Gas film cooling efficiency prediction standard flux correction method based on Reynolds stress model

Abstract

The invention discloses an air film cooling efficiency prediction standard flux correction method based on a Reynolds stress model, and relates to an end-period cooling efficiency prediction standard flux correction method. The invention aims to solve the problem that the air film cooling efficiency on a discrete hole air film cooling center line is excessively predicted by a model adopted at present. According to the method, a Reynolds time-average Navier-Stokes equation is obtained by adopting a Reynolds time-average method, a steady-state Reynolds time-average NS equation is solved, a Reynolds stress transport equation and a turbulence transport variable control equation are directly solved, and turbulent energy, specific dissipation rate, turbulence viscosity and Reynolds stress are obtained; calculating a turbulence dissipation rate; calculating a turbulence Reynolds number; calculating a turbulent heat transfer time scale factor and a turbulent heat transfer time scale; calculating an isotropic turbulence heat transfer coefficient; calculating an anisotropic turbulence heat transfer coefficient; calculating the anisotropic turbulence heat transfer amount and the isotropic turbulence heat transfer amount difference value; and calculating an anisotropic energy source item. The invention belongs to the field of aerodynamics and computational fluid mechanics.

Description

Technical Field

[0001] The present invention relates to a method for predicting the film cooling efficiency and correcting the scalar flux, belonging to the fields of aerodynamics and computational fluid dynamics. Background Art

[0002] Film cooling is applied to various high-temperature components that require thermal protection, such as gas turbine blades, rocket nozzles, and ramjet combustors. The main structural forms of film cooling are divided into slot type and discrete type. Among them, the slot type is considered an ideal cooling structure layout form, but it is restricted by various mechanical structures and thermal intensities. The discrete hole film cooling layout is more flexible and has lower requirements for the structure, so it has more practical application value, and thus a large number of studies have been carried out.

[0003] With the development of CFD technology, a large number of researchers have used RANS to analyze the regularity of discrete hole film cooling. However, the flow field of typical discrete hole film cooling is quite complex, with several large-scale vortex structures coexisting, and there are flow separation and reattachment near the film holes, which is a flow with strong anisotropy. The traditional two-equation turbulence model has insufficient prediction of the Reynolds stress anisotropy. At the same time, scalar transport also affects the prediction of film cooling efficiency. Even in the case of homogeneous turbulence, scalar transport also shows anisotropy. The turbulent viscosity used in the traditional model is a scalar and cannot accurately reflect the heat transfer anisotropy. Due to the existence of the above defects, the models currently used all over-predict the film cooling efficiency on the centerline of discrete hole film cooling.

[0004] Therefore, how to accurately predict the cooling efficiency of discrete hole film by the turbulence model is an urgent problem to be solved in this field. Summary of the Invention

[0005] In order to solve the problem that the models currently used all over-predict the film cooling efficiency on the centerline of discrete hole film cooling, the present invention further provides a method for predicting the film cooling efficiency and correcting the scalar flux based on the Reynolds stress model.

[0006] The technical solution adopted by the present invention to solve the above problems is as follows: The steps of the present invention include:

[0007] Step 1: Obtain the Reynolds-averaged NS equation by using the Reynolds-averaging method, solve the steady Reynolds-averaged NS equation, and directly solve the Reynolds stress transport equation and the control equation of the turbulent transport variable to obtain the turbulent kinetic energy k, the specific dissipation rate ω, the turbulent viscosity μ t and the Reynolds stress

[0008] Step 2: Calculate the turbulent dissipation rate ε by using the turbulent kinetic energy k and the specific dissipation rate ω;

[0009] Step 3: Calculate the turbulent Reynolds number Re using the turbulent dissipation rate ε and the kinematic viscosity μ t ;

[0010] Step 4: Calculate the turbulent heat transfer scale factor f t and the heat transfer time scale τ using the turbulent Reynolds number Re t ;

[0011] Step 5: Calculate the isotropic and anisotropic turbulent heat transfer coefficients k t ;

[0012] Step 6: Calculate the difference in anisotropic and isotropic turbulent heat transfer amounts Δq using the heat transfer coefficient i ;

[0013] Step 7: Add the obtained correction amount difference to the energy equation in the form of an energy source term to carry out the numerical calculation of multi-dimensional flow heat transfer for discrete hole film cooling.

[0014] Furthermore, in Step 1, the time-averaged Reynolds simulation method is used to solve the NS equations in a steady state as follows:

[0015]

[0016] Using the formula:

[0017]

[0018] Calculate the turbulent kinetic energy k, the specific dissipation rate ω, the turbulent viscosity μ t and the Reynolds stress

[0019] In the above equations:

[0020]

[0021]

[0022] Among them, is the partial derivative operator, t is time, ρ is density, u is velocity, δ ij is the Kronecler symbol, the subscripts i, j are spatial dimension indices, x is the coordinate axis, μ is the momentum viscosity, μ t is the turbulent viscosity, y is the distance from the wall surface, σ k,1 , σ k,2 , σ ω,1 , σ ω,2 , α, β, C1, C2 are constant parameters.

[0023] Furthermore, Step 2 includes:

[0024] Calculate the turbulent dissipation rate ε using the formula ε = kω, where k is the turbulent kinetic energy and ω is the specific dissipation rate.

[0025] Further, step 3 includes:

[0026] Using the formula to calculate the turbulent Reynolds number Re t , where ρ is the fluid density, ε is the turbulent dissipation rate, k is the turbulent kinetic energy, and μ is the momentum viscosity.

[0027] Further, step 4 includes:

[0028] Using the formula ft = 1 - exp(-(Ret / 20) 0.45 ) to calculate the turbulent heat transfer scale factor f t , where Re t is the turbulent Reynolds number;

[0029] Using the formula: τ = f t -1 k / ε to calculate the turbulent heat transfer time scale τ, where f t is the turbulent heat transfer scale factor, ε is the turbulent dissipation rate, and k is the turbulent kinetic energy.

[0030] Further, step 5 includes:

[0031] Using the formula k t = C p μ t / Pr t to calculate the isotropic turbulent heat transfer coefficient k t , where C p is the specific heat capacity, μ t is the turbulent viscosity, and Pr t is the turbulent Prandtl number;

[0032] Using the high-order generalized gradient model (HOGGDH):

[0033]

[0034] to calculate the anisotropic heat transfer coefficient k xx , k xy , k xz , k yy , k yz , k zz , where ρ is the density, C p is the specific heat capacity, C θ is the model constant, τ is the turbulent heat transfer time scale, etc. are the Reynolds stresses.

[0035] Further, step 6 includes:

[0036] Using the formula to calculate the difference in turbulent heat transfer quantity Δq between anisotropy and isotropyi , where k t is the isotropic turbulent heat transfer coefficient, and k t,ij is the anisotropic turbulent heat transfer coefficient, is the temperature gradient.

[0037] Furthermore, step 7 includes:

[0038] Adding a source term to the original energy equation where S h is the energy source term, and Δq i is the difference in turbulent heat transfer between anisotropy and isotropy.

[0039] Furthermore, in the solution process of step 7, the left and right side walls of the computational domain are set as periodic boundaries, the inlet boundary conditions are respectively set as pressure inlet boundary conditions and mass flow inlet boundary conditions, the outlet boundary condition is set as a pressure outlet boundary condition, and numerical simulation of discrete hole film cooling is carried out;

[0040] A pressure-based coupled implicit solver is used for calculation, gradient discretization is carried out based on the Green-Gauss nodal method, the convection term is discretized using a second-order upwind scheme, and the diffusion term is discretized using a central difference scheme; the residual of the continuity equation is less than 10 -3 , the residuals of the momentum equation and the energy equation are less than 10 -6 , the difference in mass flow rate at the inlet and outlet is less than 1%, and the temperature at the monitoring point is less than 1% can be regarded as the calculation convergence;

[0041] During the calculation process, the original unchanged Reynolds stress transport model is used to solve for convergence, and after the flow field temperature field reaches a steady state, a source term is further added to the energy equation for solution.

[0042] The beneficial effects of the present invention are:

[0043] 1. By directly solving the Reynolds stress transport equation, the present invention can more accurately capture the flow field result characteristics of the film jet, and the predictions of the eddy current intensity, Reynolds stress, and velocity field are all more accurate;

[0044] 2. On the basis of considering the anisotropy of Reynolds stress, by introducing the HOGGDH model, the original isotropic scalar flux model is further improved to be anisotropic, and the diffusion prediction of the film cooling jet core is more accurate, and the prediction of the film cooling efficiency is more accurate;

[0045] 3. By comparing the experimental data of different film hole patterns, blowing ratios, and density ratios respectively, the predicted normalized flux correction method for film cooling efficiency based on the Reynolds stress transport turbulence model considered in the present invention shows good consistency with the experimental data in all simulations. The relative prediction accuracy is improved by 32% compared with the traditional two-equation model, which has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the flow chart of the present invention;

[0047] Figure 2 is the schematic diagram of the computational domain of the present invention;

[0048] Figure 3 is the comparison diagram of the centerline film cooling efficiency predicted by different numerical models and the experimental data in Example 1;

[0049] Figure 4 is the comparison diagram of the film cooling efficiency predicted by different numerical models and the experimental data in Example 1;

[0050] Figure 5 is the comparison diagram of the centerline film cooling efficiency predicted by different numerical models and the experimental data in Example 2;

[0051] Figure 6 is the comparison diagram of the film cooling efficiency predicted by different numerical models and the experimental data in Example 2. DETAILED DESCRIPTION OF THE INVENTION

[0052] DETAILED DESCRIPTION OF THE INVENTION 1: As Figure 1 shown, a predicted normalized flux correction method for film cooling efficiency based on the Reynolds stress model, the specific steps include:

[0053] Step 1. Obtain the Reynolds-averaged NS equation by using the Reynolds-averaging method, solve the steady Reynolds-averaged NS equation, and directly solve the Reynolds stress transport equation and the control equation of the turbulent transport variables to obtain the turbulent kinetic energy k, the specific dissipation rate ω, the turbulent viscosity μ t and the Reynolds stress

[0054] Steadily solve the NS equation by using the time-averaged Reynolds simulation method as follows:

[0055]

[0056] Use the formula:

[0057]

[0058] Calculate the turbulent kinetic energy k, the specific dissipation rate ω, the turbulent viscosity μ t and the Reynolds stress

[0059] In the above equation:

[0060]

[0061]

[0062] wherein, is the partial derivative operator, t is time, ρ is density, u is velocity, δ ij is the Kronecker symbol, the subscripts i and j are spatial dimension indices, x is the coordinate axis, μ is the momentum viscosity, μ t is the turbulent viscosity, y is the distance from the wall surface, σ k,1 , σ k,2 , σ ω,1 , σ ω,2 , α, β, C1, and C2 are constant parameters;

[0063] Step 2: Calculate the turbulent dissipation rate ε using the turbulent kinetic energy k and the specific dissipation rate ω;

[0064] Calculate the turbulent dissipation rate ε using the formula ε = kω, where k is the turbulent kinetic energy and ω is the specific dissipation rate;

[0065] Step 3: Calculate the turbulent Reynolds number Re using the turbulent dissipation rate ε and the kinematic viscosity μ t ;

[0066] Use the formula to calculate the turbulent Reynolds number Re t , where ρ is the fluid density, ε is the turbulent dissipation rate, k is the turbulent kinetic energy, and μ is the momentum viscosity;

[0067] Step 4: Calculate the turbulent heat transfer scale factor f t and the heat transfer time scale τ using the turbulent Reynolds number Re t ;

[0068] Use the formula f t = 1 - exp(-(Re t / 20) 0.45 ) to calculate the turbulent heat transfer scale factor f t , where Re t is the turbulent Reynolds number;

[0069] Use the formula: τ = f t -1 k / ε to calculate the turbulent heat transfer time scale τ, where f t is the turbulent heat transfer scale factor, ε is the turbulent dissipation rate, and k is the turbulent kinetic energy

[0070] Step 5: Calculate the isotropic and anisotropic turbulent heat transfer coefficients k t ;

[0071] Using the formula k t = C p μ t / Pr t calculate the isotropic turbulent heat transfer coefficient k t , where C p is the specific heat capacity, μ t is the turbulent viscosity, and Pr t is the turbulent Prandtl number;

[0072] Using the high-order generalized gradient model (HOGGDH):

[0073]

[0074]

[0075] calculate the anisotropic heat transfer coefficients k xx , k xy , k xz , k yy , k yz , k zz , where ρ is the density, C p is the specific heat capacity, C θ is the model constant, τ is the turbulent heat transfer time scale, etc. are the Reynolds stresses;

[0076] Step 6. Use the heat transfer coefficient to calculate the difference in anisotropic and isotropic turbulent heat transfer amounts Δq i ;

[0077] Use the formula to calculate the difference in turbulent heat transfer amounts Δq between anisotropy and isotropy i , where k t is the isotropic turbulent heat transfer coefficient, k t,ij is the anisotropic turbulent heat transfer coefficient, is the temperature gradient;

[0078] Step 7. Add the obtained difference in correction amounts to the energy equation in the form of an energy source term to carry out numerical calculations of multi-dimensional flow heat transfer for discrete hole film cooling;

[0079] Add a source term to the original energy equation where S h is the energy source term, and Δq i is the difference in turbulent heat transfer amounts between anisotropy and isotropy;

[0080] During the solution process, the left and right side walls of the computational domain are set as periodic boundaries, the inlet boundary conditions are respectively set as the pressure inlet boundary condition and the mass flow rate inlet boundary condition, and the outlet boundary condition is set as the pressure outlet boundary condition to perform numerical simulation on discrete hole film cooling;

[0081] The calculation is carried out using a pressure-based coupled implicit solver, the gradient is discretized based on the Green-Gauss node method, the convection term is discretized using the second-order upwind scheme, and the diffusion term is discretized using the central difference scheme; the residual of the continuity equation is less than 10 -3 , the residuals of the momentum equation and the energy equation are less than 10 -6 , the difference in mass flow rate at the inlet and outlet is less than 1%, and the temperature at the monitoring point is less than 1% can be regarded as the calculation converging;

[0082] During the calculation process, the original unchanged Reynolds stress transport model is used to solve for convergence, and after the flow field temperature field reaches a steady state, a source term is further added to the energy equation for solution.

[0083] Example

[0084] Example 1

[0085] A circular hole of the film cooling hole is selected to verify the numerical prediction ability of the simulation method. The computational domain is as Figure 2 shown, including the mainstream domain, the plenum chamber and the jet holes. Among them, the mainstream velocity is 20 m / s and the temperature is 300 K. The diameter of the film hole is 12.7 mm, and the calculation origin is selected at the center of the film hole outlet. The length in front of the circular hole is 19D, the length behind the hole is 40D, the spanwise range of the computational domain is -1.5D to 1.5D, and the size of the entire plenum chamber is 6D×3D×6D.

[0086] As Figure 3 shown, the gap between the predicted results of the film cooling centerline cooling efficiency under numerical simulation of different models and the experimental data is compared. Among them, EXP represents the experimental data, and HOGGDH represents the simulation results after modifying the scalar flux model. From Figure 3 it can be observed that the numerical simulation results using the scalar flux correction method for predicting film cooling efficiency based on the Reynolds stress model proposed by the present invention are most consistent with the experimental values for the film cooling efficiency on the centerline.

[0087] As Figure 4 shown, the film cooling efficiency in the area close to the center has a certain downward trend compared with the original unmodified RSM model. At the same time, the cooling efficiency has an increasing trend in the spanwise direction, indicating that the film diffuses to both sides. At the same time, with the development of the flow, the film cooling efficiency becomes more uniform in the spanwise direction. The prediction results of the improved model based on the RSM model introducing the anisotropic scalar flux model HOGGDH are more accurate.

[0088] Embodiment 2

[0089] Select the film cooling hole pattern as the 7-7-7 forming hole to verify the numerical prediction ability of the simulation method. The diameter of the film hole is 7.75 mm, the length-diameter ratio is 6, the film inclination angle is 30°, and the expansion angle is 7°. The calculation range in the entire x-direction of the computational domain is -35D to 35D, the mainstream inlet height is 12.5D, the spanwise range of the computational domain is -3D to 3D, and the size of the plenum chamber is 6D×6D×12.5D. The mainstream inlet velocity is 10 m / s.

[0090] As Figure 5 shown, the centerline cooling efficiency distribution of the 7-7-7 forming hole under the conditions of density ratio 1.5 and blowing ratio 0.5 is presented. Among the three models, the HOGGDH has relatively higher calculation accuracy. This is mainly attributed to the step-by-step improvement and introduction from the turbulence model to the scalar flux model. Figure 6 The distribution of the wall cooling efficiency calculated by different models is shown. As shown in the figure, from the SSTk- to the HOGGDH model, the core region on the centerline of the cooling flow gradually shortens, while it expands in the spanwise direction. The prediction accuracy gradually improves from the SST k- to the HOGGDH model. The distribution of the film cooling efficiency predicted by the SST k- differs the most from the experimental results, and the core region of the film cooling is the longest. The RSM is the second, and the improved model corrected by the HOGGDH model has a difference in cooling efficiency from the experimental results of no more than 0.1, which is less than the uncertainty of the experimentally measured cooling efficiency. Although there is a gap between the corrected model and the experimental results, it is still within an acceptable range, and the model still improves the relevant prediction accuracy.

[0091] After comparing with multiple experimental data, the prediction results of the gas film cooling efficiency of the improved model in different hole patterns, density ratios, and blowing ratios are more consistent with the experimental results.

[0092] The above is only a preferred embodiment of the present invention, and it is not intended to limit the present invention in any form. Although the present invention has been disclosed above with the preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art, without departing from the technical solution of the present invention, can make some changes or modifications to the above-disclosed technical content to be equivalent change equivalent embodiments. However, as long as it does not depart from the technical solution content of the present invention, according to the technical essence of the present invention, any simple modification, equivalent replacement, and improvement of the above embodiments within the spirit and principle of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model, characterized in that: The specific steps include: Step 1: Use the Reynolds time-averaged method to obtain the Reynolds time-averaged NS equation, solve the steady-state Reynolds time-averaged NS equation, and directly solve the Reynolds stress transport equation and the turbulent transport variable control equation to obtain the turbulent kinetic energy k, specific dissipation rate ω, and turbulent viscosity μ t and Reynolds stress Step 2, calculate the turbulent dissipation rate ε using the turbulent kinetic energy k and the specific dissipation rate ω; Step 3: Calculate the turbulent Reynolds number Re using the turbulent dissipation rate ε and kinematic viscosity μ t ; Step 4: Use the turbulent Reynolds number Re t Calculate the turbulent heat transfer scale factor f t and heat transfer time scale τ; Step 5: Calculate the isotropic and anisotropic turbulent heat transfer coefficient k t ; Step 6: Use the heat transfer coefficient to calculate the difference in anisotropic and isotropic turbulent heat transfer Δq i ; Step 7: Add the obtained correction difference to the energy equation as an energy source term to carry out numerical calculation of multi-dimensional flow heat transfer of discrete pore film cooling.

2. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: In step 1, the time-averaged Reynolds simulation method is used to solve the NS equation in a steady state as follows: Using the formula: Calculate turbulent kinetic energy k, specific dissipation rate ω, and turbulent viscosity μ t and Reynolds stress In the above equation: in, is the partial derivative operator, t is time, ρ is density, u is velocity, δ ij is the Kronecler symbol, subscripts i and j are the spatial dimension indices, x is the coordinate axis, μ is the kinetic viscosity, and μ t is the turbulent viscosity, y is the distance from the object surface, σ k,1 , σ k,2 , σ ω,1 , σ ω,2 , α, β, C1, C2 are constant parameters.

3. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 2 includes: The turbulent dissipation rate ε is calculated using the formula ε=kω, where k is the turbulent kinetic energy and ω is the specific dissipation rate.

4. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 3 includes: Using the formula Calculate the turbulent Reynolds number Re t , where ρ is the fluid density, ε is the turbulent dissipation rate, k is the turbulent kinetic energy, and μ is the kinetic viscosity.

5. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 4 includes: Using formula f t =1-exp(-(Re t / 20) 0.45 ) Calculate the turbulent heat transfer scale factor f t , where Re t is the turbulent Reynolds number; Using the formula: τ = f t -1 k / ε calculates the turbulent heat transfer time scale τ, where f t is the turbulent heat transfer scale factor, ε is the turbulent dissipation rate, and k is the turbulent kinetic energy.

6. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 5 includes: Using formula k t =C p μ t / Pr t Calculate the isotropic turbulent heat transfer coefficient k t , where C p is the specific heat capacity, μ t is the turbulent viscosity, Pr t is the turbulent Prandtl number; Using the High-Order Generalized Gradient Model (HOGGDH): Calculation of anisotropic heat transfer coefficient k xx , k xy , k xz , k yy , k yz , k zz , where ρ is the density, C p is the specific heat capacity, C θ is the model constant, τ is the turbulent heat transfer time scale, is the Reynolds stress.

7. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 6 includes: Using the formula Calculate the difference in turbulent heat transfer between anisotropic and isotropic conditions Δq i , where k t is the isotropic turbulent heat transfer coefficient, k t,ij Anisotropic turbulent heat transfer coefficient, is the temperature gradient.

8. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: Step 7 includes: Adding source terms to the original energy equation Where S h is the energy source term, Δq i is the difference in turbulent heat transfer between anisotropic and isotropic conditions.

9. The method for correcting the standard flux of film cooling efficiency prediction based on the Reynolds stress model according to claim 1, characterized in that: In the solution process of step 7, the left and right walls of the computational domain are set as periodic boundaries, the inlet boundary conditions are set as pressure inlet boundary conditions and mass flow inlet boundary conditions, and the outlet boundary conditions are set as pressure outlet boundary conditions, and the discrete hole film cooling is numerically simulated; The calculation is performed using a pressure-based coupled implicit solver, the gradient is discretized based on the Green-Gauss node method, the convection term is discretized using a second-order upwind format, and the diffusion term is discretized using a central difference format; the continuity equation residual is less than 10 -3 , the residuals of momentum equation and energy equation are less than 10 -6 , the difference between the inlet and outlet mass flow is less than 1%, and the temperature at the monitoring point is less than 1%, which can be regarded as the calculation convergence; During the calculation process, the original unchanged Reynolds stress transport model is used to solve the convergence. After the flow field and temperature field reach a stable state, the source term is further added to the energy equation for solution.

Images