The wing according to claim 1, wherein, among the above-mentioned required pressure distributions, the required pressure distribution on the lower wing surface is determined based on the desired pressure distribution on the upper wing surface, as well as the distribution of the pressure difference between the upper and lower surfaces, providing an optimal combination of distribution the angle of aerodynamic twist and the curvature of the wing in scope. 3. The wing according to claim 1 or 2, wherein when the direction along the chord of the wing is represented by the X axis, the direction of the wingspan is represented by the axis Y and the length of the chord of the wing (= c (y)) is used to determine a point in the direction of the X axis along wing chord from the leading edge of the wing at each point along the wing span (Y = y) in a dimensionless form (ξ = x / s (y)),
at each point along the wing span, a shape of the required pressure distribution is created on the upper surface of the wing so that in the extremely narrow region from the leading edge of the wing, in which Δξ <0.01 is set, the gradients of rapid acceleration and deceleration of pressure are constant, and in the subsequent wide region, which is set Δξ≤ξ≤1, there is a slow increase in pressure while reducing the magnitude of the acceleration, and a slowly accelerating gradient, asymptotically approaching a given value, is constant. 4. The wing according to claim 3, in which, in addition to the above-mentioned required pressure distribution on the upper surface of the wing, for the point at which the maximum velocity of the fast acceleration gradient at each point along the wing span and the constant value of the slow acceleration gradient is reached, average pressure distributions in the previously defined ranges the length of the chord of the wing at the same points along the span of the wing for the initial pressure distribution obtained by analyzing the calculated gas dynamics method of the initial distribution form ayutsya as initial values for the minimum pressure value and a constant turbulence analysis process, and then, when there will be a maximum displacement point of turbulence of the boundary layer, both the above values are taken as optimum. 5. The wing according to claim 1, in which, in addition to the required pressure distribution on the upper surface of the wing, at each point on the leading edge of the wing, the pressure value is obtained by multiplying the pressure at the critical point, determined by the number M of the unperturbed flow and the sweep angle leading edge, at a constant value. 6. The wing according to claim 3, in which, when each point in the wing span (Y = y) is converted into a dimensionless form (η = y / s) using the half-span (s),
the required pressure distribution on the upper surface of the wing (Cp (ξ, η)) is determined by the following exponential function having the parameters {A ₀ (η), A ₁ (η), A ₂ (η), A ₃ (η), A ₄ (η), B ₁ (η), B ₂ (η), B ₃ (η)}, depending on the location of each point in the wingspan, and the parameters {P ₁ , P ₂ } not depending on the location of each point in the wingspan ,
Cp (ξ, η) = A ₀ (η) · 1 + A ₁ (η) · [exp (B ₁ (η) ξ) -1] + A ₂ (η) · [exp (B ₂ (η) ξ ) -1] + А ₃ (η) · [exp (В ₃ (η) ξ ^P1 ) -1] + А ₄ (η) ξ ^P2 ,
an analysis is made of the sensitivity of the position of the point of turbulization of the boundary layer on the upper surface of the wing to changes in the values of each of the above parameters using the turbulization analysis process, and
a search is made for the optimal combination of parameter values that ensures the maximum rearward shift of the point of turbulence of the boundary layer on the upper surface of the wing for a given Reynolds number.

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