An adaptive turbulence simulation method applicable to flow separation calculations of underwater vehicles

Abstract

This invention discloses an adaptive turbulence simulation method suitable for calculating the flow separation of underwater vehicles, the steps of which are as follows: k‑e The turbulence model stress is remodeled, and the subgrid-scale turbulence stress tensor is obtained through Reynolds stress attenuation. The resolution control function is improved based on the turbulence energy spectrum. The filtering scale coefficients in the resolution control function are calculated, and the magnitude of the resolution control function is further calculated. An adaptive transition between unsteady RANS, LES, and DNS turbulence models is achieved. The adaptive turbulence simulation modeling process is completed. Unsteady calculations are performed on the flow around underwater vehicles. The method of this invention can accurately simulate and predict the flow around underwater vehicles at large angles of attack and flow separation phenomena under relatively coarse computational grids.

Description

Technical Field

[0001] This invention belongs to the field of underwater flow separation technology, specifically relating to an adaptive turbulence simulation method suitable for calculating the flow separation of underwater vehicles. Background Technology

[0002] Underwater vehicles often experience high angles of attack during surfacing or diving, resulting in highly complex hydrodynamic fluid flow processes characterized by strong nonlinearity and multi-scale flow separation. Current semi-empirical methods or steady-state-based computational fluid dynamics (CFD) methods offer limited accuracy in predicting flow separation and calculating hydrodynamic forces, failing to meet the future demands for high reliability, maneuverability, and safety of underwater vehicles. Therefore, developing sophisticated, high-precision calculation methods for underwater vehicle flow separation is crucial for predicting maneuvering motions and ensuring safe operation.

[0003] In underwater vehicle hydrodynamics research, when the Reynolds number exceeds a certain range, the fluid transitions from laminar to turbulent flow. Turbulence contains numerous multi-scale, random vortices, exhibiting strong multi-scale irregularities, dissipation, and diffusion characteristics. Although significant progress has been made in turbulence calculation and prediction over the past century, the reliability and accuracy of calculations still cannot meet design requirements under many extreme conditions, such as highly separated flows. In underwater vehicle hydrodynamic CFD research, high-precision turbulence models are one of the core issues restricting computational accuracy.

[0004] Underwater vehicles are typically large in size, resulting in very high Reynolds numbers (Re) for external flows during operation; for example, some ships have Reynolds numbers exceeding 10⁷. The higher the Reynolds number of turbulent flow, the larger the range of turbulence involved, from the smallest to the largest scale. To effectively describe these complex nonlinear motions at different scales, the requirements for turbulence models increase with the Reynolds number. On the other hand, turbulence itself is a stochastic, unsteady process. The currently dominant Reynolds-averaged (RANS) turbulence simulation method has inherent limitations; it solves for the average of all turbulent scales, thus failing to effectively describe unsteady turbulent structures, leading to poor accuracy and reliability in hydrodynamic calculations during flow separation. Large eddy simulation (LES) is suitable for calculating unsteady flow separation processes, but it requires very fine computational grids near solid walls, resulting in enormous computational resource consumption and making it difficult to apply to the separation flow calculations of large underwater vehicles.

[0005] Significant flow separation occurs in high Reynolds number turbulent flows outside underwater vehicles under conditions such as high angles of attack. Separated flows are a complex phenomenon in fluid mechanics, prevalent in practical engineering problems in navigation, aerospace, shipbuilding, and transportation. Because flow separation significantly impacts the flow characteristics around and the forces acting on an object, long-term research has revealed that steady-state RANS methods have poor accuracy in calculating separation phenomena and their flow characteristics, while the Large Eddy Simulation (LES) method consumes excessive computational resources, severely hindering the refined development of hydrodynamics for underwater vehicles.

[0006] Due to the inherent structural characteristics of submarines, the surrounding flow is highly complex. Horseshoe vortices inevitably form at the junction of the main body and appendages. The formation of these vortices induces three-dimensional boundary layer separation at the junction, which in turn further intensifies the horseshoe vortices. Furthermore, horseshoe vortices at the conning tower and stern rudder propagate downstream, significantly impacting the wake. The three-dimensional flow field information surrounding the submarine, particularly the presence of separated vortices, is crucial to its performance. These vortex systems exhibit strong unsteady, pulsating characteristics, necessitating the development of high-precision, efficient turbulence simulation methods suitable for the complex separated flows of underwater vehicles. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, the present invention aims to provide an adaptive turbulence simulation method suitable for calculating the flow separation of underwater vehicles, thereby solving the problems of poor calculation accuracy or excessively high calculation costs in existing turbulence simulation technologies. The method of the present invention can accurately simulate and predict the flow around underwater vehicles at large angles of attack and flow separation phenomena under relatively coarse computational grids (approximately 7 million grids).

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] An adaptive turbulence simulation method for calculating the flow separation of underwater vehicles, as described in this invention, comprises the following steps:

[0010] 1) The stress in the k-ε turbulence model is remodeled, and the subgrid-scale turbulence stress tensor is obtained through Reynolds stress attenuation. in, For Reynolds stress, For the turbulent stress tensor, F r This is the resolution control function;

[0011] 2) Improved resolution control function F based on turbulent energy spectrum r The improved resolution control function F is obtained. r * The improved resolution control function F r* It includes three turbulence scales: the integral length scale L i Filtering scale L c and Kolmogorov length scale L k ;

[0012] 3) Correct the mainstream free turbulence model for the WALE subgrid stress model, and then calculate the filter scale coefficient C in the resolution control function in step 2). x And further calculate the size of the resolution control function;

[0013] 4) As the size of the three turbulence scales in step 2) changes, the resolution control function in step 2) is adaptively adjusted to achieve an adaptive transition between the unsteady RANS, LES and DNS turbulence modes.

[0014] 5) Using partially solvable numerical simulation methods and finite numerical scaling methods, The form is simplified to Where μ t sub The modified turbulent viscosity coefficient is based on the improved resolution control function F in step 2). r * This will enable the realization of the turbulent viscosity coefficient μ in the k-ε turbulence model. t RANS The model is remodeled to complete the adaptive turbulence simulation modeling process;

[0015] 6) Perform unsteady calculations on the flow of underwater vehicles.

[0016] Further, the expression for the resolution control function in step 1) is:

[0017]

[0018] In the formula, β-O(10 -3 nO(1) are constant parameters of the model, Δ is the mesh scale, and L is the model size. k The Kolmogorov length scale is defined as follows:

[0019] L k =ν 3 / 4 / ε 1 / 4

[0020] Where ε is the turbulent kinetic energy dissipation rate and ν is the molecular kinetic viscosity coefficient.

[0021] Furthermore, step 2) is based on the resolution control function F improved by the turbulent energy spectrum. r * The expression is:

[0022]

[0023] Assuming the resolution control function F in step 1) r This is applicable to the inertial sub-region scale, combined with the improved resolution control function F. r * And it is necessary to ensure that the improved resolution control function F r * ∈[0,1], the improved resolution control function F r * The expression is as follows:

[0024]

[0025] Where n = 2 and β = 0.002 are model constants, L i L c and L k These are the integration length scale, the filtering scale, and the Kolmogorov length scale, respectively, and their expressions are as follows:

[0026] L c =C x (Δ x Δ y Δ z ) 1 / 3

[0027] L i =k 3 / 2 / ε

[0028] L k =ν 3 / 4 / ε 1 / 4

[0029] Where, Δ x ,Δ y ,Δ z ε represents the grid size in the x, y, and z directions, respectively; k is the turbulent kinetic energy; ε is the turbulent kinetic energy dissipation rate; and ν is the molecular kinetic viscosity coefficient.

[0030] Furthermore, the filtering scale coefficient C in step 3) x The expression is:

[0031]

[0032]

[0033] Where the subscripts i, j = 1, 2, C wale =0.21 and C limiter =2.0 is the model constant, S ij and These are the unscented parts of the strain rate tensor and the velocity gradient tensor, respectively.

[0034] Furthermore, the adaptive transition between different turbulence modes in step 4) specifically involves:

[0035] When the resolution control function F r * When the magnitude of F approaches 1, unsteady RANS models dominate, and most turbulence is simulated using a realizable k-ε turbulence model; when the resolution control function F... r * As the mesh size gradually decreases, the proportion of unsteady RANS mode gradually decreases, while the proportion of DNS mode gradually increases. At this point, reverting to LES mode increases the proportion of direct solution; when the resolution control function F... r * As the value approaches 0, the DNS mode becomes dominant, and the turbulence is almost entirely solved directly.

[0036] Furthermore, step 5) can realize the turbulent viscosity coefficient μ in the k-ε turbulence model. t RANS The solution is:

[0037] μ t RANS =ρC μ k 2 / ε

[0038] Where ρ is the fluid density, k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, and C... μ =0.09 is the model constant for realizing the k-ε turbulence model;

[0039] For the turbulent viscosity coefficient μ in the k-ε turbulence model t RANS The modifications were made, and the modified turbulent viscosity coefficient μ t sub The expression is:

[0040] μ t sub =F r ρC μ k 2 / ε.

[0041] Further, step 6) specifically involves: using the modified turbulent viscosity coefficient μ t sub Unsteady numerical simulations were performed on the flow around and flow separation process of underwater vehicles at high angles of attack.

[0042] The beneficial effects of this invention are:

[0043] This invention proposes a method to modify the mainstream free turbulence model for the WALE subgrid stress model, and further develops a new method for calculating the filter scale coefficient in the resolution control function. Based on the k-ε turbulence model framework, it realizes the model construction for adaptive turbulence simulation. This invention can accurately capture the fine details of the flow field during the flow separation process of underwater vehicles while significantly saving computational resources, and accurately predict the separation characteristics of the boundary layer. It can be used for the refined design, development and performance optimization of underwater vehicles, and solve navigation-related engineering and technical problems. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention.

[0045] Figure 2 A comparison chart showing the calculated and experimental results of the pressure coefficient along the centerline of an underwater vehicle at zero angle of attack.

[0046] Figure 3 This is a schematic diagram of the limiting streamlines during the predicted flow separation of an underwater vehicle under a 60° angle of attack condition.

[0047] Figure 4 This is a schematic diagram of the streamlines of the cross section during the predicted flow separation of an underwater vehicle under a 60° angle of attack condition. Detailed Implementation

[0048] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0049] Reference Figure 1 As shown, the present invention provides an adaptive turbulence simulation method for calculating the flow separation of underwater vehicles, comprising the following steps:

[0050] 1) The stress in the k-ε turbulence model is remodeled, and the subgrid-scale turbulence stress tensor is obtained through Reynolds stress attenuation. in, For Reynolds stress, For the turbulent stress tensor, F r This is the resolution control function;

[0051] The expression for the resolution control function in step 1) is as follows:

[0052]

[0053] In the formula, β-O(10 -3 ), nO(1) are constant parameters of the model, Δ is the mesh scale (truncation length scale), L k The Kolmogorov length scale is defined as follows:

[0054] L k =v 3 / 4 / ε 1 / 4

[0055] Where ε is the turbulent kinetic energy dissipation rate and ν is the molecular kinetic viscosity coefficient.

[0056] 2) Improved resolution control function F based on turbulent energy spectrum r The improved resolution control function F is obtained. r * The improved resolution control function F r * It includes three turbulence scales: the integral length scale L i Filtering scale L c and Kolmogorov length scale L k ;

[0057] In step 2), the resolution control function F is based on the improved turbulent energy spectrum. r * The expression is:

[0058]

[0059] Assuming the resolution control function F in step 1) r This is applicable to the inertial sub-region scale, combined with the improved resolution control function F. r * And it is necessary to ensure that the improved resolution control function F r * ∈[0,1], the improved resolution control function F r * The expression is as follows:

[0060]

[0061] Where n = 2 and β = 0.002 are model constants, L i L c and L k These are the integration length scale, the filtering scale, and the Kolmogorov length scale, respectively, and their expressions are as follows:

[0062] L c =C x (Δ x Δ y Δ z ) 1 / 3

[0063] L i =k 3 / 2 / ε

[0064] L k =ν 3 / 4 / ε 1 / 4

[0065] Where, Δ x ,Δ y ,Δ z ε represents the grid size in the x, y, and z directions, respectively; k is the turbulent kinetic energy; ε is the turbulent kinetic energy dissipation rate; and ν is the molecular kinetic viscosity coefficient.

[0066] 3) Correct the mainstream free turbulence model for the WALE subgrid stress model, and then calculate the filter scale coefficient C in the resolution control function in step 2). x And further calculate the size of the resolution control function;

[0067] Among them, the filter scaling coefficient C in step 3) x The expression is:

[0068]

[0069]

[0070] Where the subscripts i, j = 1, 2, C wale =0.21 and C limiter =2.0 is the model constant, S ij and These are the unscented parts of the strain rate tensor and the velocity gradient tensor, respectively.

[0071] 4) As the size of the three turbulence scales in step 2) changes, the resolution control function in step 2) is adaptively adjusted to achieve an adaptive transition between the unsteady RANS, LES and DNS turbulence modes.

[0072] Specifically, the adaptive transition between different turbulence modes in step 4) is as follows:

[0073] When the resolution control function F r * When the magnitude of F approaches 1, unsteady RANS models dominate, and most turbulence is simulated using a realizable k-ε turbulence model; when the resolution control function F... r * As the mesh size gradually decreases, the proportion of unsteady RANS mode gradually decreases, while the proportion of DNS mode gradually increases. At this point, reverting to LES mode increases the proportion of direct solution; when the resolution control function F... r * As the value approaches 0, the DNS mode becomes dominant, and the turbulence is almost entirely solved directly.

[0074] 5) Using partially solvable numerical simulation methods and finite numerical scaling methods, The form is simplified to Where μ t sub The modified turbulent viscosity coefficient is based on the improved resolution control function F in step 2). r * This will enable the realization of the turbulent viscosity coefficient μ in the k-ε turbulence model. t RANS The model is remodeled to complete the adaptive turbulence simulation modeling process;

[0075] In step 5), the turbulent viscosity coefficient μ in the k-ε turbulence model can be realized. t RANS The solution is:

[0076] μ t RANS =ρC μ k 2 / ε

[0077] Where ρ is the fluid density, k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, and C... μ =0.09 is the model constant for realizing the k-ε turbulence model;

[0078] For the turbulent viscosity coefficient μ in the k-ε turbulence model t RANS The modifications were made, and the modified turbulent viscosity coefficient μ t sub The expression is:

[0079] μ t sub =F r ρC μ k 2 / ε.

[0080] 6) Use the modified turbulent viscosity coefficient μ t sub Unsteady numerical simulations were performed on the flow around and flow separation process of underwater vehicles at high angles of attack.

[0081] Example 1:

[0082] To address the problem of flow around and flow separation at large angles of attack for underwater vehicles, a submarine model was selected to establish a three-dimensional computational domain, which was divided into a structured computational mesh with a total of approximately 7 million meshes. The computational conditions were set with angles of attack α = 0° and α = 60°, and water as the fluid medium. Boundary conditions were set with a velocity inlet and a pressure outlet. The submarine surface was set as a solid wall with no slip boundary conditions.

[0083] After steps 1) to 6) above, the turbulent viscosity coefficient μ, modified using the resolution control function, is obtained. t sub The calculations were performed using computational fluid dynamics software, and the following results were obtained:

[0084] Figure 2 The horizontal axis represents the dimensionless axial length of the underwater vehicle, and the vertical axis represents the calculated centerline pressure coefficient C of the underwater vehicle. p When the angle of attack α = 0°, the calculation results are in good agreement with the experimental data. The results of this invention can effectively predict the flow problems of underwater vehicles.

[0085] Figure 3 and Figure 4 The method described above was used to simulate the flow field characteristics of underwater vehicles at high angles of attack.

[0086] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. An adaptive turbulence simulation method suitable for calculating the flow separation of underwater vehicles, characterized in that, The steps are as follows: 1) The stress in the k-ε turbulence model is remodeled, and the subgrid-scale turbulence stress tensor is obtained through Reynolds stress attenuation. in, For Reynolds stress, For the turbulent stress tensor, F r This is the resolution control function; 2) Improved resolution control function F based on turbulent energy spectrum r The improved resolution control function F is obtained. r * The improved resolution control function F r * It includes three turbulence scales: the integral length scale L i Filtering scale L c and Kolmogorov length scale L k ; 3) Correct the mainstream free turbulence model for the WALE subgrid stress model, and then calculate the filter scale coefficient C in the resolution control function in step 2). x And further calculate the size of the resolution control function; 4) As the size of the three turbulence scales in step 2) changes, the resolution control function in step 2) is adaptively adjusted to achieve an adaptive transition between the unsteady RANS, LES and DNS turbulence modes. 5) Using partially solvable numerical simulation methods and finite numerical scaling methods, The form is simplified to Where μ t sub The modified turbulent viscosity coefficient is based on the improved resolution control function F in step 2). r * This will enable the realization of the turbulent viscosity coefficient μ in the k-ε turbulence model. t RANS The model is remodeled to complete the adaptive turbulence simulation modeling process; 6) Perform unsteady calculations on the flow of underwater vehicles.

2. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 1, characterized in that, The expression for the resolution control function in step 1) is: In the formula, β-O(10 -3 nO(1) are constant parameters of the model, Δ is the mesh scale, and L is the model size. k The Kolmogorov length scale is defined as follows: L k =n 3 / 4 / e 1 / 4 Where ε is the turbulent kinetic energy dissipation rate and ν is the molecular kinetic viscosity coefficient.

3. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 2, characterized in that, Step 2) is based on the resolution control function F improved by the turbulent energy spectrum. r * The expression is: Assuming the resolution control function F in step 1) r This is applicable to the inertial sub-region scale, combined with improved resolution control. function F r * And it is necessary to ensure that the improved resolution control function F r * ∈[0,1], the improved resolution control function F r * The expression is as follows: Where n = 2 and β = 0.002 are model constants, L i L c and L k These are the integration length scale, the filtering scale, and the Kolmogorov length scale, respectively, and their expressions are as follows: L c =C x (D x D y D z ) 1 / 3 L i =k 3 / 2 / e L k =n 3 / 4 / e 1 / 4 Where, Δ x ,Δ y ,Δ z ε represents the grid size in the x, y, and z directions, respectively; k is the turbulent kinetic energy; ε is the turbulent kinetic energy dissipation rate; and ν is the molecular kinetic viscosity coefficient.

4. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 3, characterized in that, The filter scaling coefficient C in step 3) x The expression is: Where the subscripts i, j = 1, 2, C wale =0.21 and C limiter =2.0 is the model constant, S ij and These are the unscented parts of the strain rate tensor and the velocity gradient tensor, respectively.

5. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 4, characterized in that, The adaptive transition between different turbulence modes in step 4) specifically involves: When the resolution control function F r * When the magnitude of F approaches 1, unsteady RANS models dominate, and most turbulence is simulated using realizable k-ε turbulence models; when the resolution control function F... r * As the mesh size gradually decreases, the proportion of unsteady RANS mode gradually decreases, while the proportion of DNS mode gradually increases. At this point, reverting to LES mode increases the proportion of direct solution; when the resolution control function F... r * As the value approaches 0, the DNS mode becomes dominant, and the turbulence is almost entirely solved directly.

6. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 5, characterized in that, In step 5), the turbulent viscosity coefficient μ in the k-ε turbulence model can be realized. t RANS The solution is: m t RANS =ρC μ k 2 / e Where ρ is the fluid density, k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, and C... μ =0.09 is the model constant for realizing the k-ε turbulence model; For the turbulent viscosity coefficient μ in the k-ε turbulence model t RANS The modifications were made, and the modified turbulent viscosity coefficient μ t sub The expression is: μ t sub =F r ρC μ k 2 / ε。 7. The adaptive turbulence simulation method for underwater vehicle flow separation calculation according to claim 6, characterized in that, Step 6) specifically involves: using the modified turbulent viscosity coefficient μ t sub Unsteady numerical simulations were performed on the flow around and flow separation process of underwater vehicles at high angles of attack.

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