Cross-medium navigation body water outlet numerical simulation method under wave condition

Abstract

According to the cross-medium navigation body water outlet numerical simulation method under the wave condition, fluid-solid coupling of a cross-medium navigation body is processed, solved and calculated on the basis of a BDIM method, and the water outlet process of the cross-medium navigation body under the complex wave condition can be better simulated; a wave generation quantity source item based on a gravity water wave solution is introduced in wave generation, so that the numerical wave generation stability and applicability in a wave environment can be improved, and the numerical simulation precision of large and steep waves is improved while the calculation efficiency is ensured; a two-step projection method is utilized in the solution of the flow field, and the two constructed rough and encrypted grids and a dynamic time step length adjustment strategy are matched, so that the pressure coupling calculation error can be remarkably reduced, and the reliability of a simulation result in engineering application is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid mechanics of water-air amphibious navigation bodies, and in particular relates to a numerical simulation method for a cross-medium navigation body emerging from water under wave conditions. Background Art

[0002] When a cross-media vehicle enters and exits the water, it will undergo strong nonlinear interactions with the surface waves. The surface pressure distribution, posture and other aspects of the vehicle are affected by the wave load and its dynamic evolution characteristics, which in turn affects the motion stability and structural safety of the vehicle. Currently, most studies on the entry and exit processes of cross-media vehicles in this field are based on numerical simulation methods. However, these methods generally have obvious shortcomings when dealing with multi-scale coupling problems. For example, in terms of temporal and spatial scale matching, due to the significant time scale difference between wave field generation and vehicle motion simulation, it is difficult to coordinate them within a unified computational framework. The traditional single time step strategy results in a large consumption of computing resources in the low-frequency wave evolution process, which makes it difficult to meet the high temporal resolution requirements of the water exit transient process. In terms of grid adaptability, due to the order of magnitude difference between the spatial grid scale required for large-scale wave field evolution and the grid required for capturing the fine flow field on the vehicle surface, it is difficult to simultaneously analyze the large-scale wave field evolution and the flow separation in the near-wall region of the vehicle using traditional full-domain or gradient grid systems. In terms of wave-structure coupling, existing empirical interface processing methods are still insufficient to accurately transmit the bidirectional coupling effect between wave pressure fluctuations and vehicle motion. Therefore, how to improve the numerical simulation method of cross-media vehicle exit under wave conditions to improve accuracy and computational efficiency is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0003] In view of this, and in response to the technical problems existing in this field, the present invention provides a numerical simulation method for a cross-medium navigation body emerging from the water under wave conditions, which specifically includes the following steps:

[0004] Step 1: Set the computational domain range and its initial and boundary conditions based on the wave parameters and the vehicle model, and set the computational physical time for wave generation and water discharge respectively; divide the computational domain into the wave-generating area and the working area where the vehicle is located, and construct a coarse grid that meets the wave generation requirements; use the BDIM method to handle the cross-medium vehicle fluid-structure coupling and establish the governing equations for the entire computational domain to calculate the interaction between the wave field and the vehicle;

[0005] Step 2: Introduce the wave-generating momentum source term based on the gravity water wave solution into the governing equation corresponding to the wave-generating area in the computational domain, and use the finite difference method to obtain the discretized governing equation. Determine the discrete time step of wave generation based on the wave velocity and the scale of the coarse grid, and solve the discretized governing equation using the two-step projection method to obtain the fluid velocity field for the next time step.

[0006] Step 3: Use the PLIC-VOF (Piecewise Linear Interface Calculation, piecewise linear interface calculation; Volume of fluids, fluid volume fraction) method combined with a coarse grid to reconstruct the gas-liquid interface shape, and use the fluid velocity field obtained in step 2 to update the wave field volume fraction for the next time step;

[0007] Step 4: By comparing the wave generation calculation physical time with the setting of step 1, the wave field numerical simulation results including volume fraction, flow field velocity and pressure are output or the calculation is repeated in step 2;

[0008] Step 5: Based on the structure of the vehicle and the corresponding accuracy requirements, a refined grid is constructed to meet the requirements of the cross-medium vehicle exit process; the wave field volume fraction, flow field velocity and pressure parameters output in step 4 are linearly interpolated to the refined grid;

[0009] Step 6: Utilize the discretized governing equations combined with the maximum velocity of the flow field to dynamically calculate the discrete time step of the water discharge process simulation, and solve the fluid velocity field for the next time step using the two-step projection method; then, use the PLIC-VOF method combined with the refined grid to reconstruct the gas-liquid interface and update the wave field volume fraction for the next time step;

[0010] Step 7: By comparing the calculated physical time of the water outlet with the setting of step 1, the numerical simulation results of the water outlet multiphase flow including vorticity and Q-vorticity are output or the calculation is repeated in step 5 for recalculation;

[0011] Step 8: Based on the numerical simulation results of the outlet multiphase flow output in step 7, the stable outlet range of the cross-medium navigation body in the working area is optimized.

[0012] Furthermore, step 1 is based on the calculation domain range and its initial and boundary conditions according to the wave wavelength λ, wave height H s , period T, cross-medium navigation body length L, initial water depth h settings; set the wave calculation physical time to t1, the water exit calculation physical time to t2; the wave zone length is set based on the wave wavelength, and when generating the coarse grid, set the wavelength direction grid size Δx≤λ / 40, the wave height direction grid Δz≤H s / 20 to ensure the capture accuracy of the wave interface;

[0013] When dealing with fluid-solid interaction of a cross-medium vehicle based on the BDIM method, the computational domain is first divided into solid subdomains Ω based on the distance function. b , fluid subdomain Ω f and fluid-solid interface subdomain Ω s Then, the control equations of each subdomain are combined into the following control equations of the entire computational domain using the weighted summation of the kernel function: ε :

[0014] M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε ,x,t)+S ε (Φ ε ,x,t)=0

[0015]

[0016] Where x represents the x-axis in the xyz coordinate system, t is time; Φ ε represents physical quantities such as velocity and pressure; ε is the scope of the kernel function, and its value is half of the boundary thickness; symbols b, f, and s correspond to the subdomains divided respectively; B(Φ,x b ,t)=0、F(Φ,x f ,t)=0、S(Φ,x s ,t)=0 are solid subdomain Ω b , fluid subdomain Ω f and fluid-solid interface subdomain Ω s The governing equation, K ε is the integral kernel function corresponding to each subdomain; as shown below:

[0017] B(u)=uU b =0

[0018]

[0019] Where Δt is the time step, u is the flow velocity, U b is the speed of the vehicle, p is the flow field pressure, represents the gradient of the corresponding parameter, F st is the surface tension, g is the acceleration of gravity, ρ and μ are the mixture density and dynamic viscosity respectively, satisfying:

[0020]

[0021] Among them, α w , α g are the volume fractions of liquid and gas phase, respectively;

[0022] For any K ε (x,y) is the integral kernel function, satisfying ∫ Ω K ε (x,y)dy≡1, when xy|>ε, K is satisfied ε (x,y)≡0; To ensure the smoothness and tight support of the kernel function, the integral kernel function can be:

[0023]

[0024] On this basis, based on the assumption that the boundary of the vehicle has no slip, the control equation of the computational domain M is transformed into ε Simplified to the following form:

[0025] M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε , x, t);

[0026] At the same time, considering the compact support of the kernel function, the following simplified form is obtained:

[0027]

[0028] Among them, δ ε is the zero-order moment of the kernel function, that is:

[0029]

[0030] Combined with the value conditions of the integral kernel function, we get:

[0031]

[0032] Where d is the normal distance from the grid point to the fluid-solid boundary and satisfies:

[0033]

[0034] The above equations are combined to obtain the final computational domain control equation:

[0035]

[0036] Here, n represents the time step.

[0037] Furthermore, the following wave-making momentum source term based on the gravity water wave solution is specifically introduced into the control equation:

[0038]

[0039] Where z is the z-axis in the xyz coordinate system, g is the acceleration due to gravity, and a is mn is the amplitude, ω m is the angular frequency, k m is the wave number, θ n is the wave direction, ε mn is the phase; the wave has M frequency components ω and wave number components k, has N different propagation directions θ, and has M×N wave amplitudes a and phases ε;

[0040] When performing finite difference discretization, the convection term in the computational domain control equation is Specifically, the second-order upwind scheme is used to calculate the diffusion term. The central difference method is used, and the surface tension is calculated by the continuous force model. The discrete time step of wave generation is specifically set as:

[0041]

[0042] The execution process of the two-step projection method specifically includes:

[0043] The first step is to remove the pressure term in the computational domain control equation and calculate the velocity u of the previous time step. n Get the estimated speed u*, n+1 :

[0044]

[0045] And based on the pressure Poisson equation, the pressure field p of the next time step is obtained n+1 :

[0046]

[0047] The second step is to correct the estimated velocity field based on the pressure field to obtain the velocity field u of the next time step n+1 :

[0048]

[0049] Furthermore, in step 3, when executing the PLIC-VOF method, the shape of the gas-liquid interface is reconstructed using straight line segments within the grid cells, and the position of the straight line segment and the normal vector n are calculated using the volume fraction α and its gradient:

[0050]

[0051] The volume fraction α is specifically based on the transport equation, combined with the velocity field u of the next time step obtained in step 2. n+1 Perform update calculations:

[0052]

[0053] Wherein, S represents the area; the finite volume method is used to discretely solve the equation.

[0054] Furthermore, step 4 is processed according to one of the following two situations based on the physical time of wave generation calculation:

[0055] Case 1: If the calculation physical time is greater than or equal to the wave-making calculation physical time set in step 1, the wave-making calculation is terminated and the wave field numerical simulation results are output;

[0056] Case 2: If the calculation time is less than the wave generation calculation time set in step 1, then return to step 2. Furthermore, in step 5, the scale of the refined grid is set based on the diameter D of the vehicle as follows:

[0057] Δx=Δy=Δz≤D / 50

[0058] The following trilinear interpolation method is used to linearly interpolate the wave field volume fraction, flow field velocity and pressure parameters to the refined grid:

[0059] Q′(x′ p ,y q ′,z r ′)=(1-α)(1-β)(1-γ)Q i,j,k +α(1-β)(1-γ)Q i+1,j,k n

[0060] +(1-α)β(1-γ)Q i,j+1,k n+αβ(1-γ)Q i+1,j+1,k n+(1-α)(1-β)γQ i,j,k+1 n

[0061] +α(1-β)γQ i+1,j,k+1 n+(1-α)βγQ i,j+1,k+1 n+αβγQ i+1,j+1,k+1

[0062] Among them, Q′ is the interpolation to the encrypted grid point (x′ p ,y q ′,z r ′), α, β, and γ are the normalized relative positions in the x, y, and z directions, respectively, satisfying the following relationship:

[0063]

[0064] Among them, i, j, k are coarse grid node indices, satisfying:

[0065] x i ≤x′ p ≤x i+1 ,y j ≤y q′≤y j+1 ,z k ≤z r ′≤z k+1 .

[0066] Furthermore, the discrete time step Δt2 of the water discharge process simulation in step 6 is specifically calculated using the following formula:

[0067]

[0068] Among them, u, v, and w are the velocity components of the flow field in the x, y, and z directions respectively, and CFL is the Courant number;

[0069] Then, the gas-liquid interface is reconstructed through the same process as steps 2 and 3, and the wave field volume fraction for the next time step is updated and calculated.

[0070] Furthermore, step seven is processed according to one of the following two situations based on the physical time of the water discharge simulation:

[0071] Case 1: If the water-outlet simulation physical time is greater than or equal to the water-outlet calculation physical time set in step 1, the water-outlet numerical simulation of the cross-media vehicle under wave conditions is terminated, and the water-outlet multiphase flow numerical simulation results of the cross-media vehicle are output;

[0072] Case 2: If the numerical simulation calculation physical time is less than the calculation physical time set in step 1, return to step 5.

[0073] The numerical simulation method for the emergence of a cross-media vehicle under wave conditions provided by the present invention processes and solves the fluid-solid coupling of the cross-media vehicle based on the BDIM method, which can better simulate the emergence process of the cross-media vehicle under complex wave conditions; a wave-making momentum source term based on the gravity water wave solution is introduced in wave making, which can improve the stability and applicability of numerical wave making in wave environment, while ensuring the calculation efficiency, and improving the numerical simulation accuracy of large waves and steep waves; the two-step projection method is used in the solution of the flow field, combined with the constructed rough and encrypted grids and the dynamic time step adjustment strategy, which can significantly reduce the pressure coupling calculation error and improve the reliability of the simulation results in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A flow chart of the method provided by the present invention;

[0075] Figure 2 Schematic diagram of optional calculation domain settings in an embodiment of the present invention;

[0076] Figure 3 The vehicle model and fluid-solid boundary grid under the coarse grid in the embodiment of the present invention;

[0077] Figure 4 is the wave gas-liquid interface result simulated under the coarse grid in the embodiment of the present invention;

[0078] Figure 5 is the vehicle model and fluid-solid boundary grid under the encrypted grid in the embodiment of the present invention;

[0079] Figure 6 is the wave gas-liquid interface result after interpolation to the encrypted grid in the embodiment of the present invention;

[0080] Figure 7 It is the simulation result of the position of the vehicle and the multiphase flow parameters at the time of water exit in the embodiment of the present invention. DETAILED DESCRIPTION

[0081] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0082] The present invention provides a numerical simulation method for the emergence of a cross-medium navigation body under wave conditions, such as Figure 1 As shown, the specific steps include:

[0083] Step 1: Set the computational domain range and its initial and boundary conditions based on the wave parameters and the vehicle model, and set the computational physical time for wave generation and water discharge respectively; divide the computational domain into the wave-generating area and the working area where the vehicle is located, and construct a coarse grid that meets the wave generation requirements; use the BDIM method to handle the cross-medium vehicle fluid-structure coupling and establish the governing equations for the entire computational domain to calculate the interaction between the wave field and the vehicle;

[0084] Step 2: Introduce the wave-generating momentum source term based on the gravity water wave solution into the governing equation corresponding to the wave-generating area in the computational domain, and use the finite difference method to obtain the discretized governing equation. Determine the discrete time step of wave generation based on the wave velocity and the scale of the coarse grid, and solve the discretized governing equation using the two-step projection method to obtain the fluid velocity field for the next time step.

[0085] Step 3: Use the PLIC-VOF (Piecewise Linear Interface Calculation, piecewise linear interface calculation; Volume of fluids, fluid volume fraction) method combined with a coarse grid to reconstruct the gas-liquid interface shape, and use the fluid velocity field obtained in step 2 to update the wave field volume fraction for the next time step;

[0086] Step 4: By comparing the wave generation calculation physical time with the setting of step 1, the wave field numerical simulation results including volume fraction, flow field velocity and pressure are output or the calculation is repeated in step 2;

[0087] Step 5: Based on the structure of the vehicle and the corresponding accuracy requirements, a refined grid is constructed to meet the requirements of the cross-medium vehicle exit process; the wave field volume fraction, flow field velocity and pressure parameters output in step 4 are linearly interpolated to the refined grid;

[0088] Step 6: Utilize the discretized governing equations combined with the maximum velocity of the flow field to dynamically calculate the discrete time step of the water discharge process simulation, and solve the fluid velocity field for the next time step using the two-step projection method; then, use the PLIC-VOF method combined with the refined grid to reconstruct the gas-liquid interface and update the wave field volume fraction for the next time step;

[0089] Step 7: By comparing the calculated physical time of the water outlet with the setting of step 1, the numerical simulation results of the water outlet multiphase flow including vorticity and Q-vorticity are output or the calculation is repeated in step 5 for recalculation;

[0090] Step 8: Based on the numerical simulation results of the outlet multiphase flow output in step 7, the stable outlet range of the cross-medium navigation body in the working area is optimized.

[0091] In a preferred embodiment of the present invention, step 1 sets the calculation domain range and its initial conditions and boundary conditions to 1.2λ, 4D, and d+1.75L according to λ=25m, the length of the navigation body L=8m, and the diameter D=1m. The bottom of the navigation body is initially located in the inner area of ​​the cylinder at the bottom of the calculation domain, the initial velocity of the navigation body is 0m / s, the initial water depth is h=12m, the initial velocity field is u=0m / s, and the pressure above the horizontal plane is p=p0=101325Pa, and the pressure below the horizontal plane is p=p0+ρ w g(d+Ly), set the bottom boundary and the surrounding area as solid wall, and set the top as the pressure outlet boundary, such as Figure 2 As shown. Set the wave generation calculation physical time t1 = 30s and the water discharge calculation physical time t2 = 2s. Divide the wave generation area length into 0.2λ and the working area length into λ. Construct a coarse grid with the grid size Δx = λ / 200 in the wavelength direction and Δz = H in the wave height direction. s / 20, the vehicle model and fluid-solid boundary grid under the coarse grid are as follows Figure 3 As shown;

[0092] When dealing with fluid-solid interaction of a cross-medium vehicle based on the BDIM method, the computational domain is first divided into solid subdomains Ω based on the distance function. b , fluid subdomain Ω f and fluid-solid interface subdomain Ω sThen, the control equations of each subdomain are combined into the following control equations of the entire computational domain using the weighted summation of the kernel function: ε :

[0093] M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε ,x,t)+S ε (Φ ε ,x,t)=0

[0094]

[0095] Where x represents the x-axis in the xyz coordinate system, t is the time; ε is the scope of the kernel function, and its value is half of the boundary thickness; the symbols b, f, and s correspond to the subdomains divided respectively; B(Φ,x b ,t)=0、F(Φ,x f ,t)=0、S(Φ,x s ,t)=0 are solid subdomain Ω b , the governing equations of the fluid subdomain Ωf and the fluid-solid interface subdomain Ωs, K ε is the integral kernel function corresponding to each subdomain; as shown below:

[0096] B(u)=uU b =0

[0097]

[0098] Where u is the flow velocity, U b is the speed of the vehicle, p is the flow field pressure, represents the gradient of the corresponding parameter, F st is the surface tension, g is the acceleration due to gravity, ρ m 、μ m are the mixed density and dynamic viscosity respectively, satisfying:

[0099]

[0100] Among them, α w , α g are the volume fractions of liquid and gas phase, respectively;

[0101] For any K ε (x,y) is the integral kernel function, satisfying ∫ Ω K ε (x,y)dy≡1, when xy|>ε, K is satisfied ε(x,y)≡0; To ensure the smoothness and tight support of the kernel function, the integral kernel function can be:

[0102]

[0103] On this basis, based on the assumption that the boundary of the vehicle has no slip, the control equation of the computational domain M is transformed into ε Simplified to the following form:

[0104] M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε , x, t);

[0105] At the same time, considering the compact support of the kernel function, the following simplified form is obtained:

[0106]

[0107] Among them, δ ε is the zero-order moment of the kernel function, that is:

[0108]

[0109] Combined with the value conditions of the integral kernel function, we get:

[0110]

[0111] Where d is the normal distance from the grid point to the fluid-solid boundary and satisfies:

[0112]

[0113] The above equations are combined to obtain the final computational domain control equation:

[0114]

[0115] Here, n represents the time step.

[0116] In a preferred embodiment of the present invention, according to the wave height H s =2a=2.5m, angular frequency ω=1.57rad / s, and the following wave-making momentum source term based on the gravity water wave solution is introduced into the control equation:

[0117]

[0118] Where z is the z-axis in the xyz coordinate system, g is the acceleration due to gravity, and a is mn is the amplitude, ω m is the angular frequency, k mis the wave number, θ n is the wave direction, ε mn is the phase;

[0119] When performing finite difference discretization, the convection term in the computational domain control equation is Specifically, the second-order upwind scheme is used to calculate the diffusion term. The central difference method is used, and the surface tension is calculated by the continuous force model. The discrete time step of wave generation is specifically set as:

[0120]

[0121] The execution process of the two-step projection method specifically includes:

[0122] The first step is to remove the pressure term in the computational domain control equation and calculate the velocity u of the previous time step. n Get the estimated speed u*, n+1 :

[0123]

[0124] And based on the pressure Poisson equation, the pressure field p of the next time step is obtained n+1 :

[0125]

[0126] The second step is to correct the estimated velocity field based on the pressure field to obtain the velocity field u of the next time step n+1 :

[0127]

[0128] In a preferred embodiment of the present invention, when executing the PLIC-VOF method in step 3, the gas-liquid interface shape is reconstructed using straight line segments within the grid cells, and the position of the straight line segment and the normal vector n are calculated using the volume fraction α and its gradient:

[0129]

[0130] The volume fraction α is specifically based on the transport equation, combined with the velocity field u of the next time step obtained in step 2. n+1 Perform update calculations:

[0131]

[0132] Wherein, S represents the area; the finite volume method is used to discretely solve the equation.

[0133] In a preferred embodiment of the present invention, step 4 is specifically processed according to one of the following two situations based on the physical time of wave generation calculation:

[0134] Case 1: If the calculation physical time is greater than or equal to the wave-making calculation physical time t1 = 30s set in step 1, the wave-making calculation is terminated and the wave field numerical simulation results are output;

[0135] Case 2: If the calculation physical time is less than the wave-making calculation physical time t1 = 30s set in step 1, return to step 2.

[0136] For the generated liquid volume fraction field results, Tecplot is used for post-processing, and the liquid volume fraction isosurface C = 0.5 is taken, as shown in Figure 4 shown.

[0137] In a preferred embodiment of the present invention, in step 5, the scale of the encrypted grid is set based on the diameter D of the vehicle: Δx = Δy = Δz = D / 50, and the vehicle model and fluid-solid boundary grid under the encrypted grid are as follows: Figure 5 shown.

[0138] The following trilinear interpolation method is used to linearly interpolate the wave field volume fraction, flow field velocity and pressure parameters to the refined grid:

[0139] Q′(x′ p ,y q ′,z r ′)=(1-α)(1-β)(1-γ)Q i,j,k +α(1-β)(1-γ)Q i+1,j,k n

[0140] +(1-α)β(1-γ)Q i,j+1,k n+αβ(1-γ)Q i+1,j+1,k n+(1-α)(1-β)γQ i,j,k+1 n

[0141] +α(1-β)γQ i+1,j,k+1 n+(1-α)βγQ i,j+1,k+1 n+αβγQ i+1,j+1,k+1

[0142] Among them, Q′ is the interpolation to the encrypted grid point (x′ p ,y q ′,z r ′), α, β, and γ are the normalized relative positions in the x, y, and z directions, respectively, satisfying the following relationship:

[0143]

[0144] Among them, i, j, k are coarse grid node indices, satisfying:

[0145] x i ≤x′ p ≤xi+1 ,y j ≤y q ′≤y j+1 ,z k ≤z r ′≤z k+1 .

[0146] For the interpolated liquid volume fraction field results, Tecplot is used for post-processing, and the liquid volume fraction isosurface C = 0.5 is taken, as shown in Figure 6 shown.

[0147] In a preferred embodiment of the present invention, in step 6, the initial velocity of the vehicle is 12 m / s, and the discrete time step Δt2 of the water exit simulation is specifically calculated using the following formula:

[0148]

[0149] Among them, u, v, and w are the flow field velocity components in the x, y, and z directions respectively, and CFL is the Courant number. To ensure the calculation accuracy of volume fraction transport, CFL can be taken as 0.2.

[0150] Then, the gas-liquid interface is reconstructed through the same process as steps 2 and 3, and the wave field volume fraction for the next time step is updated and calculated.

[0151] In a preferred embodiment of the present invention, step seven is specifically processed according to one of the following two situations based on the physical time of water outlet simulation:

[0152] Case 1: If the water-outlet simulation physical time is greater than or equal to the water-outlet calculation physical time t2 = 2s set in step 1, the water-outlet numerical simulation of the cross-media vehicle under wave conditions is terminated, and the water-outlet multiphase flow numerical simulation results of the cross-media vehicle are output;

[0153] Case 2: If the numerical simulation calculation physical time is less than the calculation physical time t2=2s set in step 1, then return to step 5.

[0154] For the generated liquid volume fraction and velocity field results, Tecplot is used for post-processing to calculate the vorticity and Q vorticity. The liquid volume fraction isosurface C = 0.5, the Q vorticity isosurface Q = 0.25, and the Q vorticity isosurface color band is the vorticity amplitude, as shown in Figure 2. Figure 7 shown.

[0155] It should be understood that the size of the serial numbers of the steps in the embodiment of the present invention does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0156] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A numerical simulation method for a cross-medium vehicle emerging from water under wave conditions, characterized by: The specific steps include: Step 1: Set the computational domain range and its initial and boundary conditions based on the wave parameters and the vehicle model, and set the computational physical time for wave generation and water discharge respectively; divide the computational domain into the wave-generating area and the working area where the vehicle is located, and construct a coarse grid that meets the wave generation requirements; use the BDIM method to handle the cross-medium vehicle fluid-structure interaction and establish the governing equations for the entire computational domain to calculate the interaction between the wave field and the vehicle; Step 2: Introduce the wave-generating momentum source term based on the gravity water wave solution into the governing equation corresponding to the wave-generating area in the computational domain, and use the finite difference method to obtain the discretized governing equation. Determine the discrete time step of wave generation based on the wave velocity and the scale of the coarse grid, and solve the discretized governing equation using the two-step projection method to obtain the fluid velocity field for the next time step. Step 3: Use the PLIC-VOF method combined with the coarse grid to reconstruct the shape of the gas-liquid interface, and use the fluid velocity field of the next time step obtained in step 2 to update the wave field volume fraction of the next time step; Step 4: By comparing the wave generation calculation physical time with the setting of step 1, the wave field numerical simulation results including volume fraction, flow field velocity and pressure are output or the calculation is repeated in step 2; Step 5: Based on the structure of the vehicle and the corresponding accuracy requirements, a refined grid is constructed to meet the requirements of the cross-medium vehicle exit process; the wave field volume fraction, flow field velocity and pressure parameters output in step 4 are linearly interpolated to the refined grid; Step 6: Utilize the discretized governing equations combined with the maximum velocity of the flow field to dynamically calculate the discrete time step of the water discharge process simulation, and solve the fluid velocity field for the next time step using the two-step projection method; then, use the PLIC-VOF method combined with the refined grid to reconstruct the gas-liquid interface and update the wave field volume fraction for the next time step; Step 7: By comparing the calculated physical time of the water outlet with the setting of step 1, the numerical simulation results of the water outlet multiphase flow including vorticity and Q-vorticity are output or the calculation is repeated in step 5 for recalculation; Step 8: Based on the numerical simulation results of the outlet multiphase flow output in step 7, the stable outlet range of the cross-medium navigation body in the working area is optimized.

2. The method according to claim 1, wherein: Step 1: Calculate the scope of the calculation domain and its initial and boundary conditions according to the wave wavelength λ, wave height H s , period T, cross-medium navigation body length L, initial water depth h settings; set the wave calculation physical time to t1, the water exit calculation physical time to t2; the wave zone length is set based on the wave wavelength, and when generating the coarse grid, set the wavelength direction grid size Δx≤λ / 40, the wave height direction grid Δz≤H s / 20 to ensure the capture accuracy of the wave interface; When dealing with fluid-solid interaction of a cross-medium vehicle based on the BDIM method, the computational domain is first divided into solid subdomains Ω based on the distance function. b , fluid subdomain Ω f and fluid-solid interface subdomain Ω s Then, the control equations of each subdomain are combined into the following control equations of the entire computational domain using the weighted summation of the kernel function: ε : M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε ,x,t)+S ε (Φ ε ,x,t)=0 Where x represents the x-axis in the xyz coordinate system, t is time; Φ ε represents velocity or pressure; ε is the scope of the kernel function, and its value is half of the boundary thickness; symbols b, f, and s correspond to the subdomains divided respectively; B(Φ,x b ,t)=0、F(Φ,x f ,t)=0、S(Φ,x s ,t)=0 are solid subdomain Ω b , fluid subdomain Ω f and fluid-solid interface subdomain Ω s The governing equation, K ε is the integral kernel function corresponding to each subdomain; as shown below: B(u)=uU b =0 Where Δt is the time step, u is the flow velocity, U b is the speed of the vehicle, p is the flow field pressure, ▽ represents the gradient of the corresponding parameters, F st is the surface tension, g is the acceleration of gravity, ρ and μ are the mixture density and dynamic viscosity respectively, satisfying: Among them, α w , α g are the volume fractions of liquid and gas phase, respectively; For any K ε (x,y) is the integral kernel function, satisfying ∫ Ω K ε (x,y)dy≡1, when xy|>ε, K is satisfied ε (x,y)≡0; To ensure the smoothness and tight support of the kernel function, the integral kernel function can be: On this basis, based on the assumption that the boundary of the vehicle has no slip, the control equation of the computational domain M is transformed into ε Simplified to the following form: M ε (Φ ε ,x,t)≡B ε (Φ ε ,x,t)+F ε (Φ ε ,x,t); At the same time, considering the compact support of the kernel function, the following simplified form is obtained: Among them, δ ε is the zero-order moment of the kernel function, that is: Combined with the value conditions of the integral kernel function, we get: Where d is the normal distance from the grid point to the fluid-solid boundary and satisfies: The above equations are combined to obtain the final computational domain control equation: Here, n represents the time step.

3. The method according to claim 2, wherein: The following wave-making momentum source term based on the gravity water wave solution is introduced into the governing equation: Where z is the z-axis in the xyz coordinate system, g is the acceleration due to gravity, and a is mn is the amplitude, ω m is the angular frequency, k m is the wave number, θ n is the wave direction, ε mn is the phase; the wave has M frequency components ω and wave number components k, has N different propagation directions θ, and has M×N wave amplitudes a and phases ε; When performing finite difference discretization, the convection term u in the computational domain control equation is n ·▽u n Specifically, a second-order upwind scheme is used to calculate the diffusion term ▽·μ m [▽u n +(▽u n ) T ] uses central difference processing and calculates surface tension through a continuous force model; the discrete time step of wave generation is specifically set to: The execution process of the two-step projection method specifically includes: The first step is to remove the pressure term in the computational domain control equation and calculate the velocity u of the previous time step. n Get the estimated speed u*, n+1 : And based on the pressure Poisson equation, the pressure field p of the next time step is obtained n+1 : The second step is to correct the estimated velocity field based on the pressure field to obtain the velocity field u of the next time step n+1 :

4. The method according to claim 3, wherein: In step 3, when executing the PLIC-VOF method, the shape of the gas-liquid interface is reconstructed using straight line segments within the grid cells, and the position of the straight line segment and the normal vector n are calculated using the volume fraction α and its gradient: The volume fraction α is specifically based on the transport equation, combined with the velocity field u of the next time step obtained in step 2. n+1 Perform update calculations: Wherein, S represents the area; the finite volume method is used to discretely solve the equation.

5. The method according to claim 1, wherein: Step 4 is processed according to one of the following two situations based on the physical time of wave generation calculation: Case 1: If the calculation physical time is greater than or equal to the wave-making calculation physical time set in step 1, the wave-making calculation is terminated and the wave field numerical simulation results are output; Case 2: If the physical calculation time is less than the wave generation calculation physical time set in step 1, return to step 2.

6. The method according to claim 4, wherein: In step 5, the scale of the refined grid is set based on the diameter D of the vehicle as follows: Δx=Δy=Δz≤D / 50 The following trilinear interpolation method is used to linearly interpolate the wave field volume fraction, flow field velocity and pressure parameters to the refined grid: Q′(x′ p ,y q ′,z r ′)=(1-a)(1-b)(1-c)Q i,j,k +α(1-β)(1-γ)Q i+1,j,k n+(1-α)β(1-γ)Q i,j+1,k n+αβ(1-γ)Q i+1,j+1,k n+(1-α)(1-β)γQ i,j,k+1 n+α(1-β)γQ i+1,j,k+1 n+(1-α)βγQ i,j+1,k+1 n+αβγQ i+1,j+1,k+1 Among them, Q′ is the interpolation to the encrypted grid point (x′ p ,y q ′,z r ′), α, β, and γ are the normalized relative positions in the x, y, and z directions, respectively, satisfying the following relationship: Among them, i, j, k are coarse grid node indices, satisfying: x i ≤x′ p ≤x i+1 ,y j ≤y q ′≤y j+1 ,z k ≤z r ′≤z k+1 。 7. The method according to claim 6, wherein: The discrete time step Δt2 of the water discharge process simulation in step 6 is calculated using the following formula: Among them, u, v, and w are the velocity components of the flow field in the x, y, and z directions respectively, and CFL is the Courant number; Then, the gas-liquid interface is reconstructed through the same process as steps 2 and 3, and the wave field volume fraction for the next time step is updated and calculated.

8. The method according to claim 1, wherein: Step 7 is handled according to one of the following two situations based on the physical time of water discharge simulation: Case 1: If the water-outlet simulation physical time is greater than or equal to the water-outlet calculation physical time set in step 1, the water-outlet numerical simulation of the cross-media vehicle under wave conditions is terminated, and the water-outlet multiphase flow numerical simulation results of the cross-media vehicle are output; Case 2: If the numerical simulation calculation physical time is less than the calculation physical time set in step 1, return to step 5.

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