CN116070538A - Interference area wall inversion method based on three-dimensional bending shock wave interference theory - Google Patents

Interference area wall inversion method based on three-dimensional bending shock wave interference theory Download PDF

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CN116070538A
CN116070538A CN202211461757.1A CN202211461757A CN116070538A CN 116070538 A CN116070538 A CN 116070538A CN 202211461757 A CN202211461757 A CN 202211461757A CN 116070538 A CN116070538 A CN 116070538A
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张旭辉
姚冉
王兆伟
尹戈玲
辜天来
秦云鹏
杨旸
费王华
赵大海
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Abstract

The invention relates to an interference area wall inversion method based on a three-dimensional bending shock wave interference theory, which comprises the following steps: obtaining discrete point parameters: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane; determining a streamline equation: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, solving a streamline equation corresponding to each discrete point in the symmetry plane; solving an outer cone flow field; determining the wall surface of a shock interference area: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface; determining CFD flow field grid topology; establishing a CFD simulation model; and optimizing the wall surface of the shock interference area. The inversion design method provides the lip front edge interference area profile optimization scheme, and achieves the effect of reducing the wall surface heat flow.

Description

Interference area wall inversion method based on three-dimensional bending shock wave interference theory
Technical Field
The invention relates to an interference area wall inversion method based on a three-dimensional bending shock wave interference theory, and belongs to the technical field of combined power aircrafts.
Background
The hypersonic speed internal and external flow integrated aircraft air inlet lip is severe in aerodynamic heat load due to complex shock wave interference. The prior researches show that the increase of the heat flow on the wall surface of the root part of the lip front edge is directly or indirectly derived from the shock wave interference phenomenon, so that the shock wave interference intensity of the root part of the lip is weakened, and the heat flow peak value can be effectively reduced. Therefore, the method aims at giving a three-dimensional preset shock wave profile meeting the requirements of the lip according to the working requirements of the air inlet channel, and giving a lip front edge strong interference area profile optimization scheme through inversion design, so that the effect of reducing the wall surface heat flow is achieved.
Because the front edge flow field of the lip of the air inlet of the integrated aircraft with the internal and external flows has obvious three-dimensional property, the method of two-dimensional inversion and transverse flow correction commonly used at home and abroad at present can only predict the form of the initial development stage of the shock wave of the disjunctor, and obvious deviation appears at the downstream, and the method has difficulty in realizing inversion of the three-dimensional flow field of the lip and the profile of an interference zone.
Disclosure of Invention
The invention solves the technical problems that: the method for inverting the wall surface of the interference area based on the three-dimensional bending shock wave interference theory is provided to realize effective prediction of the convection field structure, and the optimization scheme of the wall surface of the shock wave interference area is determined by comparing and contrasting the simulated shock wave surface with the preset bending shock wave surface.
The solution of the invention is as follows:
an interference area wall inversion method based on a three-dimensional bending shock wave interference theory comprises the following steps:
obtaining discrete point parameters: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane;
determining a streamline equation: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, a free streamline method is applied, and a streamline equation corresponding to each discrete point in the symmetry plane is solved;
solving an outer cone flow field: determining a plurality of external cone flow fields passing through discrete points and kissing with the shock wave surface along the flow direction, and solving the corresponding external cone flow fields based on the local shock wave angle and Mach number corresponding to each discrete point in the symmetrical plane;
determining the wall surface of a shock interference area: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface;
determining CFD flow field grid topology: grid topology division is carried out on the shock wave interference area wall surface based on the inverse design generated shock wave interference area wall surface, so that gaps and overlapping areas are not formed on the geometric surface, and CFD flow field grid topology is generated;
building a CFD simulation model: introducing CFD flow field mesh topology into a flow field solver, setting the flow field solver, and establishing a CFD simulation model;
optimizing the wall surface of the shock interference area: setting initial conditions, performing steady simulation on the CFD simulation model to obtain flow field aerodynamic parameter distribution and flow field outlet parameter distribution, identifying a simulated laser surface based on the flow field aerodynamic parameter distribution and the flow field outlet parameter distribution, comparing the simulated laser surface with a preset bending laser surface, and determining a shock interference area wall optimization scheme.
Further, the local shock wave angle, mach number, pressure and expansion wave deflection angle in the symmetrical plane flow field are determined by solving the intersection relation of oblique shock waves, ipsilateral oblique shock waves and compression waves:
solving the local shock angle by the formula (1), and solving the local shock angle by the formulas (2) and (3) according to the Mach number M of the incoming flow A And pressure p A Calculation of the Mach number M after oblique shock wave B And pressure p B ：
Figure BDA0003954041070000021
Figure BDA0003954041070000022
Figure BDA0003954041070000023
In the formulas (1) - (3), M is Mach number, beta is shock angle, delta is turning angle, k is specific heat ratio,
Figure BDA0003954041070000024
subscript a represents the wavefront and subscript B represents the wave back;
according to formula (4), determining deflection angle of discrete expansion wave, forming a new oblique shock wave F after the oblique shock wave B and the oblique shock wave C are intersected, and setting the corresponding shock wave angle as beta F And generating reflected wave system and slip flow interruption, wherein the turning angle and shock angle corresponding to the oblique shock wave B are respectively delta B 、β B The turning angle and the shock angle corresponding to the oblique shock wave F are respectively delta C 、β C At this time, the discrete expansion wave deflection angle simplified from the wave-sector expansion wave is as follows:
Figure BDA0003954041070000031
wherein M is Mach number, beta is shock wave angle, delta is turning angle, k is specific heat ratio, subscript C represents parameters after oblique shock wave C, subscript F represents parameters after oblique shock wave F, subscript D represents parameters of sector expansion wave region.
Further, the method for solving the streamline equation in the symmetry plane corresponding to each discrete point is as follows:
based on the formula (5), a streamline equation in a symmetrical plane corresponding to each discrete point is given; selection (x) w ，y w ) To make it and discrete point (x s ，y s ) On the same characteristic line, if the flow on the section x is uniform, i.e. Mach number, pressure and flow direction on the section are the same as those of the wall surface parameters, the characteristic line is a straight line, and the streamline equation is expressed as independent variable x w Is defined by the parameter equation:
Figure BDA0003954041070000032
wherein x and y are coordinates, mu is Mach angle, theta is wedge angle, M is Mach number, q is heat flow, subscript s represents discrete point on shock wave, subscript w represents any point on flow line, subscript x represents section x, subscript +_infinity represents incoming flow;
for aerodynamic parameters on the flowline, mach number and pressure for each point on the flowline are determined based on equations (2) and (3), and the actual deflection angle for the point on the flowline is determined based on equations (7) and (8):
δ s ＝θ w -θ ∞ (7)
wherein delta is deflection angle, theta is wedge angle, subscript s represents discrete point on shock wave, the subscript w indicates any point on the flow line, and the subscript +..
Further, the method for solving the outer cone flow field corresponding to each discrete point comprises the following steps:
solving parameters of characteristic line intersection points through a simultaneous characteristic line equation set and a compatibility equation set, and finally obtaining the whole outer cone flow field information;
a set of feature line equations:
Figure BDA0003954041070000041
Figure BDA0003954041070000042
wherein x and y are coordinates, u and v are velocities in x and y directions, γ is an air flow angle, γ=arctan (v/u) represents an angle between an air flow and an x axis, μ is a mach angle, μ=arcsin (1/Ma), λ is a slope, subscript 0 represents a streamline, and subscript ± represents a characteristic line;
a set of compatibility equations:
ρVdV+dp＝0 (10)
dp-a 2 dρ＝0 (11)
Figure BDA0003954041070000043
where ρ is density, V is volume, p is pressure, M is Mach number, a is sound velocity, δ is turning angle, γ is air flow angle, and μ is Mach angle.
Further, the method for generating the shock wave interference area wall surface by reverse design comprises the following steps:
based on a streamline equation corresponding to each discrete point in the symmetrical plane, finally converging the streamline on the two-dimensional molded line of the outer cone flow wall surface of the symmetrical flow field; based on the solution of the outer cone flow field, the envelope curve of the outer cone flow field passing through the two-dimensional molded line of the wall surface is the wall surface of the required shock wave interference area.
Further, a flow field solver is arranged through a shock wave stabilization method, an unsteady coupling heat transfer method and an unsteady time propulsion method based on a high-resolution flux function, a turbulence model and a control equation.
Further, the high-resolution flux function is in the RoeMAS format; the shock wave stabilization method adopts a MUSCL format and a high-precision WENO format to mix; the unsteady coupling heat transfer simulation method is a radial basis function interpolation method; the unsteady time pushing method is an explicit Runge-Kutta format and an implicit post-difference time format; the turbulence model adopts a two-equation SST k-omega turbulence model; the control equation adopts a three-dimensional compressible Reynolds average N-S equation, and is specifically as follows:
Figure BDA0003954041070000051
wherein t represents time, x, y and z respectively represent three-dimensional coordinates,
Figure BDA0003954041070000052
is a conservation variable; />
Figure BDA0003954041070000053
Is a non-viscous vector flux in three directions; />
Figure BDA0003954041070000054
Is a viscous vector flux in three directions.
An interference zone wall inversion system based on three-dimensional bending shock interference theory, comprising:
discrete point parameter acquisition module: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane;
a streamline equation determination module: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, a free streamline method is applied, and a streamline equation corresponding to each discrete point in the symmetry plane is solved;
and an outer cone flow field solving module: determining a plurality of external cone flow fields passing through discrete points and kissing with the shock wave surface along the flow direction, and solving the corresponding external cone flow fields based on the local shock wave angle and Mach number corresponding to each discrete point in the symmetrical plane;
the shock interference area wall surface determining module: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface;
CFD flow field grid topology determination module: grid topology division is carried out on the shock wave interference area wall surface based on the inverse design generated shock wave interference area wall surface, so that gaps and overlapping areas are not formed on the geometric surface, and CFD flow field grid topology is generated;
CFD simulation model establishment module: introducing CFD flow field mesh topology into a flow field solver, setting the flow field solver, and establishing a CFD simulation model;
the shock interference area wall optimization module: setting initial conditions, performing steady simulation on the CFD simulation model to obtain flow field aerodynamic parameter distribution and flow field outlet parameter distribution, identifying a simulated laser surface based on the flow field aerodynamic parameter distribution and the flow field outlet parameter distribution, comparing the simulated laser surface with a preset bending laser surface, and determining a shock interference area wall optimization scheme.
Compared with the prior art, the invention has the beneficial effects that:
(1) Based on a three-dimensional bending shock wave interference theory, the three-dimensional front edge flow field structure of the lip of the air inlet channel of the internal and external integrated aircraft can be effectively predicted, and the lip front edge interference area profile optimization scheme is given out by an inversion design method, so that the effect of reducing the wall surface heat flow is achieved;
(2) According to the invention, a plurality of non-coplanar outer cone flow fields are determined according to the normal direction and the incoming flow direction of the shock wave, a streamline equation corresponding to each discrete point and aerodynamic parameters on a streamline are solved in a symmetrical plane, and a wall surface of a shock wave interference area is reversely designed and generated based on the streamline equation and the outer cone flow field of each discrete point.
Drawings
FIG. 1 is a schematic diagram of the intersection of a oblique shock wave with an on-side oblique shock wave;
FIG. 2 is a three-dimensional schematic view of a flow direction infinitesimal kissing cone;
FIG. 3 shows the three-dimensional curved wall inversion results.
Detailed Description
The invention is further illustrated below with reference to examples.
The invention is described in further detail below with reference to the accompanying drawings and examples of the reverse design of the three-dimensional bending shock flow field walls of a high-speed aircraft.
The invention discloses an interference area wall inversion design method based on a three-dimensional bending shock wave interference theory, which specifically comprises the following steps:
s1, a preset bending laser surface of a wave multiplier of a variable laser angle osculating flow field is given, a preset laser line is discretized into a plurality of discrete points in a symmetrical plane, and the wave-back parameters such as a local laser angle, mach number, pressure, expansion wave deflection angle and the like of each discrete point of the flow field in the symmetrical plane are obtained. Obtaining local shock wave angle and wave parameters such as Mach number, pressure, expansion wave deflection angle and the like by solving an oblique shock wave relation and an intersection relation of the same-side oblique shock wave and the oblique shock wave:
solving the local shock angle by the formula (1), and solving the local shock angle by the formulas (2) and (3) according to the Mach number M of the incoming flow A And pressure p A The turning angle delta can calculate the Mach number M after the oblique shock wave B And pressure p B ：
Figure BDA0003954041070000061
Figure BDA0003954041070000071
Figure BDA0003954041070000072
In the formulas (1) - (3), M is Mach number, beta is shock angle, delta is turning angle, k is specific heat ratio,
Figure BDA0003954041070000073
subscript a represents the wavefront and subscript B represents the wave back.
As shown in FIG. 1, solving the same-side oblique shock wave and oblique shock wave intersection problem
According to equation (4), the discrete expansion wave deflection angle is determined. Let the oblique shock wave B (turning angle and shock angle are delta respectively) B 、β B ) And oblique shock wave C (turning angle and shock angle are delta respectively) C 、β C ) After crossing, a new oblique shock wave F (shock angle is beta) F ) And generateReflected wave trains and slip stream discontinuities. At this time, the discrete expansion wave deflection angle simplified from the wave-sector expansion wave is as follows:
Figure BDA0003954041070000074
wherein M is Mach number, beta is shock wave angle, delta is turning angle, k is specific heat ratio, subscript C represents parameters after oblique shock wave C, subscript F represents parameters after oblique shock wave F, subscript D represents parameters of sector expansion wave region.
S2, a free streamline method is applied, and a streamline equation corresponding to each discrete point in a symmetrical plane and aerodynamic parameters such as Mach number, pressure, deflection angle and the like on a streamline are solved;
based on equation (5), a streamline equation in the symmetry plane corresponding to each discrete point is given. Selection (x) w ，y w ) To make it and discrete point (x s ，y s ) On the same characteristic line, if the flow on the section x is uniform, i.e. Mach number, pressure and flow direction on the section are the same as those of the wall surface parameters, the characteristic line is a straight line, and the streamline equation can be expressed as independent variable x w Is defined by the parameter equation:
Figure BDA0003954041070000075
wherein x and y are coordinates, μ is a Mach angle, θ is a wedge angle, M is a Mach number, q is a heat flow, subscript s represents a discrete point on the shock wave, subscript w represents any point on the flow line, subscript x represents section x, subscript ++represents incoming flow.
For aerodynamic parameters on the flowline, mach number and pressure for each point on the flowline are determined based on equations (2) and (3), and the actual deflection angle for the point on the flowline is determined based on equations (7) and (8):
δ s ＝θ w -θ ∞ (7)
wherein delta is deflection angle, theta is wedge angle, subscript s represents discrete point on shock wave, the subscript w indicates any point on the flow line, and the subscript +..
S3, making a plurality of outer cone flow fields which pass through discrete points along the flow direction and are matched with the shock wave surface, as shown in figure 2. Based on the local shock wave angle, mach number and other parameters corresponding to each discrete point in the symmetrical plane, a standard cone flow solving method is used to obtain a corresponding outer cone flow field solution;
and solving parameters of the characteristic line intersection points through a simultaneous characteristic line equation set (formulas 8 and 9) and a compatibility equation set (formulas 10, 11 and 12), and finally obtaining the whole outer cone flow field information.
A set of feature line equations:
Figure BDA0003954041070000081
Figure BDA0003954041070000082
where x and y are coordinates, u and v are velocities in x and y directions, γ is an airflow angle, γ=arctan (v/u) represents an angle between the airflow and the x axis, μ is a mach angle, μ=arcsin (1/Ma), λ is a slope, subscript 0 represents a streamline, and subscript ± represents a characteristic line.
A set of compatibility equations:
ρVdV+dp＝0 (10)
dp-a 2 dρ＝0 (11)
Figure BDA0003954041070000083
where ρ is density, V is volume, p is pressure, M is Mach number, a is sound velocity, δ is turning angle, γ is air flow angle, and μ is Mach angle.
S4, generating a shock wave interference area wall surface by reverse design based on a streamline equation of each discrete point and an outer cone flow field solution, wherein the reverse design method is based on the streamline equation corresponding to each discrete point in the symmetrical plane in the step S2, and finally converging a streamline obtained by a streamline tracking method on an outer cone flow wall surface two-dimensional molded line of the symmetrical flow field; and (3) based on the solution of the outer cone flow field in the step (S3), the envelope curve of the outer cone flow field passing through the wall surface two-dimensional molded line is the wall surface of the required shock wave interference area.
S5, selecting characteristic dimensions of the strong shock wave interference area as length units based on the wall surfaces of the shock wave interference area generated by reverse design, requiring grid topology to divide each geometric surface into areas without gaps and overlapping areas, and generating CFD flow field grid topology so as to be applied to CFD simulation calculation.
S6, leading the CFD flow field grid topology into a flow field solver, establishing a CFD simulation model, and setting specific simulation to a high-resolution flux function to use a RoeMAS format; the shock wave stabilization method adopts a MUSCL format and a high-precision WENO format to mix; the unsteady coupling heat transfer simulation method is a radial basis function interpolation method; the unsteady time pushing method is an explicit Runge-Kutta format and an implicit post-difference time format; the turbulence model adopts a two-equation SST k-omega turbulence model; the control equation adopts a three-dimensional compressible Reynolds average N-S equation, and is specifically as follows:
Figure BDA0003954041070000091
wherein t represents time, x, y and z respectively represent three-dimensional coordinates,
Figure BDA0003954041070000092
is a conservation variable; />
Figure BDA0003954041070000093
Is a non-viscous vector flux in three directions; />
Figure BDA0003954041070000094
Is a viscous vector flux in three directions.
S7, setting initial conditions, performing stationary simulation on the CFD simulation model to obtain simulation results such as flow field pneumatic parameter distribution, flow field domain outlet parameter distribution, shock wave shape and the like, comparing reverse design to generate a shock wave structure of a shock wave interference area wall surface with a preset bending shock wave result through the simulation results, and verifying the effectiveness of an interference area wall surface inversion method based on a three-dimensional bending shock wave interference theory.
Fig. 3 shows the result of an interference area wall inversion method based on the three-dimensional bending shock wave interference theory, and the effectiveness of the method is verified by reversely designing the three-dimensional bending front edge wall through a conical kissing reference flow field and comparing the three-dimensional bending front edge wall with a preset shock wave profile.
The invention provides a method for realizing three-dimensional bending shock wave interference theory modeling by combining a bending shock wave theory and a bending streamline characteristic method, and realizing effective prediction of a convection field structure;
the invention refers to a local infinitesimal osculating design method, which adopts conical flow symmetrical plane shock waves and a posterior flow field thereof to approximate to form a three-dimensional wall inversion method.
Aiming at the fourth type of shock wave interference problem of wide-range Ma 6-10 high-speed flight, the invention establishes a three-dimensional shock wave interference reverse design method of the inclined shock wave incident V-shaped front edge through a bending shock wave surface interference theoretical analysis model, and verifies the inversion method through numerical simulation and shock wave wind tunnel ground test, thereby forming a reliable three-dimensional bending shock wave interference area wall inversion design method.
An interference zone wall inversion system based on three-dimensional bending shock interference theory, comprising:
discrete point parameter acquisition module: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane;
a streamline equation determination module: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, a free streamline method is applied, and a streamline equation corresponding to each discrete point in the symmetry plane is solved;
and an outer cone flow field solving module: determining a plurality of external cone flow fields passing through discrete points and kissing with the shock wave surface along the flow direction, and solving the corresponding external cone flow fields based on the local shock wave angle and Mach number corresponding to each discrete point in the symmetrical plane;
the shock interference area wall surface determining module: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface;
CFD flow field grid topology determination module: grid topology division is carried out on the shock wave interference area wall surface based on the inverse design generated shock wave interference area wall surface, so that gaps and overlapping areas are not formed on the geometric surface, and CFD flow field grid topology is generated;
CFD simulation model establishment module: introducing CFD flow field mesh topology into a flow field solver, setting the flow field solver, and establishing a CFD simulation model;
the shock interference area wall optimization module: setting initial conditions, performing steady simulation on the CFD simulation model to obtain flow field aerodynamic parameter distribution and flow field outlet parameter distribution, identifying a simulated laser surface based on the flow field aerodynamic parameter distribution and the flow field outlet parameter distribution, comparing the simulated laser surface with a preset bending laser surface, and determining a shock interference area wall optimization scheme.
Based on the three-dimensional bending shock wave interference theory, the three-dimensional front edge flow field structure of the lip of the air inlet channel of the internal and external flow integrated aircraft can be effectively predicted, and the lip front edge interference area profile optimization scheme is given out through an inversion design method, so that the effect of reducing the wall surface heat flow is achieved.
Although the present invention has been described in terms of the preferred embodiments, it is not intended to be limited to the embodiments, and any person skilled in the art can make any possible variations and modifications to the technical solution of the present invention by using the methods and technical matters disclosed above without departing from the spirit and scope of the present invention, so any simple modifications, equivalent variations and modifications to the embodiments described above according to the technical matters of the present invention are within the scope of the technical matters of the present invention.

Claims (11)

1. An interference area wall inversion method based on a three-dimensional bending shock wave interference theory is characterized by comprising the following steps:
obtaining discrete point parameters: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane;
determining a streamline equation: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, a free streamline method is applied, and a streamline equation corresponding to each discrete point in the symmetry plane is solved;
solving an outer cone flow field: determining a plurality of external cone flow fields passing through discrete points and kissing with the shock wave surface along the flow direction, and solving the corresponding external cone flow fields based on the local shock wave angle and Mach number corresponding to each discrete point in the symmetrical plane;
determining the wall surface of a shock interference area: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface;
determining CFD flow field grid topology: grid topology division is carried out on the shock wave interference area wall surface based on the inverse design generated shock wave interference area wall surface, so that gaps and overlapping areas are not formed on the geometric surface, and CFD flow field grid topology is generated;
building a CFD simulation model: introducing CFD flow field mesh topology into a flow field solver, setting the flow field solver, and establishing a CFD simulation model;
optimizing the wall surface of the shock interference area: setting initial conditions, performing steady simulation on the CFD simulation model to obtain flow field aerodynamic parameter distribution and flow field outlet parameter distribution, identifying a simulated laser surface based on the flow field aerodynamic parameter distribution and the flow field outlet parameter distribution, comparing the simulated laser surface with a preset bending laser surface, and determining a shock interference area wall optimization scheme.
2. The interference area wall inversion method based on the three-dimensional bending shock wave interference theory according to claim 1, wherein the local shock wave angle, mach number, pressure and expansion wave deflection angle in the symmetrical plane flow field are determined by solving the intersection relation of oblique shock waves, same-side oblique shock waves and compression waves:
solving for by the formula (1)Local shock angle, based on incoming stream Mach number M by formulas (2) and (3) A And pressure p A Calculation of the Mach number M after oblique shock wave B And pressure p B ：
Figure FDA0003954041060000021
Figure FDA0003954041060000022
Figure FDA0003954041060000023
In the formulas (1) - (3), M is Mach number, beta is shock angle, delta is turning angle, k is specific heat ratio,
Figure FDA0003954041060000024
subscript a represents the wavefront and subscript B represents the wave back;
according to formula (4), determining deflection angle of discrete expansion wave, forming a new oblique shock wave F after the oblique shock wave B and the oblique shock wave C are intersected, and setting the corresponding shock wave angle as beta F And generating reflected wave system and slip flow interruption, wherein the turning angle and shock angle corresponding to the oblique shock wave B are respectively delta B 、β B The turning angle and the shock angle corresponding to the oblique shock wave F are respectively delta C 、β C At this time, the discrete expansion wave deflection angle simplified from the wave-sector expansion wave is as follows:
Figure FDA0003954041060000025
/>
wherein M is Mach number, beta is shock wave angle, delta is turning angle, k is specific heat ratio, subscript C represents parameters after oblique shock wave C, subscript F represents parameters after oblique shock wave F, subscript D represents parameters of sector expansion wave region.
3. The interference area wall inversion method based on the three-dimensional bending shock interference theory according to claim 1, wherein the streamline equation method in the symmetry plane corresponding to each discrete point is solved by:
based on the formula (5), a streamline equation in a symmetrical plane corresponding to each discrete point is given; selection (x) w ，y w ) To make it and discrete point (x s ，y s ) On the same characteristic line, if the flow on the section x is uniform, i.e. Mach number, pressure and flow direction on the section are the same as those of the wall surface parameters, the characteristic line is a straight line, and the streamline equation is expressed as independent variable x w Is defined by the parameter equation:
Figure FDA0003954041060000031
wherein x and y are coordinates, mu is Mach angle, theta is wedge angle, M is Mach number, q is heat flow, subscript s represents discrete point on shock wave, subscript w represents any point on flow line, subscript x represents section x, subscript +_infinity represents incoming flow;
for aerodynamic parameters on the flowline, mach number and pressure for each point on the flowline are determined based on equations (2) and (3), and the actual deflection angle for the point on the flowline is determined based on equations (7) and (8):
δ s ＝θ w -θ ∞ (7)
wherein delta is deflection angle, theta is wedge angle, subscript s represents discrete point on shock wave, the subscript w indicates any point on the flow line, and the subscript +..
4. The interference area wall inversion method based on the three-dimensional bending shock wave interference theory according to claim 1, wherein the outer cone flow field solving method corresponding to each discrete point is as follows:
solving parameters of characteristic line intersection points through a simultaneous characteristic line equation set and a compatibility equation set, and finally obtaining the whole outer cone flow field information;
a set of feature line equations:
Figure FDA0003954041060000032
Figure FDA0003954041060000033
wherein x and y are coordinates, u and v are velocities in x and y directions, γ is an air flow angle, γ=arctan (v/u) represents an angle between an air flow and an x axis, μ is a mach angle, μ=arcsin (1/Ma), λ is a slope, subscript 0 represents a streamline, and subscript ± represents a characteristic line;
a set of compatibility equations:
ρVdV+dp＝0 (10)
dp-a 2 dρ＝0 (11)
Figure FDA0003954041060000034
where ρ is density, V is volume, p is pressure, M is Mach number, a is sound velocity, δ is turning angle, γ is air flow angle, and μ is Mach angle.
5. The interference area wall inversion method based on the three-dimensional bending shock interference theory according to claim 1, wherein the method for generating the shock interference area wall by reverse design is as follows:
based on a streamline equation corresponding to each discrete point in the symmetrical plane, finally converging the streamline on the two-dimensional molded line of the outer cone flow wall surface of the symmetrical flow field; based on the solution of the outer cone flow field, the envelope curve of the outer cone flow field passing through the two-dimensional molded line of the wall surface is the wall surface of the required shock wave interference area.
6. The interference area wall inversion method based on the three-dimensional bending shock wave interference theory according to claim 1, wherein a flow field solver is arranged through a shock wave stabilization method, an unsteady coupling heat transfer method and an unsteady time propulsion method based on a high-resolution flux function, a turbulence model and a control equation.
7. The method for inversion of wall surface in disturbance zone based on three-dimensional bending shock disturbance theory according to claim 6, wherein,
the high-resolution flux function is in the RoeMAS format; the shock wave stabilization method adopts a MUSCL format and a high-precision WENO format to mix; the unsteady coupling heat transfer simulation method is a radial basis function interpolation method; the unsteady time pushing method is an explicit Runge-Kutta format and an implicit post-difference time format; the turbulence model adopts a two-equation SST k-omega turbulence model; the control equation adopts a three-dimensional compressible Reynolds average N-S equation, and is specifically as follows:
Figure FDA0003954041060000041
wherein t represents time, x, y and z respectively represent three-dimensional coordinates,
Figure FDA0003954041060000042
is a conservation variable; />
Figure FDA0003954041060000043
Is a non-viscous vector flux in three directions; />
Figure FDA0003954041060000044
Is a viscous vector flux in three directions.
8. An interference zone wall inversion system based on a three-dimensional bending shock interference theory is characterized by comprising:
discrete point parameter acquisition module: giving a preset bending laser surface of a wave multiplier of the variable shock angle osculating flow field, and dispersing a preset shock line into a plurality of discrete points in a symmetrical plane to obtain a local shock angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetrical plane;
a streamline equation determination module: based on the local shock wave angle, mach number, pressure and expansion wave deflection angle of each discrete point of the flow field in the symmetry plane, a free streamline method is applied, and a streamline equation corresponding to each discrete point in the symmetry plane is solved;
and an outer cone flow field solving module: determining a plurality of external cone flow fields passing through discrete points and kissing with the shock wave surface along the flow direction, and solving the corresponding external cone flow fields based on the local shock wave angle and Mach number corresponding to each discrete point in the symmetrical plane;
the shock interference area wall surface determining module: based on the streamline equation and the outer cone flow field solution of each discrete point, reversely designing and generating a shock wave interference area wall surface;
CFD flow field grid topology determination module: grid topology division is carried out on the shock wave interference area wall surface based on the inverse design generated shock wave interference area wall surface, so that gaps and overlapping areas are not formed on the geometric surface, and CFD flow field grid topology is generated;
CFD simulation model establishment module: introducing CFD flow field mesh topology into a flow field solver, setting the flow field solver, and establishing a CFD simulation model;
the shock interference area wall optimization module: setting initial conditions, performing steady simulation on the CFD simulation model to obtain flow field aerodynamic parameter distribution and flow field outlet parameter distribution, identifying a simulated laser surface based on the flow field aerodynamic parameter distribution and the flow field outlet parameter distribution, comparing the simulated laser surface with a preset bending laser surface, and determining a shock interference area wall optimization scheme.
9. The interference zone wall inversion system based on three-dimensional bending shock interference theory according to claim 8, wherein the local shock angle, mach number, pressure and expansion wave deflection angle in the symmetry plane flow field are determined by solving the oblique shock, ipsilateral oblique shock and compression wave intersection relation:
solving the local shock angle by the formula (1), and solving the local shock angle by the formulas (2) and (3) according to the Mach number M of the incoming flow A And pressure p A Calculation of the Mach number M after oblique shock wave B And pressure p B ：
Figure FDA0003954041060000051
Figure FDA0003954041060000052
Figure FDA0003954041060000061
In the formulas (1) - (3), M is Mach number, beta is shock angle, delta is turning angle, k is specific heat ratio,
Figure FDA0003954041060000062
subscript a represents the wavefront and subscript B represents the wave back;
according to formula (4), determining deflection angle of discrete expansion wave, forming a new oblique shock wave F after the oblique shock wave B and the oblique shock wave C are intersected, and setting the corresponding shock wave angle as beta F And generating reflected wave system and slip flow interruption, wherein the turning angle and shock angle corresponding to the oblique shock wave B are respectively delta B 、β B The turning angle and the shock angle corresponding to the oblique shock wave F are respectively delta C 、β C At this time, the discrete expansion wave deflection angle simplified from the wave-sector expansion wave is as follows:
Figure FDA0003954041060000063
wherein M is Mach number, beta is shock wave angle, delta is turning angle, k is specific heat ratio, subscript C represents parameters after oblique shock wave C, subscript F represents parameters after oblique shock wave F, subscript D represents parameters of sector expansion wave region.
10. The interference zone wall inversion system based on the three-dimensional bending shock interference theory according to claim 8, wherein the method for solving the streamline equation in the symmetry plane corresponding to each discrete point is as follows:
based on the formula (5), a streamline equation in a symmetrical plane corresponding to each discrete point is given; selection (x) w ，y w ) To make it and discrete point (x s ，y s ) On the same characteristic line, if the flow on the section x is uniform, i.e. Mach number, pressure and flow direction on the section are the same as those of the wall surface parameters, the characteristic line is a straight line, and the streamline equation is expressed as independent variable x w Is defined by the parameter equation:
Figure FDA0003954041060000064
wherein x and y are coordinates, mu is Mach angle, theta is wedge angle, M is Mach number, q is heat flow, subscript s represents discrete point on shock wave, subscript w represents any point on flow line, subscript x represents section x, subscript +_infinity represents incoming flow;
for aerodynamic parameters on the flowline, mach number and pressure for each point on the flowline are determined based on equations (2) and (3), and the actual deflection angle for the point on the flowline is determined based on equations (7) and (8):
δ s ＝θ w -θ ∞ (7)
wherein delta is deflection angle, theta is wedge angle, subscript s represents discrete point on shock wave, the subscript w indicates any point on the flow line, and the subscript +..
11. The interference area wall inversion system based on the three-dimensional bending shock wave interference theory according to claim 8, wherein the outer cone flow field solving method corresponding to each discrete point is as follows:
solving parameters of characteristic line intersection points through a simultaneous characteristic line equation set and a compatibility equation set, and finally obtaining the whole outer cone flow field information;
a set of feature line equations:
Figure FDA0003954041060000071
Figure FDA0003954041060000072
wherein x and y are coordinates, u and v are velocities in x and y directions, γ is an air flow angle, γ=arctan (v/u) represents an angle between an air flow and an x axis, μ is a mach angle, μ=arcsin (1/Ma), λ is a slope, subscript 0 represents a streamline, and subscript ± represents a characteristic line;
a set of compatibility equations:
ρVdV+dp＝0 (10)
dp-a 2 dρ＝0 (11)
Figure FDA0003954041060000073
where ρ is density, V is volume, p is pressure, M is Mach number, a is sound velocity, δ is turning angle, γ is air flow angle, and μ is Mach angle.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116384291A (en) * 2023-06-06 2023-07-04 中国航天空气动力技术研究院 Method for improving applicability of inverse characteristic line method by using expansion flow
CN117744282A (en) * 2024-02-20 2024-03-22 中国科学技术大学 Molded line determining method for variable cross-section shock tube
CN118171396A (en) * 2024-05-14 2024-06-11 中国空气动力研究与发展中心计算空气动力研究所 Mixed grid construction method and system for supersonic embedded put numerical simulation

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116384291A (en) * 2023-06-06 2023-07-04 中国航天空气动力技术研究院 Method for improving applicability of inverse characteristic line method by using expansion flow
CN116384291B (en) * 2023-06-06 2023-08-29 中国航天空气动力技术研究院 Method for improving applicability of inverse characteristic line method by using expansion flow
CN117744282A (en) * 2024-02-20 2024-03-22 中国科学技术大学 Molded line determining method for variable cross-section shock tube
CN118171396A (en) * 2024-05-14 2024-06-11 中国空气动力研究与发展中心计算空气动力研究所 Mixed grid construction method and system for supersonic embedded put numerical simulation

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