GKS turbulence transition calculation method based on extended Maxwell velocity distribution function

Abstract

The invention discloses a GKS turbulence transition calculation method based on an expanded Maxwell velocity distribution function, and belongs to the technical field of turbulence numerical calculation. The method comprises the following steps of: 1, adding an internal energy item of equivalent turbulent energy into a Maxwell velocity distribution function, and constructing an expanded Maxwell velocity distribution function; 2, selecting a turbulence transition model according to different incoming flow conditions and calculation model appearances, and calculating source items; according to the method, the GKS method is expanded and applied to simulation calculation of hypersonic turbulence transition, the internal energy item of equivalent turbulent energy is added into the Maxwell velocity distribution function, the expanded Maxwell velocity distribution function is constructed only by adding the turbulent energy item into the Maxwell velocity distribution function according to the expanded GKS calculation method for transition and turbulence, and the calculation efficiency is improved. And a turbulence transition model is combined to calculate a source item, so that a new expansion algorithm can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical calculation of turbulence, and specifically to a GKS turbulent transition calculation method based on an extended Maxwell velocity distribution function. Background Technique

[0002] Hypersonic flows are often accompanied by turbulent transitions. The aerodynamic heating and frictional drag in the turbulent flow regime are much higher than those in the laminar flow regime, which makes hypersonic flight in the turbulent flow regime require more fuel consumption and makes the design of the thermal protection system more difficult. Such an engineering background makes it particularly crucial to accurately calculate and predict the three flow regimes of laminar flow, turbulent flow, and transition in hypersonic CFD calculations.

[0003] Generally speaking, the laminar flow calculation method is relatively accurate and reliable; while the calculations of turbulent flow and transition have great uncertainties, which pose great challenges and difficulties to the commonly used RANS algorithm in general engineering. The traditional RANS algorithm has not perfected the physical mechanism of energy transport from the turbulent pulsating field to the mean field in its calculation system, and has not coupled molecular motion and vortex motion in the same velocity distribution function. Therefore, a GKS turbulent transition calculation method based on an extended Maxwell velocity distribution function is proposed. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art. For this reason, an object of the present invention is to propose a GKS turbulent transition calculation method based on an extended Maxwell velocity distribution function.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A GKS turbulent transition calculation method based on an extended Maxwell velocity distribution function, comprising the following steps;

[0007] Step 1: Add an internal energy term of equivalent turbulent kinetic energy to the Maxwell velocity distribution function to construct an extended Maxwell velocity distribution function;

[0008] Step 2: Select a turbulent transition model according to different oncoming flow conditions and the shape of the calculation model, and calculate the source term;

[0009] Step 3: Couple the extended Maxwell velocity distribution function and the source term of the turbulent transition model into the GKS calculation framework for numerical calculation.

[0010] As a further optimized solution of the present invention, in Step 2, it is divided into four calculation conditions of Run7, Run8, Run18, and Run21 respectively.

[0011] As a further optimized solution of the present invention, in step three, a three-dimensional semi-model shape is adopted for the calculation, and the number of grids is 200×100×25. Among them, 200 grid points are arranged in the flow direction, 100 grid points are arranged in the normal direction, 25 grid points are arranged in the circumferential direction, and the distance from the first layer of the wall surface is 1×10 -6 m.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] The present invention expands the GKS method and applies it to the simulation calculation of hypersonic turbulent transition. By adding the internal energy term of the equivalent turbulent kinetic energy to the Maxwell velocity distribution function, for the extended GKS calculation method of transition and turbulence, only the turbulent kinetic energy term needs to be added to the Maxwell velocity distribution function, constructing an extended Maxwell velocity distribution function, and combining with the turbulent transition model to calculate the source term, then a new extended algorithm can be obtained.

[0014] In the present invention, under the condition that the overall framework remains unchanged and the amount of code modification is small, the calculation program of the extended algorithm can be completed, so that the GKS calculation method based on the Maxwell velocity distribution function can more conveniently handle a certain non-conserved physical quantity that may play a dominant role in hypersonic flows. Description of the Drawings

[0015] Figure 1 It is the incoming flow condition diagram in the Run7 state of the present invention;

[0016] Figure 2 It is the incoming flow condition diagram in the Run8 state of the present invention;

[0017] Figure 3 It is the incoming flow condition diagram in the Run18 state of the present invention;

[0018] Figure 4 It is the incoming flow condition diagram in the Run21 state of the present invention;

[0019] Figure 5 It is the comparison diagram of the surface heat flux distribution in Run8 of the present invention;

[0020] Figure 6 It is the surface heat flux distribution diagram in Run18 of the present invention;

[0021] Figure 7 It is the surface heat flux distribution diagram in Run21 of the present invention. Detailed Embodiments

[0022] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0023] The present invention provides a technical solution:

[0024] Based on the GKS turbulent transition calculation method of the extended Maxwell velocity distribution function, applying the extended Maxwell distribution function, starting from the mesoscopic level, a turbulent numerical calculation method with a clearer physical image and higher simulation accuracy is developed. It includes the following steps;

[0025] Step 1: Add an internal energy term of equivalent turbulent kinetic energy to the Maxwell velocity distribution function to construct an extended Maxwell velocity distribution function;

[0026] Step 2: Select a suitable turbulent transition model according to different incoming flow conditions and the shape of the calculation model, and calculate the source term;

[0027] Specifically, it is divided into four calculation conditions: Run7, Run8, Run18, and Run21. The incoming flow conditions are as shown in the attached Figure 1 - attached Figure 4 as shown.

[0028] Step 3: Couple the extended Maxwell velocity distribution function and the source term of the turbulent transition model into the GKS calculation framework for numerical calculation.

[0029] Specifically, the calculation uses a three-dimensional semi-model shape, and the number of grids is 200×100×25. Among them, 200 grid points are arranged in the flow direction, 100 grid points are arranged in the normal direction, 25 grid points are arranged in the circumferential direction, and the distance from the first layer of the wall surface is 1×10 -6 m.

[0030] The comparison of the wall heat flux under the Run8 condition is as shown in the attached Figure 5 as shown. It can be clearly seen that in the calculation mode of tight coupling of turbulent kinetic energy, the peak value of the heat flux after transition obtained by the GKS transition calculation method can better match the experimental value. And in the laminar flow stage before transition, the heat flux can also better match the experimental value, indicating that this method has good applicability for hypersonic transition calculation.

[0031] For the calculation states Run18 and Run21 with an incoming flow Mach number of 10, the calculation results are as shown in the attached Figure 6 and 7 as shown.

[0032] In four computational states, the extended GKS method can accurately simulate the transition starting position and the peak heat flux after transition during the transition process, and can accurately predict the heat flux change during the transition process.

[0033] The calculation results show that the GKS turbulent kinetic energy coupling method can well calculate hypersonic turbulence and transitional flow. For the separation zone, the prediction of the peak pressure and heat flux is in good agreement with the experimental values, with high accuracy. The turbulent kinetic energy coupling GKS algorithm can effectively improve the pressure overshoot problem, greatly improve the heat flux prediction accuracy, and more accurately predict the size of the separation bubble.

[0034] In summary, the calculation results show that the GKS turbulent kinetic energy coupling method can well calculate hypersonic turbulence and transitional flow. For the separation zone, the prediction of the peak pressure and heat flux is in good agreement with the experimental values, with high accuracy. Especially in the calculation example of a compression corner with shock-turbulent boundary layer interference, the turbulent kinetic energy coupling GKS algorithm can effectively improve the pressure overshoot problem, greatly improve the heat flux prediction accuracy, and more accurately predict the size of the separation bubble.

[0035] The main difference between the extended GKS method coupled with turbulent kinetic energy and the uncoupled algorithm lies in the way of introducing turbulent kinetic energy. First, in the extended GKS method, an internal energy term representing equivalent turbulent kinetic energy is added to the extended Maxwell velocity distribution function, coupling the vortex motion representing turbulent kinetic energy with molecular motion, and improving the physical mechanism of energy transport from the turbulent pulsating field to the mean field. Compared with the physical process of one-way energy transport from the mean field to the pulsating field expressed in the uncoupled algorithm, the coupled extended GKS method is more in line with the real physical picture. The present invention does not require overly demanding grids, can save computing resources, and increase computing efficiency. This method currently shows high accuracy and has great development potential in the prediction and simulation of hypersonic turbulent transition flows.

[0036] Parts not involved in the present invention are the same as or can be implemented using existing technologies. Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. The GKS turbulence transition calculation method based on the extended Maxwell velocity distribution function is characterized by: The steps include: Step 1: Add the internal energy term of equivalent turbulent kinetic energy to the Maxwell velocity distribution function to construct the extended Maxwell velocity distribution function; Step 2: According to different incoming flow conditions and calculation model shapes, select the turbulent transition model and calculate the source term; Step 3: Couple the extended Maxwell velocity distribution function and turbulent transition model source term into the GKS computational framework for numerical calculation.

2. The GKS turbulence transition calculation method based on the extended Maxwell velocity distribution function according to claim 1, characterized in that: In step 2, the calculation conditions are divided into four: Run7, Run8, Run18, and Run21.

3. The GKS turbulent transition calculation method based on the extended Maxwell velocity distribution function according to claim 1, characterized in that: In step 3, the calculation adopts the three-dimensional half-mold shape, the grid volume is 200×100×25, among which 200 grid points are arranged in the flow direction, 100 grid points are arranged in the normal direction, and 25 grid points are arranged in the circumferential direction. The first layer wall distance is 1×10 -6 m.

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