Three-dimensional numerical simulation method and system for high-speed inclined water outlet of supercavitation projectile

Abstract

The invention provides a three-dimensional numerical simulation method and system for supercavitation projectile high-speed inclined water discharge, and the method comprises the steps: building a three-dimensional geometric model of a projectile and a flow field computational domain, and outputting projectile body attribute parameters; estimating the size of a projectile body motion area, performing grid division on the projectile body and a flow field calculation domain, importing fluid solving software, establishing an overlapping calculation domain, and setting projectile attribute parameters and fluid solver boundary conditions; the influence of compressibility of water on the high-speed projectile is considered, a user-defined function is adopted, and the nonlinear relation between the density and the pressure of the compressible liquid under the isothermal condition is established; initial motion parameters of the projectile are defined, numerical solution is carried out, and cavitation evolution, flow field distribution, stress and motion characteristics in the water outlet process of the high-speed inclined projectile are obtained. According to the invention, the high-speed inclined water outlet process of the projectile under different working conditions can be simulated, the cost can be effectively reduced, and a technical basis is provided for a submarine launching test.

Description

Technical Field

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

[0002] The principle of supercavitating projectiles achieving high-speed underwater movement is based on supercavitation drag reduction technology. When moving at high speed underwater, the head cavitator induces the generation of supercavitation to wrap the projectile body to achieve the drag reduction effect. 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-altitude targets near the water surface can significantly improve the penetration capability and efficiency of supercavitating projectiles. Compared with vertical water exit, underwater supercavitating projectiles have better maneuverability and safety when exiting the water obliquely. There are significant differences in the cavitation evolution and flow field distribution before and after the projectile crosses the free liquid surface under low-speed and high-speed conditions. Therefore, studying the high-speed oblique water exit process of the projectile has important practical significance for predicting the motion characteristics of the underwater submarine penetration process.

[0004] At present, the research on projectile water emergence is mainly focused on low-speed and vertical conditions, and limited research has been conducted on the high-speed inclined water emergence process of projectiles, which has more practical application value. Since high-speed water emergence tests require complex test equipment, are costly, difficult, and have poor repeatability, and the water emergence process involves the mutual coupling of solid, liquid, and gas phases, it has strong instantaneous, nonlinear, and unsteady characteristics, it is difficult to capture and monitor the process of projectiles crossing the free liquid surface using conventional test methods. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a three-dimensional numerical simulation method and system for the high-speed inclined exit of a supercavitating projectile from water, which can capture and monitor the process of the projectile crossing the free liquid surface at high speed and the projectile cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics, so as to save money and provide a technical basis for submarine launch tests.

[0006] A three-dimensional numerical simulation method for a supercavitating projectile exiting water at a high speed and at an angle comprises the following steps:

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

[0008] Step 2: Estimate the size of the projectile 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: Based on the divided flow field calculation domain and projectile property parameters, the influence of water compressibility on high-speed projectiles is considered, and the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions is established;

[0010] Step 4: Define the initial motion parameters of the projectile, and perform numerical solution 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.

[0011] Furthermore, the projectile attribute parameters include the projectile mass m, the projectile center of gravity coordinates (x, y, z), and the inertia tensor I of the projectile center of gravity determined according to the projectile body coordinate frame, and the inertia tensor I is:

[0012]

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

[0014] Furthermore, the grid division includes: dividing the background flow field calculation domain and the foreground projectile calculation domain into structured grids, encrypting the projectile motion path and the air-water interface in the background flow field calculation domain, and encrypting the projectile surface grid; the establishment of the flow field calculation domain and the overlapping calculation domain around the projectile includes: assembling the foreground projectile calculation domain and the background flow field calculation domain using overlapping grid technology; the fluid solver boundary conditions are: the bottom of the flow field calculation domain is the pressure inlet, the surroundings and the top are all pressure outlets, and the overlapping calculation domain boundary is the overlapping grid boundary condition.

[0015] Furthermore, the flow field calculation domain is divided into water domain and air domain, which specifically includes:

[0016] The volume fraction of air in the flow field calculation domain is set to 1. A water area is created according to the estimated missile motion area. 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] Where P is the static 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 area in the background domain frame coordinate system; h o is 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:

[0020]

[0021] in,

[0022]

[0023] Wherein, ρ represents the liquid density at pressure p; ρ0 represents the liquid density at reference pressure p0; n is the density index; K0 represents the bulk modulus at reference pressure p0; K represents the bulk modulus at pressure p; Δp represents the relative pressure.

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

[0025] Furthermore, the 6DOF rigid body motion model is used to solve the motion of the projectile in the flow field, specifically including:

[0026] The translational motion control equation of the projectile is established in the inertial reference coordinate system:

[0027]

[0028] Where V G is the translational velocity vector of the projectile's center of mass; m is the mass of the projectile; F G is the external force vector on the projectile;

[0029] The control equation for the rotation of the projectile in rigid body coordinates is:

[0030]

[0031] Where: p is the projectile angular velocity vector; I is the projectile's inertia tensor; M is the projectile's 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, the density, volume fraction, and pressure changes of the mixture medium in the flow field are obtained by solving the continuity equation and momentum equation of the mixture. The continuity equation and momentum equation are respectively:

[0033]

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

[0035] Furthermore, the Shear Stress Transport k-omega turbulence model is used to provide turbulence closure for the Reynolds averaged equation, including:

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

[0037]

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

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

[0040]

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

[0042] Furthermore, the gas-liquid mass transfer equation is:

[0043]

[0044] in,

[0045]

[0046] Where: R e is the evaporation rate; R c is the condensation rate, R B is the radius of the bubble, n is the number of cavitation bubbles per unit volume, and its value is 1×10 11 .

[0047] A three-dimensional numerical simulation system for supercavitating projectiles exiting water at high speed and inclination, comprising:

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

[0049] Model gridding and computational domain division unit, estimate the size of the projectile motion area, mesh the three-dimensional geometric model of the projectile and the flow field computational domain, establish the flow field computational domain and the overlapping computational domain around the projectile based on the divided grid, divide the flow field computational domain into water domain and air domain, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions;

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

[0051] The solving unit defines the initial motion parameters of the projectile, and based on the established nonlinear relationship between the density and pressure of the compressible liquid under isothermal conditions, performs numerical solution 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 present invention has the following beneficial effects:

[0053] (1) The present invention provides a three-dimensional numerical simulation method for a supercavitating projectile exiting water at a high speed and an inclined direction, which is convenient for simulating the process of projectile exiting water under different working conditions and shows extremely high flexibility and practicality. This method is helpful for in-depth research on the cavitation evolution, flow field distribution, force and motion characteristics of a projectile exiting water at a high speed and an inclined direction.

[0054] (2) The present invention provides a three-dimensional numerical simulation method for high-speed inclined water exit of a supercavitating projectile. The method can conduct an intuitive study on the three-phase coupled and unsteady water exit process, effectively avoiding the problems of complex test equipment, high test cost, great difficulty, poor repeatability, etc. in high-speed water exit tests, thereby significantly reducing the test difficulty and cost.

[0055] (3) The present invention provides a three-dimensional numerical simulation method for a supercavitating projectile exiting water at a high speed and in an inclined manner. The method provides technical support for underwater supercavitating projectile testing and can strike surface targets or low-altitude targets near the water surface, significantly improving the weapon's destructive efficiency and combat effectiveness while also having higher maneuverability and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the implementation of the present invention or the existing technical solutions, the following is a brief introduction to the drawings required for describing the embodiments.

[0057] Figure 1 A flow chart of a three-dimensional numerical simulation method for a supercavitating projectile exiting water at a high speed and at an angle provided by the present invention;

[0058] Figure 2 It is a schematic diagram of grid division of the present invention;

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

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

[0061] Figure 5 It is a cloud diagram of the wetting of the supercavitating projectile during the high-speed tilting water exit process of the projectile of the present invention;

[0062] Figure 6 is a curve diagram of the change of the water outlet angle during the water outlet process of the navigation body of the present invention, Figure 6 (a) is the curve of the roll angle changing with time. Figure 6 (b) is the curve of yaw angle changing with time. Figure 6 (c) is a graph showing the variation of the pitch angle with time;

[0063] Figure 7 The pitch moment variation curve diagram of the navigation body provided by the present invention during the process of leaving the water is shown in FIG. Figure 7 (a) is the curve of rolling moment changing with time. Figure 7 (b) is the curve of yaw moment changing with time. Figure 7 (c) is the curve of pitch moment changing with time DETAILED DESCRIPTION

[0064] In order to make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention:

[0065] like Figure 1 A three-dimensional numerical simulation method for a supercavitation projectile exiting water at a high speed and at an angle is shown, and the specific steps are as follows:

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

[0067] Step 2: Estimate the size of the projectile motion area, mesh the projectile and flow field calculation domain, import the meshed grid 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 domain and air domain, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions;

[0068] Step 3: Based on the divided flow field calculation domain and projectile property parameters, the influence of water compressibility on high-speed projectiles is considered, and a user-defined function is used to establish the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions;

[0069] Step 4: Define the initial motion parameters of the projectile, import the nonlinear relationship between the density and pressure of the compressible liquid under isothermal conditions, perform numerical calculations and solve, 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, the background domain frame coordinate system O-XYZ is set as follows Figure 3 As shown in the figure, O is the origin of the background domain, the X axis is parallel to the air-water interface, the Y axis is vertically upward and points to the air-water interface, and the Z axis is determined by the right-hand rule and points outward; the establishment of the three-dimensional projectile foreground domain, the projectile foreground domain frame coordinate system P-xyz is set as follows Figure 3 As shown, taking a truncated cone flat-head 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 plane of the projectile, 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 output of the projectile property parameters in step 1 includes:

[0073] Using Creo / Proe modeling and design software, change the model mass attributes in the established projectile 3D model, assign the projectile material attributes, and generate the projectile mass m, projectile center of gravity coordinates (x, y, z) and other basic attributes and the inertia tensor I at the projectile center of gravity, specifically:

[0074]

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

[0076] Specifically, the grid division in step 2 includes:

[0077] Convert the above generated 3D model into step format and import it into ICEM software to generate structured mesh. Figure 2 As shown in the figure, a rectangular flow field calculation domain and a projectile overlap calculation domain are established, the projectile motion path and the air-water interface in the background flow field calculation domain are encrypted, the spacing of the projectile motion path grid in the X, Y, and Z directions is ΔX=ΔY=ΔZ=2mm, and the minimum spacing of the air-water interface grid in the Y direction is ΔY=0.2mm; the projectile surface grid is encrypted, and the minimum spacing of the projectile surface grid in the y direction is Δy=0.1mm.

[0078] Specifically, dividing the flow field calculation domain in step 2 includes:

[0079] Set the volume fraction of air in the flow field calculation domain to 1, create a water area based on the estimated projectile motion area, and set the volume fraction of water in the water area 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] Where P is the static 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 area; h o is the height of point o in the background domain coordinate frame.

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

[0083] like Figure 3As shown, the foreground projectile calculation domain and the background flow field calculation domain are assembled by overlapping grid technology, and the boundary conditions of the fluid solver are: the bottom of the flow field calculation domain is the pressure inlet, and the surroundings and the top are all pressure outlets, and the boundary of the projectile overlapping calculation domain is the overlapping grid boundary condition. This method generates appropriate grids on the subdomains, and then couples the data on the donor grids of the fluid background domain and the foreground domain with the nearby receptor grids for solution, avoiding the difficulty of the traditional single grid method that requires the grid of the entire calculation area to meet the requirements of geometry, physical properties and boundary conditions, and can more flexibly design grids according to the specific needs of each subdomain, thereby significantly improving the efficiency of grid generation and the accuracy of simulation.

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

[0085] The Tait liquid state equation is introduced to establish the nonlinear relationship between the density and pressure of compressible liquid under isothermal conditions, specifically:

[0086]

[0087] in,

[0088]

[0089] Among them, the generation of shock waves is related to the propagation speed of disturbances. The propagation speed of disturbances in water is the speed of sound in water c, which is calculated as follows:

[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 index, for liquid water, n = 7.15; K0 represents the bulk modulus under reference pressure p0; K represents the bulk modulus under pressure p; Δp represents relative pressure.

[0092] Specifically, in step 4:

[0093] The present invention uses dynamic grid technology to set the attitude angles of the projectile around the x-axis, y-axis, and z-axis, i.e., the roll angle, in the configuration file. Yaw angle ψ, pitch angle θ; water exit velocity u, v, w on the x-axis, y-axis, and z-axis; displacement L of the projectile 3D model on the x-axis, y-axis, and z-axis in the background domain coordinate frame x , L y , L zThe process of projectile exiting water under different working conditions can be simulated according to the actual situation. The motion of the projectile in the flow field is solved by the 6DOF rigid body motion model. The motion of the projectile can be divided into the translation of the center of mass and the rotation around the center of mass. The translation motion control equation of the projectile is established in the inertial reference coordinate system:

[0094]

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

[0096] The governing equation for the rotation of the projectile in rigid body coordinates is:

[0097]

[0098] Where: p is the projectile angular velocity vector; I is the projectile's inertia tensor; M is the projectile's external torque vector.

[0099] The present invention aims at the problem of projectiles exiting water at an angle under high speed. Based on the finite volume method of the Navier-Stokes equation, the Volume of Fluid multiphase flow model is used to solve the multiphase flow system consisting of water, air and water vapor in the cross-medium flow field. The VOF model treats each phase as a mixed flow system of a single medium. During the calculation process, the continuity equation and momentum equation of the mixture are solved to obtain the density, volume fraction and pressure changes of the mixture medium in the flow field.

[0100] Continuity equation:

[0101]

[0102] Momentum equation:

[0103]

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

[0105] The expression of mixed phase density is:

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

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

[0108] The expression of the mixed phase dynamic viscosity 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 are the dynamic viscosities of water vapor, water and air respectively.

[0111] Energy equation:

[0112]

[0113] Where c p is the specific heat capacity, T is the temperature, k is the fluid heat transfer coefficient, S T is the viscous dissipation term.

[0114] The present invention aims at the problem of the inclined exit of the projectile from the water under high-speed conditions, and uses the Reynolds time-averaged method to simulate the process of the projectile entering the water. Since the Reynolds time-averaged method treats the instantaneous velocity as the superposition of the average velocity and the pulsating velocity, the unknown term of Reynolds stress is added to the RANS equations. The Shear Stress Transport k-omega turbulence model is used to provide turbulent closure for the Reynolds average equation. The model takes into account the turbulent shear stress transmission, combines the advantages of the k-ε model in the external area simulation and the standard k-ω turbulence model in the near-wall calculation, and can make a high-precision prediction of the flow separation and development under the adverse pressure gradient condition.

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

[0116]

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

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

[0119]

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

[0121] The present invention aims at the problem of inclined water discharge of projectiles under high-speed conditions and selects to use the Schnerr-Sauer cavitation model, which regards the steam-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:

[0123]

[0124] in,

[0125]

[0126] Where: R e is the evaporation rate; R c is the condensation rate, R B is the radius of the bubble, n is the number of cavitation bubbles per unit volume, and its value is 1×10 11 .

[0127] The above formula can accurately reflect the cavitation phenomenon around the projectile, thereby simulating the evolution of cavitation and flow field during the projectile entering the water and capturing the flow field changes around the projectile. Figure 4 , Figure 5 shown.

[0128] Calculated roll angle The curves of yaw angle ψ and pitch angle θ changing with time are as follows: Figure 6 As shown, the second-order derivative of the attitude angle with respect to time can be obtained to obtain the angular acceleration. The instantaneous total external torque of the projectile on the x-axis, y-axis, and z-axis can be obtained from the law of rigid body fixed axis rotation, as shown in Figure 7As shown, rolling moment, yaw moment and pitch moment:

[0129]

[0130] Where: M ψ 、M θ are the rolling moment, yaw moment and pitch moment of the projectile respectively; I xx ,I yy ,I zz are the moments of inertia about the x-axis, y-axis, and z-axis respectively; α ψ , α θ They are the roll acceleration, yaw acceleration and pitch acceleration of the projectile respectively.

[0131] This embodiment also provides a three-dimensional numerical simulation system for a supercavitating projectile exiting water at a high speed and at an angle, comprising:

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

[0133] Model gridding and computational domain division unit, estimate the size of the projectile motion area, mesh the three-dimensional geometric model of the projectile and the flow field computational domain, establish the flow field computational domain and the overlapping computational domain around the projectile based on the divided grid, divide the flow field computational domain into water domain and air domain, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions;

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

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

[0136] The invention can simulate the high-speed inclined water exit process of a projectile under different working conditions, can effectively reduce the cost, and provide a technical basis for submarine launch tests.

[0137] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be within the protection scope of the present invention.

Claims

1. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and inclination, characterized in that: The steps include: Step 1: Establish a three-dimensional geometric model of the projectile and flow field calculation domain, and determine the projectile attribute parameters; Step 2: Estimate the size of the projectile 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: Based on the divided flow field calculation domain and projectile property parameters, the influence of water compressibility on high-speed projectiles is considered, and the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions is established; Step 4: Define the initial motion parameters of the projectile, and perform numerical solution 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.

2. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and at an angle 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 inertia tensor I of the projectile center of gravity determined according to the projectile body coordinate frame. The inertia tensor I is: In the formula, the diagonal elements of the matrix I xx ,I yy ,I zz are the moments of inertia about the x-axis, y-axis, and z-axis respectively; the off-diagonal elements of the matrix I xy ,I yz ,I yx ,I xz ,I zx ,I zy It is called the product of inertia.

3. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and at an angle according to claim 1, characterized in that: The grid division includes: dividing the background flow field calculation domain and the foreground projectile calculation domain into structured grids, encrypting the projectile motion path and the air-water interface in the background flow field calculation domain, and encrypting the projectile surface grid; the establishment of the flow field calculation domain and the overlapping calculation domain around the projectile includes: assembling the foreground projectile calculation domain and the background flow field calculation domain by using overlapping grid technology; the boundary condition of the fluid solver is: the bottom of the flow field calculation domain is the pressure inlet, the surroundings and the top are all pressure outlets, and the overlapping calculation domain boundary is the overlapping grid boundary condition; dividing the flow field calculation domain into water domain and air domain specifically includes: The volume fraction of air in the flow field calculation domain is set to 1. A water area is created based on the estimated missile motion area. 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 ) Where P is the static 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 area in the background domain frame coordinate system; h o is the height of point o in the background domain frame coordinate system.

4. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and obliquely according to claim 1, characterized in that: The nonlinear relationship between density and pressure of a compressible liquid under isothermal conditions is: in, Wherein, ρ represents the liquid density at pressure p; ρ0 represents the liquid density at reference pressure p0; N is the density index; K0 represents the bulk modulus at reference pressure p0; K represents the bulk modulus at pressure p; Δp represents the relative pressure.

5. The three-dimensional numerical simulation method for a supercavitating projectile exiting water at a high speed and at an angle according to claim 1, characterized in that: The numerical solution specifically includes: using a 6DOF rigid body motion model to solve the motion of the projectile in the flow field, using the Volume of Fluid model to solve the multiphase flow system composed of water, air, and water vapor in the cross-medium flow field, using the Shear Stress Transport k-omega turbulence model to provide turbulent closure for the Reynolds average equation, using the Schnerr-Sauer cavitation model to treat the steam-water medium as a mixture, and using the gas-liquid mass transfer rate to calculate the water vapor volume fraction.

6. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and obliquely according to claim 5, characterized in that: The 6DOF rigid body motion model is used to solve the motion of the projectile in the flow field, including: The translational motion control equation of the projectile is established in the inertial reference coordinate system: Where V G is the translational velocity vector of the projectile's center of mass; m is the mass of the projectile; F G is the external force vector on the projectile; The control equation for the rotation of the projectile in rigid body coordinates is: Where: p is the projectile angular velocity vector; I is the projectile's inertia tensor; M is the projectile's external torque vector.

7. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and obliquely according to claim 5, characterized in that: The Volume of Fluid model is used to solve the multiphase flow system composed of water, air and water vapor in the cross-medium flow field. Specifically, the density, volume fraction and pressure changes of the mixture medium in the flow field are obtained by solving the continuity equation and momentum equation of the mixture. The continuity equation and momentum equation are respectively: In the formula, ρ m is the density of the mixed phase; t is the time; P represents the flow field pressure; μ m is the dynamic viscosity of the mixed phase; u i 、u j is the velocity component in the Cartesian coordinate system; u r is the velocity of the fluid in the direction of tensor r; δ ij is the Kronecker symbol; S represents the source phase.

8. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and obliquely according to claim 5, characterized in that: The Shear Stress Transport k-omega turbulence model is used to provide turbulence closure for the Reynolds averaged equations, including: Establish the transport equation of turbulent kinetic energy k and specific dissipation rate ω: In the formula, σ k , σ ω is the turbulent Prandtl number of turbulent kinetic energy ω and specific dissipation rate ω; G k , G ω are the turbulent kinetic energy and specific dissipation rate generation terms respectively; S k With S ω For custom items; Y k , Y ω are the divergent phases of turbulent kinetic energy and specific dissipation rate respectively; D ω is an orthogonal divergence term; Define the eddy viscosity coefficient μ t for: Where: a * is the low Reynolds number correction coefficient, a1 is the empirical coefficient, S is the average strain rate tensor, and F is the mixing function.

9. A three-dimensional numerical simulation method for a supercavitating projectile exiting water at high speed and in an inclined manner according to claim 5, characterized in that: The gas-liquid mass transfer equation is: in, Where: R e is the evaporation rate; R c is the condensation rate, R B is the radius of the bubble, n is the number of cavitation bubbles per unit volume, and its value is 1×10 11 .

10. A three-dimensional numerical simulation system for high-speed oblique water exit of a supercavitating projectile for implementing the method described in any one of claims 1 to 9, characterized in that: include: A model building unit is used to establish a three-dimensional geometric model of the projectile and the flow field calculation domain and determine the projectile attribute parameters; Model gridding and computational domain division unit, estimate the size of the projectile motion area, mesh the three-dimensional geometric model of the projectile and the flow field computational domain, establish the flow field computational domain and the overlapping computational domain around the projectile based on the divided grid, divide the flow field computational domain into water domain and air domain, establish the water-air interface, and set the projectile attribute parameters and fluid solver boundary conditions; The nonlinear relationship building unit integrates the divided flow field calculation domain and projectile property parameters, considers the effect of water compressibility on high-speed projectiles, and establishes the nonlinear relationship between density and pressure of compressible liquid under isothermal conditions; The solving unit defines the initial motion parameters of the projectile, and based on the established nonlinear relationship between the density and pressure of the compressible liquid under isothermal conditions, performs numerical solution to obtain the cavitation evolution characteristics, flow field distribution characteristics, force characteristics and motion characteristics of the projectile ejection process.

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