A wide speed range boundary layer transition prediction method using algebraic intermittency factor

Abstract

The application discloses a wide-speed-domain boundary layer transition prediction method using algebraic intermittency factor, which is based on a general Reynolds average Navier-Stokes computational fluid dynamics method, and transition indicator variables and transition criteria that can be locally solved in a flow field are calculated to construct an algebraic form of an intermittency factor function, and further, the generation term and the dissipation term of a turbulent kinetic energy transport equation of a turbulent flow model are modified by the intermittency factor function, so that the accurate prediction of subsonic to hypersonic boundary layer transition is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of hypersonic boundary layer transition prediction, and particularly relates to a wide-speed-range boundary layer transition prediction method. BACKGROUND

[0002] In recent years, with the continuous upgrading of high-speed transportation, earth-to-space transportation and other needs, aircraft are gradually developing towards large airspace, wide speed range, reusability and other directions. In such aircraft, boundary layer transition is a common flow phenomenon. Boundary layer transition represents the evolution process of flow from laminar state to turbulent state, which significantly affects the aircraft wall friction drag, heat exchange and flow separation, and has important significance for the design of aircraft aerodynamic shape, thermal protection system and propulsion system. Therefore, in the design of wide-speed-range hypersonic aircraft, boundary layer transition prediction is a key technical problem.

[0003] Transition prediction technology generally includes experimental research, direct numerical simulation, large eddy simulation, flow stability analysis, transition model, etc. Among the above methods, transition model has the advantages of convenient use, good robustness and low computational resource demand, and is a commonly used transition prediction method in current engineering practice. However, the flow scene faced by wide-speed-range hypersonic aircraft is very complex, and the transition mechanism and influencing factors are more. Compared with a single subsonic / transonic scene, the traditional transition model based on multiple transport equations faces the defects of poor computational robustness, low prediction accuracy and high model implantation difficulty when applied to wide-speed-range flow, which hinders the transition prediction and aerodynamic design of wide-speed-range hypersonic aircraft.

[0004] Therefore, it is necessary to propose a new technical solution to solve the above technical problems. SUMMARY

[0005] In view of the above problems, the present application provides a wide-speed-range boundary layer transition prediction method using algebraic intermittency factor, which aims to accurately predict the subsonic to hypersonic boundary layer transition.

[0006] In order to achieve the above purpose, the technical solutions that can be adopted by the present application are as follows:

[0007] A wide-speed-range boundary layer transition prediction method using algebraic intermittency factor, comprising the following steps,

[0008] (1) using average flow information, calculating the vortex Reynolds number Re v ;

[0009] (2) calculating the local momentum thickness Reynolds number Re θL for characterizing transition through the vortex Reynolds number Re v ;

[0010] (3) calculating the transition prediction result according to the input free stream turbulence Tu∞ and the outer edge Mach number M of the boundary layer calculated in the previous step e Calculate the transition criterion Re θt ;

[0011] (4) According to the local momentum thickness Reynolds number Re θL and the transition criterion Re θt , construct the algebraic intermittency factor γ;

[0012] (5) Use the intermittency factor γ to modify the turbulence model, including the production term P k , the dissipation term D k and the mixing function F1 of the transport equation of turbulent kinetic energy k:

[0013] P k = γP k,SST

[0014] D k = {f lim min[max(γ,0.1),1]+(1-fl lim )}D k,SST

[0015] Where P k,SST and D k,SST represent the production term and the dissipation term of the transport equation of turbulent kinetic energy k in the original k-ω SST turbulence model respectively; The function fl lim is used to ensure the reasonable dissipation of turbulent kinetic energy in the free stream.

[0016]

[0017] Where F 1SST represents the mixing function in the original k-ω SST turbulence model, F3 represents the limiter function, and R y represents the Reynolds number based on the wall distance d w and the turbulent kinetic energy k.

[0018] (6) In any computational fluid dynamics solver, the general CFD method is used to solve the turbulence model equation modified by the above steps to obtain the data of velocity, density, temperature, force coefficient, and wall heat flux of the flow.

[0019] Further, in step (1), the Re v calculation formula is:

[0020]

[0021] Where ρ is the density, d w is the wall distance, Ω is the modulus of vorticity, and μ is the molecular viscosity.

[0022] Further, in step (2), the local momentum thickness Reynolds number Re θL As follows:

[0023]

[0024] Where F ratio represents the maximum value of the vortex Reynolds number Re v,max and the integral momentum thickness Reynolds number Re θ The specific formula is as follows:

[0025]

[0026] Where c1, c2 and c3 are formula coefficients, M e represents the Mach number at the outer edge of the boundary layer, T e represents the temperature at the outer edge of the boundary layer, T w represents the wall temperature; for an isothermal wall, T w is determined by the input parameters; for an adiabatic wall, T w takes the adiabatic wall temperature γ g is the specific heat ratio, and Pr is the laminar Prandtl number.

[0027] Further, in step (2), M e and T e are solved by using the following isentropic relationship:

[0028]

[0029]

[0030] Where p ∞ represents the pressure of the free stream, ρ ∞ represents the density of the free stream, U ∞ represents the velocity of the free stream, a ∞ represents the speed of sound of the free stream; p represents the local pressure of each grid point calculated by the flow field, ρ e represents the density at the outer edge of the boundary layer, U e represents the velocity at the outer edge of the boundary layer, and a e represents the speed of sound at the outer edge of the boundary layer, and R represents the gas constant.

[0031] Further, in step (3), the calculation formula of the transition criterion Re θt is as follows:

[0032]

[0033] Re θt,high = 62.12 (Tu ∞ + 0.032)-0.745 M e

[0034]

[0035] where Re θt,low represents the transition criterion value under the free stream Mach number M ∞ ≤1.2, Re θt,hig represents the transition criterion value under the free stream Mach number M ∞ >1.2.

[0036] Further, in step (4), the algebraic intermittency factor γ is constructed in the following form:

[0037] γ=γ1+γ2

[0038]

[0039] γ2=min(10Φ1Φ2γ1,3)

[0040]

[0041] As can be seen from the above formula, when the intermittency factor γ=0, it indicates that the flow is laminar, and 0<γ<1 indicates that the flow is in the transition stage; the intermittency factor γ is composed of the first part γ1 and the second part γ2; Φ1 and Φ2 are two limiter functions for shielding the second part γ2 of the intermittency factor in the fully developed turbulent flow region and the boundary layer viscous bottom layer; F turb is a dissipation function based on the turbulent viscosity μ t and the molecular viscosity μ.

[0042] Compared with the prior art, the present application has the beneficial effects that:

[0043] The transition prediction can be performed through the local information of the flow field, no additional transport equation or non-local variable solving strategy needs to be added, and accurate prediction of the subsonic to hypersonic boundary layer transition and aerodynamic force and heat can be realized.

[0044] The design method provided by the present application can be stored on a storage medium as a computer program, and comprises the following technical scheme: an electronic device comprising: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the above-mentioned prediction method.

[0045] and:

[0046] A computer readable medium having a computer program stored thereon, the program being executed by a processor to implement the above-mentioned prediction method. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The flow chart of the new algebraic transition model proposed in the application.

[0048] Figure 2 The schematic diagram of the grid and boundary conditions of the flat plate example calculation.

[0049] Figure 3 The comparison of the prediction results of the new algebraic transition model proposed in the application and the traditional two-equation transport transition model in the subsonic flat plate transition example.

[0050] Figure 4 The comparison of the prediction results of the new algebraic transition model proposed in the application and the traditional two-equation transport transition model in the supersonic flat plate transition example.

[0051] Figure 5 The comparison of the prediction results of the new algebraic transition model proposed in the application and the traditional two-equation transport transition model in the hypersonic flat plate transition example. DETAILED DESCRIPTION

[0052] In order to make the purpose, design process, technical method and advantages of the application clearer, the application will be further described in detail below with reference to the drawings.

[0053] The application discloses a wide-speed-range boundary layer transition prediction method using algebraic intermittency factors, comprising the following steps:

[0054] (1) using average flow information, the vortex Reynolds number Re v is calculated as follows:

[0055]

[0056] Wherein, ρ is the density, d w is the wall distance, Ω is the modulus of vorticity, and μ is the molecular viscosity.

[0057] (2) further calculating the local momentum thickness Reynolds number Re v used for representing the transition of the flow field through the vortex Reynolds number Re θL as follows:

[0058]

[0059] Wherein, F ratio represents the ratio relationship between the maximum vortex Reynolds number Re v,max and the integral momentum thickness Reynolds number Re θ , and the specific formula is as follows:

[0060]

[0061] Among them, c1, c2 and c3 are formula coefficients, M e represents the Mach number at the outer edge of the boundary layer, T e represents the temperature at the outer edge of the boundary layer, T w represents the wall temperature. For an isothermal wall, T w Determined by input parameters; for an adiabatic wall, T w Take the adiabatic wall temperature γ g is the specific heat ratio, Pr is the laminar Prandtl number. For ideal air, γ g It is usually set to 1.4, and Pr is usually set to 0.72. e and T e represent the Mach number and temperature at the outer edge of the boundary layer respectively, and are solved using the following isentropic relationship:

[0062]

[0063] Among them, p ∞ represents the free flow pressure, ρ ∞ represents the density of the free flow, U ∞ represents the velocity of the free stream, a ∞ represents the sound velocity of the free flow. These four quantities are given by the boundary conditions of the calculation input. p represents the local pressure of each grid point in the flow field calculation, ρ e represents the density at the outer edge of the boundary layer, U e represents the velocity at the outer edge of the boundary layer and a e represents the speed of sound at the outer edge of the boundary layer. These four variables are obtained in CFD (Computational Fluid Dynamics) calculations. R represents the gas constant, which is given by the fluid properties and is usually taken as 287 for ideal air.

[0064] (3) According to the input free flow turbulence Tu ∞ and the boundary layer outer edge Mach number M calculated in the previous step e Calculate the transition criterion Re θt Value

[0065]

[0066] Re θt,high =62.12(Tu ∞ +0.032) -0.745 M e

[0067]

[0068] Among them, Re θt,low Indicates low-speed flow (i.e., free-flow Mach number M ∞ ≤1.2) under the transition criterion value, Reθt,high represents the transition criterion value under high-speed flow (i.e. free stream Mach number M ∞ >1.2).

[0069] (4) The local momentum thickness Reynolds number Re θL calculated in step (2) and the transition criterion Re θt calculated in step (3) are used to construct the algebraic intermittency factor γ in the following form:

[0070] γ = γ1 + γ2

[0071]

[0072] γ2 = min(10Φ1Φ2γ1,3)

[0073]

[0074] At the end of this step, the intermittency factor γ for transition prediction is obtained. When γ = 0, the flow is laminar; when 0 < γ < 1, the flow is in the transition regime; and when γ = 1, the flow is fully turbulent. The intermittency factor γ is composed of two parts: γ1 and γ2. Φ1 and Φ2 are two limiter functions to shield the second part γ2 of the intermittency factor in the fully turbulent region and the viscous sublayer of the boundary layer. turb F is a dissipation function based on the turbulent viscosity μ t and the molecular viscosity μ, which makes the transition criterion value decrease rapidly after the onset of turbulence, thus ensuring the accurate generation of the intermittency factor.

[0075] (5) In order to obtain the influence of transition on aerodynamic forces, aerodynamic heating, etc., the intermittency factor γ can be further used to modify the turbulence model after step (4). Taking the k-ω SST turbulence model as an example, the production term P k and the dissipation term D k of the transport equation of the turbulent kinetic energy k are modified as follows:

[0076] P k = γP k,SST

[0077] D k = {f lim min[max(γ, 0.1), 1] + (1 - fl lim )}D k,SST

[0078] where P k,SST and D k,SST represent the production term and the dissipation term of the transport equation of the turbulent kinetic energy k in the original k-ω SST turbulence model, respectively. The function fl lim is used to ensure the reasonable dissipation of the turbulent kinetic energy in the free stream:

[0079]

[0080] where S is the modulus of the strain rate. Finally, the blending function F1 in the original k-ω SST turbulence model is modified as follows:

[0081] F1 = max(F 1SS ,F3),

[0082] where F 1SST represents the blending function in the original k-ω SST turbulence model, F3 represents a limiter function, R y represents the Reynolds number based on the wall distance d w and the turbulent kinetic energy k.

[0083] (6) The turbulence model equation modified by the above steps is solved by using a general CFD method in any computational fluid dynamics (CFD) solver, so that the velocity, density, temperature, force coefficient, and wall heat flux of the flow can be obtained.

[0084] The specific effects of the present application are verified below by taking a subsonic to hypersonic flat plate example. The calculation conditions refer to the experimental conditions in the published literature, and are specifically shown in Table 1. The calculation grid and boundary conditions are shown in Figure 2 The streamwise x normal grid numbers upstream and downstream of the wedge are 21 x 151 and 301 x 151, respectively, and the dimensionless height y + of the first layer of grid is 1.

[0085]

[0086] The transition model proposed in the present application can be implanted in any computational fluid dynamics solver, and the specific implementation process and calculation results of the present application are described below by taking the open-source wind thunder software of the China Aerodynamics Research and Development Center as an example. First, a new subprogram is established in the structural grid Reynolds averaged Navier-Stokes equation (RANS) solver of the wind thunder software to program and realize steps (1)-(4) of the technical scheme, so as to calculate the algebraic intermittency factor function. The flow field variable information required in the calculation process can be directly obtained from the structural grid RANS solver of the wind thunder software. Then the calculated algebraic intermittency factor function is transmitted to the k-ω SST turbulence model module of the structural grid RANS solver of the wind thunder software, and step (5) of the technical scheme is programmed and realized, so as to modify the k-ω SST turbulence model. After the above programming is completed, the structural grid RANS solver of the wind thunder software is called to read in the grid to start the CFD flow field calculation, i.e. step (6) of the technical scheme. When the calculation is completed, the wind thunder software can automatically output the flow field calculation results.

[0087] Figures 3 to 5 The flat plate wall friction resistance coefficient and Stanton number distribution calculated by the new algebraic transition model proposed by the application and used by the wind and thunder software are given, and the γ-Re θ The calculation results of the two-equation transport transition model and the experimental results in the published literature are compared. It can be seen that the new algebraic transition model proposed by the application and the traditional γ-Re θ The two-equation transport transition model achieves similar transition prediction results; in the supersonic and hypersonic working conditions, the method proposed by the application obtains results more consistent with the experimental values, indicating the beneficial effects of the application.

[0088] In addition, there are many specific implementation methods and approaches of the application, and the above description is only the preferred embodiment of the application. It should be pointed out that for ordinary skilled persons in the technical field, some improvements and refinements can be made without departing from the principles of the application, and these improvements and refinements should also be regarded as the protection scope of the application.

Claims

1. A wide speed range boundary layer transition prediction method using algebraic intermittency factor, characterized by, comprising the steps of (1) Using the average flow information, the vortex Reynolds number is calculated ; (2) Vortex Reynolds number , calculate the local momentum thickness Reynolds number of the flow field used to characterize the transition ; (3) From the input free stream turbulence and the outer edge Mach number of the boundary layer calculated in the previous step Calculate the transition criterion value; (4) Constructing the algebraic intermittency factor according to the local momentum thickness Reynolds number of the flow field and the transition criterion ;​ Construction of algebraic intermittency factor The form is as follows: ； ； ； ； ； ； As seen from the above equation, when the intermittency factor represents that the flow is laminar, represents that the flow is in the transition phase; the intermittency factor is composed of a first part and a second part ; and are two limiter functions for shielding the second part of the intermittency factor in the fully developed turbulent region and the viscous sublayer of the boundary layer ; is a dissipation function based on the turbulent viscosity and the molecular viscosity ; (5) Use of intermittency factor correcting the turbulence model, including the production term of the transport equation for the turbulent kinetic energy the dissipation term the mixing function of the transport equation for the turbulent kinetic energy ； ； wherein and respectively represent the original k is the turbulent kinetic energy generation and dissipation terms of the transport equation; the function is used to ensure a reasonable dissipation of turbulent kinetic energy in the free stream; ； wherein represents the original mixing function in SST turbulence model, represents the limiter function, represents the wall distance based Reynolds number; and turbulent kinetic energy (6) solving the turbulence model equation modified by the above steps by using a general CFD method in any computational fluid dynamics solver to obtain the data of velocity, density, temperature, force coefficient, wall heat flux of the flow.

2. The prediction method of claim 1, wherein: In step (1), The calculation formula is: ； wherein is the density, is the wall distance, is the modulus of vorticity, is the molecular viscosity.

3. The prediction method of claim 2, wherein: In step (2), the local momentum thickness Reynolds number of the flow field is as follows: ； in, Represents the maximum vortex Reynolds number The momentum thickness Reynolds number obtained by integrating The specific formula is as follows: ； ； ； ； where , and are formula coefficients, denotes the Mach number at the outer edge of the boundary layer, denotes the temperature at the outer edge of the boundary layer, denotes the wall temperature; for an isothermal wall, is determined from the input parameters; for an adiabatic wall, the adiabatic wall temperature is taken , is the Prandtl number, is the laminar Prandtl number.

4. The prediction method of claim 3, wherein: In step (2), and Solving is performed using the following isentropic relation: ； ； ； ； ； wherein P∞ represents the pressure of the free stream, ρ∞ represents the density of the free stream, V∞ represents the velocity of the free stream, a∞ represents the speed of sound of the free stream; P represents the local pressure of the flow field calculation at each grid point, ρ represents the density of the boundary layer outer edge, V represents the velocity of the boundary layer outer edge and a represents the speed of sound of the boundary layer outer edge, R represents the gas constant.

5. The prediction method of claim 4, wherein: In step (3), the transition criterion The calculation formula is: ; ； ； wherein represents the transition criterion value at a free stream Mach number represents the transition criterion value at a free stream Mach number represents the transition criterion value at a free stream Mach number represents the transition criterion value at a free stream Mach number 6. An electronic device, comprising: one or more processors; and a storage device for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the prediction method of any one of claims 1-5.

7. A computer readable medium having stored thereon a computer program, characterized in that The program is executed by the processor to implement the prediction method of any one of claims 1-5.

Images