CN115828418A - Strong interference area profile design method based on two-dimensional bending characteristic line theory - Google Patents

Abstract

The invention develops a strong interference area profile design method based on a two-dimensional bending characteristic line theory, which comprises the following steps: step (1), acquiring a preset shock wave shape; step (2), acquiring flow field data i; step (3), determining the shape i of the wall surface according to the preset shock wave shape and the flow field data i; step (4), performing flow field simulation according to the shape i of the wall surface to obtain flow field data i +1; step (5), judging whether the similarity of the simulated shock wave shape i and the preset shock wave shape meets the requirement or not according to the flow field parameters corresponding to the flow field data i +1 and the wall surface shape i; and (6) outputting the wall shape i if the requirement is met, and if the requirement is not met, i = i +1 and re-executing the steps (2) to (6). Therefore, the technical blank in the field of reverse design of the appearance of the aircraft in the shock wave strong interference area in China is filled, and support is provided for aerodynamic thermal protection of the high-speed aircraft and analysis of the aerodynamic thermal environment of strong shock wave interference in the future.

Description

A Surface Design Method for Strong Interference Area Based on Two-dimensional Curved Characteristic Line Theory

technical field

This application relates to the technical field of combined propulsion aircraft, in particular to a method for designing the surface of a strong interference area based on the theory of two-dimensional curved characteristic lines.

Background technique

The leading edge of the inlet lip of a hypersonic aircraft with integrated internal and external flow has quasi-two-dimensional characteristics in the symmetrical plane. In the early stage of engineering application, the solution of the flow field in the symmetrical plane is generally regarded as a two-dimensional problem. The three-dimensional effect of the flow field brings The influence of is only considered in the boundary conditions. In order to make the air intake system of the aircraft work normally under the predetermined flight conditions, it is necessary to design the profile of the lip strong interference area, and to weaken the shock wave interference characteristics as much as possible (ideally without shock wave interference) under the premise of meeting the working conditions, so as to To achieve the effect of reducing the wall heat flow.

Shock interference profile design methods at home and abroad are currently mainly based on Oswatitsch wave distribution theory and isentropic compression theory. The oblique shock wave characteristic line is alternately advanced to solve the flow field after the shock wave, and the wall centerline profile is finally designed through repeated iterations. This method is often used in the traditional binary inlet design, but considering that the inlets of hypersonic vehicles are mostly curved surfaces, and the shock wave is in the form of curved compression shock waves, it is necessary to study a new method for the design of the interference area. At the same time, the scope of application of Oswatitsch wave distribution theory is limited, and the original formula is no longer applicable under hypersonic conditions.

Contents of the invention

This application provides a surface design method for strong interference areas based on the two-dimensional bending characteristic line theory. The purpose is to solve the problem of two-dimensional design of strong interference areas through the combination of bending shock wave compression and isentropic compression based on the characteristic line theory. . This fills the technical gap in the field of reverse design of aircraft shape in the area of strong shock wave interference in my country, and provides support for the aerodynamic thermal protection of high-speed aircraft in the future and the analysis of the aerodynamic thermal environment of strong shock wave interference.

In the first aspect, a wall design method is provided, including:

Step (1), obtaining a preset shock wave shape;

Step (2), obtaining flow field data i;

Step (3), according to the preset shock wave shape and the flow field data i, determine the wall shape i, the wall shape if _W,i () satisfies:

y _W,i =f _W,i (x _W,i ),0≤x _W,i ≤L,

x _W,i is the x coordinate of the wall surface, y _W,i is the y coordinate of the wall surface, y _st0,i is the y coordinate of the streamline starting point, M _x,i is the Mach number of section x, q _∞ is the standard heat flow, q _x,i is the heat flow of section x, μ is the Mach angle of section x, θ _x,i is the air flow angle of section x;

Step (4), performing flow field simulation according to the wall shape i, to obtain flow field data i+1;

Step (5), according to the flow field data i+1 and the flow field parameters corresponding to the wall shape i, determine whether the similarity between the simulated shock wave shape i and the preset shock wave shape meets the requirements;

Step (6), if the requirement is met, output the wall shape i, if the requirement is not met, then i=i+1, and re-execute steps (2)-(6).

Compared with the prior art, the solution provided by this application at least includes the following beneficial technical effects:

(1) By enhancing the stability of shock wave capture and the high-resolution characteristics of the boundary layer, the accuracy of existing numerical methods for predicting aerodynamic heat in complex flow regions is effectively improved.

(2) Based on the basic characteristics that need to be satisfied by hypersonic aerothermal prediction flux function: shock wave stability and boundary layer solution ability, develop and construct new flux functions, and obtain high precision under micro-scale, high-energy region, and strong shock wave interference Heat flow prediction method.

(3) Propose the flow regulation and heat reduction scheme in the rough zone, and give the flow field regulation and heat reduction mechanism. By changing the size of the separation bubble, the reattachment occurs at a suitable angle under the corresponding Mach number flow condition, and the jet flows along the outer edge of the separation bubble in the form of a shear layer, and finally reattaches at a small angle.

With reference to the first aspect, in some implementation manners of the first aspect, the preset shock wave shape is used to indicate at least one of the following: distribution of aerodynamic parameters on a compression surface, distribution of outlet parameters, and shape of a bending shock wave.

By setting the preset shock wave shape at multiple angles, the inverted wall shape can better meet the application requirements.

With reference to the first aspect, in some implementation manners of the first aspect, the flow field data i include at least one of the following: parameters before and after the shock wave, wall parameters, outlet parameters, and streamline data in the flow field.

The amount of process data is relatively large, and the shape of the wall can be deduced more accurately.

With reference to the first aspect, in some implementations of the first aspect, for the case where oblique shock wave 1 and oblique shock wave 2 intersect on the same side, the streamline data i satisfies:

Discrete expansion wave turning angle

Among them, M represents the Mach number, p represents the pressure, k represents the specific heat ratio of the gas, the subscript BC represents the area where the incoming flow passes through the turning angle δ _BC = δ _B + δ _C , and the area B is the oblique shock wave 1 and the In the area between the oblique shock waves 2, the area B is located upstream of the oblique shock wave 2, and the area C is the downstream area of the oblique shock wave 2.

Before deriving the shape of the wall, determining the streamline data for the intersection of oblique shock wave 1 and oblique shock wave 2 on the same side will help make the input data of wall inversion closer to the actual situation and make the deduction process more accurate.

With reference to the first aspect, in some implementations of the first aspect, the wall shape i and f _W,i () satisfy:

δ_W,i表示壁面处的转折角。

δ _W,i represents the turning angle at the wall.

The wall shape i also needs to meet some constraints of the airflow field to make the deduction process more accurate.

With reference to the first aspect, in some implementations of the first aspect, the wall shape i is the wall shape of the supersonic curved leading edge section and the subsonic root region, and the supersonic curved leading edge section and the subsonic root region Determined by bending shock morphology and wall heat flow.

The application can be designed for the wall part, which is beneficial to reduce the amount of data introduced in the wall shape deduction and improve the data processing efficiency.

With reference to the first aspect, in some implementations of the first aspect, the wall shape i also satisfies:

θ _st = θ _W

δ _st ＝(θ _W -2δ _exp )-(θ _W,st0 -2δ _exp,st0 )

Where θ is the air flow angle, δ is the turning angle, the subscript st is the point on the streamline, the subscript w is the point on the wall, the subscript w, st0 is the starting point of the streamline on the wall, and the subscript exp is the expansion wave, the subscripts exp, st0 represent the streamline starting point of the expansion wave region.

In this way, the influence of the reflected expansion wave on the shock wave and the re-reflection of the expansion wave on the wall surface can be considered, so that the deduction process is more accurate.

With reference to the first aspect, in some implementations of the first aspect, the flow field parameters include Mach number Ma _st and pressure p _st :

M _st ＝f _PM,M (M _st0 ,δ _st )

p _st ＝f _PM,p (Ma _st0 ,p _st0 ,δ _st )

M represents the Mach number, p represents the pressure, δ represents the turning angle, the subscript st represents the point on the streamline, the subscript st0 represents the starting point of the streamline, and f _PM,p () represents the Prandtl-Meyer flow function.

Using Mach number and pressure to verify whether the wall shape deduction is reasonable can improve the design verification process and make it more reasonable.

With reference to the first aspect, in some implementation manners of the first aspect, the wall shape i satisfies the assumptions of isentropic fan separation, cross-sectional average, and two-dimensional isentropic steady flow.

By assuming that the calculation model is reasonably simplified, it is beneficial to improve the efficiency of data processing.

With reference to the first aspect, in some implementation manners of the first aspect, the determining the shape i of the wall surface includes:

Use the chord intercept method to calculate the parameters of the shock wave, expansion wave and after-wave airflow in different flow fields, until all internal units and the intersection positions of the incident shock wave and the slip line are calculated, and the streamline from the starting point of the shock wave is traced to obtain The wall shape i.

With reference to the first aspect, in some implementations of the first aspect, the performing flow field simulation includes:

Generate CFD flow field grid topology based on the wall surface obtained by inverse design;

Import the grid topology into the flow field solver, establish a CFD simulation model, and select the shock wave stabilization method, time-advancing method, turbulence model and control equation;

Initial conditions are set, and a steady state simulation is performed on the CFD simulation model to obtain the flow field data i+1.

In a second aspect, an electronic device is provided, and the electronic device is configured to execute the method described in any one of the implementation manners of the foregoing first aspect.

Description of drawings

Figure 1 is a flow chart of the two-dimensional surface design method.

Figure 2 is a schematic diagram of the flow field near the wall in the two-dimensional profile design.

Fig. 3 is a schematic diagram of an oblique shock wave on a wedge.

Fig. 4 is a schematic diagram of the intersection of an oblique shock wave and an oblique shock wave on the same side.

Figure 5 is a schematic diagram of the reflection of expansion waves.

Fig. 6 Schematic diagram of segmental inversion of curved front flow field.

Fig. 7 is a schematic diagram of the preset shock wave, the inversion wall and the numerical verification wall.

Fig. 8 is a schematic diagram of the comparison of the Mach number cloud images of the numerical simulation near the wall before and after the inversion design.

Detailed ways

The application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

In the present invention, the design method of the strong interference area is based on the two-dimensional bending characteristic line theory. Figure 1 shows a schematic flowchart of the method. Figure 2 is a schematic diagram of the flow field near the wall in the two-dimensional profile design. Specifically include the following steps.

S1, based on the characteristics of two-dimensional shock wave interference, the simplified assumptions for establishing isentropic wave fan separation, section average and two-dimensional isentropic steady flow are as follows.

(1) discrete wave fan

When calculating the turning angle caused by the reflected wave, the dispersed fan expansion wave is simplified to the discrete expansion wave reflected by the compression fan concentration intersecting with the shock wave, which is approximately calculated as a discrete expansion wave.

(2) Section average

For approximate calculations, the outlet section is defined as the left-handed feature line emanating from the end of the wall. The Mach number, pressure, and total pressure are taken as the average values of the parameters of the wall, after the shock wave, and at the end of the streamline:

In the formula, n is the number of streamlines, and i is its serial number. M represents the Mach number, P represents the pressure, P* represents the total pressure, the subscript x represents the section x, the subscript W represents the wall surface, the subscript st, i represents the i-th streamline, and the subscript s represents the shock wave. From this, the approximate values of the performance parameters such as the Mach number of the outlet section, the pressure ratio, and the total pressure recovery coefficient can be calculated.

(3) Two-dimensional isentropic steady flow

In order to solve the flow under two-dimensional shock disturbance, it is necessary to derive the characteristic line equations (including characteristic line equations, streamline equations and corresponding compatibility equations) from the Euler equation, and then use the finite difference method to solve the ordinary differential equations. Therefore, in the present invention, the design method is applicable to two-dimensional steady isentropic flow. If there is a flow field with strong shock wave (pressure ratio exceeding 2.0) inside, the calculation is still continued according to the isentropic situation.

S2. According to the specified aerodynamic parameter distribution of the compression surface, outlet parameter distribution and bending shock shape, establish an approximate method for calculating the parameters before and after the shock, wall parameters, outlet parameters and streamlines in the flow field. The calculated relations are all in the form of is given in the form of an explicit analytical solution.

(1) oblique shock wave

As shown in Fig. 3, the shock angle β can be determined by applying the oblique shock wave before and after relationship:

In the formula, M represents the Mach number, p represents the pressure, δ represents the turning angle (representing the turning change of the gas flow direction), β represents the shock angle (the angle between the shock wave and the wall surface), k is the specific heat ratio of the gas, and the subscript A and B represent the area shown in Figure 3. Region A may be the region upstream of the shock. Region B is the downstream region of Region A, located downstream of the shock wave.

An explicit expression for the exact solution of the shock tangent can be obtained after some algebraic transformations:

均为来流参数确定的变量。in

Both are variables determined by incoming flow parameters.

(2) Oblique shock wave and oblique shock wave intersect on the same side

As shown in Fig. 2 and Fig. 4, oblique shock wave 1 (airflow turning angle and shock angle are δ _B , β _B ) and oblique shock wave 2 (airflow turning angle and shock angle are δ _C , β _C ) After the intersection, a new oblique shock wave 3 (shock angle β _F ) is formed, and a reflected wave system and slip flow discontinuity are generated. At this time, the turning angle of the discrete expansion wave simplified by the fan expansion wave is as follows:

Among them, M represents the Mach number, p represents the pressure, k represents the specific heat ratio of the gas, the subscript C represents the C region in Figure 4, D represents the expansion wave D region, and the subscript BC represents the incoming flow through the turning angle δ _BC = δ _B + _δC region. Region B is the region between oblique shock 1 and oblique shock 2. Area B is located upstream of oblique shock wave 2 and is the upstream area of area C. Area C is the downstream area of oblique shock wave 2. Oblique shock wave 1 and oblique shock wave 2 intersect to form oblique shock wave 3 and slip line, the slip line is the slip line of oblique shock wave 1, and the F area is located between oblique shock wave 3 and slip line SL shown in 2) between. The intersection of oblique shock wave 1 and oblique shock wave 2 will also form an expansion wave, and the area D shows the expansion sector. The area between the D area and the F area is the E area. A jet can form between the E area and the F area.

(3) The expansion wave is reflected on the wall

As shown in Figure 5, the discrete expansion wave with an expansion angle of δ is reflected on the wall parallel to the incoming flow, which is easy to analyze. The air flow is expanded from area A to area B and then to area C, and the expanded angle is twice the original expansion angle . Area A is the upstream area of the incident expansion wave, B is the area between the incident expansion wave and the reflected expansion wave, and C is the downstream area of the reflected expansion wave.

S3. According to the shape of the bending shock wave and the heat flow on the wall, given the bending shock wave, and taking the streamline from the starting point of the bending shock wave as the boundary, decompose the flow field of the bending front section into the flow field of the bending shock wave section (the streamline in the area Both pass through the bending shock) and the flow field of the straight leading edge section (the streamlines in the area all pass through the straight leading shock), as shown in Figure 6.

(1) Divide the flow field into a supersonic curved front section and a subsonic root region, and then invert the wall in partitions. At the boundary point of the flow field, where the shock wave upstream of the subsonic region intersects the shock wave of the supersonic curved leading edge section, the shock angles of the two are equal.

(2) Due to the lack of theoretical solution methods in the subsonic region, it is proposed to select a flow field with a suitable root shock wave shape from the existing SRR configuration, and intercept the subsonic flow field not affected by the shock wave interference as the subsonic root area. The incoming flow Mach number, pressure, and flow direction angle are M _∞ , p _∞ , and θ _∞ respectively, and the curved compression profile (that is, the wall at the supersonic curved front section and the subsonic root region) is determined by the following formula:

y _W ＝f _W (x _W ),0≤x _W ≤L

Among them, x and y represent the coordinates, the f function represents the profile function of the curved wall, the subscript W represents the wall, and L represents the length of the wall. Select the coordinate system so that the direction of the abscissa is the same as the direction of the incoming flow, and the origin is the starting point of the wall. The distribution of wall angles can be obtained:

Where δ _W δ represents the turning angle at the wall, x represents the coordinate, f function represents the shape function of the curved wall, and the subscript w represents the wall.

(3) According to the matching conditions of the existing subsonic section, refer to the reverse design method of the supersonic inlet/special-shaped supersonic inner flow channel, respectively construct the flow field of the curved shock wave section and the shock wave of the straight leading edge section with reasonable shapes. Discrete bending shock wave, calculate shock wave, expansion wave and airflow parameters after wave in different flow field domains, until all internal elements and the intersection positions of incident shock wave and slip line are calculated.

S4, use the chord intercept method to calculate the parameters of the shock wave, expansion wave, and post-wave airflow in different flow fields, until all internal units and the intersection positions of the incident shock wave and the slip line are calculated, and the streamline from the start point of the shock wave is traced , which is the wall surface required by the inverse design. The wall inverse design method is summarized below.

The coordinates of the shock wave at each interference point are calculated according to the parameters of each area. Starting from the shock wave interference point, the intersection point between the compression wave and the wall is reversed, and the streamline from the start point of the shock wave is traced, which is the target wall shape obtained by inversion. According to the X direction (that is, the X abscissa direction in S3) cross section (the cross section is perpendicular to the X direction), the flow rate on the cross section (the cross section is perpendicular to the X direction) is equal to the flow rate of the incoming flow capture cross section, and the streamline equation with x _w as the independent variable can be obtained:

Among them, x and y represent the coordinates, μ is the Mach angle, θ is the air flow angle, M is the Mach number, q is the heat flow, the subscript st represents the point on the streamline, the subscript st0 represents the starting point of the streamline, and the subscript w represents the wall surface The point above, the subscript x indicates the cross-section x, the subscript x can be a discrete value in the X direction, q _∞ is the standard heat flow, which is used to define the standard value of the incoming flow, which can be determined artificially according to the needs, for example, the peak heat flow of the sharp leading edge as a reference value.

Combined with Fig. 2, considering the influence of the reflected expansion wave on the shock wave and the re-reflection of the expansion wave on the wall, the flow direction θ _st at a point on the streamline and the compressed turning angle δ _st from the starting point of the streamline are approximately taken as for:

θ _st = θ _W

δ _st ＝(θ _W -2δ _exp )-(θ _W,st0 -2δ _exp,st0 )

Where θ is the air flow angle, δ is the turning angle, the subscript st is the point on the streamline, the subscript w is the point on the wall, the subscript w, st0 is the starting point of the streamline on the wall, and the subscript exp is the expansion wave, the subscripts exp, st0 represent the streamline starting point of the expansion wave region.

Solve the corresponding Mach number M _st and pressure p _st from the starting point parameters of the streamline (i.e. parameters after the shock wave):

M _st ＝f _PM,M (M _st0 ,δ _st )

p _st ＝f _PM,p (M _st0 ,p _st0 ,δ _st )

In the formula, M represents the Mach number, p represents the pressure, δ represents the turning angle, the subscript st represents the point on the streamline, the subscript st0 represents the starting point of the streamline, and f _PM represents the Prandtl-Meyer flow function. Finally, the expression for solving the coordinates on the streamline with x _w as the independent variable can be obtained, and the Mach number, pressure and flow direction of the corresponding position can be obtained at the same time. That is to say, the flow near the wall satisfies the Prandtl-Meyer flow, that is, the airflow presents a two-dimensional isentropic steady flow in which the supersonic speed expands and accelerates around an obtuse outer angle.

S5, based on the wall surface obtained by the inverse design, generate the CFD flow field grid topology. Requirements: Select the characteristic size of the strong shock wave interference area of the aircraft as the length unit, and there are no gaps or overlapping areas in each geometric surface of the mesh topology division.

S6, importing the grid topology into the flow field solver to establish a CFD simulation model. The high-resolution flux function constructed is RoeMAS format; the shock wave stabilization method adopts MUSCL format mixed with high-precision WENO format; the unsteady coupled heat transfer simulation method is radial basis function interpolation method; the unsteady time-advancing method is explicit Runge -Kutta scheme and implicit post-difference time scheme; the turbulence model adopts the two-equation SST k-turbulence model; the governing equation adopts the three-dimensional compressible Reynolds-averaged N-S equation, which is as follows:

为守恒变量；

为三个方向的无粘矢通量；

为三个方向的粘性矢通量。Among them, x, y, z represent three-dimensional coordinates,

is a conserved variable;

is the inviscid vector flux in three directions;

is the viscous vector flux in three directions.

S7, setting initial conditions, performing steady state simulation on the CFD simulation model, and verifying the shock wave structure of the reverse design wall through the numerical simulation results such as flow field aerodynamic parameter distribution, flow field outlet parameter distribution and shock wave shape.

Simulation results may include simulated Mach numbers and pressures. Compare the simulated Mach number with the previous Mach number M _st , compare the simulated pressure with the previous pressure p _st , and judge whether the similarity between the simulated shock wave shape and the preset shock wave shape meets the requirements. If the requirements are met, the inverted wall shape is determined as the final wall design shape. If the requirements are not met, re-execute the above S1 to S7 according to the simulated flow field data and the preset shock wave shape until the similarity between the simulated shock wave shape and the preset shock wave shape meets the requirements.

FIG. 7 is a schematic diagram showing that the similarity between the simulated shock wave shape and the preset shock wave shape meets the requirements. The simulated shock wave shape, the preset shock wave shape and the wall surface in FIG. 7 may all refer to the central simulated shock wave shape, the central preset shock wave shape and the central wall surface.

Figure 8 shows a verification example of the two-dimensional bending shock flow field. The shape of the two-dimensional bending shock wave is constructed with the ellipse parametric equation (incoming flow Ma=6, shock wave expression: x=cos(θ), y =2sin(θ), θ=-60°～-15°). The gray scale of the preset shock wave in Fig. 8 is the same as the gray scale of the wall simulation results. It can be seen from the figure that the shock shape obtained by the numerical simulation of the inverted wall is in good agreement with the preset shock wave shape, which shows that the method has a good performance in solving two-dimensional problems.

In this application, through the two-dimensional bow shock wave and oblique shock wave interference theoretical model, the flow field of the curved leading edge section is decomposed into the curved shock wave section and the straight leading edge section flow field and solved separately, and the two-dimensional curved surface flow field in the shock wave interference area is obtained parameter. This application proposes a flow field iterative method for two-dimensional bow shock and bending shock interference under shock interference on the same side to realize the calculation of flow field parameters for bending shock and bow shock interference. This application forms a two-dimensional design method for the strong interference area based on the characteristic line theory. According to the shape of the preset bending shock wave and the boundary conditions of the three-dimensional effect of the flow field, the flow field is recursively calculated to obtain the bending shock wave section and the straight forward The aerodynamic parameters and coordinate conditions of the flow field in the edge section are tracked according to the characteristic line theory to form the two-dimensional surface of the strong interference area after the heat reduction design. This application relates to a design method for the strong interference area based on the two-dimensional bending characteristic line theory. Through the bending shock wave characteristic line theory, the reverse design method of the lip is developed, which can adapt to the wall boundary design of two sets of bow shock wave interference. , can be widely used in high-speed aircraft aerodynamic thermal environment assessment, aerodynamic thermal protection design and other fields.

Although the present invention is disclosed above with preferred embodiments, it is not intended to limit the present invention, and any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the present invention The protection scope of the invention shall be defined by the claims of the present invention.

Claims (12)

1. A wall design method, characterized in that, comprising: Step (1), obtaining a preset shock wave shape; Step (2), obtaining flow field data i; Step (3), according to the preset shock wave shape and the flow field data i, determine the wall shape i, the wall shape if _W,i () satisfies: y _W,i =f _W,i (x _W,i ),0≤x _W,i ≤L,

x _W,i is the x coordinate of the wall surface, y _W,i is the y coordinate of the wall surface, y _st0,i is the y coordinate of the streamline starting point, M _x,i is the Mach number of section x, q _∞ is the standard heat flow, q _x,i is the heat flow of section x, μ is the Mach angle of section x, θ _x,i is the air flow angle of section x; Step (4), performing flow field simulation according to the wall shape i, to obtain flow field data i+1; Step (5), according to the flow field data i+1 and the flow field parameters corresponding to the wall shape i, determine whether the similarity between the simulated shock wave shape i and the preset shock wave shape meets the requirements; Step (6), if the requirement is met, output the wall shape i, if the requirement is not met, then i=i+1, and re-execute steps (2)-(6). 2 . The method according to claim 1 , wherein the preset shock shape is used to indicate at least one of the following: distribution of aerodynamic parameters on a compression surface, distribution of outlet parameters, and bending shock shape. 3 . 3 . The method according to claim 1 , wherein the flow field data i include at least one of the following: parameters before and after the shock wave, wall parameters, outlet parameters, and streamline data in the flow field. 4 . 4. The method according to claim 1, characterized in that, for the intersection of oblique shock wave 1 and oblique shock wave 2 on the same side, the streamline data i satisfy: Discrete expansion wave turning angle

Among them, M represents the Mach number, p represents the pressure, k represents the specific heat ratio of the gas, the subscript BC represents the area where the incoming flow passes through the turning angle δ _BC = δ _B + δ _C , and the area B is the oblique shock wave 1 and the In the area between the oblique shock waves 2, the area B is located upstream of the oblique shock wave 2, and the area C is the downstream area of the oblique shock wave 2. 5. method according to claim 1, is characterized in that, described wall shape i also f _{W, i} () satisfies:

δ _W,i represents the turning angle at the wall. 6. The method according to claim 1, wherein the wall shape i is the wall shape of the supersonic curved leading section and the subsonic root region, and the supersonic curved leading section and the subsonic root region pass through Bending shock morphology and wall heat flow determination. 7. The method according to claim 1, characterized in that, the wall shape i also satisfies: θ _st = θ _W δ _st ＝(θ _W -2δ _exp )-(θ _W,st0 -2δ _exp,st0 ) Where θ is the air flow angle, δ is the turning angle, the subscript st is the point on the streamline, the subscript w is the point on the wall, the subscript w, st0 is the starting point of the streamline on the wall, and the subscript exp is the expansion wave, the subscripts exp, st0 represent the streamline starting point of the expansion wave region. 8. method according to claim 1, is characterized in that, described flow field parameter comprises Mach number Ma _st and pressure p _st : M _st ＝f _PM,M (M _st0 ,δ _st ) p _st ＝f _PM,p (Ma _st0 ,p _st0 ,δ _st ) M represents the Mach number, p represents the pressure, δ represents the turning angle, the subscript st represents the point on the streamline, the subscript st0 represents the starting point of the streamline, and f _PM,p () represents the Prandtl-Meyer flow function. 9 . The method according to claim 1 , wherein the wall shape i satisfies the assumptions of isentropic fan separation, section average and two-dimensional isentropic steady flow. 10. The method according to claim 1, wherein said determining the wall shape i comprises: Use the chord intercept method to calculate the parameters of the shock wave, expansion wave and after-wave airflow in different flow fields, until all internal units and the intersection positions of the incident shock wave and the slip line are calculated, and the streamline from the starting point of the shock wave is traced to obtain The wall shape i. 11. The method according to claim 1, wherein said performing flow field simulation comprises: Generate CFD flow field grid topology based on the wall surface obtained by inverse design; Import the grid topology into the flow field solver, establish a CFD simulation model, and select the shock wave stabilization method, time-advancing method, turbulence model and control equation; Initial conditions are set, and a steady state simulation is performed on the CFD simulation model to obtain the flow field data i+1. 12. An electronic device, characterized in that the electronic device is configured to execute the method according to any one of claims 1 to 11.

Images