DE2337992A1 - HYDRODYNAMIC PROFILES - Google Patents

Description

ΡΑΤΕ \ τ.Λ, \ ίν. -.

Dr. - Ing.! :, \ _; ; s ·, -, ._
Dipl. -Ing. UL * r PV. ..
Dipl.-Ing. H, "i \ s £. Kuv ^ HKfc,

1 B E R L 1 f J 3 3 Auguste-Viktoria-Strasse 65

The Boeing Company, Seattle, Washington, V.St.ν.Α,

Hydrodynamic Profiles

The present invention relates to hydrodynamic profiles and a method of constructing the same.

Hydrofoils are well known as a means of carrying boats across the water while in motion, compared to conventional ones To achieve improved sailing characteristics and lower power requirements for watercraft. It's in the past various designs for hydrofoil profiles have been proposed. These constructions were for the application on the propellers and wings of aircraft have been developed with the stated aim of compressibility effects, which are known as were deemed detrimental to aircraft performance. A comparison of the results of wind tunnel tests The hydrodynamic profiles of the prior art show that there is a considerable improvement in the buoyancy ratio to achieve flow resistance at low Reynolds numbers

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if one delays the compressibility effects. Some of these hydrodynamic profiles are known as the ¹¹ NACA 16-XXX "series and have been shown to have the most desirable properties, including low top surface overspeed, of the prior art hydrofoil profiles.

However, some of the characteristics of the 16-XXX series are undesirable, when viewed from the standpoint of hydrodynamic applications at full-scale Reynolds numbers, viz the high negative pressure at the run-up edge and the steep positive pressure gradient at the run-down edge, which causes the profile flow fluctuations including cavitation and boundary layer separation. The sensitivity of the flow to surface irregularities can also affect the driving quality and the operating characteristics of the vehicle. The so far for the Proposed aerodynamic profiles do not provide use in an environment where hydrofoils operate similarly Potential for particular improvements in terms of operating characteristics and the ride quality.

Applications of hydrofoil systems to boats are known in the art. In the development of this technique, however, one has So far most of the effort has been devoted to the control systems and methods of attaching the wings, the construction of the struts, the drives etc. used.

The method of the present invention sets for construction of the hydrodynamic profiles disclosed here a well-known computer programs which have been written to perform tasks of the Aerospace and water engineering to solve, as well as experimental data derived from the operation of the previously known hydrofoil systems emerged. To define the pressure distribution and the boundary layer properties required for the application are considered desirable for full-scale hydrofoils to produce the desired hydrodynamic profile, became a: .Pressure profile for a given speed

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ability set up by a fluid moving hydrodynamic profile, the profile having an area of positive pressure the leading edge of the wing profile, an area negative Pressure over an upper surface of the hydrofoil with a kinked area segment in the pressure profile in a rearward one Section of the upper surface that creates lowered negative pressures to control cavitation and an area positive Pressure over the entire lower surface of the airfoil profile, also here in a rear section of the lower Area in which low positive pressures are observed, a kinked area in the pressure profile to control cavitation is provided. Furthermore, an area of positive pressure must be provided on the trailing edge of the airfoil. as if you had a pressure profile that met the design criteria mentioned above, a hydrodynamic airfoil was used, which exhibited these properties, analytically using computer calculation methods developed. One of the hydrodynamic aerofoil profiles that, as it turned out, met the design criteria, runs flat over a substantial portion of the lower surface, with a substantial portion of the upper surface being of a plurality is formed by arcs.

These objects, properties and features of the present invention result in detail from an evaluation of the following discussion of the preferred embodiment used in conjunction with the accompanying drawings.

Fig. 1 shows a pressure profile for a typical airfoil profile According to the state of the art;

Fig. 2 shows a pressure profile for a typical hydrofoil profile According to the state of the art;

Figure J shows a pressure profile for use in engineering a hydrofoil profile according to the present invention;

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Pig. 4 shows an actually occurring water bearing surface with Cavitation;

Fig. 5 shows a linearized wing plane with the at Operation of the hydrofoil observed boundary conditions;

FIG. 6 graphically shows a portion of the conformal mapping that occurs in the construction of the hydrodynamic profiles according to FIG of the present invention was used;

7 shows a further graphic representation of a subsequent one Step in the conformal mapping that is used to solve the construction tasks set out here became;

Figure 8 shows an airfoil that meets many of the design criteria met for the hydrodynamic airfoil according to the present invention;

9 shows an example of the airfoil profiles for comparison the NACA I6-XXX series;

Fig. 10 shows a graph of the operational characteristics the airfoil profile of FIG. 8; and

Fig.11 is a calculated two-dimensional pressure distribution for the airfoil profile of FIG. 8.

The method of generating an airfoil with the improvements noted above uses available analytical computer programs and experimental data to define the pressure distribution and boundary layer properties that are desirable for the full-scale application of hydrofoils being held. A pressure distribution was defined based on a non-deformed aerofoil profile, with certain requirements differed from those used for hydrofoils such as the series

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NACA 16-XXX included in the Pig. 2 and 9 apply. Of the negative pressure at the leading edge of the wing profiles Series I6-OCXX is high and makes you sensitive to the Leading edge cavitation As a result of fluctuations in the angle of attack. To improve this situation, the pressure coefficient and gradient over the front part of the was proposed Airfoil profile changed.

The pressure gradient over the rear part of the wing profiles of the series I6-XXX remains negative up to about 60 Jo of the profile depth and then increases rapidly when approaching the trailing edge. Such a pressure distribution is particularly sensitive to a turbulent boundary layer separation in the entire range of the fully wet Reynolds numbers, since the rapid slowing down of the flow lowers the energy of the boundary layer so that it can no longer follow the surface. This phenomenon becomes even more serious when a flap is used on the trailing edge, with the flow more likely to detach on the side of the wing profile opposite the flap deflection. For the airfoil profile of the exemplary embodiment, the pressure distribution over the rear part of the profile depth was set in such a way that the flow gradually slows down and thus the possibility of a turbulent separation is reduced. The resulting pressure distribution contains a concave or kinked area in the rear part of the wing profile. This characteristic concave area results from the criterion for preventing or delaying a turbulent separation. The extent and gradient of the pressures in this area depend on the Reynolds area in which the airfoil is to be operated. Another effect of this distribution is that the point of transition from a laminar to a turbulent boundary layer is shifted to a more favorable point from the point of view of flow resistance.

Fig. 3 shows the pressure field around the hydrodynamic airfoil profile according to the present invention. For a buoyant working with its angle of attack near the free surface

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Area, the present invention includes the following properties.

(1) The pressure decreases from the dew point 21 near the run-up edge 20 gradually decreases towards a negative area near the center 22. The size of the minimum of the negative pressure is determined by the vapor pressure the liquid. The Druekayf the rear part 24 of the The profile gradually increases from the minimum of the negative pressure near the center to a positive value, that near the Storage area 26 is located on the drainage edge.

(2) The pressure distribution on the rear part of the profile contains a concave or bent part. The purpose of this kink is to stabilize the transition area of the boundary layer in order to protect it against fluctuations in the flow as a result of wave rotation speeds to make insensitive; it also serves to prevent flow separation. Shape and extent the kink are determined by the Reynolds number range, within whose profile should work.

(3) The pressure on the lower surface JO gradually decreases from the dynamic pressure near the leading edge to a positive minimum near the center of the profile. The pressure distribution on the rear part gradually decreases from the positive minimum near the center to the trailing edge 28. The pressure distribution for the lower surface can also contain a kinked section. The amount of pressure on the lower surface is determined by the lift desired by the profile. Since the minimum suction force on the upper surface is limited by the vapor pressure, the lower surface generates a considerable proportion of the lift.

(4) The pressure distribution on either side of a symmetrical The strut profile corresponds to the pressure distribution on the upper surface of the wing profile.

Fig. 1 shows the pressure distribution of a typical one for comparison Air wing profile, Fig. 2 for comparison the pressure distribution of a typical water wing profile.

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The following theory describes a method for constructing profiles with the desired properties.

LINEARIZED THEORY

If one assumes that a steady two-dimensional incompressible and rotation-free flow exists everywhere in the physical plane outside the space enclosed by the profile, one can furthermore assume that a complex velocity function UJ - / * x * - i / y exists, where the complex velocity function , * / ΊΓ are the total horizontal speed component and S ^ T are the total vertical speed component. The complex total velocity function Uj is known from elementary fluid mechanics and can be obtained as follows: Let 0 and Λ £ τ be the velocity potential and flow function of an incompressible, rotation-free, continuous two-dimensional flow fluid. If one defines Q, = 0 + i as the complex potential and forms the partial derivatives with respect to x, the following results:

- \ x ~ \ x -Ί χ dz 2 ^{X dz}

From ζ = χ + iy follows -jj z / ^ x - 1. If one leads the velocity components _{with V, r and V}

V = -. "% JL .. and V = -for χ Qx ^{n v} y ^ x

one, one obtains the following relationship after insertion j_

where -dQ / dz is called the complex velocity.

Since 0 and \ ts satisfy the Cauchy-Riemann equations, this " must also hold for ti /, since both V and V are analytical

χ y ν

Functions of 0 and J> are. This makes U / an analytical funk

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tion of the complex variables ζ ^ x + iy, where (x, y) are the rectangular coordinates in the flow field of the Pig. H- are. So it applies

UJ (z) = V (x, y) - iV (x, y).

A complete description of the terms outlined above can be found in every textbook on fluid mechanics.

If you write Uj to

(z) = V ⁰⁰ ZfI + u (x, y) - iV (x, y) _7,

it follows, that a new function Us (z) + u (x, y) - iV (x, y), called the complex perturbation rate, is also an analytic function in the same range as LO (z). Lt / (z) satisfies the Cauchy-Riemann equations; consequently both the continuity equation,

as well as the condition of rotation-free flow

, y)

3 y

Fulfills. It applies

^v - ^(x i ^y) " ^v ^ - · ^v - ^(x ' ^y)

'v

(, y)
u (x, y) = Ο? and v (x, y) -

so that u and ν are dimensionless quantities, i.e. the ratio in each case the speed component caused by the profile to the speed of the free flow. Furthermore, all length measurements normalized with respect to the profile depth C.

The basic assumption of the linearized theory is that the size of the perturbation disturbance velocities (u, v) is due to

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the presence of these two in the main flow are small compared to the velocity of the free flow, V ζφ. as As a consequence of the assumption of the small disturbance, the flow conditions can be applied to the actual body and evaluate cavity surfaces in the horizontal plane y - 0 aligned with the speed of the free flow. The boundary conditions of this exercise can be determined as follows: If ζ = <? O and u = ν - 0 this condition is exact Fulfills. To simplify the boundary condition on the cavity interface and the wetted surface of a water bearing surface, it is assumed that both the curvature and the angle of attack are small, large ones of the first order. The second and higher powers of these magnitudes can be neglected. Since ö ~ * - 0, the cavity that extends on a Arbitrarily chosen location along the profile depth on the upper surface and the trailing edge of the lower surface of the wing begins with a slim figure to infinity. One can reasonably assume that with the exception of the effects of the Gravity, which can be neglected, the cavity is aligned with the free flow. For the cavity interface it is assumed that the flow velocity there is equal to the velocity of the free flow; it follows u on the wetted surface of the water bearing surface, the flow must be tangential to the solid surface; it follows from this

1 + u with y as the wing coordinate.

On the free surface, y = h, the linearized Bernoul Ils ehe equation becomes u - -g, ^ V. / V ^ Ci o, if the Froude number based on the wave height γ ** is very large. With Bernoulli's equation and after linearization, it follows for the wetted surface

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The above boundary conditions are shown in FIG. COMPLIANT IMAGE

1. χ - 2. χ = 3. X -

after V ₁ - - OC Il V ₁ - - a Il ^ν ι - O It ^ν 1 ⁼ + «Σ

By using the Schwarz-Christoffel transformation, the Line y = h and the semi-infinite line y - · 0, χ> 0, transformed to the real axis of the v-plane, where ν - ν, + iVpj while the entire z-plane is transformed into the lower half of the v-plane; cf. Fig. 6. The required transformation is then:

If- = C ₁ C ₂ Av - (-a ^ ⁰ - ¹ (v - 0) 2- ^ 1 of »Av = A v / a, (at P) (at N) (at L) (at M)

by specifying the following points in the transformation: <P , y = h
o, y - ο

If one integrates the above equation and applies the condition, v ^ O at z ^ O, one obtains the following transformation:

ζ = Aa / ~ V / a _ in (+ v / a) _7 and after equating the real and imaginary components

χ = AaA ₁ A - In (I + v / a) "J y = AaA ₂ A - arg v_7

If you also specify that the run-off edge of the plate χ = 1, y - 0 ~ to v-, = + 1 and the ventilation point on the upper surface x = e, y = O ⁺ to transform into v-, - - f and that the change in the imaginary part of ζ when ν passes through v-, = -a equals y = h / c, the following equations are obtained:

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- aln (l -i-l)

e = Aa / "~ -f / g - In (I - f / g) J7

and ,_

since V ₂ - 0 and the z-plane is mapped into the lower v-half-plane, arg ν - - ^ 'applies to ν-, = -a.

The conformal mapping was applied to the ν plane to map the upper half of the z-plane outside the unit circle y =, as shown in FIG. 6. The first transformation

v ¹ = ^λ - ^f - ^2v

1 + f

stretches the ventilation point ν of the water surface to the point +1 on the real ν -axis and maps the lower half of the v-plane to the upper half of the ν -plane _o The second transformation is a Joukowsky transformation of the form

r ¹ = 7 + 1 nrl ^ T »T? = Vr ¹

v * = or Tl = v * +

^ Ί ^J

which depicts the wetted surface of the water-bearing surface in the upper half of the unit circle "C = I.

For points on the unit circle for which "^ = l.e" became the corresponding value for χ found on the wetted surface by

= eo s9 + isin © = v ¹ + i Yl - (v ¹ ) ² = - v ¹ + i \ fiT- (ν ¹ ),

da V ₂ - ο

χ + χ

l + f - f - (1 ₊ f) cos θ ₌

1 - f - (1 ₊ f) cos θ _{= K} _ _cos 1 L - - _L

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with K - and L- ^L

Hence χ _ Aa / ~ ILzCOB-A _ mc ^ cos 9) -j ₌

- d.Jj d.lj -

· - in 7 with P = K + al.

After the differentiation it results

dx A,. κ -
ηΠ ι COS θ L ^ ^ol COS θ.

The leading edge of the profile in the ^ -plane is given by

COS 0 - y - = - § - K.

(Exponents are reference symbols)

For a profile shape with a given h / cj and a given one Basic distribution C is given by the center line

r ¹ Ό \ - 1/77 "cp9sic sin θ

yj - - ^ - ^ / cos θ - cos θ _ο ^aw

and the thickness distribution to

^{rl +} ( ^θ ο) _ 2 y / a / A

1 + f COSJ2T - cos with yρ = parabolic thickness term.

These are the basic parameters necessary for the construction of a hydrodynamic wing profile with the desired Pressure profile are required.

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Figures 8, 10 and 11 show a particular hydrodynamic airfoil profile that meets many of the design criteria noted above Fulfills. This airfoil has a substantially flat lower surface and a substantial part of it The upper surface is made up of three arcs, as shown in the figures. The nose and drainage contours are constructed as shown to be a positive pressure in the jam area of the leading edge and also to cause a positive pressure on the profile in the jam area at the drainage edge. The shape shown creates in the pressure profiles of both the upper and the lower kinked areas in order to have the desired influence on the cavitation and to get a dewetting of the wing.

For comparison, FIG. 9 shows the NACA profile 16-30 (7.5). the curved lower surface creates a negative pressure on the lower surface to create a curved passage through a liquid to allow; see Fig. 2.

While the inventors here their invention with reference to particular Embodiments have described, is apparent to the person skilled in the art, that various modifications can be made within the scope of the invention.

- patent claims -

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Claims (1)

Patent claims Hydrodynamic profile for hydrofoils, all in one Body with an upper and a lower surface and an elongated axis extending in the direction of movement of the Profile runs through a liquid, the airfoil profile when the liquid passes through the liquid A pressure profile develops over its surface, which has an area of positive pressure at the leading edge, an area of negative pressure above the top surface that includes a kinked portion that extends over a rear section of the upper surface is located, in which decreasing negative pressures change the cavitation location, as well an area of positive pressure over the lower surface, which also has a kinked section over a rear Includes part of the lower surface in which decreasing positive pressures change the cavitation location, and one Area of positive pressure on the trailing edge. 2. Hydrodynamic profile according to claim 1, wherein a substantial Part of the lower surface is flat. 3. Hydrodynamic profile according to claim 1 or 2, wherein a A substantial part of the upper surface is formed from a large number of arcs. 4. Hydrodynamic profile according to claim 1, 2 or j5, in which in the negative pressure area, the pressure above the upper surface 509807/0093 gradually increases from the dynamic pressure at the leading edge Minimum decreases near the center of the profile and in the course of the bent part up to the area of positive pressure gradually increases again at the trailing edge. Method of constructing a hydrodynamic profile for water yield areas. By creating a for a hydrodynamic Profile that runs through a liquid at a target speed without being curved and that specifies a desired pressure profile, that has an area of positive pressure on the leading edge, an area of negative pressure above the top surface of the wing profile with a bent section in the pressure profile, which is in a rear part of the upper Area in which decreasing negative pressures cause cavitation, as well as with an area of positive pressure above the lower surface of the wing, which also has a bent section in a rear part of the lower Contains area in which decreasing positive pressures cause cavitation and an area of positive pressure at the drainage edge of the wing, and by determining the shape of the hydrodynamic profile, the aforementioned pressure profile generated. 6. The method according to claim 5 * in which in the range of the negative Pressure above the upper surface of the wing the pressure from the dynamic pressure at the leading edge gradually approaches a minimum decreases towards the center of the profile and then gradually increases to the positive pressure in the course of the bent section the trailing edge increases. 7. Hydrodynamic profile for hydrofoils, which is essentially is constructed as described with reference to the drawings. 509807/0093 B 1032 8. Method of constructing a hydrodynamic profile for water bearing surfaces as described herein with reference to the Drawings is described. Cl./Br. 509807/0093 Blank page