Response prediction method for ventilation supercavity flow pattern in navigation depth change process

Abstract

The invention discloses a response prediction method for a ventilation supercavity flow pattern in a navigation depth change process. The method comprises the following steps: step 1, constructing a mathematical model; 2, on the basis of the mathematical model, boundary condition setting and mesh generation are carried out on the watershed of the aircraft, and a numerical calculation model is obtained; 3, verifying the numerical calculation model to obtain a ventilation supercavitation numerical calculation model suitable for the variable navigation depth condition; and 4, based on the supercavitation numerical calculation model, performing simulation calculation on the ventilation supercavitation flow field under the variable navigation depth condition to obtain a simulation result. According to the response prediction method for the ventilation supercavity flow pattern in the navigation depth change process, the problem that the flow pattern change and response of the cavity in the navigation depth dynamic change process of the supercavity vehicle cannot be predicted in the prior art is solved.

Description

Technical Field

[0001] This invention belongs to the field of supercavitating vehicle cavitation flow pattern prediction technology, specifically relating to a method for predicting the response of ventilated supercavitating flow patterns during changes in navigation depth. Background Technology

[0002] Supercavitating vehicles generate cavitation bubbles by introducing non-condensable gases, significantly reducing drag and overcoming the speed bottleneck of traditional underwater weapons, attracting widespread attention from scholars both domestically and internationally. The hydrodynamics of supercavitating vehicles differs from that of fully wetted vehicles; their hydrodynamics depends on the positional and kinematic coupling relationship between the vehicle body and the cavitation flow pattern. During actual operation, supercavitating vehicles undergo depth adjustments. Due to the cavitation delay effect, the vehicle's motion response and the cavitation response are inconsistent, making it difficult to determine the supercavitation morphology and relative bubble position, thus posing challenges to navigation control and trajectory prediction. According to published literature, when the navigation depth changes, factors such as free surface effects and hydrostatic pressure significantly impact the cavitation flow pattern, and cavitation development exhibits a lag. The response characteristics of this process lead to enhanced nonlinearity in cavitation hydrodynamics, further affecting the stability of cavitation navigation. Current research mainly focuses on the impact of steady-state navigation depth on supercavitation, with limited research on the flow pattern changes and response characteristics of cavitation during dynamic changes in navigation depth. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the response of supercavitating flow patterns during changes in navigation depth, which solves the problem that existing technologies cannot predict the changes in flow patterns and responses of supercavitating vehicles during dynamic changes in navigation depth.

[0004] The technical solution adopted in this invention is a method for predicting the response of ventilated supercavitation flow patterns during changes in navigation depth, comprising the following steps: Step 1: Construct a mathematical model; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

[0005] The invention is further characterized by: The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model.

[0006] The multiphase flow model uses a phase-separated flow model to obtain clear phase interfaces and internal flow structures of cavitation bubbles; the basic governing equations of the phase-separated flow model include the continuity equation, momentum equation, and volume fraction equation. The continuity equation is shown in equation (1); (1); in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. c m For the first m Phase volume fraction; r m The density of the phase; v The velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); (2); (3); in, p It is static pressure; m m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; M These are forces acting between different phases; C D It is a constant; r n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α Phase 1 velocity, u α2 for α 2-phase velocity; The volume fraction equation is shown in equation (4); (4).

[0007] The turbulence model selected is SST. k-oh Model, SST k-oh The basic equations of the model are shown in equations (5) and (6); (5); (6); in, r m Density; U For speed; k It is turbulent kinetic energy; m For fluid dynamic viscosity; mt This is the eddy viscosity coefficient; oh The turbulence frequency; p k The turbulence generation rate; s ω3 , s k3 , α 3, β 3 and β' These are model constants; SST k-oh The formulas for the mixture function of the model are shown in equations (7), (8) and (9); (7); (8); (9); in, y It is the distance to the wall.

[0008] The cavitation model selected is the Singhal model, and the mass transfer between phases in the Singhal model is shown in equations (10), (11) and (12); (10); (11); (12); in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. s It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; r l The density is the far-field fluid density.

[0009] Step 2 is as follows: Step 2.1: Set the computational domain scale: Set the total axial length of the computational domain to 5 times the length of the aircraft, the distance from the computational domain inlet to the cavitation device at the nose of the aircraft to 1 time the length of the aircraft, and the distance from the computational domain outlet to the tail jet outlet to 3 times the length of the aircraft; Set the total radial length of the computational domain to 6.5 times the length of the aircraft. Step 2.2: Set the boundary conditions of the computational domain: Set the inlet boundary of the computational domain to a velocity inlet of 100 m / s, set the outlet boundary of the computational domain to a pressure outlet of 0.2 MPa, and allow free entry and exit around the computational domain; Step 2.3: Perform structured meshing on the computational domain to obtain the numerical computational model: the mesh size in the cavitation densification zone of the computational domain does not exceed 0.5 mm, the number of mesh layers in the cavitation densification zone of the computational domain is not less than 70 layers, and more than 60% of the mesh in the computational domain is concentrated in the area affected by ventilation supercavitation and tail jet.

[0010] Step 3 includes verification of the supercavitation test of a large-scale ventilated supercavitating underwater vehicle model on a lake and verification of grid independence. The verification of the supercavitation test of the large-size ventilated supercavitating underwater vehicle model on the lake is specifically as follows: the supercavitation size of the ventilated supercavitating flow pattern obtained in the free navigation state of the large-size ventilated supercavitating underwater vehicle model on the lake is compared with the supercavitation size obtained by numerical calculation. The error of the supercavitation size does not exceed 2.1%, indicating that the numerical calculation model meets the requirements. The grid independence verification specifically requires that the number of grid cells be no less than 3.64 million, which satisfies both computational accuracy and avoids wasting computational resources, thus satisfying the grid independence verification.

[0011] Step 4 involves simulating the supercavitation flow field under varying depth conditions, specifically including simulation calculations under conditions of decreasing depth step and increasing depth step.

[0012] The simulation calculation under the step reduction of depth is as follows: using the method of step change of environmental pressure, the pressure is stepped from 0.2 MPa to 0.15 MPa based on the stable cavitation corresponding to environmental pressure. The characteristics of the supercavitation characteristic scale and the change characteristics of the pressure inside the cavitation are analyzed, and the cavitation flow pattern is compared with that under the same steady working condition to explore the change of cavitation flow pattern and response characteristics. For a cavitator of a fixed size, when the cavitation number is small and the influence of gravity is neglected, the characteristic scale of the supercavitation is determined by the magnitude of the cavitation number, which is defined as shown in equation (13): (13); in, P ∞ For far-field static pressure; P c This refers to the static pressure of the gas inside the cavitation bubble; UThe incoming flow velocity. The simulation calculation under the condition of step increase in navigation depth is as follows: the supercavitation morphology of the supercavitation bubble is simulated and calculated according to the numerical calculation model of supercavitation cavitation, and the supercavitation flow field is obtained; the supercavitation flow field is analyzed to obtain the supercavitation bubble radius and half-length of the supercavitation bubble under the step increase in navigation depth; the change of supercavitation flow pattern is analyzed and compared with that of steady supercavitation at the same navigation depth to analyze the reasons for the difference in flow pattern.

[0013] The beneficial effects of this invention are: The method for predicting the response of supercavitary flow patterns during depth changes provided by this invention, based on a phase-separated flow model, achieves numerical simulation of the step-deep change process of a supercavitary vehicle by setting the environmental pressure boundary conditions as a function of time, and obtains the influence law of the step-deep change mode on the cavitary flow pattern. When the depth decreases stepwise, the cavitary characteristic scales exhibit an oscillating upward trend, accompanied by repeated elongation and breakage of the cavitary tail, eventually stabilizing after 1.5 s. The evolution of supercavitation exhibits significant time lag characteristics. When the depth increases stepwise, the cavitary characteristic scales exhibit an oscillating downward trend, and the cavitary tail undergoes significant shedding due to the increase in environmental pressure, eventually stabilizing after 0.9 s. The time lag characteristics of the depth increase stepwise increase are weaker than those of the depth decrease stepwise decrease condition. When the navigation depth is reduced from 10m to 5m, the size of the fully developed supercavitation is not significantly different from that of the steady supercavitation at a navigation depth of 5m. When the navigation depth is increased from 5m to 10m, the maximum cross-sectional radius of the supercavitation after the flow field is fully developed is 8.3% larger and the half-length of the cavitation is 22% larger than that of the steady supercavitation at a navigation depth of 10m. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the geometric model of the supercavitating vehicle in Embodiment 8 of the present invention; Figure 2 This is a schematic diagram of the computational domain and boundary conditions in Embodiment 8 of the present invention; Figure 3 This is a schematic diagram of the mesh division result in Embodiment 8 of the present invention; Figure 4 This is a schematic diagram showing the comparison results of cavitation flow patterns in Embodiment 8 of the present invention; Figure 5 This is a schematic diagram illustrating the impact of the depth step reduction on the cavitation characteristic scale in Embodiment 8 of the present invention; Figure 6 This is a schematic diagram of the bubble profile during the depth step reduction from 0 to 0.45s in Embodiment 8 of the present invention; Figure 7 This is a schematic diagram of the space bubble profile during the 0 to 1s depth step reduction in Embodiment 8 of the present invention; Figure 8This is a schematic diagram illustrating the changes in pressure and cavitation number within the bubble during the depth-step reduction in Embodiment 8 of the present invention. Figure 9 This is a schematic diagram illustrating the effect of the step increase in navigation depth on the characteristic scale of cavitation in Embodiment 8 of the present invention; Figure 10 This is a schematic diagram of the cavity profile during the step increase in depth from 0 to 0.3s in Embodiment 8 of the present invention; Figure 11 This is a schematic diagram illustrating the changes in pressure and cavitation number within the bubble during a step increase in depth, as described in Embodiment 8 of the present invention. Detailed Implementation

[0015] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0016] Example 1 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

[0017] Example 2 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

[0018] Example 3 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model; The multiphase flow model uses a phase-separated flow model to obtain clear phase interfaces and internal flow structures of cavitation bubbles; the basic governing equations of the phase-separated flow model include the continuity equation, momentum equation, and volume fraction equation. The continuity equation is shown in equation (1); (1); in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. c m For the first m Phase volume fraction; r m The density of the phase; v The velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); (2); (3); in, p It is static pressure; m m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; M These are forces acting between different phases; C D It is a constant; r n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α Phase 1 velocity, u α2 for α 2-phase velocity; The volume fraction equation is shown in equation (4); (4); The turbulence model selected is SST. k-oh Model, SST k-oh The basic equations of the model are shown in equations (5) and (6); (5); (6); in, r m Density; U For speed; k It is turbulent kinetic energy; m For fluid dynamic viscosity; m tThis is the eddy viscosity coefficient; oh The turbulence frequency; p k The turbulence generation rate; s ω3 , s k3 , α 3, β 3 and β' These are model constants; SST k-oh The formulas for the mixture function of the model are shown in equations (7), (8) and (9); (7); (8); (9); in, y It is the distance to the wall; The cavitation model selected is the Singhal model, and the mass transfer between phases in the Singhal model is shown in equations (10), (11) and (12); (10); (11); (12); in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. s It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; r l The far-field fluid density; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

[0019] Example 4 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model; The multiphase flow model uses a phase-separated flow model to obtain clear phase interfaces and internal flow structures of cavitation bubbles; the basic governing equations of the phase-separated flow model include the continuity equation, momentum equation, and volume fraction equation. The continuity equation is shown in equation (1); (1); in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. c m For the first m Phase volume fraction; r m The density of the phase; v The velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); (2); (3); in, p It is static pressure; m m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; M These are forces acting between different phases; C D It is a constant; r n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α Phase 1 velocity, u α2 for α 2-phase velocity; The volume fraction equation is shown in equation (4); (4); The turbulence model selected is SST. k-oh Model, SST k-ohThe basic equations of the model are shown in equations (5) and (6); (5); (6); in, r m Density; U For speed; k It is turbulent kinetic energy; m For fluid dynamic viscosity; m t This is the eddy viscosity coefficient; oh The turbulence frequency; p k The turbulence generation rate; s ω3 , s k3 , α 3, β 3 and β' These are model constants; SST k-oh The formulas for the mixture function of the model are shown in equations (7), (8) and (9); (7); (8); (9); in, y It is the distance to the wall; The cavitation model selected is the Singhal model, and the mass transfer between phases in the Singhal model is shown in equations (10), (11) and (12); (10); (11); (12); in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. s It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F cThey are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; r l The far-field fluid density; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 2 is as follows: Step 2.1: Set the computational domain scale: Set the total axial length of the computational domain to 5 times the length of the aircraft, the distance from the computational domain inlet to the cavitation device at the nose of the aircraft to 1 time the length of the aircraft, and the distance from the computational domain outlet to the tail jet outlet to 3 times the length of the aircraft; Set the total radial length of the computational domain to 6.5 times the length of the aircraft. Step 2.2: Set the boundary conditions of the computational domain: Set the inlet boundary of the computational domain to a velocity inlet of 100 m / s, set the outlet boundary of the computational domain to a pressure outlet of 0.2 MPa, and allow free entry and exit around the computational domain; Step 2.3: Perform structured meshing on the computational domain to obtain the numerical calculation model: the mesh size in the cavitation densification zone of the computational domain does not exceed 0.5 mm, the number of mesh layers in the cavitation densification zone of the computational domain is not less than 70 layers, and more than 60% of the mesh in the computational domain is concentrated in the area affected by ventilation supercavitation and tail jet flow. Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

[0020] Example 5 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model; The multiphase flow model uses a phase-separated flow model to obtain clear phase interfaces and internal flow structures of cavitation bubbles; the basic governing equations of the phase-separated flow model include the continuity equation, momentum equation, and volume fraction equation. The continuity equation is shown in equation (1); (1); in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. c m For the first m Phase volume fraction; r m The density of the phase; vThe velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); (2); (3); in, p It is static pressure; m m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; M These are forces acting between different phases; C D It is a constant; r n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α Phase 1 velocity, u α2 for α 2-phase velocity; The volume fraction equation is shown in equation (4); (4); The turbulence model selected is SST. k-oh Model, SST k-oh The basic equations of the model are shown in equations (5) and (6); (5); (6); in, r m Density; U For speed; k It is turbulent kinetic energy; m For fluid dynamic viscosity; m t This is the eddy viscosity coefficient; oh The turbulence frequency; p k The turbulence generation rate; s ω3 , s k3 , α 3, β 3 and β' These are model constants; SST k-oh The formulas for the mixture function of the model are shown in equations (7), (8) and (9); (7); (8); (9); in, y It is the distance to the wall; The cavitation model selected is the Singhal model, and the mass transfer between phases in the Singhal model is shown in equations (10), (11) and (12); (10); (11); (12); in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. s It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; r l The far-field fluid density; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 2 is as follows: Step 2.1: Set the computational domain scale: Set the total axial length of the computational domain to 5 times the length of the aircraft, the distance from the computational domain inlet to the cavitation device at the nose of the aircraft to 1 time the length of the aircraft, and the distance from the computational domain outlet to the tail jet outlet to 3 times the length of the aircraft; Set the total radial length of the computational domain to 6.5 times the length of the aircraft. Step 2.2: Set the boundary conditions of the computational domain: Set the inlet boundary of the computational domain to a velocity inlet of 100 m / s, set the outlet boundary of the computational domain to a pressure outlet of 0.2 MPa, and allow free entry and exit around the computational domain; Step 2.3: Perform structured meshing on the computational domain to obtain the numerical calculation model: the mesh size in the cavitation densification zone of the computational domain does not exceed 0.5 mm, the number of mesh layers in the cavitation densification zone of the computational domain is not less than 70 layers, and more than 60% of the mesh in the computational domain is concentrated in the area affected by ventilation supercavitation and tail jet flow. Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 3 includes verification of the supercavitation test of a large-scale ventilated supercavitating underwater vehicle model on a lake and verification of grid independence. The verification of the supercavitation test of the large-size ventilated supercavitating underwater vehicle model on the lake is specifically as follows: the supercavitation size of the ventilated supercavitating flow pattern obtained in the free navigation state of the large-size ventilated supercavitating underwater vehicle model on the lake is compared with the supercavitation size obtained by numerical calculation. The error of the supercavitation size does not exceed 2.1%, indicating that the numerical calculation model meets the requirements. The grid independence verification specifically requires that the number of grid cells be no less than 3.64 million, which satisfies both computational accuracy and avoids waste of computational resources, thus satisfying the grid independence verification. Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field under varying navigation depth conditions and obtain the simulation results; Step 4 involves simulating the cavitation flow field under varying depth conditions, specifically including simulation calculations under conditions of decreasing depth step and increasing depth step. The simulation calculation under the step reduction of depth is as follows: using the method of step change of environmental pressure, the pressure is stepped from 0.2 MPa to 0.15 MPa based on the stable cavitation corresponding to environmental pressure. The characteristics of the supercavitation characteristic scale and the change characteristics of the pressure inside the cavitation are analyzed, and the cavitation flow pattern is compared with that under the same steady working condition to explore the change of cavitation flow pattern and response characteristics. For a cavitator of a fixed size, when the cavitation number is small and the influence of gravity is neglected, the characteristic scale of the supercavitation is determined by the magnitude of the cavitation number, which is defined as shown in equation (13): (13); in, P ∞ For far-field static pressure; P c This refers to the static pressure of the gas inside the cavitation bubble; U The incoming flow velocity. The simulation calculation under the condition of step increase in navigation depth is as follows: the supercavitation morphology of the supercavitation bubble is simulated and calculated according to the numerical calculation model of supercavitation cavitation, and the supercavitation flow field is obtained; the supercavitation flow field is analyzed to obtain the supercavitation bubble radius and half-length of the supercavitation bubble under the step increase in navigation depth; the change of supercavitation flow pattern is analyzed and compared with that of steady supercavitation at the same navigation depth to analyze the reasons for the difference in flow pattern.

[0021] Example 6 The response prediction method for supercavitation flow patterns during changes in navigation depth proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; Multiphase flow model; The non-condensable gas introduced into the supercavitation exhibits a clear stratified flow with the surrounding water, with gas / water mixing only present to a certain extent in the cavitation closure region and at the two-phase interface. In the multiphase flow model, each phase exists independently, making it suitable for accurately describing complex flow fields with varying flow patterns and interactions. This model better reflects the physical nature of the ventilated supercavitation flow field and offers higher computational accuracy in predicting the morphology and flow structure characteristics of ventilated supercavitation. Numerical calculation models include governing equations, turbulence models, and cavitation models. The governing equations of the phase-separated flow model include the continuity equation, momentum equation, and energy equation. Mass transfer and interaction between the two phases are transmitted through the phase interface. Due to the underwater working environment, the cooling rate of the gas introduced into the supercavitating vehicle is relatively fast, so it can be treated as a normal temperature gas. Since water has a large specific heat capacity, there is no obvious temperature change in the flow field, and the energy exchange between the gas and liquid phases is ignored, so the energy equation is ignored. The continuity equation is shown in equation (1); (1); in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. c m For the first m Phase volume fraction; r m The density of the phase; v The velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); (2); (3); in, p It is static pressure; m m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; MThese are forces acting between different phases; C D It is a constant; r n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α1 Phase velocity, u α2 for α2 Phase velocity; The volume fraction equation is shown in equation (4); (4); Turbulence model; Based on the characteristics of turbulence models and the research results of relevant literature, SST is adopted. The model accurately captures changes in ventilation bubble flow patterns, air mass shedding, and jet flow phenomena within bubbles under varying navigation depth conditions. SST k-oh The basic equations of the model are shown in equations (5) and (6); (5); (6); in, r m Density; U For speed; k It is turbulent kinetic energy; m For fluid dynamic viscosity; m t This is the eddy viscosity coefficient; oh The turbulence frequency; p k The turbulence generation rate; s ω3 , s k3 , α 3, β 3 and β' These are model constants; SST k-oh The formulas for the mixture function of the model are shown in equations (7), (8) and (9); (7); (8); (9); in, y It is the distance to the wall; Cavitation model; The Singhal et al. cavitation model, proposed by scholars Singhal et al., is based on the Rayleigh-Plesset cavitation dynamics equation. It considers the effects of phase change, cavitation hydrodynamics, turbulent pressure fluctuations, and non-condensable gases in the supercavitating flow field and is used for simulation calculation of the flow pattern of supercavitating vehicles under varying depth conditions. The mass transfer between phases in this model is based on equations (10), (11), and (12). (10); (11); (12); in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. s It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; r l The far-field fluid density; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; The research object is a typical supercavitating vehicle, such as Figure 1 As shown, where D n It is 100mm long. It mainly consists of a cavitation unit, vent, conical section, cylindrical section, and engine exhaust nozzle. When the radial ratio of the watershed is less than 50, the watershed has a significant impact on the scale of the ventilated supercavitation and the pressure distribution characteristics. To eliminate the influence of the watershed, this paper adopts a radial ratio of 50, and the specific boundary conditions are set as follows: Figure 2 As shown. The left boundary of the computational domain uses a velocity inlet; the right boundary uses a pressure outlet, the vent uses a mass flow inlet, and the ventilation is compressed ambient air. The computational domain is surrounded by no-slip wall boundary conditions. The inlet velocity is 100 m / s, the ventilation flow rate is 2 kg / s, and the ambient pressure is determined according to specific operating conditions. High-speed ventilation supercavitation degassing occurs in a jet flow pattern. To better capture the jet flow phenomenon and cavitation flow pattern, mesh refinement is required in the ventilation supercavitation region, especially the supercavitation closure region. Meshing software is used to mesh the computational domain, employing a hexahedral structured mesh throughout. The mesh distribution characteristics of the computational domain are as follows: Figure 3 As shown, most of the total grid size is concentrated in the ventilated supercavitation region. Furthermore, the grid fineness may affect the morphology and venting mechanism of the ventilated supercavitation. Grid independence verification shows that the grid independence requirement is met, with a grid size of 3.64 million. Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; The coupling relationship between the supercavitation morphology and the position of the vehicle was acquired using an underwater high-speed camera system. The experimental launch device was an open-grid launch tube, which was fixed to a lifting launcher. To verify the accuracy of the numerical model's calculation of ventilated supercavitation, Northwestern Polytechnical University conducted a free-sailing supercavitation test on a lake using a large-scale ventilated supercavitating underwater vehicle model. The supercavitating underwater vehicle model consisted of a disc cavitator, a ventilation device, a conical section of the projectile body, a cylindrical section of the projectile body, and a tail nozzle. High-speed ventilated supercavitation numerical simulations were performed under the same flow conditions as the free-sailing test, obtaining the ventilated supercavitation flow pattern under free-sailing conditions. Using the numerical model established above, simulation calculations were performed for this experimental condition to verify the calculation accuracy of the ventilated supercavitation numerical model. The experimental results and numerical simulation results are as follows: Figure 4 As shown. The cavitation profile curve uses the cavitation diameter... d c Dimensionless processing was performed. As shown in the figure, under the same flow conditions, the relative deviation between the supercavitation size obtained by numerical simulation and the experimental results does not exceed 2.1%, further proving that the calculation accuracy of the high Froude number ventilation supercavitation numerical model constructed in this application is high; as shown in Table 1; Table 1 Comparison of cavitation flow patterns

[0022] Furthermore, the mesh fineness can affect the morphology and venting mechanism of the ventilated supercavitation. Three sets of meshes were created: a coarser mesh with 1.81 million grid points, a medium mesh with 3.64 million grid points, and a finer mesh with 5.21 million grid points, while maintaining the same distribution of edge nodes. Numerical simulations were conducted under the target operating conditions. The results showed that compared to the medium mesh, the coarse mesh resulted in deviations of 14.1% in the half-length of the cavitation bubble and 9.2% in the maximum cross-sectional radius. However, there was no significant difference in the half-length of the cavitation bubble and the maximum cross-sectional radius between the fine mesh and the medium mesh. To ensure computational accuracy and avoid wasting computational resources, the mesh size should be no less than 3.64 million. Therefore, the computational model with a medium mesh size of 3.64 million grid points was selected for subsequent work. Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field under varying navigation depth conditions and obtain the simulation results; In control systems, dynamic performance indicators under step signal input are the most intuitive way to evaluate system response characteristics. To obtain the hysteresis characteristics of the supercavitating supercavitating vehicle under varying depth conditions, a step signal input is used to measure depth changes. By analyzing the changes in cavitation characteristic scales and internal pressure characteristics, the response characteristics and changes in the ventilated supercavitating flow pattern are revealed when the depth changes. Unsteady evolution characteristics of supercavitating flow patterns with reduced depth step; To investigate the variation characteristics of the supercavitation characteristic scale and internal pressure of the supercavitation bubble when the navigation depth decreases stepwise from 10m to 5m, a step-change method of ambient pressure was adopted, starting from a stable bubble corresponding to an ambient pressure of 0.2MPa and gradually increasing to 0.15MPa. The variation characteristics of the supercavitation characteristic scale over time are as follows: Figure 5 As shown in the figure, the dashed lines represent the cavitation characteristic scale of steady supercavitation at a depth of 5m. The cavitation characteristic scale curves have been dimensionlessly processed using the cavitation diameter Dn.

[0023] The results show that when the depth is stepped down to 5m, the cavitation characteristic scale exhibits a certain degree of hysteresis and oscillation during the change process. The ventilated supercavitation characteristic scale needs to wait for T1=1.5s to increase to a new stable state, and there is no significant difference from the steady supercavitation characteristic scale at a depth of 5m. This indicates that the supercavitation characteristic scale exhibits strong time hysteresis characteristics when the depth is stepped down.

[0024] The cavitation profile of the interval with larger oscillation amplitude, from 0s to 0.45s, is shown below. Figure 6 As shown. From 0 to 0.1 s, the depth drops abruptly to 5 m, accompanied by a decrease in environmental pressure. The gas velocity at the vent increases, and the cavitation bubble begins to expand from the vent towards the tail. The half-length and maximum cross-sectional radius of the cavitation bubble increase rapidly, thus exhibiting an irregular elliptical shape in the longitudinal section of the cavitation bubble, as shown. Figure 7As shown, the cavitation profile exhibits significant expansion in certain regions due to rapid gas expansion. This expansion divides the original cavitation into two parts: a new cavitation that has undergone gas expansion and the original cavitation that has not. From 0.1s to 0.2s, the cavitation characteristic scale decreases rapidly. As the cavitation characteristic scale gradually approaches the characteristic scale of a steady supercavitation at a depth of 5m, its oscillation amplitude weakens. After reaching a new stable state, the cavitation characteristic scale becomes identical to that corresponding to a steady supercavitation at a depth of 5m. Simultaneously with gas expansion, gas from the cavitation tail continuously enters the cavitation under the influence of the back jet. This results in a decrease in the amount of gas released from the cavitation tail and an increase in the cavitation volume. Once the cavitation volume reaches a certain level, it ruptures under the influence of the high-pressure region at the tail, causing the cavitation volume to decrease and repeating the previous process until a new stable state is reached. During the step descent at depth, the elongation of the tail cavitation continuously decreases. After 0.45s, the oscillation amplitude of the cavitation characteristic scale decreases significantly and eventually passes through... T After 1 = 1.5s, it increases to a stable state, and then the curve of the cavitation characteristic scale changing with time shows an oscillating upward trend.

[0025] The half-length of the cavitation bubble changes from 50.4 mm in the time interval from 0 to 0.05 s. D n The figure decreased slightly to 49.8. D n The maximum cross-sectional radius of the cavitation bubble is 3.26. D n It increased significantly to 3.62. D n When the navigation depth drops to 5m in a step, the cavitation bubble begins to expand from the vent to an axial depth of 49.8 m within 0.05 s. D n At this point, the radius of the new cavitation cutoff section is larger than the radius of the original cavitation's maximum cross-section. Furthermore, in the axial dimension, the new cavitation cutoff section is smaller than the location of the original maximum cross-section. Therefore, the half-length of the cavitation appears to decrease slightly, while the radius of the maximum cross-section appears to increase significantly. Accompanying the response of the cavitation gas to the decrease in flight depth, the gas within the cavitation gradually expands towards the tail, reaching 93.1 at 0.1 s. D n This point marks the cutoff point for new cavitation. At 0.1 s, the new cavitation bubble, after gas expansion, is already at 68.5 axial angle. D n The maximum cross-section appears at this point, which is larger than the cross-section at the new cavitation stop point. At this point, the radius of the maximum cross-section of the cavitation is 68.5. D n The radius of the cross section at that location; For a cavitator of a fixed size, when the cavitation number is small and the influence of gravity is neglected, the characteristic scale of the supercavitation is determined by the magnitude of the cavitation number, as defined by equation (13): (13); in, P ∞ For far-field static pressure; P c This refers to the static pressure of the gas inside the cavitation bubble; U The incoming flow velocity; As defined by the cavitation number, the cavitation number of a supercavitating vehicle under this operating condition is determined by the pressure inside the bubble. To reveal the changing characteristics of the supercavitation morphology, such as... Figure 8 As shown, the variation characteristics of internal pressure and cavitation number are presented. The results show that when the environmental pressure decreases abruptly, the pressure inside the bubble cannot change abruptly to the pressure inside the steady supercavitation at a depth of 5m. Instead, it takes about T1=1.5s to reach the corresponding pressure of 86.3kPa. This indicates that the hysteresis characteristics of the characteristic scale of the cavitation bubble are determined by the time hysteresis characteristics of the pressure inside the cavitation bubble.

[0026] Unsteady evolution characteristics of supercavitating flow patterns with increasing depth; By increasing the navigation depth from 5m to 10m in a step, the characteristic scale of cavitation and the variation characteristics of pressure within the cavitation bubble were obtained. For example... Figure 9 The figure shows the variation characteristics of the supercavitation characteristic scale over time. The results indicate that when the depth increases stepwise to 10m, the cavitation characteristic scale does not respond directly; the supercavitation characteristic scale requires a transition time. T It takes 2 = 0.9 seconds to reach a new steady state. T 2 is approximately the time required to reduce the depth step to a steady state. T 0.6 times that of 1, indicating that the time hysteresis characteristics of the supercavitation characteristic scale are weak when the depth of travel increases stepwise; The cavitation flow pattern within the range of 0s to 0.3s, where the oscillation amplitude is relatively large, is shown in the figure below. Figure 10 As shown; from 0 to 0.1 s, the cavitation characteristic scale decreases rapidly, and from 0.1 to 0.2 s, it increases rapidly. The oscillation amplitude of the cavitation characteristic scale decreases with increasing time. Due to the increase in environmental pressure, the tail of the cavitation bubble detaches significantly under high pressure. After 0.3 s, the oscillation amplitude of the cavitation characteristic scale weakens, and finally, after 0.9 s, the cavitation bubble reaches a new stable state. The maximum cross-sectional radius of the cavitation bubble at a steady operating depth of 10 m is 3.26. D n The cavitation half-length is 50.4. D n The cruising depth increased in a step from 5m to 10m, and the diameter of the fully developed supercavitation reached 3.53m. D n The cavitation half-length is 61.5. D nCompared to the steady operating condition at a depth of 10m, the values ​​increased by 8.3% and 22%, respectively. With increasing depth, the supercavitation shrinks, and the final size of the supercavitation is influenced by its previous state. This conclusion is consistent with the hysteresis characteristics of ventilated supercavitation found in the literature. like Figure 11 The figure shows the changes in bubble pressure and cavitation number as the depth increases stepwise. The results indicate that as the depth increases stepwise, approximately... T It takes 2 = 0.9 seconds to reach the steady-state bubble pressure corresponding to a navigation depth of 10m, which is approximately the time required for a step decrease in navigation depth. T The pressure inside the cavitation bubble is 0.6 times that of a step depth, therefore the time lag characteristic of the cavitation bubble is weaker when the depth increases by a step depth, resulting in a weaker time lag characteristic of the cavitation bubble characteristic scale compared to the decrease in depth. Furthermore, after increasing the depth to 10m, the pressure inside the stable cavitation bubble is 141.3kPa, which is 7.5% higher than the 131.5kPa pressure of the stable cavitation bubble at a steady depth of 10m. This results in the characteristic scale of the stable cavitation bubble obtained after increasing the depth by a step depth being larger than the characteristic scale of the stable cavitation bubble at a steady depth of 10m.

[0027] Based on a phase-separated flow model, by setting the environmental pressure boundary conditions to vary over time, a numerical simulation of the step-dependent depth variation process of a supercavitating vehicle was achieved, and the influence of the step-dependent depth variation on the cavitation flow pattern was obtained. The main conclusions are as follows: 1) As the depth of travel decreases stepwise, the characteristic scale of the cavitation bubble exhibits an oscillating upward trend, accompanied by repeated elongation and rupture of the cavitation tail, eventually stabilizing after 1.5 seconds. The evolution of supercavitation shows obvious time lag characteristics; 2) When the depth increases stepwise, the characteristic scale of the cavitation bubble shows an oscillating downward trend, and the tail of the cavitation bubble detaches significantly due to the increase in environmental pressure, eventually stabilizing after 0.9 s. The time hysteresis characteristic of the depth-increasing stepwise increase is weaker than that of the depth-decreasing stepwise decrease. 3) After the navigation depth is reduced from 10m to 5m, the size of the fully developed supercavitation is not significantly different from that of the steady supercavitation at a navigation depth of 5m; after the navigation depth is increased from 5m to 10m, the maximum cross-sectional radius of the supercavitation after the flow field is fully developed is 8.3% larger and the half-length of the cavitation is 22% larger than that of the steady supercavitation at a navigation depth of 10m.

Claims

1. A method for predicting the response of ventilated supercavitation flow patterns during changes in navigation depth, characterized in that, Includes the following steps: Step 1: Construct a mathematical model; Step 2: Based on the mathematical model, set boundary conditions and mesh the watershed of the vehicle to obtain the numerical calculation model; Step 3: Verify the numerical calculation model to obtain a numerical calculation model for ventilation overcavitation under varying navigation depth conditions; Step 4: Based on the supercavitation numerical calculation model, simulate the supercavitation flow field of ventilation under varying navigation depth conditions and obtain the simulation results.

2. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 1, characterized in that, The mathematical models described in step 1 include multiphase flow models, turbulence models, and cavitation models.

3. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The multiphase flow model uses a phase-separated flow model to obtain clear phase interfaces and internal flow structures of cavitation bubbles; the basic governing equations of the phase-separated flow model include the continuity equation, momentum equation, and volume fraction equation. The continuity equation is shown in equation (1); （1）； in, m In this context, 1 and 2 represent the liquid phase and the gas phase, respectively. γ m For the first m Phase volume fraction; ρ m The density of the phase; v The velocity vector of the fluid element; t For time; The momentum equations are shown in equations (2) and (3); （2）； （3）； in, p It is static pressure; μ m Let be the dynamic viscosity of the fluid element; g It is the acceleration due to gravity; M These are forces acting between different phases; C D It is a constant; ρ n The average density of the gas-liquid two-phase mixture; A The area of ​​the phase interface per unit volume; u α1 for α Phase 1 velocity, u α2 for α 2-phase velocity; The volume fraction equation is shown in equation (4); （4）。 4. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The turbulence model used is SST. k-ω Model, the SST k-ω The basic equations of the model are shown in equations (5) and (6); （5）； （6）； in, ρ m Density; U For speed; k It is turbulent kinetic energy; μ For fluid dynamic viscosity; μ t This is the eddy viscosity coefficient; ω The turbulence frequency; p k The turbulence generation rate; σ ω3 , σ k3 , α 3, β 3 and β' These are model constants; The SST k-ω The formulas for the mixture function of the model are shown in equations (7), (8) and (9); （7）； （8）； （9）； in, y It is the distance to the wall.

5. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The cavitation model is the Singhal model, and the mass transfer between phases in the Singhal model is based on equations (10), (11) and (12); （10）； （11）； （12）； in, Evaporation rate; Condensation rate; k This represents the local turbulence intensity. σ It is the surface tension coefficient of the liquid phase; f v This refers to the mass fraction of the vapor phase. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ Far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; p sat This is the theoretical saturated vapor pressure; ρ l The density is the far-field fluid density.

6. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The specific process of step 2 is as follows: Step 2.1: Set the computational domain scale: Set the total axial length of the computational domain to 5 times the length of the aircraft, the distance from the computational domain inlet to the cavitation device at the nose of the aircraft to 1 time the length of the aircraft, and the distance from the computational domain outlet to the tail jet outlet to 3 times the length of the aircraft; Set the total radial length of the computational domain to 6.5 times the length of the aircraft. Step 2.2: Set the boundary conditions of the computational domain: The inlet boundary of the computational domain is set to a velocity inlet of 100 m / s, and the outlet boundary of the computational domain is set to a pressure outlet of 0.2 MPa. The area around the computational domain is free to enter and exit. Step 2.3: Perform structured meshing on the computational domain to obtain the numerical computational model: the mesh size in the cavitation densification zone of the computational domain does not exceed 0.5 mm, the number of mesh layers in the cavitation densification zone of the computational domain is not less than 70 layers, and more than 60% of the mesh in the computational domain is concentrated in the area affected by ventilation supercavitation and tail jet.

7. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The verification described in step 3 includes verification of the supercavitation test of a large-size ventilated supercavitating underwater vehicle model on a lake and verification of grid independence; The verification of the supercavitation test of the large-size ventilated supercavitating underwater vehicle model on the lake is specifically as follows: the supercavitation size of the ventilated supercavitating flow pattern obtained in the free navigation state of the large-size ventilated supercavitating underwater vehicle model on the lake is compared with the supercavitation size obtained by numerical calculation. The error of the supercavitation size does not exceed 2.1%, indicating that the numerical calculation model meets the requirements. The grid independence verification specifically involves ensuring that the number of grid cells is not less than 3.64 million, which satisfies both computational accuracy and avoids wasting computational resources, thereby satisfying the grid independence verification.

8. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 2, characterized in that, The simulation calculation of the supercavitation flow field under varying depth conditions described in step 4 specifically includes simulation calculations under conditions of step reduction in depth and simulation calculations under conditions of step increase in depth.

9. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 8, characterized in that, The simulation calculation under the step reduction of the navigation depth is as follows: using the method of step change of environmental pressure, the pressure is stepped from the stable cavitation corresponding to 0.2MPa to 0.15MPa. The characteristic scale of supercavitation and the change characteristics of pressure inside the cavitation are analyzed, and the cavitation flow pattern under the same steady working condition is compared to explore the change of cavitation flow pattern and response characteristics. For a cavitator of a fixed size, when the cavitation number is small and the influence of gravity is neglected, the characteristic scale of the supercavitation is determined by the magnitude of the cavitation number, which is defined as shown in equation (13): （13）； in, P ∞ For far-field static pressure; P c This refers to the static pressure of the gas inside the cavitation bubble; U The incoming flow velocity.

10. The method for predicting the response of ventilated supercavitation flow patterns during depth changes according to claim 8, characterized in that, The simulation calculation under the condition of step increase in navigation depth is specifically as follows: the morphology of supercavitation bubble under step increase in navigation depth is simulated and calculated according to the numerical calculation model of supercavitation, and the supercavitation flow field is obtained. The supercavitation flow field of the ventilation system was analyzed to obtain the supercavitation radius and half-length of the supercavitation under a step increase in navigation depth. The changes in the supercavitation flow pattern were analyzed and compared with those of the steady supercavitation at the same navigation depth to analyze the reasons for the differences in flow pattern.

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