A prediction method for transition turbulence of an adiabatic wall trans-medium vehicle

Abstract

The present invention proposes a method for predicting transition turbulence of an adiabatic-wall trans-medium vehicle. First, a three-dimensional model of the trans-medium vehicle is established. Based on the three-dimensional model of the trans-medium vehicle, computational grids are created and flow field boundary conditions are applied to obtain a computational model of the trans-medium vehicle. Then, a CFD solver embedded with an improved transition turbulence model is used to solve the flow field of the computational model of the trans-medium vehicle established in step 1 to obtain the transition position. The present invention modifies the local momentum thickness Reynolds number and the transition momentum thickness Reynolds number involved in the boundary layer transition prediction model by introducing a pressure gradient factor, and proposes a model function corrected according to the transition momentum thickness Reynolds number and the Mach number at the boundary layer edge, obtaining a boundary layer transition prediction model suitable for the trans-medium fluid environment, which can provide accurate and efficient boundary layer transition-turbulence prediction for the flow noise control of the trans-medium vehicle to meet the actual engineering requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational fluid dynamics, and in particular relates to a transition turbulence prediction method suitable for an adiabatic wall cross-medium vehicle. Background Art

[0002] An airdrop underwater working robot is a cross-medium vehicle that can quickly reach the marine working area and is widely used in the fields of marine oil exploration, underwater scientific research and target detection. Flow field calculation based on computational fluid dynamics for airdrop underwater working robots is an important means to analyze the working performance of robots, and transition turbulence prediction is an important part of flow field calculation.

[0003] Boundary layer transition is a physical phenomenon widely existing in nature, which describes the transition process from laminar state to turbulent state. When the flow transitions from a stable laminar state to a turbulent state, the physical quantities of the flow will fluctuate violently, thereby affecting the distribution of friction, heat flow, noise, etc. on the surface of the object. For cross-medium vehicles, flow transition will not only affect its resistance performance in the air and underwater cruising stages, but also the flow noise generated by the pressure pulsation in the boundary layer of the transition zone and the pressure pulsation in the turbulent zone at the head of the vehicle will interfere with its underwater sonar detection. Therefore, studying the prediction and control of boundary layer transition is of great significance to improving the performance of cross-medium vehicles.

[0004] With the rapid development of computers, numerical simulation methods have become an important means of studying transitional flows due to their advantages of low cost, short cycle, and freedom from field conditions. Commonly used numerical methods for predicting flow transitions can be divided into four categories: methods based on linear stability theory (LST), parabolic stability equations (PSE), transition criteria, and transition models. Among them, the transition prediction method based on stability theory involves integral operations, which is difficult to apply in simulations involving a large amount of calculations, while the transition criteria are highly dependent on the experience of researchers, and the established transition criteria often lack universality. The transition model represented by the combination of the transition model and the RANS turbulence model cleverly avoids the dependence of the transition empirical formula on non-local variables by using the relationship between the vorticity Reynolds number and the momentum thickness Reynolds number obtained in the Brautius boundary layer. The flow variables in the transition model can be solved locally, so it is easier to parallelize. At the same time, the transition criterion established in the transition model also eliminates the dependence on the researcher's experience, and thus has been widely used in transition flow simulation.

[0005] Traditionally, the prediction of boundary layer transition on the surface of aircraft is mainly carried out in a single medium environment, and there is no effective solution for the prediction of boundary layer transition on the surface of cross-medium aircraft. During the research process, the applicant found that when the mainstream boundary layer transition turbulence model is applied When the model simulates and predicts the boundary layer flow of a trans-medium vehicle, the following problems still exist: First, the existing theory believes that the model function mainly affects the transition length of the boundary layer. Therefore, the model function generally uses fixed values. However, the applicant found that the model function also has a great influence on the transition trigger moment. Moreover, under different Reynolds number conditions, the influence of the model function on the transition trigger moment varies greatly. For a trans-medium vehicle, since it needs to perform transition prediction in environments with a large difference in Reynolds numbers such as underwater and air, therefore, using the traditional fixed-value model function will lead to a large difference between the transition prediction result and the actual situation; Second, the existing relationship of the transition momentum thickness Reynolds number is not sensitive to the pressure gradient, while the flow often has a pressure gradient; in the presence of a pressure gradient, when the transition position is in the adverse pressure region and the favorable pressure region, it will respectively lead to an overestimation and an underestimation of the transition momentum thickness Reynolds number. The above problems in the prior art result in inaccurate transition prediction for trans-medium vehicles, which hinders the development and research of noise prediction and suppression technologies for trans-medium vehicles. Therefore, facing the requirements of the trans-medium working environment, constructing an efficient and accurate transition-turbulence prediction method has important academic value and engineering practical significance. Summary of the Invention

[0006] To solve the problems existing in the prior art, the present invention proposes a transition-turbulence prediction method applicable to an adiabatic wall trans-medium vehicle. This method is based on model. According to the characteristics of the trans-medium working environment, by introducing a pressure gradient factor to modify the local momentum thickness Reynolds number and the transition momentum thickness Reynolds number involved in the model function in the source term of the intermittency factor transport equation (i.e., the boundary layer transition prediction model), considering the pressure gradient information when calculating the model function of the transition prediction, a modified model function is proposed according to the transition momentum thickness Reynolds number and the Mach number at the edge of the boundary layer , avoiding the use of a model function with a fixed value , obtaining a boundary layer transition prediction model applicable to the trans-medium fluid environment, and being able to provide accurate and efficient boundary layer transition-turbulence prediction for the flow noise control of trans-medium vehicles to meet the actual engineering requirements.

[0007] The present invention is realized through the following technical solutions:

[0008] A transition-turbulence prediction method applicable to an adiabatic wall trans-medium vehicle, comprising the following steps:

[0009] Step 1: Establish a three-dimensional model of the cross-media vehicle, create a computational grid based on the three-dimensional model of the cross-media vehicle, and apply flow field boundary conditions to obtain a computational model of the cross-media vehicle;

[0010] Step 2: Use a CFD solver embedded with an improved transition turbulence model to solve the flow field of the computational model of the cross-media vehicle established in Step 1 to obtain the transition position;

[0011] The improved transition turbulence model is obtained through the following process:

[0012] Step 2.1: Based on the transition turbulence model, establish a boundary layer transition prediction model applicable to the cross-media fluid environment

[0013] ∂ (ργ) ∂ t + ∂ (ρ u j γ) ∂ x j = P γ - D γ + ∂ ∂ x j [(μ+ μ t σ f ) ∂ γ ∂ x j ]

[0014] where represents the intermittency factor, represents laminar flow, represents turbulent flow, and when its value is between 0 and 1, it corresponds to the transition process; is the fluid density; is the time; is the coordinate component in the th direction, corresponding to , , directions in the Cartesian coordinate system in sequence; represents the velocity component of the fluid in the th direction, corresponding to directions in the Cartesian coordinate system in sequence; is the dynamic viscosity coefficient, is the turbulent dynamic viscosity coefficient; is a model constant, generally taken as 1; and correspond to the generation source term and destruction source term of the intermittency factor in sequence:

[0015]

[0016]

[0017] where is the modulus of the velocity strain rate tensor, is the modulus of the vorticity, and are model constants, which are respectively , and is the model function; controls the starting position of transition, controls the length of the transition region and the transition triggering moment, controls the destruction source term to remain closed outside the laminar boundary layer and the viscous sublayer of the turbulent boundary layer, and the form is as follows:

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] where , , are all triggering functions related to , is an intermediate variable, is the local momentum thickness Reynolds number, is the transition momentum thickness Reynolds number, is the Mach number at the edge of the boundary layer;

[0025] Step 2.2: According to the boundary layer transition prediction model applicable to the cross-medium fluid environment obtained in Step 2.1, modify the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model to obtain an improved transition turbulence model; the improved transition turbulence model consists of a turbulent kinetic energy transport equation, a turbulent specific dissipation rate transport equation, and a boundary layer transition prediction model applicable to the cross-medium fluid environment (i.e., the intermittency factor transport equation).

[0026] The core innovation point of the above solution is to propose a modified model function based on the transition momentum thickness Reynolds number and the Mach number at the edge of the boundary layer, avoiding the use of a model function with a fixed value , so that the obtained boundary layer transition prediction model is applicable to the cross-medium fluid environment, and accurate transition positions and occurrence times can be obtained in different media.

[0027] Furthermore, in step 2.1, the local momentum thickness Reynolds number is corrected by the local pressure gradient factor to obtain:

[0028]

[0029]

[0030] where is the vorticity Reynolds number, is a function of the local pressure gradient factor .

[0031] Furthermore, the local pressure gradient factor is calculated using the following expression:

[0032]

[0033] where is the local momentum thickness, is the velocity at the boundary layer edge, is the displacement of the fluid element.

[0034] Furthermore, the velocity at the boundary layer edge is calculated according to the formula:

[0035] U e = U ∞ 2 + 2τ τ-1 [1- ( p p ∞ ) (τ-1) / τ ] p ∞ ρ ∞

[0036] where is the velocity of the free stream at infinity; is the density of the free stream at infinity, is the local pressure, is the pressure of the free stream at infinity, is the specific heat ratio.

[0037] Furthermore, in step 2.1, the transition momentum thickness Reynolds number is calculated according to the formula

[0038]

[0039] where is the Mach number at the boundary layer edge, is the turbulence intensity of the incoming flow at infinity, is the pressure gradient factor.

[0040] Furthermore, the Mach number at the edge of the boundary layer is calculated according to the isentropic relation:

[0041] M e = [ 1+(τ-1) / 2 M ∞ 2 (p / p ∞ ) (τ-1) / τ -1] 2 τ-1

[0042] wherein is the Mach number of the far-field incoming flow.

[0043] Furthermore, in step 2.2, the turbulent kinetic energy transport equation is:

[0044]

[0045] wherein is the turbulent kinetic energy, is a model constant, and its value is consistent with that in the original Menter SST turbulence model, and are the modified turbulent kinetic energy production source term and destruction source term:

[0046] ,

[0047] wherein and are respectively the production source term and destruction source term of the turbulent kinetic energy transport equation in the original Menter SST turbulence model.

[0048] Beneficial effects:

[0049] The present invention provides a transition-turbulence prediction method applicable to an adiabatic-wall trans-medium vehicle. The method is based on model. According to the characteristics of the trans-medium fluid environment, by introducing a pressure gradient factor to correct the local momentum thickness Reynolds number and transition momentum thickness Reynolds number involved in the model function in the source term of the intermittency factor transport equation, and considering the influence of the pressure gradient on the transition of the trans-medium fluid environment when calculating the model parameters of the transition prediction, a modified model function is creatively proposed according to the transition momentum thickness Reynolds number and the Mach number at the edge of the boundary layer , so as to obtain a boundary layer transition prediction model applicable to the trans-medium fluid environment, which can provide accurate and efficient boundary layer transition turbulence prediction for the trans-medium vehicle in air and underwater scenarios to meet the actual engineering requirements. Description of the Drawings

[0050] Figure 1Schematic diagram of the forebody model of a body of revolution according to an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of the computational grid and boundary conditions of the forebody of a body of revolution according to an embodiment of the present invention;

[0052] Figure 3 Comparison of the calculation results of the surface pressure coefficient of the forebody of a body of revolution according to an embodiment of the present invention;

[0053] Figure 4 Comparison of the calculation results of the friction drag coefficient on the symmetry plane of the forebody of a body of revolution according to an embodiment of the present invention;

[0054] Figure 5 Comparison of the transition prediction positions using different transition prediction models and experimental data of different flow states of the forebody of a body of revolution according to an embodiment of the present invention at different Reynolds numbers. Detailed implementation manners

[0055] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer and more understandable, and to enable those skilled in the art to better understand the present invention, the present invention will be further described in detail and completely below in conjunction with the accompanying drawings and implementation cases. It should be understood that the specific implementation cases described herein are only used to explain the present invention and are not used to limit the present invention.

[0056] In this embodiment, taking the 4620-3 body of revolution as an example, a transition turbulence prediction method applicable to an adiabatic wall trans-medium vehicle is used to numerically simulate the experimental state of the 4620-3 body of revolution, predict the transition position, and compare it with the experimental results to verify the beneficial effects of the method of the present invention.

[0057] Specifically, a transition turbulence prediction method applicable to an adiabatic wall trans-medium vehicle in this embodiment includes the following steps:

[0058] Step 1: Establish a three-dimensional model of a trans-medium vehicle, create a computational grid based on the three-dimensional model of the trans-medium vehicle and apply flow field boundary conditions to obtain a computational model of the trans-medium vehicle;

[0059] In this embodiment, the three-dimensional model of the trans-medium vehicle is as shown in Figure 1 shown, and the computational grid and flow field boundary conditions are as shown in Figure 2 shown.

[0060] Step 2: Use a CFD solver embedded with an improved transition turbulence model to solve the flow field of the computational model of the trans-medium vehicle established in Step 1 to obtain the transition position.

[0061] The method for obtaining the improved transition turbulence model is: based on the model, according to the characteristics of the trans-medium fluid environment, it is proposed that according to the transition momentum thickness Reynolds number and the Mach number at the edge of the boundary layer Modified model function , and introduce the pressure gradient factor to the intermittency factor Modify the local momentum thickness Reynolds number and transition momentum thickness Reynolds number involved in the model function in the source term of the transport equation (boundary layer transition prediction model), obtain a boundary layer transition prediction model applicable to the trans-medium fluid environment, and then couple it to the Menter SST turbulence model framework to obtain an improved transition turbulence model.

[0062] The establishment process of the improved transition turbulence model is specifically as follows:

[0063] Step 2.1: Based on the transition turbulence model, establish a boundary layer transition prediction model applicable to the trans-medium fluid environment

[0064] ∂ (ργ) ∂ t + ∂ (ρ u j γ) ∂ x j = P γ - D γ + ∂ ∂ x j [(μ+ μ t σ f ) ∂ γ ∂ x j ]

[0065] where represents the intermittency factor, represents laminar flow, represents turbulent flow, and when its value is between 0 and 1, it corresponds to the transition process; is the fluid density; is the time; is the coordinate component in the th direction, corresponds to , , in the Cartesian coordinate system in turn; represents the velocity component of the fluid in the th direction, corresponds to in the Cartesian coordinate system in turn; is the dynamic viscosity coefficient, is the turbulent dynamic viscosity coefficient; is a model constant, generally taken as 1; and correspond to the generation source term and destruction source term of the intermittency factor in turn:

[0066]

[0067]

[0068] where is the modulus of the velocity strain rate tensor, is the modulus of the vorticity, and are model constants, which are respectively , and is the model function; controls the starting position of transition, controls the length of the transition region and the transition triggering moment, controls the destruction source term to remain closed outside the laminar boundary layer and the viscous sublayer of the turbulent boundary layer, and the form is as follows:

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] where , , are all triggering functions related to , is an intermediate variable, is the local momentum thickness Reynolds number, is the transition momentum thickness Reynolds number, is the Mach number at the edge of the boundary layer.

[0076] Local momentum thickness Reynolds number is corrected through the local pressure gradient factor as follows:

[0077]

[0078]

[0079] where is the vorticity Reynolds number, is a function of the local pressure gradient factor .

[0080] Localized pressure gradient factor It is calculated by using the following expression:

[0081]

[0082] Where is the localized momentum thickness, is the velocity at the edge of the boundary layer, is the displacement of the fluid element, is the velocity at the edge of the boundary layer and is the derivative of the displacement of the fluid element with respect to.

[0083] The velocity at the edge of the boundary layer is calculated according to the compressible Bernoulli equation:

[0084] U e = U ∞ 2 + 2τ τ-1 [1- ( p p ∞ ) (τ-1) / τ ] p ∞ ρ ∞

[0085] It is calculated that where is the velocity of the free stream at infinity; is the density of the free stream at infinity, is the local pressure, is the pressure of the free stream at infinity, is the specific heat ratio.

[0086] The transition momentum thickness Reynolds number is calculated according to the formula based on the incoming flow turbulence intensity, the Mach number at the edge of the boundary layer and the pressure gradient factor by using the Simple-AHD criterion :

[0087]

[0088] Where is the Mach number at the edge of the boundary layer, is the incoming flow turbulence intensity at infinity, is the pressure gradient factor.

[0089] The Mach number at the edge of the boundary layer is calculated according to the isentropic relation:

[0090] M e = [ 1+(τ-1) / 2 M ∞ 2 (p / p ∞ ) (τ-1) / τ -1] 2 τ-1

[0091] In the formula, is the Mach number of the incoming flow at infinity.

[0092] In this embodiment, the corrected transitional momentum thickness Reynolds number as the applicable range of the transition criterion is 0.0 ≤ ≤ 1.1, ≤ 1%.

[0093] Step 2.2: According to the boundary layer transition prediction model applicable to the trans-medium fluid environment obtained in Step 2.1, modify the generation source term and destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model to obtain an improved transition turbulence model; the improved transition turbulence model consists of a turbulent kinetic energy transport equation, a turbulent specific dissipation rate transport equation, and a boundary layer transition prediction model applicable to the trans-medium fluid environment.

[0094] Among them, the turbulent kinetic energy transport equation is:

[0095]

[0096] In the formula, is the turbulent kinetic energy, is a model constant, and its value is the same as that in the original Menter SST turbulence model, and are the modified turbulent kinetic energy generation source term and destruction source term:

[0097] ,

[0098] Among them and are respectively the generation source term and destruction source term of the turbulent kinetic energy transport equation in the original Menter SST turbulence model.

[0099] The transport equation of the turbulent specific dissipation rate adopts the form in the original Menter SST turbulence model. Finally, a three-equation improved transition turbulence model is formed. Embedding the improved transition turbulence model into the CFD solver can realize the numerical prediction of the transition turbulent flow field of the trans-medium vehicle.

[0100] In order to verify the transition prediction effect of the above technical solution of the present invention in trans-medium flow, transition model, transition model are selected as controls to simulate the transition turbulent flow field of the 4620-3 body of revolution, and compare with the data published in the literature. The calculation conditions are shown in the following table:

[0101] Table 1. Inflow velocity and Reynolds number conditions for numerical simulation on the 4620-3 body of revolution

[0102]

[0103] Figure 3 Shown is the comparison of the surface pressure coefficient from numerical simulations of different models with the pressure coefficient given in the literature. From Figure 3 it can be seen that the transition model, the transition model, and the results of the pressure coefficient calculated by the method of the present invention are in good agreement with the results given in the literature, initially verifying the reliability of the calculation by the method of the present invention.

[0104] Figure 4 and Figure 5 respectively show the comparison of the surface friction drag coefficient and the transition position on the symmetric plane of the forebody of the 4620-3 body of revolution predicted by three transition models. From the figure, it can be seen that for the fixed of the transition model, due to the too large fixed coefficient, the transition is triggered in advance, so the predicted transition position is the most forward. While the transition model is less affected by the adverse pressure gradient, and the predicted transition positions are generally more backward. The transition position of the method of the present invention is between the transition positions predicted by the above two transition models; Figure 5 The flow states observed at each monitoring point in the experiment are marked above, including laminar state, disturbance wave development state, intermittent state, turbulent state, and the combination of disturbance wave development state and intermittent state and the combination of intermittent state and turbulent state. The numerical simulation results of the method of the present invention are highly consistent with the literature results and the experiment, verifying the high accuracy of the present invention in predicting the boundary layer transition for the cross-medium flow scenario, and can provide accurate and efficient boundary layer transition-turbulence prediction for cross-medium vehicles to meet the actual engineering requirements.

[0105] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall, characterized by: The following steps are involved: Step 1: Establish a three-dimensional model of a cross-media vehicle, create a computational grid based on the three-dimensional model of the cross-media vehicle, and apply flow field boundary conditions to obtain a computational model of the cross-media vehicle; Step 2: Use the CFD solver embedded with the improved transition turbulence model to solve the flow field of the cross-medium vehicle calculation model established in step 1 to obtain the transition position; The improved transition turbulence model is obtained through the following process: Step 2.1: Based on Transition turbulence model, establish boundary layer transition prediction model suitable for cross-medium fluid environment in represents the intermittent factor, represents laminar flow, Indicates turbulence, and its value between 0 and 1 corresponds to the transition process; is the fluid density; For time; For the The coordinate components in the directions, Corresponding to the Cartesian coordinate system , , direction; Indicates that the fluid The velocity components in the directions, Corresponding to the Cartesian coordinate system direction; is the dynamic viscosity coefficient, is the turbulent dynamic viscosity coefficient; is the model constant, generally 1; and They correspond to the generation source term and the destruction source term of the intermittent factor respectively: in is the modulus of the velocity strain rate tensor, is the modulus of vorticity, and are model constants, respectively , and is the model function; Control the starting position of the transition, Control the length of the transition zone and the transition triggering time, The control destruction source term is kept closed outside the laminar boundary layer and the viscous bottom layer of the turbulent boundary layer, and the form is as follows: in , , Both Related trigger functions, is the intermediate variable, is the localized momentum thickness Reynolds number, is the transition momentum thickness Reynolds number, is the Mach number at the edge of the boundary layer; Step 2.2: According to the boundary layer transition prediction model suitable for cross-medium fluid environment obtained in step 2.1, modify the generation source term and destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model to obtain an improved transition turbulence model; the improved transition turbulence model consists of the turbulent kinetic energy transport equation, the turbulent specific dissipation rate transport equation and the boundary layer transition prediction model suitable for cross-medium fluid environment.

2. A method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 1, characterized in that: In step 2.1, the localized momentum thickness Reynolds number By localizing the pressure gradient factor Corrected to get: in is the vorticity Reynolds number, is the localized pressure gradient factor function.

3. A method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 2, characterized in that: Localized pressure gradient factor The calculation is done using the following expression: in is the localized momentum thickness, is the velocity at the edge of the boundary layer, is the displacement of the fluid element.

4. A method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 3, characterized in that: The velocity at the edge of the boundary layer According to the formula: Calculated, where is the speed of the free stream at infinity; is the density of the free flow at infinity, For local pressure, The pressure of the infinite free flow, is the specific heat ratio.

5. The method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 1, characterized in that: In step 2.1, the transition momentum thickness Reynolds number According to the formula Calculated, where is the Mach number at the edge of the boundary layer, is the turbulence of the infinite incoming flow, is the pressure gradient factor.

6. A method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 5, characterized in that: Mach number at the edge of the boundary layer According to the isentropic relationship, we can calculate: In the formula, is the Mach number of the incoming flow at infinite distance, is the specific heat ratio, For local pressure, is the pressure of the free flow at infinity.

7. The method for predicting transition turbulence for a vehicle crossing a medium with an adiabatic wall according to claim 1, characterized in that: In step 2.2, the turbulent kinetic energy transport equation is: In the formula, is the turbulent kinetic energy, is a model constant whose value is consistent with that in the original Menter SST turbulence model. and Generate and destroy source terms for the modified turbulent kinetic energy: ， in and They are respectively the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the original Menter SST turbulence model.

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