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

Abstract

The application discloses a k-epsilon turbulent flow model enhanced mixing correction method suitable for air film cooling, provides a mixing function C for describing two different state fluids for the k-epsilon turbulent flow model m , so as to improve the fluid mixing prediction situation of the mixing area of the two fluids, and corrects the mixing function C m of the turbulent flow viscosity coefficient μ of the different mixing degree areas t , realizes the correction of the different mixing intensity areas of the two fluids, and improves the numerical prediction accuracy of the air film cooling efficiency mixing area.

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 k-ε turbulence models with 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-ε 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 stream. However, this turbulence model is still a two-equation turbulence model and cannot improve the calculation accuracy of the mixing zone of two streams in film cooling. Therefore, this invention proposes an enhanced mixing correction method for the k-ε turbulence model suitable for film cooling, adding an additional scalar transport equation to distinguish between the two streams, resulting in a three-equation turbulence model. The invention patent (CN 113158340 B) discloses a method for correcting the turbulent length scale of the k-ε turbulence model. However, it corrects the turbulent kinetic energy dissipation rate transport equation by adding a source term to the right side. This added source term does not involve the mixing of the two fluids, so it cannot distinguish between the mixing region and the non-mixing region 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-ε turbulence model applicable to 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-ε turbulence model suitable for film cooling, wherein the method involves 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] Blending function C m The 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 The component transport equations are obtained by solving them. Since film cooling involves the mixing of two streams, the other component can be transported via 1-C. A Calculated; and 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 ε is the turbulent kinetic energy dissipation rate.

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

[0016]

[0017] Where D A Let Sc be the molecular diffusion coefficient of cooling gas A. t U is the turbulent Schmidt number. j Let μ be the velocity in tensor form. t is the turbulent viscosity coefficient of the turbulence model.

[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 turbulent kinetic energy dissipation rate ε are calculated by the turbulent kinetic energy transport equation and the turbulent kinetic energy dissipation rate transport equation, respectively.

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

[0021]

[0022] Turbulent kinetic energy dissipation rate transport equation:

[0023]

[0024] Where, x j The coordinate axes are in tensor form, μ is the molecular dynamic viscosity coefficient, and P is the coordinate axis. k C is the turbulent kinetic energy generation term in the turbulent kinetic energy equation. ε1 C ε2 , σ k , σ ε and P k C is obtained based on the constants of the turbulence model and the solutions of each transport equation. ε1 C ε2 σ is an adjustable empirical constant for the turbulence model. k Let σ be the Prandtl number of the k-equation. ε The Prandtl number of the ε equation is given by the Prandtl number. The calculation methods and ranges of the above parameters are well known to those skilled in the art.

[0025] The k-ε turbulence model enhancement and mixing correction method for film cooling disclosed in this invention uses three turbulent transport equations—turbulent kinetic energy transport equation, 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 as a correction method for the viscosity coefficient of the turbulence model. The turbulent viscosity coefficient is required to solve all three turbulent transport equations; that is, the three equations are coupled through the turbulent viscosity coefficient, with the mixing function serving as a weighting function for the coupling relationship between the three equations.

[0026] Furthermore, the method of the present 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.

[0027] 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 that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by the present invention, and will not be exhaustively listed here.

[0028] The beneficial effects of this invention are:

[0029] 1. The method of this invention considers the mixing effect of two fluids on the turbulent viscosity coefficient of the k-ε turbulence model, which greatly improves the prediction accuracy of film cooling efficiency. The error between the predicted film cooling efficiency of the k-ε turbulence model and the experiment can be reduced from more than 30% to less than 20%.

[0030] 2. The method of the present invention can be applied to the numerical prediction of film cooling problems under subsonic and supersonic flow conditions.

[0031] 3. The 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

[0032] Figure 1 This is a schematic diagram of the gas film cooling efficiency calculation domain in Embodiment 1 of the present invention;

[0033] 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;

[0034] 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;

[0035] 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;

[0036] 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

[0037] 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.

[0038] 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.

[0039] Example 1:

[0040] The transport equations for the k-ε turbulence model are as follows:

[0041] Component transport equations:

[0042]

[0043] Turbulent kinetic energy transport equation:

[0044]

[0045] Turbulent kinetic energy dissipation rate transport equation:

[0046]

[0047] This invention discloses a k-ε turbulence model enhancement mixing correction method suitable for film cooling. The k-ε turbulence model enhancement mixing correction method utilizes a mixing function C... m The turbulent viscosity coefficient μ describes the region with different mixing degrees. t This allows for the correction of regions with different mixing intensities between the two fluids.

[0048] Specifically, the k-ε turbulence model describes the mixing function of two fluids in different states, which is used to improve the prediction of fluid mixing in the mixing region of the two fluids. The mixing function describes the increase of turbulent viscosity coefficient in regions with different mixing degrees, thereby correcting regions with different mixing intensities of the two fluids. The more uniform the mixing, the larger the value of the mixing function.

[0049] The turbulent viscosity coefficients of the turbulence model are as follows:

[0050] Turbulent viscosity coefficient:

[0051]

[0052] That is, the mixing function C was used. m As the viscosity coefficient μ in the turbulence model t Corrections.

[0053] Mixing function:

[0054]

[0055] Among them, D A Let Sc be the molecular diffusion coefficient of cooling gas A. t Let x be the turbulent Schmidt number. j U represents the coordinate axis directions 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 ε is the turbulent kinetic energy generation term in the turbulent kinetic energy equation, and ε is the turbulent kinetic energy dissipation rate.

[0056] C ε1 C ε2 , σ k , σ ε and P k All of these can be obtained based on the constants of the turbulence model and the solutions to each transport equation. n is the mixing constant, which is related to the densities of the two fluids; in this example, n = 2.

[0057] This example provides the following turbulence model constants and related parameter values:

[0058] C ε1 =1.44, C ε2 =1.92, σ k =1,σ ε =1.3, C μ =0.09, Pr t =0.9,Sc t =0.9.

[0059] The k-ε turbulence model enhancement and mixing correction method of the present invention is to modify the component transport based on the original k-ε turbulence model. The original k-ε turbulence model has turbulence transport equations (2) and (3). In this scheme, the component transport equation (1) of the two gases cooled by film cooling is calculated in addition to this, and the modified turbulence viscosity coefficient (4) is used to perform iterative calculation of all transport equations.

[0060] 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 length of the contraction section is 330d, and the length of the expansion section is 963d. 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 distance from the first exhaust film hole to the inlet is 66d, the film holes 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 holes are located is 0.67d, the cold air channel is 88d long, 13.5d wide, and 40d high, where d represents the diameter of the film hole, and there are a total of 10 film holes.

[0061] The specific implementation process is as follows:

[0062] Step 1: Given an initial flow field value for the desired flow field domain, including velocity, pressure, density, temperature, composition, turbulent kinetic energy, and turbulent kinetic energy dissipation rate.

[0063] Step 2: Calculate the turbulent viscosity coefficient using the turbulent viscosity coefficient equation (4) described in this invention.

[0064] 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.

[0065] 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.

[0066] Step 5: Use the turbulent viscosity coefficient obtained in Step 4 to solve the equation described in Step 3, and obtain the solution.

[0067] Step 6: Subtract the solution from Step 3 from the solution from Step 5, and calculate the residual.

[0068] 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.

[0069] Step 8: Obtain the solution from Step 7 and use it for subsequent data processing and related design.

[0070] 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.

[0071] 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 5 The 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.

[0072] 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 the mixing correction of a k-ε turbulence model suitable for film cooling, characterized in that, The k-ε 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. Mixing function The 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; and in the unmixed region, Or another component 1- The value tends to 0; Turbulent viscosity coefficient for: Where ρ is the gas density and k is the turbulent kinetic energy. The turbulent kinetic energy dissipation rate.

2. The k-ε turbulence model enhancement and mixing correction method 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, The coordinate axes are in tensor form. Velocity in tensor form, is the turbulent viscosity coefficient of the turbulence model.

3. The k-ε turbulence model enhancement and mixing correction method as described in claim 1, characterized in that, n takes a value between 1 and 3.

4. The k-ε turbulence model enhancement and mixing correction method as described in claim 1, characterized in that, Turbulent kinetic energy k and turbulent kinetic energy dissipation rate The results were obtained by calculation using the turbulent kinetic energy transport equation and the turbulent kinetic energy dissipation rate transport equation, respectively.

5. The k-ε turbulence model enhancement and mixing correction method as described in claim 4, characterized in that, Turbulent kinetic energy transport equation: Turbulent kinetic energy dissipation rate transport equation: in, The coordinate axes are 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. , , , 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 be the Prandtl number of the ε equation.

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