A three-dimensional numerical simulation method and system for high-speed tilting of a supercavitating projectile out of water

Abstract

This invention provides a three-dimensional numerical simulation method and system for high-speed inclined water ejection of a supercavitating projectile. The method includes: establishing a three-dimensional geometric model of the projectile and the flow field computational domain, and outputting the projectile's property parameters; estimating the size of the projectile's motion region, meshing the projectile and flow field computational domains, importing the meshes into fluid dynamics software, establishing an overlapping computational domain, and setting the projectile's property parameters and the fluid dynamics solver's boundary conditions; considering the influence of water compressibility on the high-speed projectile, using a user-defined function to establish the nonlinear relationship between density and pressure of a compressible liquid under isothermal conditions; defining the initial motion parameters of the projectile, performing numerical solutions, and obtaining the cavitation evolution, flow field distribution, force and motion characteristics of the high-speed inclined projectile during water ejection. This invention can simulate the high-speed inclined water ejection process of a projectile under different operating conditions, effectively reducing costs and providing a technical basis for submarine-launched tests.

Description

Technical Field

[0001] This invention belongs to the field of cross-medium water discharge technology, and in particular relates to a three-dimensional numerical simulation method and system for high-speed inclined water discharge from a supercavitating projectile. Background Technology

[0002] The principle behind supercavitating projectiles achieving high-speed underwater motion is based on supercavitation drag reduction technology. When moving at high speed underwater, the projectile is induced by a cavitation device at the nose to generate supercavitation that envelops the projectile body, thereby achieving drag reduction. Theoretically, the drag reduction effect can reach more than 90%.

[0003] Due to the natural concealment of seawater, launching supercavitating projectiles from underwater to strike surface targets or low-flying targets near the water surface can significantly improve the penetration capability and efficiency of supercavitating projectiles. Compared to vertical launch, underwater supercavitating projectiles launch at an angle, offering better maneuverability and safety. The cavitation evolution and flow field distribution before and after the projectile crosses the free liquid surface differ significantly between low-speed and high-speed scenarios. Therefore, studying the high-speed angled launch process of projectiles is of significant practical importance for predicting the motion characteristics of underwater submarine-launched penetration.

[0004] Current research on projectile water ejection mainly focuses on low-speed and vertical scenarios, with limited research on the high-speed, inclined water ejection process of projectiles, which has more practical application value. High-speed water ejection tests require complex equipment, are costly and difficult, have poor repeatability, and involve the coupling of solid, liquid, and gas phases, exhibiting strong transient, nonlinear, and unsteady characteristics. Conventional testing methods struggle to capture and monitor the process of a projectile crossing a free liquid surface. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a three-dimensional numerical simulation method and system for high-speed tilting water ejection of supercavitating projectiles. This method can capture and monitor the process of the projectile crossing the free liquid surface at high speed, as well as the projectile's cavitation evolution characteristics, flow field distribution characteristics, force characteristics, and motion characteristics. This saves costs and provides a technical basis for submarine-launched tests.

[0006] A three-dimensional numerical simulation method for high-speed inclined water ejection of a supercavitating projectile includes the following steps:

[0007] Step 1: Establish a three-dimensional geometric model of the projectile and the flow field computational domain, and determine the projectile property parameters;

[0008] Step 2: Estimate the size of the projectile's motion area, mesh the three-dimensional geometric model of the projectile and the flow field calculation domain, establish the flow field calculation domain and the overlapping calculation domain around the projectile based on the mesh, divide the flow field calculation domain into water and air domains, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions.

[0009] Step 3: Combining the defined flow field calculation domain and projectile property parameters, and considering the influence of water compressibility on high-speed projectiles, establish the nonlinear relationship between density and pressure of compressible liquids under isothermal conditions.

[0010] Step 4: Define the initial motion parameters of the projectile. Based on the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions, perform numerical solutions to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics, and motion characteristics of the projectile ejection process.

[0011] Furthermore, the projectile attribute parameters include the projectile mass m, the projectile center of gravity coordinates (x, y, z), and the inertial tensor I that determines the projectile center of gravity based on the projectile coordinate frame. The inertial tensor I is:

[0012]

[0013] In the formula, the diagonal elements I of the matrix xx I yy I zz These are the moments of inertia about the x-axis, y-axis, and z-axis, respectively; the off-diagonal elements I of the matrix. xy I yz I yx I xz I zx I zy It is called the product of inertia.

[0014] Furthermore, the mesh generation includes: dividing the background flow field computational domain and the foreground projectile computational domain into structured meshes; refining the mesh of the projectile motion path and the air-water interface in the background flow field computational domain; and refining the mesh of the projectile surface. The establishment of the flow field computational domain overlapping with the computational domain around the projectile includes: assembling the foreground projectile computational domain and the background flow field computational domain using overlapping mesh technology. The boundary conditions of the fluid solver are: the bottom of the flow field computational domain is a pressure inlet, and the surrounding area and top are pressure outlets; the boundary of the overlapping computational domain is an overlapping mesh boundary condition.

[0015] Furthermore, dividing the flow field computational domain into water and air domains specifically includes:

[0016] The volume fraction of air in the flow field computation domain is set to 1. A water area is created based on the estimated projectile motion region, and the volume fraction of water in the water area is set to 1. The pressure gradient distribution in the water area is defined by the designed field function, which is:

[0017] P o =ρ*g*(Hh) o )

[0018] In the formula, P is the hydrostatic pressure of the fluid at point o in the fluid domain; ρ is the fluid density; g is the gravitational acceleration; H is the height of the water body in the background domain frame coordinate system; h o The height of point o in the background domain frame coordinate system.

[0019] Furthermore, the nonlinear relationship between density and pressure of a compressible liquid under isothermal conditions is as follows:

[0020]

[0021] in,

[0022]

[0023] In the formula, ρ represents the liquid density under pressure p; ρ0 represents the liquid density under reference pressure p0; n is the density exponent; K0 represents the bulk modulus under reference pressure p0; K represents the bulk modulus under pressure p; and Δp represents the relative pressure.

[0024] Furthermore, the numerical solution process specifically includes: using a 6DOF rigid body motion model to solve the projectile's motion in the flow field; using a Volume of Fluid model to solve the multiphase flow system consisting of water, air, and water vapor in the transmedium flow field; using a Shear Stress Transport k-omega turbulence model to provide turbulent closure for the Reynolds-averaged equations; using a Schnerr-Sauer cavitation model to treat the steam-water medium as a mixture; and using the gas-liquid mass transport rate to calculate the water vapor volume fraction.

[0025] Furthermore, the solution to the projectile's motion in the flow field using a 6DOF rigid body motion model specifically includes:

[0026] The translational motion control equations for the projectile are established in the inertial reference coordinate system as follows:

[0027]

[0028] In the formula, V G F is the translational velocity vector of the projectile's center of mass; m is the mass of the projectile; F G It is the vector of external forces acting on the projectile;

[0029] The governing equations for the projectile's rotation in rigid body coordinates are as follows:

[0030]

[0031] In the formula: ω p I is the projectile angular velocity vector; I is the projectile inertia tensor; M is the projectile external torque vector.

[0032] Furthermore, the Volume of Fluid model is used to solve the multiphase flow system consisting of water, air, and water vapor in the cross-medium flow field. Specifically, this involves solving the continuity equation and momentum equation of the mixture to obtain the density, volume fraction, and pressure changes of the mixture medium in the flow field. The continuity equation and momentum equation are as follows:

[0033]

[0034] In the formula, ρ m t represents the mixed phase density; t represents time; P represents the flow field pressure; μ m The dynamic viscosity of the mixed phase; u i u j The velocity component in the Cartesian coordinate system; u r δ is the velocity of the fluid in the direction of the tensor r. ij For Kronecker notation; S represents the source phase.

[0035] Furthermore, the Shear Stress Transportk-omega turbulence model is used to provide turbulence closure for the Reynolds-averaged equations, specifically including:

[0036] Establish the transport equations for turbulent kinetic energy k and specific dissipation rate ω:

[0037]

[0038] In the formula, σ k σ ω G is the Prandtl number of turbulent flow, which is the turbulent kinetic energy ω and the specific dissipation rate ω. k G ω These are the turbulent kinetic energy and specific dissipation rate generation terms, respectively; S k With S ω For custom items; Y k Y ω The divergent phases, representing turbulent kinetic energy and specific dissipation rate, respectively; D ω It is an orthogonal divergent term;

[0039] Define the eddy viscosity coefficient μ t for:

[0040]

[0041] In the formula: a * is the low Reynolds number correction factor, a1 is the empirical coefficient, S is the mean strain rate tensor, and F is the mixing function.

[0042] Furthermore, the gas-liquid mass transport equation is as follows:

[0043]

[0044] in,

[0045]

[0046] In the formula: R e R is the evaporation rate. c R is the condensation rate. B Let be the radius of the bubble, and n be the number of cavitation bubbles per unit volume, with a value of 1 × 10⁻⁶. 11 .

[0047] A three-dimensional numerical simulation system for high-speed inclined water ejection of a supercavitating projectile includes:

[0048] The model building unit is used to establish a three-dimensional geometric model of the projectile and flow field computational domain and determine the projectile attribute parameters;

[0049] Model meshing and computational domain division units are used to estimate the size of the projectile's motion area. The three-dimensional geometric model of the projectile and the flow field computational domain is meshed. Based on the mesh, the flow field computational domain and the overlapping computational domain around the projectile are established. The flow field computational domain is divided into water and air domains. A water-air interface is established, and the projectile attribute parameters and fluid solver boundary conditions are set.

[0050] The nonlinear relationship construction unit integrates the divided flow field calculation domain and projectile attribute parameters, considers the influence of water compressibility on high-speed projectiles, and establishes the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions.

[0051] The solution unit defines the initial motion parameters of the projectile and performs numerical solutions based on the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics of the projectile ejection process.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] (1) This invention provides a three-dimensional numerical simulation method for high-speed inclined water ejection of supercavitating projectiles, which facilitates the simulation of the water ejection process of projectiles under different working conditions, demonstrating extremely high flexibility and practicality. This method helps to conduct in-depth research on the cavitation evolution, flow field distribution, force and motion characteristics of projectiles during high-speed inclined water ejection.

[0054] (2) This invention provides a three-dimensional numerical simulation method for high-speed inclined water discharge of supercavitating projectiles. This method can intuitively study the three-phase coupled and unsteady water discharge process, effectively avoiding the problems of complex test equipment, high test cost, high difficulty and poor repeatability required for high-speed water discharge test, and significantly reducing the test difficulty and cost.

[0055] (3) This invention provides a three-dimensional numerical simulation method for high-speed inclined exit of a supercavitating projectile from water. This method provides technical support for underwater supercavitating projectile testing and can strike surface targets or low-altitude targets flying near the water surface, significantly improving the weapon's damage efficiency and combat effectiveness, while also possessing higher maneuverability and safety. Attached Figure Description

[0056] To more clearly illustrate the implementation of the present invention or the existing technical solutions, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0057] Figure 1 A flowchart of a three-dimensional numerical simulation method for high-speed inclined water ejection of a supercavitating projectile provided by the present invention;

[0058] Figure 2 This is a schematic diagram of the mesh division of the present invention;

[0059] Figure 3 This is a schematic diagram of the computational domain and boundary conditions of the present invention;

[0060] Figure 4 This is a schematic diagram of the cavitation evolution during the high-speed inclined water exit process of the supercavitating projectile of the present invention;

[0061] Figure 5 This is a cloud diagram of the supercavitating projectile during its high-speed, tilted water ejection process according to the present invention.

[0062] Figure 6 This is a graph showing the change in the water exit angle of the vehicle body during the water exit process of the present invention. Figure 6 (a) in the graph shows the roll angle as a function of time. Figure 6 (b) in the figure is a graph showing the change of yaw angle over time. Figure 6 (c) in the figure is the pitch angle as a function of time.

[0063] Figure 7 This is a curve showing the change in pitching moment during the water emergence process of the aircraft provided by the present invention. Figure 7 (a) in the figure is the curve of rolling torque changing with time. Figure 7 (b) in the figure is the curve of yaw moment changing with time. Figure 7 (c) in the figure represents the pitching moment as a function of time. Detailed Implementation

[0064] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention:

[0065] like Figure 1 The following are the specific steps of a three-dimensional numerical simulation method for high-speed inclined water ejection of a supercavitating projectile:

[0066] Step 1: Establish a three-dimensional geometric model of the projectile and flow field computational domain, and output the projectile property parameters;

[0067] Step 2: Estimate the size of the projectile's motion area, mesh the projectile and the flow field calculation domain, import the mesh into the fluid solver software, establish the flow field calculation domain and the overlapping calculation domain around the projectile, divide the flow field calculation domain into water and air domains, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions.

[0068] Step 3: Combining the defined flow field computational domain and projectile attribute parameters, and considering the influence of water compressibility on high-speed projectiles, a user-defined function is used to establish the nonlinear relationship between density and pressure of compressible liquids under isothermal conditions.

[0069] Step 4: Define the initial motion parameters of the projectile, import the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions, perform numerical calculations to solve the problem, and obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics of the projectile ejection process.

[0070] Specifically, the establishment of the three-dimensional geometric model in step 1 includes:

[0071] The establishment of the three-dimensional fluid background domain, and the setting of the background domain frame coordinate system O-XYZ are as follows: Figure 3 As shown, O is the origin of the background domain, the X-axis is parallel to the air-water interface, the Y-axis points vertically upwards towards the air-water interface, and the Z-axis is determined by the right-hand rule, pointing outwards; the three-dimensional projectile foreground domain is established, and the coordinate system P-xyz of the projectile foreground domain framework is set as follows. Figure 3 As shown, taking a truncated cone flat-nosed projectile as an example, P is the center of mass of the projectile, the x-axis is parallel to the axis of the projectile and points in the direction of the projectile plane, the z-axis is parallel to the Z-axis and points outward, and the y-axis is determined by the right-hand rule and is perpendicular to the P-xz plane.

[0072] Specifically, the projectile property parameters output in step 1 include:

[0073] Using Creo / Proe modeling software, the model's mass attribute is modified in the established 3D projectile model. After assigning the projectile's material properties, basic attributes such as the projectile's mass m, the projectile's center of gravity coordinates (x, y, z), and the inertial tensor I at the projectile's center of gravity are generated. Specifically:

[0074]

[0075] In the formula, the diagonal elements I of the matrix xx I yy I zzThese are the moments of inertia about the x-axis, y-axis, and z-axis, respectively; the off-diagonal elements I of the matrix. xy I yz I yx I xz I zx I zy It is called the product of inertia.

[0076] Specifically, the mesh generation in step 2 includes:

[0077] The generated 3D model is converted to STEP format and imported into ICEM software to generate a structured mesh. For example... Figure 2 As shown, a cuboid flow field computational domain and a projectile overlap computational domain are established. The projectile motion path and air-water interface in the background flow field computational domain are refined. The spacing of the projectile motion path mesh in the X, Y, and Z directions is ΔX = ΔY = ΔZ = 2 mm, and the minimum spacing of the air-water interface mesh in the Y direction is ΔY = 0.2 mm. The mesh of the projectile surface is also refined, and the minimum spacing of the projectile surface mesh in the y direction is Δy = 0.1 mm.

[0078] Specifically, step 2, which involves dividing the flow field computational domain, includes:

[0079] The volume fraction of air in the flow field computation domain is set to 1. A water area is created based on the estimated projectile motion region, and the volume fraction of water in the water area is set to 1. The pressure gradient distribution in the water area is defined by a user-defined field function, as shown below:

[0080] P o =ρ*g*(Hh) o )

[0081] In the formula, P is the hydrostatic pressure of the fluid at point o in the fluid domain; ρ is the fluid density; g is the acceleration due to gravity; H is the height of the water body; h o The height of point O within the background domain coordinate frame.

[0082] Specifically, the boundary conditions for the fluid solver in step 2 are set as follows:

[0083] like Figure 3As shown, an overlapping mesh technique is used to assemble the foreground projectile computational domain and the background flow field computational domain. The boundary conditions of the fluid solver are: the bottom of the flow field computational domain is a pressure inlet, and the sides and top are pressure outlets. The boundary of the projectile overlapping computational domain is an overlapping mesh boundary condition. This method generates appropriate meshes on subdomains and then couples the data from the donor meshes of the fluid background domain and the foreground domain with the nearby receiver meshes for solution. This avoids the difficulty of traditional single-mesh methods, which require the mesh of the entire computational domain to meet the requirements of geometry, physical properties, and boundary conditions. It allows for more flexible mesh design for the specific needs of each subdomain, thereby significantly improving the efficiency of mesh generation and the accuracy of simulation.

[0084] Specifically, considering the compressibility of the liquid in step 3 includes:

[0085] By introducing Tait's equation of state for liquids, a nonlinear relationship between density and pressure of compressible liquids under isothermal conditions is established, specifically:

[0086]

[0087] in,

[0088]

[0089] The generation of shock waves is related to the propagation speed of the disturbance, which is the speed of sound in water, c, calculated using the following formula:

[0090]

[0091] In the above formula, ρ represents the liquid density under pressure p; ρ0 represents the liquid density under reference pressure p0; n is the density exponent, which is taken as n = 7.15 for liquid water; K0 represents the bulk modulus under reference pressure p0; K represents the bulk modulus under pressure p; and Δp represents the relative pressure.

[0092] Specifically, in step 4:

[0093] This invention uses dynamic mesh technology, which allows the attitude angles (roll angles) of the projectile around the x-axis, y-axis, and z-axis to be set in the configuration file. Yaw angle ψ, pitch angle θ; water exit velocity along the x, y, and z axes u, v, w; displacement L of the projectile's 3D model along the x, y, and z axes within the background domain coordinate frame. x L y L zThe projectile's exit from the water under different operating conditions can be simulated based on actual circumstances. The projectile's motion in the flow field is solved using a 6DOF rigid body motion model. The projectile's motion can be divided into translational motion of the center of mass and rotation about the center of mass. The governing equations for the projectile's translational motion are established in an inertial reference coordinate system:

[0094]

[0095] In the formula: V G F is the translational velocity vector of the projectile's center of mass; m is the mass of the projectile; F G It is the vector of external forces acting on the projectile.

[0096] The governing equations for the projectile's rotation in rigid body coordinates are:

[0097]

[0098] In the formula: ω p I is the projectile angular velocity vector; I is the projectile inertia tensor; M is the projectile external torque vector.

[0099] This invention addresses the problem of projectiles launching water at high speeds. Based on the Navier-Stokes equations and the finite volume method, it employs the Volume of Fluid (VOF) model to solve the multiphase flow system consisting of water, air, and water vapor in a cross-medium flow field. The VOF model treats each phase as a single-medium mixed flow system. During the calculation, the continuity and momentum equations of the mixture are solved to obtain the density, volume fraction, and pressure changes of the mixture in the flow field.

[0100] Continuity equation:

[0101]

[0102] Momentum equation:

[0103]

[0104] In the formula: ρ m t represents the mixed phase density; t represents time; P represents the flow field pressure; μ m The dynamic viscosity of the mixed phase; u i u j The velocity component in the Cartesian coordinate system; u r δ is the velocity of the fluid in the direction of the tensor r. ij For Kronecker notation (δ when i = j) ij =1; when i≠j, δ ij =0; S represents the source phase.

[0105] The expression for the mixed phase density is:

[0106] ρ m =α v ρ v +α g ρ g +(1-α v -α g )ρ1

[0107] In the formula: α v α g These are the volume fractions of water vapor and air, respectively; ρ v , ρ1, ρ g These are the densities of water vapor, water, and air, respectively.

[0108] The expression for the dynamic viscosity of the mixed phase is:

[0109] μ m =α v μ v +α g μ g +(1-α v -α g μ1

[0110] Where: μ v μ1, μ g These are the dynamic viscosities of water vapor, water, and air, respectively.

[0111] Energy equation:

[0112]

[0113] In the formula c p Specific heat capacity, T is temperature, k is the fluid heat transfer coefficient, and S is the specific heat capacity. T It is a viscous dissipation term.

[0114] This invention addresses the problem of projectiles exiting water at high speeds by employing the Reynolds-averaged method to simulate the projectile's entry into the water. Since the Reynolds-averaged method treats instantaneous velocity as a superposition of average and fluctuating velocities, the RANS equations introduce an unknown term: Reynolds stress. The Shear Stress Transport k-omega turbulence model is used to provide turbulent closure for the Reynolds-averaged equations. This model considers the transport of turbulent shear stress and combines the advantages of the k-ε model in simulating the external region with the standard k-ω turbulence model in near-wall calculations, enabling high-accuracy predictions of flow separation and development under adverse pressure gradient conditions.

[0115] The transport equations for turbulent kinetic energy k and specific dissipation rate ω are as follows:

[0116]

[0117] Where: σk σ ω G is the Prandtl number of turbulent flow, which is the turbulent kinetic energy ω and the specific dissipation rate ω. k G ω These are the turbulent kinetic energy and specific dissipation rate generation terms, respectively; S k With S ω For custom items; Y k Y ω The divergent phases, representing turbulent kinetic energy and specific dissipation rate, respectively; D ω It is an orthogonal divergent term.

[0118] Eddy viscosity coefficient μ t The expression is:

[0119]

[0120] In the formula: a * is the low Reynolds number correction factor, a1 is the empirical coefficient, S is the mean strain rate tensor, and F is the mixing function.

[0121] This invention addresses the problem of water ejection from projectiles at high speeds by employing the Schnerr-Sauer cavitation model, which treats the vapor-water medium as a mixture and calculates the water vapor volume fraction using the gas-liquid mass transfer rate.

[0122] The transport equations for the volume fractions of the air and water vapor phases are as follows:

[0123]

[0124] in,

[0125]

[0126] In the formula: R e R is the evaporation rate. c R is the condensation rate. B Let be the radius of the bubble, and n be the number of cavitation bubbles per unit volume, with a value of 1 × 10⁻⁶. 11 .

[0127] The above formula accurately reflects the cavitation phenomenon around the projectile, thereby simulating the evolution of cavitation and flow field during the projectile's entry into water and capturing changes in the flow field around the projectile. Figure 4 , Figure 5 As shown.

[0128] Calculated roll angle The curves showing the changes in yaw angle ψ and pitch angle θ over time are as follows: Figure 6 As shown, the second derivative of the attitude angle with respect to time yields the angular acceleration. The instantaneous net external torques of the projectile about the x, y, and z axes can be calculated using the rigid body rotation law. Figure 7As shown, these are the roll moment, yaw moment, and pitch moment:

[0129]

[0130] In the formula: M ψ M θ These are the projectile's rolling moment, yaw moment, and pitching moment, respectively; I xx I yy I zz These are the moments of inertia about the x-axis, y-axis, and z-axis, respectively. α ψ α θ These are the projectile's roll acceleration, yaw acceleration, and pitch acceleration, respectively.

[0131] This embodiment also provides a three-dimensional numerical simulation system for high-speed inclined water exit of a supercavitating projectile, including:

[0132] The model building unit is used to establish a three-dimensional geometric model of the projectile and flow field computational domain and determine the projectile attribute parameters;

[0133] Model meshing and computational domain division units are used to estimate the size of the projectile's motion area. The three-dimensional geometric model of the projectile and the flow field computational domain is meshed. Based on the mesh, the flow field computational domain and the overlapping computational domain around the projectile are established. The flow field computational domain is divided into water and air domains. A water-air interface is established, and the projectile attribute parameters and fluid solver boundary conditions are set.

[0134] The nonlinear relationship construction unit integrates the divided flow field calculation domain and projectile attribute parameters, considers the influence of water compressibility on high-speed projectiles, and establishes the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions.

[0135] The solution unit defines the initial motion parameters of the projectile and performs numerical solutions based on the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics of the projectile ejection process.

[0136] This invention can simulate the high-speed tilting water ejection process of a projectile under different operating conditions, effectively reducing costs and providing a technical basis for submarine-launched tests.

[0137] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be within the scope of protection of the present invention.

Claims

1. A three-dimensional numerical simulation method for high-speed inclined water ejection of a supercavitating projectile, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional geometric model of the projectile and the flow field computational domain, and determine the projectile property parameters; Step 2: Estimate the size of the projectile's motion area, mesh the three-dimensional geometric model of the projectile and the flow field calculation domain, establish the flow field calculation domain and the overlapping calculation domain around the projectile based on the mesh, divide the flow field calculation domain into water and air domains, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions. Step 3: Combining the defined flow field calculation domain and projectile property parameters, and considering the influence of water compressibility on high-speed projectiles, establish the nonlinear relationship between density and pressure of compressible liquids under isothermal conditions. Step 4: Define the initial motion parameters of the projectile. Based on the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions, perform numerical solutions to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics, and motion characteristics of the projectile during the water ejection process. The numerical solution process specifically includes: using the 6DOF rigid body motion model to solve the projectile motion in the flow field; using the Volume of Fluid model to solve the multiphase flow system consisting of water, air, and water vapor in the cross-medium flow field; using the Shear Stress Transport k-omega turbulence model to provide turbulence closure for the Reynolds-averaged equations; using the Schnerr-Sauer cavitation model to treat the steam-water medium as a mixture; and using the gas-liquid mass transport rate to calculate the water vapor volume fraction. The Volume of Fluid model is used to solve a multiphase flow system consisting of water, air, and water vapor in a cross-medium flow field. Specifically, this involves solving the continuity and momentum equations of the mixture to obtain the density, volume fraction, and pressure changes of the mixture in the flow field. The continuity and momentum equations are as follows: In the formula, ρ m t represents the mixed phase density; t represents time; P represents the flow field pressure; μ m The dynamic viscosity of the mixed phase; u i u j The velocity component in the Cartesian coordinate system; u r δ is the velocity of the fluid in the direction of the tensor r. ij Kronecker notation; S represents the source phase; The Shear Stress Transportk-omega turbulence model is used to provide turbulence closure for the Reynolds-averaged equations, specifically including: Establish the transport equations for turbulent kinetic energy k and specific dissipation rate ω: In the formula, σ k σ ω G is the Prandtl number of turbulent flow, which is the turbulent kinetic energy ω and the specific dissipation rate ω. k G ω These are the turbulent kinetic energy and specific dissipation rate generation terms, respectively; S k With S ω For custom items; Y k Y ω The divergent phases, representing turbulent kinetic energy and specific dissipation rate, respectively; D ω It is an orthogonal divergent term; Define the eddy viscosity coefficient μ t for: In the formula: a * , where a1 is the low Reynolds number correction factor, S is the mean strain rate tensor, and F is the mixing function; The gas-liquid mass transport equation is: in, In the formula: R e R is the evaporation rate. c R is the condensation rate. B Let be the radius of the bubble, and n be the number of cavitation bubbles per unit volume, with a value of 1 × 10⁻⁶. 11 .

2. The three-dimensional numerical simulation method for high-speed inclined water exit of a supercavitating projectile according to claim 1, characterized in that, The projectile attribute parameters include the projectile mass m, the projectile center of gravity coordinates (x, y, z), and the inertial tensor I that determines the projectile center of gravity based on the projectile coordinate frame. The inertial tensor I is: In the formula, the diagonal elements I of the matrix xx I yy I zz These are the moments of inertia about the x-axis, y-axis, and z-axis, respectively; the off-diagonal elements I of the matrix. xy I yz I yx I xz I zx I zy It is called the product of inertia.

3. The three-dimensional numerical simulation method for high-speed inclined water exit of a supercavitating projectile according to claim 1, characterized in that, The mesh generation includes: dividing the background flow field computational domain and the foreground projectile computational domain into structured meshes; refining the mesh for the projectile's motion path and the air-water interface in the background flow field computational domain; and refining the mesh on the projectile's surface. Establishing an overlapping computational domain between the flow field computational domain and the surrounding projectile includes: assembling the foreground projectile computational domain and the background flow field computational domain using overlapping mesh technology. The fluid solver boundary conditions are: the bottom of the flow field computational domain is a pressure inlet, and the surrounding area and top are pressure outlets; the overlapping computational domain boundary is an overlapping mesh boundary condition. Dividing the flow field computational domain into water and air domains specifically includes: The volume fraction of air in the flow field computation domain is set to 1. A water area is created based on the estimated projectile motion region, and the volume fraction of water in the water area is set to 1. The pressure gradient distribution in the water area is defined by the designed field function, which is: P o =ρ*g*(H-h o ) In the formula, P is the hydrostatic pressure of the fluid at point o in the fluid domain; ρ is the fluid density; g is the gravitational acceleration; H is the height of the water body in the background domain frame coordinate system; h o The height of point O in the background domain frame coordinate system.

4. The three-dimensional numerical simulation method for high-speed inclined water exit of a supercavitating projectile according to claim 1, characterized in that, The nonlinear relationship between density and pressure of a compressible liquid under isothermal conditions is as follows: in, In the formula, ρ represents the liquid density under pressure p; ρ0 represents the liquid density under reference pressure p0; n is the density exponent; K0 represents the bulk modulus under reference pressure p0; K represents the bulk modulus under pressure p; and Δp represents the relative pressure.

5. The three-dimensional numerical simulation method for high-speed inclined water exit of a supercavitating projectile according to claim 1, characterized in that, Solving the projectile's motion in the flow field using a 6DOF rigid body motion model specifically includes: The translational motion control equations for the projectile are established in the inertial reference coordinate system as follows: In the formula, V G F is the translational velocity vector of the projectile's center of mass; m is the mass of the projectile; F G It is the vector of external forces acting on the projectile; The governing equations for the projectile's rotation in rigid body coordinates are as follows: In the formula: ω p I is the projectile angular velocity vector; I is the projectile inertia tensor; M is the projectile external torque vector.

6. A three-dimensional numerical simulation system for high-speed inclined water exit of a supercavitating projectile implementing the method of any one of claims 1-5, characterized in that, include: The model building unit is used to establish a three-dimensional geometric model of the projectile and flow field computational domain and determine the projectile attribute parameters; Model meshing and computational domain division units are used to estimate the size of the projectile's motion area. The three-dimensional geometric model of the projectile and the flow field computational domain is meshed. Based on the mesh, the flow field computational domain and the overlapping computational domain around the projectile are established. The flow field computational domain is divided into water and air domains. A water-air interface is established, and the projectile attribute parameters and fluid solver boundary conditions are set. The nonlinear relationship construction unit integrates the divided flow field calculation domain and projectile attribute parameters, considers the influence of water compressibility on high-speed projectiles, and establishes the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions. The solution unit defines the initial motion parameters of the projectile and performs numerical solutions based on the established nonlinear relationship between density and pressure of compressible liquid under isothermal conditions to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics of the projectile ejection process.

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