CN117408189B - Transition prediction method, device and equipment of hypersonic boundary layer and storage medium - Google Patents

Transition prediction method, device and equipment of hypersonic boundary layer and storage medium Download PDF

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CN117408189B
CN117408189B CN202311719536.4A CN202311719536A CN117408189B CN 117408189 B CN117408189 B CN 117408189B CN 202311719536 A CN202311719536 A CN 202311719536A CN 117408189 B CN117408189 B CN 117408189B
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reynolds number
boundary layer
calculation
ratio
momentum thickness
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CN117408189A (en
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张毅锋
陈琦
王新光
万钊
毛枚良
向星皓
袁先旭
陈坚强
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The application discloses a transition prediction method, a transition prediction device, transition prediction equipment and a storage medium for a hypersonic boundary layer, and belongs to the technical field of transition prediction technology. The transition prediction method of the hypersonic boundary layer comprises the following steps: drawing a calculation grid according to the model appearance of the aircraft, and performing flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field; selecting a target station in the basic flow field, and generating a ratio change profile curve along the normal direction at the target station; obtaining algebraic relation of maximum Reynolds number ratio to Mach number, wall temperature and incoming flow temperature; determining a momentum thickness Reynolds number calculation formula according to algebraic relation; and determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is positioned by using a momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number. The method and the device can improve the transition prediction precision of the hypersonic boundary layer.

Description

Transition prediction method, device and equipment of hypersonic boundary layer and storage medium
Technical Field
The application relates to the technical field of transition prediction, in particular to a transition prediction method, a transition prediction device, transition prediction equipment and a storage medium of a hypersonic boundary layer.
Background
Turbulence in hypersonic flow fields can lead to serious aerodynamic heating problems and aerodynamic problems, which can bring challenges to thermal protection design, aerodynamic manipulation and the like. In order to ensure flight safety, conventional aircraft designs typically estimate the wall heat flow and aerodynamic forces of the aircraft according to turbulent conditions, but such designs are relatively conservative with a resultant reduction in payload and aerodynamic performance. The turbulence is caused by transition of the boundary layer, if the transition can be accurately predicted when and where, the change of aerodynamic characteristics caused by the turbulence can be more accurately predicted, and more reliable and accurate flow data is provided for the design of the aircraft, so that the performance of the aircraft is improved, and transition research is attracting attention.
The prediction of the boundary layer transition mainly comprises four methods of a stability theory, a direct numerical simulation, an engineering empirical formula and a transition model, and the latter two methods generally relate to calculation of boundary layer characteristic physical quantities, such as momentum thickness, local Reynolds number, boundary layer thickness, momentum thickness Reynolds number, cross flow Reynolds number, vorticity, boundary layer outer edge Mach number and the like. The momentum thickness Reynolds number and the boundary layer transition position have better relativity, and are adopted by most empirical formulas and models.
At present, two methods are generally adopted in engineering practice to calculate the Reynolds number Re of the momentum thickness of the boundary layer θ One is an integral method, and the other is a method based on the ratio of the vortex reynolds number and the momentum thickness reynolds number. The integration method is a direct calculation according to the definition of the Reynolds number of the thickness of the momentum, wherein the thickness of the momentum is related toθIs not suitable for use in CFD (computational fluid dynamics) -based transition modelIn particular, there are difficulties in searching directions and transferring information in multi-block parallel computing. In early studies, the scholars found the vortex Raynaud Reynolds number Re v And momentum thickness Reynolds number Re θ There is a special relation between the two, in the Blasius boundary layer profile, the maximum value of the ratio is close to a constant of 2.193, and Re can be calculated by using the constant θ . Therefore, the function of the Reynolds number of the momentum thickness is realized by utilizing the special relation in the related technology, and the momentum thickness Reynolds number is applied to the judgment of the transition start of low-speed flow, so that the traditional integral operation method is avoided, and the momentum thickness Reynolds number can be conveniently integrated into numerical calculation based on the local physical quantity completely. However, the constant 2.193 reflects only the physical properties of the low velocity boundary layer, for hypersonic boundary layers (free stream Mach numberM a >5) And is not applicable. Re in boundary layer at different Mach numbers v And Re (Re) θ The ratio of the Mach number to the boundary layer increases gradually with the Mach numberM e When=8, the flow rate is far higher than the case of low-speed flow. It follows that the correct momentum thickness reynolds number will not be obtained if the original 2.193 is used to calculate the momentum thickness reynolds number. For hypersonic boundary layers, i.e. boundary layers with the speed of an object exceeding 5 times of sonic velocity, the transition of the boundary layer cannot be accurately predicted by using the empirical values at present.
Therefore, how to improve the transition prediction precision of the hypersonic boundary layer is a technical problem that needs to be solved by the skilled person at present.
Disclosure of Invention
The purpose of the application is to provide a transition prediction method and device of a hypersonic boundary layer, a storage medium and electronic equipment, and the transition prediction precision of the hypersonic boundary layer can be improved.
In order to solve the technical problems, the application provides a transition prediction method of a hypersonic boundary layer, which comprises the following steps:
drawing a calculation grid according to the model appearance of the aircraft, and performing flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
selecting a target station in the basic flow field, and generating a ratio change profile curve along a normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number;
determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve, and obtaining algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
and determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
Optionally, the performing flow calculation in the calculation grid by using a three-dimensional wiener-stokes equation includes:
and carrying out flow calculation in the calculation grid by taking a three-dimensional Navier-Stokes equation as a control equation through a numerical calculation platform.
Optionally, before the target station generates the ratio variation profile along the normal direction, the method further comprises:
calculating the vortex Reynolds number and the momentum thickness Reynolds number of the basic flow field according to the strain rate, the momentum thickness, the boundary layer thickness and the boundary layer outer edge parameters of the basic flow field;
correspondingly, generating a ratio variation profile curve along a normal direction at the target station comprises:
and determining to generate the ratio variation profile curve along the normal direction at the target station according to the vortex quantity Reynolds number and the momentum thickness Reynolds number of the basic flow field.
Optionally, the boundary layer peripheral parameters include mach number, density, viscosity coefficient, and velocity at boundary layer peripheral locations, the boundary layer peripheral locations being determined from the total enthalpy.
Optionally, generating a ratio variation profile along a normal direction at the target station includes:
generating a ratio variation profile Re along the normal direction at the target station v /2.193Re θ The method comprises the steps of carrying out a first treatment on the surface of the Wherein Re is v Represents the vortex Raynaud number, re θ The momentum thickness reynolds number is expressed.
Optionally, obtaining an algebraic relation of the maximum reynolds number ratio with respect to the mach number, the wall temperature, and the incoming flow temperature includes:
obtaining algebraic relation VDBmax of the maximum Reynolds number ratio with respect to Mach number, wall surface temperature and incoming flow temperatureM e ,Tw/To)；
Wherein VDBmax represents the algebraic relation of the maximum Reynolds number ratio with respect to Mach number, wall temperature and incoming flow temperature,M e indicating the mach number at the outer edge location of the boundary layer,Twthe temperature of the wall surface is indicated,Toindicating the total incoming flow temperature.
Optionally, determining a calculation formula of the reynolds number of the momentum thickness according to the algebraic relation comprises:
according to the algebraic relation VDBmaxM e ,Tw/To) Calculation formula Re for determining momentum thickness Reynolds number θ =max(Re v )/VDBmax(M e ,Tw/To)/2.193。
The application also provides a hypersonic boundary layer transition prediction device, which comprises:
the flow calculation module is used for drawing a calculation grid according to the model appearance of the aircraft, and carrying out flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
the profile extraction module is used for selecting a target station in the basic flow field and generating a ratio change profile curve along the normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number;
the algebraic relation determining module is used for determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve and obtaining an algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
the calculation formula determining module is used for determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
and the transition judging module is used for determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
The application also provides a storage medium, on which a computer program is stored, wherein the computer program realizes the steps executed by the transition prediction method of the hypersonic boundary layer when being executed.
The application also provides electronic equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps executed by the transition prediction method of the hypersonic boundary layer when calling the computer program in the memory.
The application provides a transition prediction method of a hypersonic boundary layer, which comprises the following steps: drawing a calculation grid according to the model appearance of the aircraft, and performing flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field; selecting a target station in the basic flow field, and generating a ratio change profile curve along a normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number; determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve, and obtaining algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature; determining a momentum thickness Reynolds number calculation formula according to the algebraic relation; and determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
According to the method, a calculation grid is drawn according to the model appearance of the aircraft, flow calculation is carried out in the calculation grid to obtain a basic flow field, and then a corresponding ratio change profile curve is generated according to the ratio change of the vortex Reynolds number and the momentum thickness Reynolds number. And an algebraic relation of the maximum Reynolds number ratio to Mach number, wall surface temperature and incoming flow temperature can be determined according to the ratio change profile curve, and a momentum thickness Reynolds number calculation formula is determined according to the algebraic relation. The momentum thickness Reynolds number calculation formula considers Mach number and wall temperature effect of the hypersonic boundary layer, can estimate the momentum thickness Reynolds number of the hypersonic boundary layer more accurately, and can improve the transition prediction precision of the hypersonic boundary layer. The application also provides a hypersonic boundary layer transition prediction device, a storage medium and an electronic device, which have the beneficial effects and are not repeated here.
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For a clearer description of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described, it being apparent that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a transition prediction method of a hypersonic boundary layer provided in an embodiment of the present application;
FIG. 2 is a Blasius boundary layer profile Re provided in an embodiment of the present application v And Re (Re) θ A relationship diagram of the ratio;
FIG. 3 shows a Re according to an embodiment of the present application v And Re (Re) θ A schematic diagram of the ratio as a function of Mach number;
FIG. 4 shows a novel momentum thickness based Reynolds number Re according to an embodiment of the present application θ Calculating a transition prediction technology roadmap;
FIG. 5 shows a Re according to an embodiment of the present application v A distribution map;
FIG. 6 is a schematic diagram of Re provided in an embodiment of the present application θ A distribution map;
FIG. 7 shows Re under the first flow conditions provided in the examples of this application v /2.193Re θ Schematic change in normal y;
FIG. 8 shows Re under the second flow conditions provided in the examples of this application v /2.193Re θ Schematic change in normal y;
FIG. 9 is a graph showing Re under third flow conditions provided in the examples of the present application v /2.193Re θ Schematic change in normal y;
FIG. 10 shows Re under the fourth flow conditions provided in the examples of this application v /2.193Re θ Schematic change in normal y;
FIG. 11 shows a max (Re v )/(2.193Re θ ) Profile in the boundary layer;
FIG. 12 shows a VDBmax-based scheme according to an embodiment of the present applicationM e ,Tw/To) Calculated Re θ A distribution diagram;
FIG. 13 shows a VDBmax-based scheme according to an embodiment of the present applicationM e ,Tw/To) Calculated Re θ /M e Schematic distribution diagram.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Referring to fig. 1, fig. 1 is a flowchart of a transition prediction method of a hypersonic boundary layer according to an embodiment of the present application.
The specific steps may include:
s101: drawing a calculation grid according to the model appearance of the aircraft, and performing flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
the embodiment can be applied to electronic equipment with an aerodynamic analysis function. A model of the aircraft that is capable of hypersonic flight to be analyzed can be obtained prior to this step. And drawing a calculation grid according to the model of the aircraft, and obtaining a calculation domain.
After the calculation grid is obtained, the flow calculation is carried out in the calculation grid by utilizing a three-dimensional Navier-Stokes equation, and the corresponding basic flow field is obtained. As a possible implementation manner, the step may be that a HTNS (hypersonic flow transition numerical simulation software) numerical calculation platform performs flow calculation in the calculation grid by using a three-dimensional nano-Stokes equation (Navier-Stokes equation) as a control equation, so as to obtain a basic flow field. The basic flow field comprises flow information such as density, speed, temperature, pressure and the like of a flow field space region.
S102: selecting a target station in a basic flow field, and generating a ratio change profile curve along a normal direction at the target station;
the step can select a target station along the flow direction, and generate a ratio variation profile curve along the normal direction on the target station, wherein the ratio variation profile curve is used for describing the ratio variation of the vortex Reynolds number and the momentum thickness Reynolds number observed from the target station along the normal direction of the flow direction.
S103: determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve, and obtaining algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
after the ratio change profile curve is obtained, the ratio of the vortex quantity Reynolds number to the momentum thickness Reynolds number, namely the maximum Reynolds number ratio, is determined in the ratio change profile curve. After the maximum Reynolds number ratio is obtained, the embodiment can draw the change curves of the maximum Reynolds number ratio, the outer edge Mach number, the wall surface temperature and the incoming flow temperature, and the algebraic relation is obtained by fitting the change curves by adopting a polynomial fitting method.
S104: determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
the algebraic relation describes the ratio of the maximum Reynolds number ratio to Mach number, wall temperature and incoming flow temperature, and therefore the ratio can be used to back-extrapolate the calculation of the Reynolds number for the thickness of the momentum.
S105: and determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
In the movement process of the aircraft, the current vortex Reynolds number, the current wall surface temperature and the current incoming flow temperature of the hypersonic boundary layer where the aircraft is located can be determined, and the current vortex Reynolds number, the current wall surface temperature and the current incoming flow temperature are substituted into a momentum thickness Reynolds number calculation formula to obtain the transition position of the aircraft.
According to the embodiment, a calculation grid is drawn according to the model appearance of the aircraft, flow calculation is carried out in the calculation grid to obtain a basic flow field, and a corresponding ratio change profile curve is generated according to the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number. And an algebraic relation of the maximum Reynolds number ratio to Mach number, wall surface temperature and incoming flow temperature can be determined according to the ratio change profile curve, and a momentum thickness Reynolds number calculation formula is determined according to the algebraic relation. The momentum thickness Reynolds number calculation formula considers Mach number and wall temperature effect of the hypersonic boundary layer, can estimate the momentum thickness Reynolds number of the hypersonic boundary layer more accurately, and can improve the transition prediction precision of the hypersonic boundary layer.
As a further introduction to the corresponding embodiment of FIG. 1, prior to the target site generating the ratio profile along the normal direction, it further comprises: calculating the vortex Reynolds number and the momentum thickness Reynolds number of the basic flow field according to the strain rate, the momentum thickness, the boundary layer thickness and the boundary layer outer edge parameters of the basic flow field; correspondingly, generating a ratio variation profile curve along a normal direction at the target station comprises: and determining to generate the ratio variation profile curve along the normal direction at the target station according to the vortex quantity Reynolds number and the momentum thickness Reynolds number of the basic flow field. The boundary layer peripheral parameters include Mach number, density, viscosity coefficient and velocity at boundary layer peripheral locations determined from the total enthalpy.
As a further introduction to the corresponding embodiment of fig. 1, the process of generating a ratio profile along the normal direction at the destination site includes: generating a ratio variation profile Re along the normal direction at the target station v /2.193Re θ The method comprises the steps of carrying out a first treatment on the surface of the Wherein Re is v Represents the vortex Raynaud number, re θ The momentum thickness reynolds number is expressed.
Further, the algebraic relation can be obtained by: obtaining algebraic relation VDBmax of the maximum Reynolds number ratio with respect to Mach number, wall surface temperature and incoming flow temperatureM e ,Tw/To) The method comprises the steps of carrying out a first treatment on the surface of the Wherein VDBmax represents the algebraic relation of the maximum Reynolds number ratio with respect to Mach number, wall temperature and incoming flow temperature,M e indicating the mach number at the outer edge location of the boundary layer,Twthe temperature of the wall surface is indicated,Toindicating the total incoming flow temperature.
Correspondingly, the process for determining the momentum thickness Reynolds number calculation formula according to the algebraic relation comprises the following steps: according to the algebraic relation VDBmaxM e ,Tw/To) Calculation formula Re for determining momentum thickness Reynolds number θ =max(Re v )/VDBmax(M e , Tw/To) And/2.193, max represents taking the maximum value.
The flow described in the above embodiment is explained below by way of an embodiment in practical application.
The constant 2.193 is used to calculate the momentum thickness reynolds number in the related art, but the constant 2.193 is only applicable to the calculation of the momentum thickness reynolds number in the low-speed boundary layer, and is not applicable to the hypersonic boundary layer. Referring to fig. 2 and 3, fig. 2 is a boundary layer profile Re of blast provided in an embodiment of the present application v And Re (Re) θ FIG. 3 is a schematic diagram showing the relationship between ratios of Re according to one embodiment of the present application v And Re (Re) θ A schematic diagram of the ratio as a function of Mach number, where eta represents the dimensionless wall distance,M e representing boundary layer peripheral Mach number, FIG. 3M e The values of (2) may be 8.0, 7.0, 6.0, 5.0, 4.0. The present embodiment is directed to low-speed Re v And Re (Re) θ The defect of the ratio relation is that hypersonic flow correction is carried out, and a novel Re capable of considering main hypersonic physical factors such as Mach number, wall temperature and the like is established v And Re (Re) θ The ratio relation is suitable for calculating the hypersonic momentum thickness Reynolds number, and a hypersonic boundary layer transition prediction technology is established based on the novel ratio relation.
The method and the device are used for solving the problem of complete localized calculation of the hypersonic boundary layer momentum thickness Reynolds number. By using the vortex Reynolds number Re in the boundary layer v And momentum thickness Reynolds number Re θ Ratio characterization to calculate momentum thickness Reynolds number Re θ Can avoid integral operation of physical quantity, but has Reynolds number Re for vortex quantity of hypersonic boundary layer v And momentum thickness Reynolds number Re θ Analysis of the ratio found Re in both the low velocity boundary layer and hypersonic boundary layer v /Re θ The ratio is several times different, and the existing momentum thickness Reynolds number calculation method based on 2.193 is not applicable in hypersonic speed.
Aiming at the technical problem, the embodiment provides a new momentum thickness Reynolds number calculation method suitable for hypersonic flow, and provides technical support for the criterion of hypersonic boundary layer transition initiation. The method accords with hypersonic physical characteristics, and has the characteristics of low cost, easy realization and high reliability; compared with the traditional calculation method of the momentum thickness Reynolds number of the boundary layer, the novel method avoids integral operation, and can more conveniently and reliably play the role of the momentum thickness Reynolds number in hypersonic transition initiation judgment.
The embodiment can simulate flow field extraction and vortex quantity Reynolds number Re based on CFD (computational fluid dynamics) numerical values v And momentum thickness Reynolds number Re θ Related physical quantity, and then obtain Re v /Re θ The characteristic law of the ratio along with Mach number and wall temperature change is finally summarized to obtain the calculated momentum thickness Reynolds number Re θ Algebraic relation of (c).
Referring to fig. 4, fig. 4 shows a new momentum thickness based reynolds number Re according to an embodiment of the present application θ The calculated transition prediction technology roadmap also describes the serial number and Mach number of the Level line LevelM a The procedure shown in fig. 4 is as follows: calculating basic flow field, calculating relative physical quantity and extracting Re v /Re θ Section, construction algebraic relation VDBmaxM e ,Tw/To) And calculating the Reynolds number of the momentum thickness and predicting transition. The present embodiment employs Re reflecting hypersonic boundary layer characteristics v And Re (Re) θ The ratio relation can accurately judge the physical quantity of the momentum thickness Reynolds number in the high-transition starting.
The basic flow field is calculated as follows:
and drawing a calculation grid (establishing a calculation domain) according to the geometric model appearance, setting boundary conditions, adopting an HTNS numerical calculation platform, and expanding flow calculation by taking a three-dimensional Navier-Stokes equation as a control equation. Under the conditions of no disturbance, no volume force and no external heat source, the control equation is specifically expressed as follows:
；
；
；
；
；
in the above formula, t is time, x, y and z are Cartesian coordinates,is a conservation variable, ++>、/>、/>For the flux in the x, y and z directions, ρ and u, v, w, e are the density, x-direction velocity, y-direction velocity, z-direction velocity and total energy per unit mass of gas, respectively, p represents the pressure,/represents>For shear stress, q is heat flow. And adopting a second-order precision calculation format capable of stably capturing shock wave interruption and precisely calculating boundary layers, properly encrypting the calculation grids near the wall surface, and calculating to obtain the basic flow information such as density, speed, temperature, pressure and the like of the space region of the flow field.
Flow condition range of basic flow field:M a =3~12，Tw/To=0.1~1.25，Re=1.0×10 7 /m。M a in order to achieve the mach number of the incoming stream,Twthe temperature of the wall surface is set to be the temperature of the wall surface,Tore is the unit Reynolds number for the total incoming flow temperature.
The calculation of the relevant physical quantity is explained as follows:
the method comprises the steps of carrying out a first treatment on the surface of the Formula (1)
The method comprises the steps of carrying out a first treatment on the surface of the Formula (2)
The method comprises the steps of carrying out a first treatment on the surface of the Formula (3)
The method comprises the steps of carrying out a first treatment on the surface of the Formula (4)
The above formula is、/>、/>The density at the boundary layer periphery, the velocity at the boundary layer periphery and the viscosity coefficient at the boundary layer periphery,θis momentum thickness, y is wall distance, < ->For local speed +.>The critical transition momentum thickness Reynolds number is S, the absolute value of strain rate is +.>Is a transition switching function. />Indicating speed, & lt->Indicate density,/->Representing the coefficient of viscosity.
And calculating relevant physical quantities of the momentum thickness Reynolds number and the vortex quantity Reynolds number based on the obtained basic flow field, wherein the relevant physical quantities comprise strain rate S, momentum thickness theta, boundary layer thickness delta and boundary layer outer edge parameters. The vorticity refers to a vorticity modulus value synthesized by vorticity in the x, y and z directions, the momentum thickness is obtained by carrying out integral operation along the normal direction by a formula (2), the outer edge position of the boundary layer is determined according to 98% of the total enthalpy, and the method is used for calculating Mach numbers at the outer edge of the boundary layerM e Density ofViscosity coefficient->And speed->. Finally, calculating the vortex quantity Reynolds number Re of the whole field according to formulas (1) and (4) v And momentum thickness Reynolds number Re θ 。
With respect to Re v /(2.193Re θ ) The description of profile extraction is as follows:
selecting a specific station along the flow direction, extracting Re calculated in the above v And Re (Re) θ And draw Re along the normal direction v /(2.193Re θ ) From the ratio change profile curve, max (Re v )/ (2.193Re θ ) Ratio of Re in boundary layer v /(2.193Re θ ) And the ratio is analyzed along with Mach number and wall temperature change rule, and max represents maximum value.
Regarding max (Re) v )/ (2.193Re θ ) The algebraic relational structure is described as follows:
according to the extracted max (Re v )/ (2.193Re θ ) The ratio is plotted against the peripheral Mach numberM e And wall temperature ratioTw/ToIs fitted by a polynomial fitting method, and max (Re v )/ (2.193Re θ ) Algebraic relation VDBmax regarding Mach number and wall temperatureM e ,Tw/To) And finally, a calculation formula of the Reynolds number of the thickness of the dynamic quantity can be reversely deduced by utilizing the ratio.
With respect to Re θ The calculation of (2) is described as follows:
VDBmax using structureM e ,Tw/To) Relationship and vortex Raynaud number, boundary layer outer edge Mach numberM e And wall temperature ratioTw/ToCan calculate Re θ The formula is as follows:
Re θ =max(Re v )/VDBmax(M e ,Tw/To)/2.193；
finally according to the momentum thickness Reynolds number Re calculated hereinabove θ And calculated boundary layer peripheral Mach numberM e Adopts transition criterion empirical formula (C=Re) θ /M e ) And the transition position can be predicted, namely when the ratio of the Reynolds number of the momentum thickness to the Mach number of the outer edge of the boundary layer is larger than the critical value C, the transition is judged to occur, and for the conventional wind tunnel experiment, C=110 is generally adopted.
According to the boundary layer momentum thickness Reynolds number calculation method suitable for the hypersonic flow field, mach number effect and wall temperature effect are considered, the momentum thickness Reynolds number of the hypersonic flow layer can be given more accurately, meanwhile, due to the fact that only local physical quantity of the flow field is adopted, original integral operation is avoided, the difficulty in calculating the momentum thickness Reynolds number in complex multiple grids is solved, and a foundation is laid for establishing a localized hypersonic boundary layer transition prediction technology based on the momentum thickness Reynolds number.
And calculating the momentum thickness Reynolds number by using the method with the half cone angle of 7 degrees as a geometric model. The length of the pointed cone is 1 meter, and the flow conditions are as follows: free stream Mach number ofM a =3 to 12, the unit reynolds number is re=1×10 7 Wall temperature ratio of modelTw/To=0.1 to 1.25. The flow conditions are centered on hypersonic flow, taking into account a wide range of speeds and wall temperature conditions.
And (3) calculating a basic flow field: and taking an N-S equation as a control equation, dispersing the non-sticky items by adopting a 2-order precision MUSCL format, dispersing the sticky items by adopting a 2-order center format, and performing time propulsion by adopting an LU-SGS format. The calculated domain is a circumferential 180-degree half field, flows to 181 grids, and is normal to 131 grids and circumferential 31 grids. Referring to fig. 4, fig. 4 is a graph showing a mach number distribution of a basic flow field after convergence, which is provided in the embodiment of the present application, so that the spatial distribution of the oblique shock wave and the mach number of the tip can be clearly seen. In FIG. 4M a Indicating the incoming stream mach number.
Calculating related physical quantities: calculating the vortex quantity, the momentum thickness and the boundary layer thickness by using rho, u, v, w and e of the basic flow field, and further calculating the boundary layer outer edge parameters、/>And->Calculating the vortex Raynaud number Re under all flow conditions according to the formulas (1) and (4) v And momentum thickness Reynolds number Re θ . FIG. 5 shows a Re according to an embodiment of the present application v Distribution diagram, FIG. 6 shows a Re provided in the embodiment of the present application θ Distribution diagrams are shown in fig. 5 and 6M a =6，Tw/ToRe on flow field symmetry plane in condition of=0.6 v And Re (Re) θ Distribution, also shows Re v Correspondence with Level line Level and Re θ And the corresponding relation with the Level line Level.
Re v /2.193Re θ Section extraction: according to the second step of calculationAs a result, the station x=300 mm was selected and Re was extracted v /2.193Re θ The ratio, a curve varying along the normal is plotted. FIG. 7 shows Re under the first flow conditions provided in the examples of this application v /2.193Re θ FIG. 8 is a schematic representation of the change in normal y, re under the second flow conditions provided by the examples of the present application v /2.193Re θ FIG. 9 is a schematic representation of the variation in normal y, re under a third flow condition provided by an embodiment of the present application v /2.193Re θ FIG. 10 is a schematic representation of the variation in normal y, re under fourth flow conditions provided by the examples of the present application v /2.193Re θ In the change schematic diagram of the normal y, the ratio reaches the maximum near the outer edge of the boundary layer, and is larger than 1, and the change amplitude is larger by 1.5-3.0. dn denotes the distance along the normal, delta denotes the boundary layer thickness.
max(Re v )/ (2.193Re θ ) Algebraic relational construction: according to Re in the previous step v /(2.193Re θ ) The dn curve gives Re in the boundary layer v /(2.193Re θ ) Maximum value, which is plotted as a function of the peripheral Mach numberM e And wall temperature ratioTw/ToSee FIG. 11, FIG. 11 is a graph of max (Re v )/(2.193Re θ ) The distribution diagram in boundary layer adopts polynomial fitting method to construct algebraic relation VDBmax between themM e ,Tw/To) The expression is as follows:
VDBmax(M e ,Tw/To)=0.15081+0.10084M e +(0.66094+0.28338M e )Tw/To-(0.12442+0.0864M e )(Tw/To) 2 ；
Re θ the calculation process of (2) is as follows: by using the expression, according to VDBmax #M e ,Tw/To) Algebraic relation Re v Can calculate and obtain Re θ Referring to fig. 12, fig. 12 shows a VDBmax-based flowchart according to an embodiment of the present applicationM e ,Tw/To) Calculated Re θ Distribution diagram, FIG. 12 shows typical calculation results, and Re θ The flow conditions of FIG. 12 and FIG. 6 are the same, re calculated for both θ The values are relatively close.
The momentum thickness reynolds number can be finally calculated by the following formula:
Re θ =max(Re v )/VDBmax(M e ,Tw/To)/2.193；
the method comprises the influence of Mach number and wall temperature effect in hypersonic boundary layer, and Re v Is the local physical quantity of the flow field, so VDBmax is used for the flow fieldM e ,Tw/To) Algebraic formula and Re v Localized calculation of the hypersonic boundary layer momentum thickness can be achieved.
Transition position prediction: re calculated above θ Used for calculating Re through transition criterion empirical formula θ /M e FIG. 13 shows a distribution of the ratio of VDBmax-based values according to the embodiment of the present applicationM e ,Tw/To) Calculated Re θ /M e Schematic distribution diagram showing Re θ /M e As shown in fig. 13, when the corresponding relation with the Level line Level is greater than the threshold 110, the transition is considered to occur. For flow conditionsM a =6，Re =1×10 7 /m，Tw/ToThe transition position at xT=295 mm can be calculated by the flow of=0.6, and accords with the wind tunnel test result (xT=300 mm).
The embodiment provides a momentum thickness Reynolds number calculation method suitable for a hypersonic boundary layer. Compared with the traditional integral method, the new method does not need normal integral operation on physical quantity of the flow field, and avoids the difficulty of flow direction searching and judging and information transmission between different calculation areas in multi-block parallel numerical calculation; meanwhile, compared with the vortex Raynaud number method with the constant of 2.193, the novel method considers the basic characteristics of hypersonic flow such as Mach number, wall temperature and the like, and can reflect hypersonic boundary layer characteristics more accurately. Compared with the prior art, the transition prediction technology based on the novel method can more conveniently and reliably acquire and judge the transition occurrence momentum thickness Reynolds number, and provides technical support for physical applications such as prediction of hypersonic boundary layer transition initiation and the like.
Compared with a calculation method of transition prediction technology based on the traditional integral momentum thickness Reynolds number, the embodiment has the following effects and advantages: (1) The realization is simple, normal integral operation and search of different partition physical quantities are not required to be carried out on the flow field, and the realization can be realized through a simple algebraic relational expression; (2) The calculation result is reliable, the Mach number and the wall temperature effect of the hypersonic boundary layer are considered, the momentum thickness Reynolds number of the hypersonic boundary layer can be estimated more accurately, and more accurate criterion judgment can be provided for the high-hyper-transition initiation; (3) Can be popularized to other more complex hypersonic flow conditions.
The embodiment of the application provides a transition prediction device of hypersonic boundary layer, and the device may include:
the flow calculation module is used for drawing a calculation grid according to the model appearance of the aircraft, and carrying out flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
the profile extraction module is used for selecting a target station in the basic flow field and generating a ratio change profile curve along the normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number;
the algebraic relation determining module is used for determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve and obtaining an algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
the calculation formula determining module is used for determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
and the transition judging module is used for determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
According to the embodiment, a calculation grid is drawn according to the model appearance of the aircraft, flow calculation is carried out in the calculation grid to obtain a basic flow field, and a corresponding ratio change profile curve is generated according to the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number. And an algebraic relation of the maximum Reynolds number ratio to Mach number, wall surface temperature and incoming flow temperature can be determined according to the ratio change profile curve, and a momentum thickness Reynolds number calculation formula is determined according to the algebraic relation. The momentum thickness Reynolds number calculation formula considers Mach number and wall temperature effect of the hypersonic boundary layer, can estimate the momentum thickness Reynolds number of the hypersonic boundary layer more accurately, and can improve the transition prediction precision of the hypersonic boundary layer.
Optionally, the process of the flow calculation module performing flow calculation within the calculation grid using the three-dimensional wiener-stokes equation includes: and carrying out flow calculation in the calculation grid by taking a three-dimensional Navier-Stokes equation as a control equation through an HTNS numerical calculation platform.
Optionally, the method further comprises:
the Reynolds number calculation module is used for calculating the vortex Reynolds number and the momentum thickness Reynolds number of the basic flow field according to the strain rate, the momentum thickness, the boundary layer thickness and boundary layer outer edge parameters of the basic flow field before the target station generates a ratio change profile curve along the normal direction;
correspondingly, generating a ratio variation profile curve along a normal direction at the target station comprises:
and determining to generate the ratio variation profile curve along the normal direction at the target station according to the vortex quantity Reynolds number and the momentum thickness Reynolds number of the basic flow field.
Further, the boundary layer peripheral parameters include Mach number, density, viscosity coefficient, and velocity at boundary layer peripheral locations, the boundary layer peripheral locations being determined from the total enthalpy.
Further, the process of generating the ratio variation profile curve along the normal direction by the profile extraction module at the target station comprises the following steps: generating a ratio variation profile Re along the normal direction at the target station v /2.193Re θ The method comprises the steps of carrying out a first treatment on the surface of the Wherein Re is v Represents the vortex Raynaud number, re θ The momentum thickness reynolds number is expressed.
Further, the process of obtaining the algebraic relation of the maximum Reynolds number ratio with respect to Mach number, wall temperature and incoming flow temperature by the algebraic relation determining module includes: obtaining algebraic relation VDBmax of the maximum Reynolds number ratio with respect to Mach number, wall surface temperature and incoming flow temperatureM e ,Tw/To) The method comprises the steps of carrying out a first treatment on the surface of the Wherein VDBmax represents the algebraic relation of the maximum Reynolds number ratio with respect to Mach number, wall temperature and incoming flow temperature,M e indicating the mach number at the outer edge location of the boundary layer,Twthe temperature of the wall surface is indicated,Toindicating the total incoming flow temperature.
Further, the process of determining the momentum thickness reynolds number calculation formula by the calculation formula determining module according to the algebraic relation comprises the following steps: according to the algebraic relation VDBmaxM e ,Tw/To) Calculation formula Re for determining momentum thickness Reynolds number θ =max(Re v )/VDBmax(M e ,Tw/To)/2.193。
Since the embodiments of the apparatus portion and the embodiments of the method portion correspond to each other, the embodiments of the apparatus portion are referred to the description of the embodiments of the method portion, and are not repeated herein.
The present application also provides a storage medium having stored thereon a computer program which, when executed, performs the steps provided by the above embodiments. The storage medium may include: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The application also provides an electronic device, which may include a memory and a processor, where the memory stores a computer program, and the processor may implement the steps provided in the foregoing embodiments when calling the computer program in the memory. Of course the electronic device may also include various network interfaces, power supplies, etc.
In the description, each embodiment is described in a progressive manner, and each embodiment is mainly described by the differences from other embodiments, so that the same similar parts among the embodiments are mutually referred. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section. It should be noted that it would be obvious to those skilled in the art that various improvements and modifications can be made to the present application without departing from the principles of the present application, and such improvements and modifications fall within the scope of the claims of the present application.
It should also be noted that in this specification, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

Claims (10)

1. The transition prediction method of the hypersonic boundary layer is characterized by comprising the following steps of:
drawing a calculation grid according to the model appearance of the aircraft, and performing flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
selecting a target station in the basic flow field, and generating a ratio change profile curve along a normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number;
determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve, and obtaining algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
and determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
2. The hypersonic boundary layer transition prediction method as set forth in claim 1, wherein the flow calculation in the calculation grid using a three-dimensional nano-stokes equation includes:
and carrying out flow calculation in the calculation grid by taking a three-dimensional Navier-Stokes equation as a control equation through a numerical calculation platform.
3. The hypersonic boundary layer transition prediction method according to claim 1, further comprising, before the target station generates the ratio change profile along the normal direction:
calculating the vortex Reynolds number and the momentum thickness Reynolds number of the basic flow field according to the strain rate, the momentum thickness, the boundary layer thickness and the boundary layer outer edge parameters of the basic flow field;
correspondingly, generating a ratio variation profile curve along a normal direction at the target station comprises:
and determining to generate the ratio variation profile curve along the normal direction at the target station according to the vortex quantity Reynolds number and the momentum thickness Reynolds number of the basic flow field.
4. The method of claim 3, wherein the boundary layer peripheral parameters include mach number, density, viscosity coefficient, and velocity at boundary layer peripheral locations, the boundary layer peripheral locations being determined from total enthalpy.
5. The hypersonic boundary layer transition prediction method of claim 1, wherein generating a ratio variation profile along a normal direction at the target station comprises:
generating a ratio variation profile Re along the normal direction at the target station v /2.193Re θ The method comprises the steps of carrying out a first treatment on the surface of the Wherein Re is v Represents the vortex Raynaud number, re θ The momentum thickness reynolds number is expressed.
6. The hypersonic boundary layer transition prediction method of claim 5, wherein obtaining the algebraic relation of the maximum reynolds number ratio with respect to mach number, wall temperature, and incoming flow temperature comprises:
obtaining algebraic relation VDBmax of the maximum Reynolds number ratio with respect to Mach number, wall surface temperature and incoming flow temperatureM e , Tw/To)；
Wherein VDBmax represents the algebraic relation of the maximum Reynolds number ratio with respect to Mach number, wall temperature and incoming flow temperature,M e indicating the mach number at the outer edge location of the boundary layer,Twthe temperature of the wall surface is indicated,Toindicating the total incoming flow temperature.
7. The hypersonic boundary layer transition prediction method of claim 6, wherein determining a momentum thickness reynolds number calculation formula according to the algebraic relation comprises:
according to the algebraic relation VDBmax(M e ,Tw/To) Calculation formula Re for determining momentum thickness Reynolds number θ =max(Re v )/VDBmax(M e ,Tw/To)/2.193。
8. The transition prediction device of the hypersonic boundary layer is characterized by comprising:
the flow calculation module is used for drawing a calculation grid according to the model appearance of the aircraft, and carrying out flow calculation in the calculation grid by utilizing a three-dimensional Navier-Stokes equation to obtain a basic flow field;
the profile extraction module is used for selecting a target station in the basic flow field and generating a ratio change profile curve along the normal direction at the target station; the ratio change profile curve is used for describing the ratio change of the vortex quantity Reynolds number and the momentum thickness Reynolds number;
the algebraic relation determining module is used for determining the maximum Reynolds number ratio of the vortex quantity Reynolds number and the momentum thickness Reynolds number according to the ratio change profile curve and obtaining an algebraic relation of the maximum Reynolds number ratio on Mach number, wall temperature and incoming flow temperature;
the calculation formula determining module is used for determining a momentum thickness Reynolds number calculation formula according to the algebraic relation;
and the transition judging module is used for determining the current momentum thickness Reynolds number of the hypersonic boundary layer where the aircraft is located by using the momentum thickness Reynolds number calculation formula, and predicting the transition position of the aircraft according to the current momentum thickness Reynolds number.
9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and wherein the processor, when invoking the computer program in the memory, performs the steps of the method for predicting transition of the hypersonic boundary layer according to any one of claims 1 to 7.
10. A storage medium having stored therein computer executable instructions which, when loaded and executed by a processor, implement the steps of the method of transition prediction of a hypersonic boundary layer according to any one of claims 1 to 7.
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