Method for estimating ventilation supercavity form under action of tail jet flow

Abstract

The invention discloses a method for estimating the form of a ventilation supercavity under the action of tail jet flow. 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 tail jet flow effect; and 4, based on the supercavitation numerical calculation model, performing simulation calculation on the ventilation supercavitation flow field under the action of the tail jet flow to obtain a simulation result. According to the method for estimating the ventilation supercavitation form under the action of the tail jet flow, the problems that the ventilation supercavitation flow is high in unsteady performance, and the ventilation supercavitation form under the action of the tail jet flow is difficult to calculate when the attack angle exists or not are solved.

Description

Technical Field

[0001] This invention belongs to the field of ventilated supercavitating vehicles, specifically relating to a method for predicting the morphology of ventilated supercavitation under the action of a tail jet. Background Technology

[0002] Supercavitating underwater vehicles (SUVs) are underwater weapons that utilize supercavitation technology. By artificially introducing non-condensable gases, most of the vehicle's surface is covered by cavitation bubbles, theoretically reducing drag by more than 90% and achieving higher speeds than traditional underwater vehicles. Supercavitating vehicles typically use jet engines as their power source. The exhaust jet causes velocity and pressure pulsations within the cavitation bubble. The exhaust jet acts on the cavitation interface, causing deformation, fluctuations, and instability of the interface, altering its relative position to the vehicle, and changing the leakage mechanism at the supercavitation tail, resulting in strong unsteadiness of the supercavitation.

[0003] According to existing technology, research on the supercavitation unsteady ventilation supercavitation morphology mainly focuses on the prediction of supercavitation morphology under conditions such as changes in ventilation volume and periodic incoming flow, while research on the changes in ventilation supercavitation morphology under the action of tail jet is rare. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the supercavitation morphology of ventilation under the action of the jet stream, which solves the problem that the supercavitation flow of ventilation is highly unsteady and it is difficult to calculate the supercavitation morphology of ventilation under the action of the jet stream with or without an angle of attack.

[0005] The technical solution adopted in this invention is a method for predicting the supercavitation morphology under the action of the tail jet, 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 suitable for ventilation supercavitation under the action of the tail jet; Step 4: Based on the supercavitation numerical calculation model, the supercavitation flow field of the ventilation under the action of the tail jet is simulated and the simulation results are obtained.

[0006] The invention is further characterized by: The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model.

[0007] The multiphase flow model uses a phase-separated flow model to obtain a clear phase interface and the internal flow structure of the cavitation bubble: the basic governing equations of the phase-separated flow model include the continuity equation, the momentum equation, and the 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).

[0008] The turbulence model selected is SST. k-ω Model, 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; 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.

[0009] 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. σ It is the surface tension coefficient of the liquid phase; f v This refers to the vapor phase mass fraction. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ For 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.

[0010] 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.

[0011] Step 3 includes verification under low-speed conditions and verification under high-speed conditions. The verification of low-speed operating conditions is as follows: the cavitation scale and venting pattern obtained from the water tunnel test are compared with the cavitation scale and venting pattern obtained from the numerical calculation. The error of the cavitation scale does not exceed 5%, and the venting pattern is consistent, indicating that the numerical calculation model meets the requirements of low-speed operating conditions. The high-speed operating condition verification is as follows: the cavitation profile of the flow field is compared with the cavitation profile obtained by the Logvinovich empirical formula. The cavitation diameter error does not exceed 5%, indicating that the numerical calculation model meets the requirements of high-speed operating conditions. The Logvinovich empirical formula is shown in Equation (13). (13); In the formula, R c Where cavitation radius is ; x This refers to the distance from the cavitation device; L c The length of the cavitation bubble; x The distance from the cavitation cross section to the cavitation device.

[0012] Step 4 involves simulating the supercavitation flow field under the influence of the tail jet, specifically including simulation calculations under horizontal straight-line conditions and simulation calculations under angle-of-attack conditions.

[0013] The specific process of simulation calculation under horizontal straight-line conditions is as follows: Under horizontal straight-line conditions, simulation calculations of the supercavitation morphology under different tail jet intensities are performed based on the numerical calculation model of supercavitation, and the supercavitation flow field is obtained; the supercavitation flow field is analyzed to obtain the flow field parameters of the supercavitation radius and length and the flow field structure inside the supercavitation under different tail jet intensities; the flow field structure inside the supercavitation is analyzed to obtain the motion of the gas introduced at the head and the gas in the tail jet under different tail jet intensities, and to obtain the reasons for the changes in the radius and length of the supercavitation caused by tail jets of different intensities; The tail jet intensity is shown in equation (14); (14); in, For gas mass flow rate, v For gas outlet velocity, F D The drag experienced by the cavitation system of the aircraft.

[0014] The specific process of simulation calculation under angle of attack conditions is as follows: Under angle of attack conditions, based on the numerical calculation model of supercavitation, simulation calculations of the supercavitation morphology under different jet intensities are performed to obtain the supercavitation flow field; the supercavitation flow field is analyzed to obtain the cavitation morphology characteristics of the supercavitation morphology under different jet intensities with angle of attack, including radius, length, cavitation closure position, and wetted area; the morphology characteristics of the supercavitation morphology are analyzed to obtain the changes in the cavitation tail exhaust mode under different jet intensities with angle of attack.

[0015] The beneficial effects of this invention are: The method for predicting the supercavitation morphology under the influence of a tail jet provided by this invention can simulate and calculate the supercavitation morphology and flow structure under the influence of a tail jet. The tail jet disrupts the original backflow structure within the supercavitation, altering the supercavitation size and venting pattern. Under weak tail jet intensity, some tail jet gas recirculates, replenishing the supercavitation and significantly increasing the supercavitation size; under strong tail jet intensity, a single vortex forms at the tail of the supercavitation, reducing the supercavitation size. At an angle of attack of 0.5 degrees, the vehicle under tail jet intensity... J Within a range of <3, there is no wetting, and cavitation is released through a single vortex tube at the tail. At an angle of attack of 1.5 degrees, as the intensity of the tail jet increases, the single vortex tube at the tail of the vehicle gradually develops into a pair of parallel vortex tubes, and the vehicle exhibits a pattern of wetting-full enclosure-wetting in sequence. At an angle of attack of 1.5 degrees, after the tail jet is activated, a large amount of tail jet gas flows back, and the cavitation size continuously increases. After 100 ms, the vehicle transitions from a wetting state to a fully enclosed state, developing into a single vortex tube venting mode. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the external shape of the aircraft in Embodiment 6 of the present invention; Figure 2 This is a schematic diagram of the aircraft mesh model in Embodiment 6 of the present invention; Figure 3 This is a schematic diagram comparing the experimental results of a low-speed water tunnel with a ventilation rate of 0.81 in Embodiment 6 of the present invention with numerical simulation. Figure 4 This is a schematic diagram comparing the experimental results of a low-speed water tunnel with an air permeability of 1.32 and numerical simulation in Embodiment 6 of the present invention; Figure 5 This is a schematic diagram of the mesh independence verification in Embodiment 6 of the present invention; Figure 6 This is a schematic diagram illustrating the variation characteristics of supercavitation morphology with tail jet intensity in Embodiment 6 of the present invention; Figure 7 This is a schematic diagram illustrating the variation characteristics of supercavitation radius and length with tail jet intensity in Embodiment 6 of the present invention; Figure 8 This is a schematic diagram of the velocity vector under the tailless jet condition in Embodiment 6 of the present invention; Figure 9 This is a schematic diagram of the velocity vector of the weak tail jet in Embodiment 6 of the present invention; Figure 10 This is a schematic diagram of the weak tail jet flow structure in Embodiment 6 of the present invention; Figure 11 This is a schematic diagram of the velocity vector of the strong tail jet in Embodiment 6 of the present invention; Figure 12 This is a schematic diagram of the strong tail jet flow structure in Embodiment 6 of the present invention; Figure 13 This is a schematic diagram illustrating the variation characteristics of the supercavitation morphology with the tail jet intensity when the angle of attack is 0.5° in Embodiment 6 of the present invention. Figure 14 This is a schematic diagram illustrating the variation characteristics of the supercavitation morphology with the tail jet intensity when the angle of attack is 1.5° in Embodiment 6 of the present invention. Figure 15 This is a schematic diagram of the cavitation profile on section 1 in Embodiment 6 of the present invention; Figure 16 This is a schematic diagram of the velocity vector at section 1 in Embodiment 6 of the present invention; Figure 17 This is a schematic diagram illustrating the time-dependent cavitation morphology characteristics in Embodiment 6 of the present invention. Figure 18 This is a schematic diagram of the gas volume fraction in Embodiment 6 of the present invention; Figure 19 This is a schematic diagram of the cavitation profile on section 2 in Embodiment 6 of the present invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to specific embodiments.

[0018] Example 1 The method for predicting the supercavitation morphology under the action of the tail jet 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 suitable for ventilation supercavitation under the action of the tail jet; Step 4: Based on the supercavitation numerical calculation model, the supercavitation flow field of the ventilation under the action of the tail jet is simulated and the simulation results are obtained.

[0019] Example 2 The method for predicting the supercavitation morphology under the action of the tail jet proposed in this embodiment includes the following steps: Based on Example 1; The mathematical models in step 1 include multiphase flow model, turbulence model and cavitation model.

[0020] The multiphase flow model uses a phase-separated flow model to obtain a clear phase interface and the internal flow structure of the cavitation bubble: the basic governing equations of the phase-separated flow model include the continuity equation, the momentum equation, and the 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); The turbulence model selected is SST. k-ω Model, 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; 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; 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. σ It is the surface tension coefficient of the liquid phase; f v This refers to the vapor phase mass fraction. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ For 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.

[0021] Example 3 The method for predicting the supercavitation morphology under the action of the tail jet proposed in this embodiment includes the following steps: Based on Example 2; 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.

[0022] Example 4 The method for predicting the supercavitation morphology under the action of the tail jet proposed in this embodiment includes the following steps: Based on Example 3; Step 3 includes verification under low-speed conditions and verification under high-speed conditions. The verification of low-speed operating conditions is as follows: the cavitation scale and venting pattern obtained from the water tunnel test are compared with the cavitation scale and venting pattern obtained from the numerical calculation. The error of the cavitation scale does not exceed 5%, and the venting pattern is consistent, indicating that the numerical calculation model meets the requirements of low-speed operating conditions. The high-speed operating condition verification is as follows: the cavitation profile of the flow field is compared with the cavitation profile obtained by the Logvinovich empirical formula. The cavitation diameter error does not exceed 5%, indicating that the numerical calculation model meets the requirements of high-speed operating conditions. The Logvinovich empirical formula is shown in Equation (13). (13); In the formula, R c Where cavitation radius is ; x This refers to the distance from the cavitation device; L c The length of the cavitation bubble; x The distance from the cavitation cross section to the cavitation device.

[0023] Example 5 The method for predicting the supercavitation morphology under the action of the tail jet proposed in this embodiment includes the following steps: Based on Example 4; Step 4 involves simulating the supercavitation flow field under the action of the tail jet, specifically including simulation calculations under horizontal straight-line conditions and simulation calculations under angle-of-attack conditions. The specific process of simulation calculation under horizontal straight-line conditions is as follows: Under horizontal straight-line conditions, simulation calculations of the supercavitation morphology under different tail jet intensities are performed based on the numerical calculation model of supercavitation, and the supercavitation flow field is obtained; the supercavitation flow field is analyzed to obtain the flow field parameters of the supercavitation radius and length and the flow field structure inside the supercavitation under different tail jet intensities; the flow field structure inside the supercavitation is analyzed to obtain the motion of the gas introduced at the head and the gas in the tail jet under different tail jet intensities, and to obtain the reasons for the changes in the radius and length of the supercavitation caused by tail jets of different intensities; The tail jet intensity is shown in equation (14); (14); in, For gas mass flow rate, v For gas outlet velocity, F D The drag experienced by the cavitation system of the aircraft; The specific process of simulation calculation under angle of attack conditions is as follows: Under angle of attack conditions, based on the numerical calculation model of supercavitation, simulation calculations of the supercavitation morphology under different jet intensities are performed to obtain the supercavitation flow field; the supercavitation flow field is analyzed to obtain the cavitation morphology characteristics of the supercavitation morphology under different jet intensities with angle of attack, including radius, length, cavitation closure position, and wetted area; the morphology characteristics of the supercavitation morphology are analyzed to obtain the changes in the cavitation tail exhaust mode under different jet intensities with angle of attack.

[0024] Example 6 The method for predicting the supercavitation morphology under the action of the tail jet proposed in this embodiment includes the following steps: Step 1: Construct a mathematical model; Multiphase flow model; The phase-separated flow model has high computational accuracy in predicting the morphology and internal flow structure of supercavitating bubbles during ventilation, and its solution method conforms to the physical nature of supercavitating flow. Therefore, the phase-separated flow model is selected to describe the multiphase flow problem in the supercavitating flow field during ventilation. In this embodiment, the ventilation medium is a room-temperature gas, the same as the ambient water temperature. The temperature of the supercavitating flow field is assumed to remain constant. The governing equations omit the flow energy equations and only involve the continuity equation, momentum equation, and volume fraction equation. The continuity equation is as follows: (1); In the formula, 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 equation is: (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, (4).

[0025] Turbulence model; The characteristics of a supercavitating flow field are high flow velocity, water-air mixing, and venting pulsations. The effects of turbulence must be considered in numerical simulations. SST is selected. k-ω The model solves the turbulence problem in the flow field. It has high accuracy in the calculation of ventilation supercavitation and can capture the backflow phenomenon caused by air mass separation, shedding and high adverse pressure gradient in the flow field. The basic equation is as follows: (5); (6); In the formula, 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; SST k-ω The formula for the mixed function is: (7); (8); (9); In the formula, y It is the distance to the wall; Cavitation model; The cavitation model selected is the Singhal model, which describes the mass transfer between phases as follows: (10); (11); In the formula, 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 vapor phase mass fraction. f g This refers to the mass fraction of non-condensable gases. p v This refers to the pressure inside the bubble; p ∞ For far-field pressure; model constants F e and F c They are 0.02 and 0.01 respectively; The cavitation pressure correction formula is as follows: (12); In the formula, p sat This is the theoretical saturated vapor pressure; ρ 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; This paper takes a spacecraft consisting of a cavitation generator, a conical section, a cylindrical section, and a tailpipe as the object of study, investigating the influence of the tail jet on the supercavitation morphology. An excessively large computational domain will cause a sharp increase in mesh size, wasting computational resources; an excessively small computational domain will cause cavitation blockage, affecting the supercavitation scale. The computational domain and boundary condition settings, such as... Figure 1 As shown in the figure D n The diameter of the cavitation unit. L For the entire vehicle length, the axial length of the computational domain is set to 5 times the vehicle length, the distance from the computational domain inlet to the cavitation generator at the vehicle's nose is set to 1 time the vehicle length, and the distance from the computational domain outlet to the tail jet outlet is set to 3 times the vehicle length; the radial length of the computational domain is set to 6.5 times the vehicle length; the left boundary is set as a velocity inlet of 100 m / s; the right boundary is set as a pressure outlet of 0.2 MPa; and free entry and exit are allowed around the computational domain. The supercavitation flow field is accompanied by strong interphase mass transfer, momentum exchange, and turbulent flow. The mesh refinement affects the flow and development of cavitation bubbles. Mesh generation is based on O-block technology, with over 60% of the mesh concentrated in the supercavitation region. The mesh generation details are as follows: Figure 2 As shown; Step 3: Verify the numerical calculation model to obtain a numerical calculation model suitable for ventilation supercavitation under the action of the tail jet; Low-speed operating condition verification; To verify the accuracy of the numerical calculation model, a series of experiments on aerated supercavitating water tunnels with varying ventilation rates were conducted at the water tunnel laboratory of Northwestern Polytechnical University. Fr The cavitation scale of a thin straight rod model with a disk cavitation device was experimentally studied under conditions of 24.8°C and ventilation rates of 0.81 and 1.32, respectively. (Froude number) Fr The definition of is: ; in, v ∞ The inflow velocity is the air permeability; the ventilation rate is defined as: ; in, Q The volumetric flow rate of the ventilation; a comparison of experimental and simulation results, such as... Figure 3 As shown, d c The maximum diameter of the cavitation bubble. L c For the cavitation length, when the ventilation rate is 0.81, the simulated deviations for the cavitation diameter and length are 3.72% and 3.52%, respectively. Figure 4 As shown, when the ventilation rate is 1.32, the simulated deviations for the bubble diameter and length are 4.03% and 3.23%, respectively. The venting mechanism at the bubble tail is consistent between the numerical simulation and the experiment. High-speed operating condition verification; Existing water tunnel experiments are insufficient to simulate flow velocities exceeding 100 m / s. Therefore, the semi-empirical formula for cavitation shape established by scholar Logvinocich is used to verify the accuracy of the computational model under high-speed conditions. This formula is based on the principle of independent expansion of cavitation cross-sections, and the equation is as follows: (13); In the formula, R c Where cavitation radius is ; x This refers to the distance from the cavitation device; L c The length of the cavitation bubble; x This represents the distance from the cavitation cross-section to the cavitation device. Fr =252、 C q =0.89, the supercavitation morphology was calculated under ambient pressures of 0.2 MPa and 0.25 MPa. The calculation results show that the maximum deviations of the cavitation radius from the empirical formula under the 0.2 MPa and 0.25 MPa conditions are 2.32% and 3.98%, respectively. Mesh independence verification; To maintain a constant distribution of grid edge nodes, coarse grids with 1.33 million grid points, medium grids with 1.8 million grid points, and fine grids with 2.35 million grid points were established. Under an environmental pressure of 0.2 MPa... Fr =252、 C q Numerical simulations were conducted under the condition of 0.89, and the results were compared with those of... Figure 5 As shown, the coarse mesh deviates by 9.81% and 7.13% in cavitation length and maximum diameter compared to the medium mesh, while the fine mesh has cavitation length and maximum diameter that are close to those of the medium mesh. Therefore, the computational model with a medium mesh size was selected for subsequent work. Step 4: Based on the supercavitation numerical calculation model, the supercavitation flow field of the ventilation under the action of the tail jet is simulated and calculated to obtain the simulation results; The effect of jet intensity on supercavitation morphology; dimensionless numbers J The formula for representing the intensity of the jet stream is: (14); in, For gas mass flow rate, v For gas outlet velocity, F DThis refers to the drag experienced by the cavitation system of the aircraft. In this embodiment, based on the supercavitating jet flow pattern, the jet flow rate is gradually increased to achieve a change in jet intensity from weak to strong, thus studying the influence of jet intensity on the supercavitation morphology.

[0026] The characteristics of the supercavitation morphology changing with the increase of the tail jet intensity are as follows: Figure 6 As shown. Without the influence of a tail jet, the supercavitation bubble vents in a jet-like pattern, and its shape is approximately elliptical. With the presence of a tail jet, the bubble shape changes significantly. The gas introduced into the nose of the vehicle mixes with the combustion gases and flows downstream, disrupting the original jet-like venting pattern, causing the tail to vent in a single-vortex pattern. In this embodiment, the minimum cross-section of the bubble behind the tail jet outlet is defined as the bubble closure position. When the tail jet intensity is weak, the bubble closure position is far from the tail jet outlet; when the tail jet intensity is strong, the bubble closure position gradually moves closer to the tail jet outlet as the tail jet intensity increases. Figure 7 As shown, regarding the cavitation radius, when the jet intensity increases to 0.13, the cavitation radius increases from 3.04. D n Significantly increased to 3.83 D n This represents a 25.99% increase compared to the case without a tail jet; when the tail jet intensity changes to 1, the cavitation radius decreases to 3.16. D n The rate of change of the cavitation radius gradually slows down; when the jet intensity is greater than 2, the rate of change of the cavitation radius is small, and further increasing the jet intensity has limited effect on the cavitation radius, and the front cavitation at this point is smaller than the cavitation in the case without a jet; when the jet intensity increases to 3, the cavitation radius further shrinks to 2.8. D n This represents an 8.01% reduction compared to the tailless jet condition; Regarding cavitation length, when the jet intensity increases to 0.13, the cavitation length increases sharply, and the cavitation closure position shifts significantly backward; when the jet intensity increases to 0.65, the cavitation length is 146.54 mm. D n Compared to the case without a tail jet, the length increased by 64.66%, at which point the cavitation closure position began to move forward; when the tail jet intensity increased to 2, the change in cavitation length became slow. It can be seen that the changes in cavitation radius and length are almost identical; when the tail jet intensity increased to 3, the cavitation length decreased to 68.29. D n Compared to the case without a tail jet, the size was reduced by 23.26%. The above changes in cavitation size indicate that a weaker tail jet helps increase the radius and length of the supercavitation, while a stronger tail jet reduces the size of the cavitation. Study on the flow structure inside a supercavitation under the action of a tail jet; The study on the variation characteristics of supercavitation morphology with jet intensity shows that the jet disrupts the original jet discharge pattern of the supercavitation, causing a change in supercavitation morphology. This embodiment explains the reason for the change in supercavitation morphology from the perspective of the internal flow structure of the supercavitation. Figure 8 This is a velocity vector distribution diagram inside a supercavitation bubble under tailless jet conditions, based on... Figure 8 As shown, the gas flows downstream along the cavitation bubble wall, converges at the tail of the bubble, decelerates under the influence of the adverse pressure gradient, and begins to flow in the opposite direction, forming a backflow. The returning gas flows along the vehicle wall towards the nose, and is entrained by newly introduced gas near the cavitation vent and flows downstream. Figure 9 This is a velocity vector distribution diagram of the tail flow field of a cavitation jet under weak tail flow conditions. Figure 10 The corresponding flow field structure diagram is as follows: Figure 9 , 10 As shown, under weak tailjet conditions, a small amount of recirculated gas near the nozzle is drawn downstream along the tailjet flow by the jet. After the combustion gas exits the nozzle, the gas in the non-tailjet core region rapidly decays and flows in the opposite direction; while the gas in the tailjet core region is hindered by the recirculated gas at the cavitation tail, causing the gas at its head to slow down and spread outwards. Some of the gas merges with the recirculated gas and flows upstream, while some is carried downstream by the gas in the downstream region near the cavitation wall. At this time, the recirculation structure within the main cavitation is less affected. The tailjet continuously replenishes the gas to the preceding cavitation, which is equivalent to increasing the ventilation volume and helps to increase the cavitation size. Figure 11 , 12 As shown, the cavitation size is further reduced, the cavitation closure position is closer to the tail jet outlet, and the gap between the tail jet and the cavitation wall becomes smaller. The artificially introduced gas flows into the tailpipe and is divided into three parts: one part is unaffected by the backflowing gas and continues to flow downstream along the cavitation wall; another part, under the influence of the tail jet ejection, flows downstream with the tail jet, but is hindered by the tail jet core area and the cavitation wall and begins to flow back, encountering the gas in the downstream region, and some of the gas flows in the opposite direction again, forming a swirling structure; the gas in the downstream region, after encountering the backflowing gas, carries some of the backflowing gas towards the tailpipe wall and flows back along the wall towards the nose of the vehicle. After the gas flows out from the tail jet outlet, most of it is discharged through the tailpipe single pipe, and a small portion of the gas outside the tail jet core area decays and is entrained into the swirling structure by the artificially introduced gas near the outlet. This portion of gas moves to the tailpipe wall and flows forward along the wall, accumulating in the cylindrical section and the stepped surface of the tailpipe; a small amount of gas continues to flow forward into the front cavitation. The effect of the tail jet on the hypercavitation flow field under angle of attack; like Figure 13As shown, this illustrates the change in the cavitation profile as the jet intensity increases at an angle of attack of 0.5°. The change in the cavitation profile at this point is similar to that during horizontal straight-line flight, with the cavitation continuously dissipating through a single vortex formed by the jet at the tail. Due to the angle of attack, the tail of the cavitation deflects upwards to some extent. J Within the range of <3, the increase in jet intensity will not cause the cavitation bubble to close into the cylindrical section of the vehicle. At the end of the large cylindrical section, the lower side of the cavitation bubble is very close to the vehicle, while the upper side of the cavitation bubble is relatively far from the vehicle.

[0027] like Figure 14 The diagram illustrates how the cavitation profile changes with increasing jet intensity at an angle of attack of 1.5°. The changes in the cavitation profile can be categorized into... J =0~0.13、 J The jet flow intensity is divided into three stages: =0.13~0.65 and J≥0.65. In the first stage, when the jet flow intensity is 0, the cylindrical section of the vehicle's frontal surface has already contacted the seawater, causing the gas on the lower side to flow obliquely upward around the cylindrical section, resulting in a crescent-shaped cavitation bubble. At this time, the cavitation bubble can be regarded as two parts: the front cavitation bubble starts from the cavitation unit, develops obliquely upward due to the obstruction of the cylindrical section wall, and forms a very small vortex above the tailpipe; the rear cavitation bubble starts from the tail of the vehicle, deforms inward due to the influence of environmental pressure, and forms a pair of parallel double vortices. The front and rear cavitation bubbles partially merge at the tailpipe, and the gas introduced from the head flows into the rear cavitation bubble through the connection.

[0028] When the jet intensity increases to 0.13, the preceding and following cavitation bubbles, replenished by the return flow of the combustion gas, gradually merge and grow into a single complete cavitation bubble, significantly increasing its size. At this point, the closure point of the cavitation bubble is relatively far from the jet outlet. When the jet intensity increases to the second stage, the nozzle at the cavitation closure point moves, causing the cavitation size to gradually decrease, but the vehicle still does not contact the seawater. At this time, the tail of the cavitation bubble degassing in the form of a single vortex.

[0029] When the jet intensity increases to the third stage, the lower wall of the cylindrical section re-contacts the seawater, disrupting the integrity of the cavitation bubble. The disturbance caused by the wetting of the wall is transmitted downstream, altering the shape of the tail vent pipe and causing the lower half of the cavitation bubble wall to be compressed and elongated on both sides.

[0030] Figure 15 It is based on the tail jet outlet 60 D n Cavitation profile diagram at the cross-section, the cross-section location is as follows Figure 14 As indicated, when the exhaust jet intensity is 0.65, the upper part of the vent pipe remains semi-circular, while the lower part is approximately elliptical, giving the vent pipe an overall "mushroom" shape. When the exhaust jet intensity increases to 1, the cavitation bubble tends to split into two separate cavitation bubbles. (Combined with...) Figure 14 and Figure 15 The increased wetted area of ​​the cylindrical section exacerbates the separation of the front and rear cavitation bubbles. The single vortex of the front cavitation bubble benefits from the replenishment of gas from the tail jet, resulting in an increase in its diameter and length. The rear cavitation bubble vents in a single-tube mode, but its upper side undergoes some inward deformation due to environmental pressure. As the intensity of the tail jet continues to increase, the wetted area gradually increases, the cavitation bubble closure position shifts forward, and a high-pressure zone forms at the tail of the vehicle, inhibiting the development of the front cavitation vortex. This also causes the upper side of the tail cavitation bubble formed by the tail jet to be compressed and deformed, forming a pair of centrally spiraling vortices, such as... Figure 16 As shown in the figure, the circle represents the aircraft, and the curve represents the cavitation profile on the cross section.

[0031] The development process of supercavitation morphology in the initial stage of the tail jet under angle of attack; At an angle of attack of 1.5°, the cavitation morphology evolved from two separate cavitation bubbles to a single, complete cavitation bubble as the jet began to open. Ten ms after the jet opened, the cavitation profile was as follows: Figure 17 As shown, the profile of the front cavitation is less affected, while the size of the rear cavitation gradually increases with the inflow of gas from the tail jet.

[0032] Figure 18 This is a volume fraction diagram of the combustion gas. It can be seen that at this point, the lower side of the back cavity is almost filled with combustion gas, while the artificially introduced gas occupies part of the space on the upper side of the tailpipe. Because the tail jet intensity is relatively low at this point, a small portion of the combustion gas rapidly decays to zero after exiting the nozzle and flows in the opposite direction. Figure 19 This is a graph showing the change of the cavitation profile on section 2 over time. The section position is as follows: Figure 16 As indicated. At this point, the connection between the front and rear cavitation bubbles is very narrow, forming a channel resembling a "triangle". Due to the obstruction of artificially introduced gas, the gas backflow mostly occurs in the lower region of the tailpipe and cannot flow into the front cavitation bubble. Most of the gas leaks directly from the vortex tube at the tail, causing the diameter of the double vortex tube to increase.

[0033] 30ms after the tailpipe starts flowing, the wetted surface on the upper side of the tailpipe is gradually enveloped by cavitation bubbles. At this point, the size of the rear cavitation bubbles increases, leading to an increase in the flow area at the connection between the cylindrical section and the tailpipe. The suppression of fuel gas backflow by artificially introduced gas weakens. The volume fraction diagram shows that a small amount of fuel gas flows back forward through the connection at this time, causing the cavitation bubble size to increase.

[0034] 50ms after the exhaust jet begins to flow, the tailpipe is completely enveloped by cavitation bubbles, which have grown significantly in size, leaving only the lower part of the cylindrical section wetted; for example... Figure 19 As shown, the flow area at the connection point increases significantly, and the upper part becomes arc-shaped, indicating that the front bubble rapidly elongates and gradually merges with the rear bubble. As shown in the gas volume fraction diagram, the gas flows to the front bubble through the connection point, obstructing the flow of artificially introduced gas into the upper bubble, with most of it flowing to the rear bubble through the lower half of the bubble. At this time, the tail-end double-vortex tubes tend to merge into a single-vortex tube.

[0035] 100ms after the tail jet begins to open, the cavitation bubble is fully enclosed, and the single-vortex venting mode at the tail is fully formed. The size of the cavitation bubble is much larger than that in the case without a tail jet. The front and rear cavitation bubbles merge into one, and the shape of the connection point is approximately a complete circle. Because the intensity of the gas tail jet is relatively low at this time, most of the gas attenuates rapidly after exiting and flows back, which greatly increases the size of the cavitation bubble.

[0036] from Figure 19 As can be seen, the shape of the connection point evolved from a triangle to a quadrilateral and finally to a circle. It is evident that the flow area of ​​the front and rear cavities continuously increases over time, which is beneficial for the backflow of gas. The gas supplied to the front increases the volume of the front cavity, causing the lower closing point of the cavity to continuously move backward until it merges with the rear cavity to form a complete cavity.

Claims

1. A method for predicting ventilated supercavitation shape under the action of a tail jet, characterized in that, The method comprises the following steps: Step 1, constructing a mathematical model; Step 2, based on the mathematical model, setting boundary conditions and dividing grids for a flow field of the vehicle to obtain a numerical calculation model; Step 3, verifying the numerical calculation model to obtain a numerical calculation model suitable for supercavitation under the action of tail jet flow; Step 4, based on the supercavitation numerical calculation model, simulating and calculating the supercavitation flow field under the action of tail jet flow to obtain simulation results.

2. The method of claim 1, wherein, The mathematical model in step 1 comprises a multiphase flow model, a turbulence model and a cavitation model.

3. The method of claim 2, wherein, The multiphase flow model selects a phase separation flow model for obtaining clear phase interface and internal flow structure of the cavity: the basic control equations of the phase separation flow model comprise continuity equation, momentum equation and volume fraction equation; The continuity equation is shown as formula (1); （1）； wherein, m 1 and 2 represent liquid and gas phases, respectively; The momentum equation is shown as formula (2) and (3); m the first m volume fraction of the phase; The volume fraction equation is shown as formula (4); m the density of the phase; v the velocity vector of the fluid element; t time; The cavitation model selects a Singhal model, and the Singhal model is used for mass transfer between phases according to formula (10), (11) and (12); （2）； （3）； wherein, p is the static pressure; The specific process of step 2 is as follows: m is the dynamic viscosity of the fluid element; g is the acceleration due to gravity; M is the force acting between different phases; C D is a constant; Step 2.1, setting the size of the calculation domain: the total length of the calculation domain in the axial direction is determined as 5 times the length of the vehicle, the distance from the inlet of the calculation domain to the head of the vehicle is determined as 1 times the length of the vehicle, and the distance from the outlet of the calculation domain to the outlet of the tail jet flow is determined as 3 times the length of the vehicle; the total length of the calculation domain in the radial direction is determined as 6.5 times the length of the vehicle; n is the average density of the gas-liquid two-phase mixture; A is the interfacial area per unit volume; u α1 is α 1 the phase velocity, u α2 is α 2 the phase velocity; Step 2.2, setting the boundary conditions of the calculation domain: the inlet boundary of the calculation domain is set as a velocity inlet of 100 m / s, the outlet boundary of the calculation domain is set as a pressure outlet of 0.2 MPa, and the calculation domain is free in and out; （4）。 4. The method of claim 2, wherein, The turbulence model is selected as SST Step 2.3, structuring the grid of the calculation domain to obtain a numerical calculation model: the grid size in the cavitation encryption area of the calculation domain is not more than 0.5 mm, the number of layers of the grid in the cavitation encryption area of the calculation domain is not less than 70 layers, and more than 60% of the grids of the calculation domain are concentrated in the supercavitation and tail jet flow affected area. The basic equations of the SST The verification in step 3 comprises low-speed working condition verification and high-speed working condition verification; model are shown in equations (5) and (6). （5）； （6）； where The low-speed working condition verification is specifically: comparing the cavitation scale and the air release mode obtained in the water tunnel test with the cavitation scale and the air release mode obtained by numerical calculation, the error of the cavitation scale is not more than 5%, and the air release modes are consistent, which indicates that the numerical calculation model meets the low-speed working condition requirement; m is the density; U is the velocity; k is the turbulent kinetic energy; The high-speed working condition verification is specifically: comparing the cavitation profile of the flow field with the cavitation profile obtained by the Logvinovich empirical formula, the error of the cavitation diameter is not more than 5%, which indicates that the numerical calculation model meets the high-speed working condition requirement; the Logvinovich empirical formula is shown as formula (13); is the kinematic viscosity; The simulation calculation of the supercavitation flow field under the action of the tail jet flow in step 4 specifically comprises simulation calculation under horizontal straight sailing condition and simulation calculation under attack angle condition. t is the eddy viscosity coefficient; ​ is the turbulent frequency; p k is the turbulent production rate; ​ ω3 , ​ k3 , α 3, β 3 and β' is a model constant; The SST ​ The mixing function formula of the model is shown in equations (7), (8) and (9). （7）； （8）； （9）； wherein y is the distance to the wall surface.

5. The method of claim 2, wherein, ​ （10）； （11）； （12）； where, is the evaporation rate; is the condensation rate; k is the local turbulence intensity; ​ is the liquid surface tension coefficient; f v is the vapor mass fraction; f g is the non-condensable gas mass fraction; p v is the bubble internal pressure; p ∞ is the far field pressure; model constant F e and F c are 0.02 and 0.01, respectively; p sat is the theoretical saturation vapor pressure; ​ l is the far field fluid density.

6. The method of claim 2, wherein, ​ ​ ​ ​ 7. The method of claim 2, wherein, ​ ​ ​ （13）； wherein R c R is the radius of the cavitator; x D is the distance from the cavitator; L c L is the length of the cavitation bubble; x D is the distance from the cavitator; 8. The method of claim 2, wherein, ​ 9. The method of claim 8, wherein, The simulation calculation under the horizontal straight sailing condition comprises the following steps: under the horizontal straight sailing condition, the simulation calculation of the air-breathing supercavitation flow field under different tail jet intensities is performed according to the air-breathing supercavitation numerical calculation model, so as to obtain the air-breathing supercavitation flow field; The air-breathing supercavitation flow field is analyzed to obtain the flow field parameters of the air-breathing supercavitation radius and length under different tail jet intensities and the flow field structure in the air-breathing supercavitation; the flow field structure in the air-breathing supercavitation is analyzed to obtain the movement of the head gas and the tail jet gas in the air-breathing supercavitation under different tail jet intensities, and the reasons for the changes of the air-breathing supercavitation radius and length caused by different tail jet intensities are obtained; The tail jet intensity is shown in formula (14); （14）； wherein, is the gas mass flow rate, v is the gas exit velocity, F D is the drag experienced by the vehicle cavitator.

10. The method of claim 8, wherein, The simulation calculation under the angle of attack condition comprises the following steps: under the angle of attack condition, the simulation calculation of the air-breathing supercavitation flow field under different tail jet intensities is performed according to the air-breathing supercavitation numerical calculation model, so as to obtain the air-breathing supercavitation flow field; The air-breathing supercavitation flow field is analyzed to obtain the air-breathing supercavitation radius, length, cavity closure position and wetted area under different tail jet intensities under the angle of attack; the air-breathing supercavitation shape characteristics are analyzed to obtain the change of the air-breathing supercavitation tail gas leakage mode under different tail jet intensities under the angle of attack.

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