A k-omega SST turbulence model enhanced mixing correction method suitable for film cooling

Abstract

The application discloses a k-omega SST turbulent flow model enhanced mixing correction method suitable for air film cooling. m The turbulent viscosity coefficient μ of different mixing degree regions is described t The turbulent viscosity coefficient μ is further used t The correction of different mixing intensity regions of two fluids is completed, and the air film cooling efficiency and the numerical prediction accuracy of the mixing region are improved through the method.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine turbulence simulation technology, and particularly relates to an enhanced mixing correction method for the k-ωSST turbulence model for film cooling. Background Technology

[0002] In the cooling technology of high-temperature components of aero-engines, film cooling (FSV) is currently the most commonly used thermal protection technology. FSV works by delivering a cooler gaseous coolant to the wall surface requiring thermal protection through holes or slits in the wall. This coolant forms a thin film along the direction of the high-temperature airflow, isolating the solid wall surface from the high-temperature airflow and preventing overheating damage from direct contact. In high-temperature components such as aero-engine combustion chambers, turbines, and nozzles, the flow complexity in the FSV cooling region is high due to the significant differences in the flow environment and the involvement of multiple flow types, making thermal protection design challenging. The definition of FSV efficiency η is as follows:

[0003]

[0004] Where T r T is the recovery temperature of the high-temperature airflow. aw To achieve the insulated wall temperature for airflow close to the wall surface, T c This is the recovery temperature of the coolant gas.

[0005] In modern design, due to the high cost of experiments, computational fluid dynamics (CFD) methods are commonly used to simulate the cooling design of film cooling systems in engines. Solving the Reynolds-averaged Navier-Stokes equations and the corresponding turbulence models is currently the most widely used method. However, the k-ωSST turbulence model is insufficient in predicting the turbulence intensity in the mixing zone, causing the predicted coolant coverage to deviate from reality. Invention patent (CN 110727996 B) discloses a turbulence model correction method suitable for flow around a moving boundary. This patent uses a filtering function to divide the vortex and non-vortex regions to correct the turbulent viscosity coefficient, improving the accuracy of numerical calculations of flow around the moving boundary of a single flow. However, this turbulence model is still a two-equation turbulence model and cannot improve the calculation accuracy of the mixing zone of two flows in film cooling. Therefore, this invention proposes an enhanced mixing correction method for the k-ωSST turbulence model suitable for film cooling, adding an additional scalar transport equation to distinguish between the two flows, resulting in a three-equation turbulence model. The invention patent (CN 113158339 B) discloses a method for correcting the turbulence length scale of the SST turbulence model. However, it corrects the turbulence by adding a source term to the right side of the specific turbulence kinetic energy dissipation rate transport equation. This added source term does not involve the mixing of the two fluids, so it cannot distinguish between the mixing and non-mixing regions of film cooling, and thus cannot make a reasonable prediction of the film cooling efficiency. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of the prior art by disclosing an enhanced mixing correction method for the k-ωSST turbulence model for film cooling. This method improves the accuracy of numerical prediction of the mixing region for film cooling efficiency.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for enhancing the mixing correction of the k-ωSST turbulence model applicable to film cooling, wherein the method enhances the mixing correction of the k-ωSST turbulence model by using the mixing function C m The turbulent viscosity coefficient μ describes the region with different mixing degrees. t Furthermore, through the turbulent viscosity coefficient μ t Corrections were made for regions with different mixing intensities between the two fluids.

[0009] The mixing function expression is as follows:

[0010]

[0011] Where n is the mixing constant, C A C represents the mass fraction of cooling gas A in film cooling. A This was obtained by solving the component transport equations. Since film cooling involves the mixing of two streams, the other component passes through 1-C. A Calculated; in the unmixed region, C A Or another component 1-C A The value tends to 0;

[0012] Turbulent viscosity coefficient μ t for:

[0013]

[0014] Where ρ is the gas density, k is the turbulent kinetic energy, and ω is the specific turbulent kinetic energy dissipation rate.

[0015] According to a preferred embodiment, the component transport equation is:

[0016]

[0017] Among them, D A Let Sc be the molecular diffusion coefficient of cooling gas A. t U is the turbulent Schmidt number. j Velocity in tensor form.

[0018] According to a preferred embodiment, n takes a value between 1 and 3.

[0019] According to a preferred embodiment, the turbulent kinetic energy k and the local specific turbulent kinetic energy dissipation rate ω are calculated by the turbulent kinetic energy transport equation and the specific turbulent kinetic energy dissipation rate transport equation, respectively.

[0020] According to a preferred embodiment, the turbulent kinetic energy transport equation is:

[0021]

[0022] The transport equation for the specific turbulent kinetic energy dissipation rate is:

[0023]

[0024] Where, x j The coordinate axes are in tensor form, and represents the molecular dynamic viscosity coefficient. k P represents the turbulent kinetic energy generation term in the turbulent kinetic energy equation, and F1 is the weighting function describing the transformed turbulence model; k ,F1,σ k ,β′,σ ω γ is obtained based on the constants of the turbulence model and the solutions of each transport equation, β′ and γ are adjustable empirical constants of the turbulence model, and σ k Let σ be the Prandtl number of the k-equation. ω Let ω be the Prandtl number of the equation. The calculation methods and ranges of the above parameters are well known to those skilled in the art.

[0025] Blending function C m turbulent viscosity coefficient μ t The equations are coupled with the component transport equations, meaning that solving the component transport equations depends on the turbulent viscosity coefficient μ. t However, the expression for the turbulent viscosity coefficient depends on the solution of the component transport equation. The turbulent viscosity coefficient μ of this invention... t It needs to be represented by the solutions of the three turbulent transport equations. By assigning a fluid initial field to the continuity equation, momentum equation, energy equation, and component transport equation, the prediction results of the film cooling mixing zone can be improved through iterative calculations.

[0026] The k-ωSST turbulence model enhancement and mixing correction method of this invention uses three turbulent transport equations—turbulent kinetic energy transport equation, specific turbulent kinetic energy dissipation rate transport equation, and component transport equation—as the governing equations of the modified turbulence model. The turbulent viscosity coefficient is calculated using the solutions of these three turbulent transport equations. A mixing function is used to correct the viscosity coefficient of the turbulence model. All three turbulent transport equations require the use of turbulent viscosity coefficients for solution; that is, the three equations are coupled through turbulent viscosity coefficients, with the mixing function serving as a weighting function for the coupling relationship between the three equations.

[0027] Furthermore, the k-ωSST turbulence model enhanced mixing correction method of this invention can also guide the design of cooling structures and flow field analysis in the field of aero-engines based on the prediction results of film cooling efficiency, and solve engineering and technical problems related to cooling technology in the field of aero-engines.

[0028] The aforementioned main solution of the present invention and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed by the present invention. Those skilled in the art, after understanding the solution of the present invention, will realize, based on existing technology and common knowledge, that there are many combinations, all of which are technical solutions to be protected by the present invention; therefore, no exhaustive list is provided here.

[0029] The beneficial effects of this invention are:

[0030] 1. The present invention provides an enhanced mixing correction method for the k-ωSST turbulence model, which considers the influence of the mixing effect of two fluids on the turbulent viscosity coefficient of the k-ωSST turbulence model, greatly improving the prediction accuracy of film cooling efficiency. The error between the k-ωSST turbulence model's predicted film cooling efficiency and the experimental result can be reduced from 40% to less than 8%.

[0031] 2. The k-ωSST turbulence model enhancement mixing correction method of this invention can be applied to the numerical prediction of film cooling problems under subsonic and supersonic flow conditions.

[0032] 3. The k-ωSST turbulence model enhanced mixing correction method of the present invention can be applied to the prediction of film cooling efficiency in the field of aero-engines, and solves the related engineering and technical problems of predicting the mixing of two flows. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the gas film cooling efficiency calculation domain in Embodiment 1 of the present invention;

[0034] Figure 2 This is a partially enlarged schematic diagram of the air film cooling efficiency calculation domain air film orifice in Embodiment 1 of the present invention;

[0035] Figure 3 This is a comparison diagram of the two-dimensional distribution of film cooling efficiency before and after turbulence model correction and experimental results in Embodiment 1 of the present invention;

[0036] Figure 4 This is a comparison chart of the spanwise mean of film cooling efficiency before and after turbulence model correction and experimental results in Embodiment 1 of the present invention;

[0037] Figure 5 This is a comparison chart of the spanwise mean of the film cooling efficiency before and after the turbulence model correction in Embodiment 1 of the present invention with the experimental error. Detailed Implementation

[0038] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0039] It should be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, it should be pointed out that unless otherwise specified, the structures, connections, positional relationships, power source relationships, etc., involved in this invention are all things that those skilled in the art can discover without creative effort based on existing technology.

[0040] Example 1:

[0041] This embodiment discloses an enhanced mixing correction method for the k-ωSST turbulence model suitable for film cooling. The transport equations of the k-ωSST turbulence model include:

[0042] Component transport equations:

[0043]

[0044] Turbulent kinetic energy transport equation:

[0045]

[0046] Specific turbulent kinetic energy dissipation rate transport equation:

[0047]

[0048] The k-ωSST turbulence model enhancement and mixing correction method applicable to film cooling is to use the mixing function C m The turbulent viscosity coefficient μ describes the region with different mixing degrees. t Furthermore, through the turbulent viscosity coefficient μ t Correction was completed for regions with different mixing intensities between the two fluids.

[0049] Specifically, a mixing function C is provided for the k-ωSST turbulence model to describe two fluids in different states. m This is used to improve the prediction of fluid mixing in the mixing region of two fluids. The mixing function C is used... m The turbulent viscosity coefficient μ describes the region with different mixing degrees. tThis allows for correction of regions with different mixing intensities between the two fluids; the more uniform the mixing, the larger the value of the mixing function.

[0050] Turbulent viscosity coefficient:

[0051]

[0052] Mixing function:

[0053]

[0054] Among them, D A Let Sc be the molecular diffusion coefficient of cooling gas A. t Let x be the turbulent Schmidt number. j Let U be the coordinate axis direction in tensor form. j Let k be the velocity in tensor form, k be the turbulent kinetic energy, and μ be the molecular dynamic viscosity coefficient. t P is the turbulent dynamic viscosity coefficient. k P represents the turbulent kinetic energy generation term in the turbulent kinetic energy equation, ω represents the specific turbulent kinetic energy dissipation rate, and F1 is the weighting function describing the converted turbulence model. k ,F1,σ k ,β′,σ ω Both γ and γ can be obtained based on the constants of the turbulence model and the solutions of each transport equation.

[0055] n is the mixing constant, which is related to the densities of the two fluids. In this example, n = 2. The following turbulence model constants and related parameter values ​​are given in this example:

[0056] σ k1 =1.176, σ ω1 =2,σ k2 =1,σ ω2 =1.168, β′=0.075, β=0.0828, γ1=0.556,

[0057] γ2=0.44, Pr t =0.9,Sc t =0.9.

[0058] The enhanced mixing correction method of the k-ωSST turbulence model of the present invention is to modify the component transport based on the original k-ωSST turbulence model. The turbulence transport equations of the original k-ωSST turbulence model are (2) and (3). Based on this, the scheme performs additional calculation of the component transport equation (1) for the two gases cooled by film gas cooling, and uses the modified turbulence viscosity coefficient (4) to perform iterative calculation of all transport equations.

[0059] This embodiment provides the following: Figure 1The fluid domain shown has a Mach number of 0.4 on the high-temperature gas side and a momentum ratio of 0.52 on the low-temperature gas side. The contraction section is 330d long, and the expansion section is 963d long. The contraction and expansion sections are smoothly connected by a 37.5d circular arc. The spanwise width is 13.5d, the inlet channel height is 362.5d, the outlet channel height is 290.7d, the first exhaust film orifice is 66d from the inlet, the film orifices are arranged in a staggered pattern with a spanwise spacing of 3d and a flowwise spacing of 3.5d, the wall thickness where the film orifices are located is 0.67d, the cold gas channel is 88d long, 13.5d wide, and 40d high, where d represents the orifice diameter. There are a total of 10 film orifices. The specific implementation process is as follows:

[0060] Step 1: Given an initial flow field value for the desired flow field domain, including velocity, pressure, density, temperature, composition, turbulent kinetic energy, and specific turbulent kinetic energy dissipation rate.

[0061] Step 2: Calculate the turbulent viscosity coefficient using the turbulent viscosity coefficient equation (4) described in this invention.

[0062] Step 3: Solve the continuity equation, momentum equation, energy equation, and turbulent transport equations (1), (2) and (3) of the turbulent model described in this invention to obtain the solutions to all equations.

[0063] Step 4: Using the solutions of all equations in Step 3, calculate the turbulent viscosity coefficient used in the next iterative calculation using the turbulent viscosity coefficient equation (4) described in this invention.

[0064] Step 5: Use the turbulent viscosity coefficient obtained in Step 4 to solve the equation described in Step 3, and obtain the solution.

[0065] Step 6: Subtract the solution from Step 3 from the solution from Step 5, and calculate the residual.

[0066] Step 7: Define the convergence residual criterion, repeat steps 3 to 6 until the residual in step 6 satisfies the convergence criterion, end the iteration, and output the final solution to the equation.

[0067] Step 8: Obtain the solution from Step 7 and use it for subsequent data processing and related design.

[0068] It should be noted that the initial flow field value described in step one of this embodiment needs to be assigned to every point in the entire flow field domain, and the relevant values ​​can be given by those skilled in the art based on the actual situation.

[0069] like Figure 3 The figure shows a comparison of the film cooling efficiency distributions of the original model, experimental results, and the modified model. Figure 4 The figure shows a comparison of the spanwise mean of film cooling efficiency for the experimental results, the original model, and the modified model. Figure 5The figure shows a comparison between the spanwise mean of film cooling efficiency and the experimental error before and after the turbulence model correction. The results both indicate that the corrected turbulence model significantly improves the prediction of film cooling efficiency.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for enhancing mixing correction in a k-ω SST turbulence model suitable for film cooling, characterized in that, The k-ω SST turbulence model enhancement mixing correction method is achieved through a mixing function. Turbulent viscosity coefficients describing regions with different degrees of mixing Furthermore, through the turbulent viscosity coefficient Corrections were made for regions with different mixing intensities between the two fluids. The mixing function expression is as follows: Where n is the mixing constant, This indicates the mass fraction of cooling gas A in film cooling. This was obtained by solving the component transport equations. Since film cooling involves the mixing of two streams, the other component passes through 1- Calculated; in the unmixed region, Or another component 1- The value tends to 0; Turbulent viscosity coefficient for: Where ρ is the gas density, k is the turbulent kinetic energy, and ω is the specific turbulent kinetic energy dissipation rate.

2. The method for enhancing mixing correction of the k-ω SST turbulence model as described in claim 1, characterized in that, The component transport equation is as follows: in, Let A be the molecular diffusion coefficient of cooling gas A. For turbulent Schmidt number, Velocity in tensor form, The coordinate axes are in tensor form.

3. The method for enhancing mixing correction in the k-ω SST turbulence model as described in claim 1, characterized in that, n takes a value between 1 and 3.

4. The method for enhancing mixing correction of the k-ω SST turbulence model as described in claim 1, characterized in that, The turbulent kinetic energy k and the local specific turbulent kinetic energy dissipation rate ω are calculated by the turbulent kinetic energy transport equation and the specific turbulent kinetic energy dissipation rate transport equation, respectively.

5. The k-ω SST turbulence model enhancement and mixing correction method as described in claim 4, characterized in that, The turbulent kinetic energy transport equation is: The transport equation for the specific turbulent kinetic energy dissipation rate is: in, The coordinate axes are in tensor form. Velocity in tensor form, The viscosity coefficient is the molecular dynamics coefficient. This refers to the turbulent kinetic energy generation term in the turbulent kinetic energy equation. The weighting function describes the converted turbulence model; , , , , and Obtained based on the constants of the turbulence model and the solutions of each transport equation; , These are adjustable empirical constants for the turbulence model. Let be the Prandtl number of the k-equation. Let ω be the Prandtl number of the equation ω.

Images