A fast calculation method and system for the trajectory of truncated oval projectile entering water

Abstract

The present invention proposes a fast calculation method for the trajectory of a truncated oval projectile entering water, establishes a fixed coordinate system and a projectile coordinate system; establishes a 3DOF projectile motion equation and initial conditions in the projectile coordinate system; calculates the radius of the cavitation section of the truncated oval projectile entering water, and then obtains the upper vertex coordinates and lower vertex coordinates of each cavitation section in the plane of the fixed coordinate system; calculates the component model of the fluid dynamics of the projectile head in the projectile coordinate system, the resultant moment model of the fluid dynamics of the projectile head on the projectile mass center, the projectile wetted area model, the projectile tail sliding lift model, the projectile tail resultant moment model, the projectile tail friction calculation model, and the component model of the projectile mass center gravity in the projectile coordinate system; substitutes the calculation result of the projectile external force into the 3DOF projectile motion equation in the projectile coordinate system, and performs time advancement solution. The present invention can comprehensively obtain some details of the truncated oval projectile entering water, and the calculation speed is fast.

Description

Technical Field

[0001] The present invention relates to cross-medium weapon launching technology, and in particular to a method and system for quickly calculating the trajectory of a truncated oval projectile entering water. Background Art

[0002] The water entry problem has a wide range of applications in the field of engineering technology. The water entry trajectory refers to the trajectory of the projectile from entering the water to the end of the movement. When the speed of the projectile in the water exceeds 50m / s, supercavitation will be generated around the projectile. The determination of the supercavitation morphology after entering the water is the key to predicting the underwater trajectory in the initial stage of entering the water. Moreover, the different head structures, water entry angles and speeds of the projectile when entering the water will make the trajectory very different. When designing large-caliber water-entering projectiles, the internal charge and water entry stability are taken into consideration. The head is mostly designed to be a truncated oval. The problem of solving the water entry trajectory of truncated oval projectiles has been a hot topic of research in recent years.

[0003] The process of projectile entering water involves the interaction between solid, liquid and vapor, which is a complex transient time-varying physical process. Currently, there are few studies on the trajectory of truncated oval projectile entering water, and the main methods are experimental research and numerical simulation.

[0004] The paper "Experimental investigation of oblique water entry of high-speed truncated cone projectiles: Cavity dynamics and impact load" uses high-speed photography technology to analyze the effects of different truncated cone projectiles on flow field characteristics and structural forces. The paper "Velocity attenuation and cavitation expansion characteristics of truncated oval projectiles entering water horizontally" uses high-speed photography technology to study the effects of different projectile shapes on water entry trajectory stability and velocity attenuation laws. During the experiment, a high-speed camera was placed at a fixed position on the water surface to observe the process of the projectile entering the water at a certain angle. The trajectory characteristics were analyzed by recording images and experimental results. However, due to the limitations of the test technology, the experimental observation can only observe a limited field of view, and the changes in the projectile attitude angle, fluid dynamics, and tail slapping effects cannot be observed.

[0005] The document "Numerical Simulation of Multiphase Flow Field of Cavitation of High-speed Projectile Entering Water" analyzes the ballistic characteristics, projectile forces and cavitation characteristics of truncated oval projectiles during water entry through numerical simulation. The document "Research on Trajectory and Stability of Supercavitating Vehicle Entering Water" analyzes the influence of wetted area and pitch angle of water entry on cavitation morphology and underwater trajectory when the projectile enters water at an angle through numerical simulation. In numerical simulation, the cavitation characteristics and ballistic characteristics of water entry trajectory are mainly studied through differential equation iteration. In simulation, it is necessary to select appropriate physical models and large-scale grid calculations to obtain effective accuracy. Each calculation is a single working condition, which will consume a lot of computing power and time, and cannot efficiently and quickly calculate the cavitation characteristics and ballistic characteristics of the truncated oval projectile entering water. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for quickly calculating the water-entering trajectory of a truncated oval projectile.

[0007] The technical solution to achieve the purpose of the present invention is: a method for quickly calculating the trajectory of a truncated oval projectile entering water, comprising the following steps:

[0008] Step 1, establish a fixed coordinate system and a projectile coordinate system;

[0009] Step 2, establish the 3DOF projectile motion equation in the projectile coordinate system;

[0010] Step 3, setting initial conditions, including the velocity of the center of mass of the projectile, the initial attitude angle of the projectile when the projectile enters the water, and the angular velocity of the projectile in the fixed coordinate plane;

[0011] Step 4, establish a calculation model for the radius of the cavitation section of the truncated oval projectile entering the water, substitute the velocity of the projectile's center of mass, calculate the radius of the cavitation section of the truncated oval projectile entering the water, and then obtain the upper vertex coordinates and lower vertex coordinates of each cavitation section in the plane of the fixed coordinate system;

[0012] Step 5, establish the projectile external force model, calculate the component model of the projectile head fluid dynamics in the projectile body coordinate system, the resultant torque model of the projectile head fluid dynamics on the projectile mass center, the projectile wetted area model, the projectile tail sliding lift model, the projectile tail resultant torque model, the projectile tail friction calculation model, and the component model of the projectile mass center gravity in the projectile body coordinate system;

[0013] Step 6, substitute the calculated results of the projectile's external force into the 3DOF projectile motion equation in the projectile coordinate system, and perform time-advancing solution in combination with the time step to obtain the fluid dynamic change curve of the truncated egg-shaped projectile during water entry, the projectile center of mass velocity curve, the projectile attitude angle curve, the displacement curve of the projectile center of mass in the fixed coordinate system, and the cavitation morphology of the truncated egg-shaped projectile entering the water.

[0014] Further, step 1, establish a fixed coordinate system (o E xE z E ) and the projectile coordinate system (o B x B z B ), the specific method is:

[0015] Fixed coordinate system origin o E Placed at the horizontal surface, x E The axis is parallel to the horizontal plane, z E The positive direction of the axis is perpendicular to the horizontal plane and upward; the origin of the projectile coordinate system is o B Located at the center of gravity of the projectile, x B The positive direction of the axis points to the projectile head along the projectile axis, z B The positive direction of the axis is perpendicular to x B Axial direction; x B Axis and x E The angle between the axes is the projectile attitude angle θ, located at x E The upper side of the axis is positive.

[0016] Further, step 2, establish the 3DOF projectile motion equation in the projectile coordinate system, the specific method is:

[0017] The 3DOF projectile motion equation in the projectile coordinate system is:

[0018]

[0019]

[0020]

[0021] Where m is the mass of the projectile, u and w are the components of the velocity of the center of mass of the projectile in the projectile coordinate system, and q is the velocity of the center of mass of the projectile in the fixed coordinate system x. E o E z E Angular velocity of the plane, G x and G z is the component of the projectile's gravity in the projectile's coordinate system, θ is the projectile's attitude angle, and F D and F L is the component of the fluid dynamics of the projectile head in the projectile body coordinate system, F f and F p is the fluid friction and gliding lift of the wetted part of the projectile tail, I y is the moment of inertia of the projectile, M c M is the resultant moment of the fluid dynamics of the projectile head on the center of mass of the projectile, p is the resultant moment of the fluid dynamics at the tail of the projectile on the center of mass of the projectile;

[0022] The calculation formulas for the projectile mass center velocity, projectile attitude angle and projectile mass center coordinates in a fixed coordinate system are:

[0023] V=u 2 +w 2

[0024] θ=θ 0 -qt

[0025]

[0026]

[0027] Where V is the velocity of the projectile center of mass, θ 0 is the initial projectile attitude angle when the projectile enters the water, t is the sailing time after the projectile enters the water, (x Et , z Et ) is the coordinate of the center of mass of the projectile in the fixed coordinate system.

[0028] Further, in step 4, a calculation model for the cross-sectional radius of the cavitation bubble of a truncated oval projectile entering water is established, and the velocity of the center of mass of the projectile is substituted to calculate the cross-sectional radius of the cavitation bubble of the truncated oval projectile entering water, and then the upper vertex coordinates and the lower vertex coordinates of each cavitation bubble cross section in the plane of the fixed coordinate system are obtained. The specific method is:

[0029] Considering the variation law of the radius of the truncated oval projectile and the principle of independent expansion of cavitation, the first cavitation section generated when the projectile enters the water is numbered as 1. By analogy, the i-th cavitation section generated when the projectile enters the water is numbered as i. For the i-th cavitation section, its radius calculation model is:

[0030]

[0031] Where t is the sailing time after the projectile enters the water, τ i is the moment when the i-th cavitation section is formed, R c (t,τ i ) is the cavitation radius of the i-th cavitation section at time t, R 0 R is the radius of the projectile head plane, n is the radius of the projectile; ρ is the density of water, m is the mass of the projectile, V 0 is the velocity of the center of mass of the projectile at t = 0, C dx is the resistance coefficient of the disk cavitation device, N is the empirical coefficient, which is taken as 1.4; V(τ i ) is τ i The velocity of the center of mass of the projectile at the moment, σ(τ i ) is τ i The projectile cavitation number at time ;

[0032] Drag coefficient C of disc cavitator dx The calculation formula is:

[0033] C dx =Cd0 (1+σ(τ i ))

[0034] In the formula, C d0 is the drag coefficient of the disc cavitator when the cavitation number is 0, which is taken as 0.827;

[0035] τ i The projectile cavitation number σ(τ i ) is calculated as:

[0036]

[0037] In the formula, p ∞ The local pressure at the head of the truncated cone projectile, p is the saturated vapor pressure of water at ambient temperature;

[0038] Based on the principle of independent expansion of cavitation, the shape position of cavitation in the longitudinal plane can be determined by the upper and lower vertices of each cavitation section. In a fixed coordinate system, the calculation formula for the vertex coordinates of each cavitation section in the longitudinal plane is:

[0039] Upper vertex:

[0040] Lower vertex:

[0041] In the formula, x Ei and z Ei is the coordinate of the vertex of the i-th cavitation section in the fixed coordinate system, x Eoi and z Eoi is τ i The coordinates of the center of mass of the projectile in the fixed coordinate system at the moment, θ(τ i ) is the projectile τ i The pitch angle of the projectile at time, x c It is the distance from the plane of the truncated cone projectile head to the center of mass.

[0042] Further, step 5, establish the projectile external force model, calculate the component model of the projectile head fluid dynamics in the projectile body coordinate system, the resultant torque model of the projectile head fluid dynamics on the projectile mass center, the projectile wetted area model, the projectile tail sliding lift model, the projectile tail resultant torque model, the projectile tail friction calculation model, and the component model of the projectile mass center gravity in the projectile body coordinate system. The specific method is:

[0043] After entering the water, the truncated oval projectile head can be regarded as a disc cavitator. The component of the fluid dynamics of the projectile head in the projectile body coordinate system is F D 、F L and the resultant moment M of the fluid dynamics of the projectile head on the center of mass of the projectile c The calculation formula is:

[0044]

[0045] F L =0

[0046] M c =0

[0047] Where ρ is the density of water, V is the velocity of the projectile center of mass, and the characteristic area of ​​the cavitator is C dx is the drag coefficient of the disk cavitator, and the cavitator angle of attack u and w are the velocity of the center of mass of the projectile in the projectile coordinate system (o B x B z B ), x c is the distance from the plane of the truncated cone projectile head to the center of mass;

[0048] The cavitation coordinates in the fixed coordinate system are converted into coordinates in the projectile coordinate system. In the projectile coordinate system, the projectile is evenly sliced ​​into a finite number of sections, numbered starting from the tail, the bottom of the projectile is numbered 1, and the projectile sections are numbered in sequence. The wetting depth of each projectile section penetrating into the cavitation wall is calculated, and the wetting depth of the projectile at the first section of the bottom of the projectile is defined as h. When the wetting depth is 0, the distance between the projectile section and the tail section of the projectile is calculated as the projectile's wetting length l, and the projectile's wetting area S w Approximately fan-shaped, the projectile wetted area S w The calculation formula is:

[0049]

[0050] Where h is the wetting depth of the projectile, l is the wetting length of the projectile, r is the radius of the tail of the projectile, R is the radius of the cavitation bubble at the tail of the projectile, ΔR = Rr;

[0051] The tail of the projectile glides and lifts F p The calculation formula is:

[0052]

[0053] Where r is the radius of the projectile tail, R is the radius of the cavitation bubble at the projectile tail, ΔR = Rr, ρ is the density of water, V is the velocity of the projectile center of mass, h is the wetting depth of the projectile, and the velocity of the projectile tail V is 1 =-w+q(Lx c )+V wc , L is the length of the truncated cone projectile, V wc is the cavitation lateral velocity, V 2 is the contraction velocity of the tail cavitation bubble, contraction is positive;

[0054] Resultant moment at the projectile tail M p The calculation formula is:

[0055]

[0056] In the formula, x c is the distance from the plane of the truncated cone projectile head to the center of mass, l is the wetted length of the projectile;

[0057] Friction force at the projectile tail F f The calculation formula is:

[0058]

[0059]

[0060] In the formula, ρ is the density of water, u is the flow rate of water, S w is the wetted area, C f is the friction coefficient, Reynolds number Re = ρul / μ, μ is the viscosity coefficient of water;

[0061] The component of the projectile's center of mass gravity in the projectile's body coordinate system G x and G z The calculation formula is:

[0062] G x = -mg sinθ

[0063] G z =-mg cosθ.

[0064] A fast calculation system for a truncated oval projectile entering water trajectory realizes fast calculation of a truncated oval projectile entering water trajectory based on the fast calculation method for the truncated oval projectile entering water trajectory.

[0065] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the fast calculation of the water-entry trajectory of a truncated oval projectile is realized based on the fast calculation method of the water-entry trajectory of the truncated oval projectile.

[0066] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the fast calculation of the water-entry trajectory of a truncated oval projectile is realized based on the fast calculation method of the water-entry trajectory of the truncated oval projectile.

[0067] Compared with the prior art, the present invention has the following significant advantages: 1) Compared with other water entry trajectory calculation methods, the calculation method provided by the present invention is more suitable for projectiles with a truncated oval head shape. 2) Compared with the limitations brought by experimental observation, the technical method provided by the present invention can more comprehensively obtain some details of the truncated oval projectile entering the water. 3) Compared with the long calculation cycle of numerical simulation, the technical method provided by the present invention can quickly calculate while ensuring effectiveness and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of the fixed coordinate system and the projectile coordinate system established for the present invention.

[0069] Figure 2 Schematic diagram of the cross-section of each cavitation bubble during the process of the truncated oval projectile entering the water.

[0070] Figure 3 Schematic diagram of the head fluid dynamics of a truncated oval projectile during its entry into water.

[0071] Figure 4 Schematic diagram of the tail fluid dynamics during the entry of a truncated oval projectile into water. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0073] The present invention is based on the principle of independent expansion of cavitation, takes into account the body characteristics of truncated oval projectiles, and can effectively calculate the cavitation characteristics, fluid dynamics and ballistic trajectory of truncated oval projectiles during water entry by establishing new cavitation morphology algorithms and wetting characteristics algorithms, thus providing an efficient and accurate calculation method for studying the water entry trajectory of truncated oval projectiles. A fast calculation method for the water entry trajectory of a truncated oval projectile specifically comprises the following steps:

[0074] Step 1: Establish a fixed coordinate system (o E x E z E ) and the projectile coordinate system (o B x B z B ).

[0075] like Figure 1 , fix the origin of the coordinate system o E Placed at the horizontal surface, x E The axis is parallel to the horizontal plane, z E The positive direction of the axis is perpendicular to the horizontal plane and upward. The origin of the projectile coordinate system is o B Located at the center of gravity of the projectile, x BThe positive direction of the axis points to the projectile head along the projectile axis, z B The positive direction of the axis is perpendicular to x B Axis direction. x B Axis and x E The angle between the axes is the projectile attitude angle θ, located at x E The upper side of the axis is positive.

[0076] Step 2: Establish the 3DOF projectile motion equation in the projectile coordinate system, calculate the projectile center of mass velocity V, projectile attitude angle θ and the coordinates of the projectile center of mass in the fixed coordinate system (x Et , z Et ).

[0077] The 3DOF projectile motion equation in the projectile coordinate system is:

[0078]

[0079]

[0080]

[0081] Where m is the mass of the projectile, u and w are the components of the velocity of the center of mass of the projectile in the projectile coordinate system, and q is the velocity of the center of mass of the projectile in the fixed coordinate system x. E o E z E Angular velocity of the plane, G x and G z is the component of the projectile's gravity in the projectile's coordinate system, θ is the projectile's attitude angle, and F D and F L is the component of the fluid dynamics of the projectile head in the projectile body coordinate system, F f and F p is the fluid friction and gliding lift of the wetted part of the projectile tail, I y is the moment of inertia of the projectile, M c M is the resultant moment of the fluid dynamics of the projectile head on the center of mass of the projectile, p It is the resultant moment of the fluid dynamics at the tail of the projectile on the center of mass of the projectile.

[0082] The calculation formulas for the projectile mass center velocity, projectile attitude angle and projectile mass center coordinates in a fixed coordinate system are:

[0083] V=u 2 +w 2

[0084] θ=θ 0 -qt

[0085]

[0086]

[0087] Where V is the velocity of the projectile center of mass, θ 0 is the initial projectile attitude angle when the projectile enters the water, t is the sailing time after the projectile enters the water, (x Et , z Et ) is the coordinate of the center of mass of the projectile in the fixed coordinate system.

[0088] Set the initial conditions, V 0 is the initial projectile mass center velocity, u=V 0 sinθ 0 and w = V 0 cosθ 0 ,θ 0 is the initial projectile attitude angle when the projectile enters the water, (0, 0) is the initial coordinate of the center of mass of the projectile in the fixed coordinate system, and the projectile is in the fixed coordinate system x E o E z E The angular velocity of rotation of the plane is q=0.

[0089] Step 3, establish a calculation model for the cross-sectional radius of the cavitation bubble when the truncated oval projectile enters the water, substitute the center of mass velocity of the projectile, and obtain the cross-sectional radius of the cavitation bubble when the truncated oval projectile enters the water.

[0090] like Figure 2 , considering the variation law of the radius of the truncated oval projectile and the principle of independent expansion of cavitation, the first cavitation section generated when the projectile enters the water is numbered as 1, and by analogy, the i-th cavitation section generated when the projectile enters the water is numbered as i. For the i-th cavitation section, its radius calculation model is:

[0091]

[0092] Where t is the sailing time after the projectile enters the water, τ i is the moment when the i-th cavitation section is formed, R c (t,τ i ) is the cavitation radius of the i-th cavitation section at time t, R 0 R is the radius of the projectile head plane, n is the radius of the projectile. ρ is the density of water, m is the mass of the projectile, V 0 is the velocity of the center of mass of the projectile at t = 0, C dx is the resistance coefficient of the disk cavitator, and N is an empirical coefficient, which is taken as 1.4. i ) is τ i The velocity of the center of mass of the projectile at the moment, σ(τ i ) is τ i The projectile cavitation number at time .

[0093] Drag coefficient C of disc cavitator dx The calculation formula is:

[0094] C dx =C d0 (1+σ(τ i ))

[0095] C d0 is the drag coefficient of the disc cavitator when the cavitation number is 0, which is taken as 0.827.

[0096] τ i The projectile cavitation number σ(τ i ) is calculated as:

[0097]

[0098] p ∞ The local pressure at the head of the truncated cone projectile, p, is the saturated vapor pressure of water at ambient temperature.

[0099] Step 4: Calculate the fixed coordinate system x E o E z E The upper and lower vertex coordinates of each cavitation section in the plane.

[0100] like Figure 2 Based on the principle of independent expansion of cavitation, the shape position of cavitation in the longitudinal plane can be determined by the upper and lower vertices of each cavitation section. In a fixed coordinate system, the calculation formula for the vertex coordinates of each cavitation section in the longitudinal plane is:

[0101] Upper vertex:

[0102] Lower vertex:

[0103] In the formula, x Ei and z Ei is the coordinate of the vertex of the i-th cavitation section in the fixed coordinate system, x Eoi and z Eoi is τ i The coordinates of the center of mass of the projectile in the fixed coordinate system at the moment, θ(τ i ) is the projectile τ i The pitch angle of the projectile at time, x c It is the distance from the plane of the truncated cone projectile head to the center of mass.

[0104] Step 5: Calculate the component F of the fluid dynamics of the projectile head in the projectile body coordinate system D 、F L and the resultant moment M of the fluid dynamics of the projectile head on the center of mass of the projectile c .

[0105] like Figure 3After entering the water, the truncated oval projectile head can be regarded as a disk cavitator. The component of the fluid dynamics of the projectile head in the projectile body coordinate system is F D 、F L and the resultant moment M of the fluid dynamics of the projectile head on the center of mass of the projectile c The calculation formula is:

[0106]

[0107] F L =0

[0108] M c =0

[0109] Where ρ is the density of water, V is the velocity of the projectile center of mass, and the characteristic area of ​​the cavitator is C dx is the drag coefficient of the disk cavitator, and the cavitator angle of attack u and w are the velocity of the center of mass of the projectile in the projectile coordinate system (o B x B z B ), x c It is the distance from the plane of the truncated cone projectile head to the center of mass.

[0110] Step 6: Calculate the projectile wetted area S w .

[0111] like Figure 3 , convert the cavitation coordinates in the fixed coordinate system of step 4 into the coordinates in the projectile coordinate system. In the projectile coordinate system, slice the projectile equally into a finite number of sections, numbering them starting from the tail. The bottom of the projectile is numbered 1, and the projectile sections are numbered in sequence. The wetting depth of each projectile section penetrating the cavitation wall is calculated. The wetting depth of the projectile at the first section of the bottom of the projectile is defined as h. When the wetting depth is 0, the distance between the projectile section and the tail section of the projectile is calculated as the projectile's wetting length l, and the projectile's wetting area S is w It is approximately fan-shaped. The projectile wetted area S w The calculation formula is:

[0112]

[0113] Where h is the wetting depth of the projectile, l is the wetting length of the projectile, r is the radius of the tail of the projectile, R is the radius of the cavitation bubble at the tail of the projectile, and ΔR = Rr.

[0114] Step 7: Calculate the lift F of the projectile tail p and the resultant moment M at the projectile tail p .

[0115] The tail of the projectile glides and lifts F p The calculation formula is:

[0116]

[0117] Where r is the radius of the projectile tail, R is the radius of the cavitation bubble at the projectile tail, ΔR = Rr, ρ is the density of water, V is the velocity of the projectile center of mass, h is the wetting depth of the projectile, and the velocity of the projectile tail V is 1 =-w+q(Lx c )+V wc , L is the length of the truncated cone projectile, V wc is the cavitation lateral velocity, V 2 is the contraction velocity of the tail cavitation bubble, contraction is positive.

[0118] Resultant moment at the projectile tail M p The calculation formula is:

[0119]

[0120] x c is the distance from the plane of the truncated cone projectile head to the center of mass, and l is the wetted length of the projectile.

[0121] Step 8: Calculate the friction force F at the tail of the projectile f .

[0122] Friction force at the projectile tail F f The calculation formula is:

[0123]

[0124]

[0125] In the formula, ρ is the density of water, u is the flow rate of water, S w is the wetted area, C f is the friction coefficient, Reynolds number Re = ρul / μ, μ is the viscosity coefficient of water.

[0126] Step 9: Calculate the component G of the projectile's center of mass gravity in the projectile coordinate system x and G z .

[0127] The component of the projectile's center of mass gravity in the projectile's body coordinate system G x and G z The calculation formula is:

[0128] G x = -mg sinθ

[0129] G z = -mg cosθ

[0130] Step 10, perform time-marching solution.

[0131] Combined with the initial conditions, the external forces of the projectile calculated in steps 5, 6, 7, 8, and 9 are brought into the motion equation in step 2, the time step is set, and the time-marching solution is performed using the Euler method.

[0132] Step 11, visualize the results obtained by time solution, and obtain the projectile center of mass velocity Vt curve, projectile attitude angle θ-t curve, projectile center of mass displacement curve in a fixed coordinate system and fluid dynamic change curve during the truncated egg-shaped projectile entering the water.

[0133] The results of step 10 are visualized to obtain the velocity Vt curve of the center of mass of the truncated egg-shaped projectile during the water entry process, the curve of the projectile attitude angle θ-t, and the displacement curve of the center of mass of the projectile in the fixed coordinate system. The results of step 4 are visualized to obtain the cavitation morphology of the truncated egg-shaped projectile entering the water, and the results calculated in steps 5, 6, 7, and 8 are visualized to obtain the fluid dynamic change curve of the truncated egg-shaped projectile during the water entry process.

[0134] The present invention also proposes a system for quickly calculating the water-entry trajectory of a truncated oval projectile. Based on the method for quickly calculating the water-entry trajectory of a truncated oval projectile, the system can realize the quick calculation of the water-entry trajectory of a truncated oval projectile.

[0135] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the fast calculation of the water-entry trajectory of a truncated oval projectile is realized based on the fast calculation method of the water-entry trajectory of the truncated oval projectile.

[0136] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the fast calculation of the water-entry trajectory of a truncated oval projectile is realized based on the fast calculation method of the water-entry trajectory of the truncated oval projectile.

[0137] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0138] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A fast calculation method for the trajectory of a truncated oval projectile entering water. It is characterized in that The steps include: Step 1, establish a fixed coordinate system and a projectile coordinate system; Step 2, establish the 3DOF projectile motion equation in the projectile coordinate system; Step 3, setting initial conditions, including the velocity of the center of mass of the projectile, the initial attitude angle of the projectile when the projectile enters the water, and the angular velocity of the projectile in the fixed coordinate plane; Step 4, establish a calculation model for the radius of the cavitation section of the truncated oval projectile entering the water, substitute the velocity of the projectile's center of mass, calculate the radius of the cavitation section of the truncated oval projectile entering the water, and then obtain the upper vertex coordinates and lower vertex coordinates of each cavitation section in the plane of the fixed coordinate system; Step 5, establish the projectile external force model, calculate the component model of the projectile head fluid dynamics in the projectile body coordinate system, the resultant torque model of the projectile head fluid dynamics on the projectile mass center, the projectile wetted area model, the projectile tail sliding lift model, the projectile tail resultant torque model, the projectile tail friction calculation model, and the component model of the projectile mass center gravity in the projectile body coordinate system; Step 6, substituting the calculated result of the projectile external force into the 3DOF projectile motion equation in the projectile body coordinate system, performing time advancement solution in combination with the time step, and obtaining the fluid dynamic change curve of the truncated egg-shaped projectile during water entry, the velocity curve of the projectile center of mass, the projectile attitude angle curve, the displacement curve of the projectile center of mass in the fixed coordinate system, and the cavitation morphology of the truncated egg-shaped projectile when entering the water; Step 4, establish a calculation model for the cross-sectional radius of the cavitation bubble of a truncated oval projectile entering water, substitute the velocity of the projectile's center of mass, calculate the cross-sectional radius of the cavitation bubble of a truncated oval projectile entering water, and then obtain the upper vertex coordinates and lower vertex coordinates of each cavitation cross section in the plane of the fixed coordinate system. The specific method is: Considering the variation law of the radius of the truncated oval projectile and the principle of independent expansion of cavitation, the first cavitation section generated when the projectile enters the water is numbered as 1. By analogy, the i-th cavitation section generated when the projectile enters the water is numbered as i. For the i-th cavitation section, its radius calculation model is: Where t is the sailing time after the projectile enters the water, τ i is the moment when the i-th cavitation section is formed, R c (t,τ i ) is the cavitation radius of the i-th cavitation section at time t, R 0 R is the radius of the projectile head plane, n is the radius of the projectile; ρ is the density of water, m is the mass of the projectile, V 0 is the velocity of the center of mass of the projectile at t = 0, C dx is the resistance coefficient of the disk cavitation device, N is the empirical coefficient, which is taken as 1.4; V(τ i ) is τ i The velocity of the center of mass of the projectile at the moment, σ(τ i ) is τ i The projectile cavitation number at the moment; Drag coefficient C of disc cavitator dx The calculation formula is: C dx =C d0 (1+σ(τ i )) In the formula, C d0 is the drag coefficient of the disc cavitator when the cavitation number is 0, which is taken as 0.827; τ i The projectile cavitation number σ(τ i ) is calculated as: In the formula, p ∞ The local pressure at the head of the truncated cone projectile, p is the saturated vapor pressure of water at ambient temperature; Based on the principle of independent expansion of cavitation, the shape position of the cavitation in the longitudinal plane can be determined by the upper and lower vertices of each cavitation section. In a fixed coordinate system, the calculation formula for the vertex coordinates of each cavitation section in the longitudinal plane is: Upper vertex: Lower vertex: In the formula, x Ei and z Ei is the coordinate of the vertex of the i-th cavitation section in the fixed coordinate system, x Eoi and z Eoi is τ i The coordinates of the center of mass of the projectile in the fixed coordinate system at the moment, θ(τ i ) is the projectile τ i The pitch angle of the projectile at time, x c is the distance from the plane of the truncated cone projectile head to the center of mass; Step 5, establish the projectile external force model, calculate the component model of the projectile head fluid dynamics in the projectile body coordinate system, the resultant torque model of the projectile head fluid dynamics on the projectile mass center, the projectile wetted area model, the projectile tail sliding lift model, the projectile tail resultant torque model, the projectile tail friction calculation model, and the component model of the projectile mass center gravity in the projectile body coordinate system. The specific method is: After entering the water, the truncated oval projectile head can be regarded as a disc cavitator. The component of the fluid dynamics of the projectile head in the projectile body coordinate system is F D 、F L and the resultant moment M of the fluid dynamics of the projectile head on the center of mass of the projectile c The calculation formula is: F L ＝0 M c ＝0 Where ρ is the density of water, V is the velocity of the projectile center of mass, and the characteristic area of ​​the cavitator is C dx is the drag coefficient of the disk cavitator, and the cavitator angle of attack u and w are the velocity of the center of mass of the projectile in the projectile coordinate system o B x B z B The component in x c is the distance from the plane of the truncated cone projectile head to the center of mass; The cavitation coordinates in the fixed coordinate system are converted into coordinates in the projectile coordinate system. In the projectile coordinate system, the projectile is evenly sliced ​​into a finite number of sections, numbered starting from the tail, the bottom of the projectile is numbered 1, and the projectile sections are numbered in sequence. The wetting depth of each projectile section penetrating into the cavitation wall is calculated, and the wetting depth of the projectile at the first section of the bottom of the projectile is defined as h. When the wetting depth is 0, the distance between the projectile section and the tail section of the projectile is calculated as the projectile's wetting length l, and the projectile's wetting area S w Approximately fan-shaped, the projectile wetted area S w The calculation formula is: Where h is the wetting depth of the projectile, l is the wetting length of the projectile, r is the radius of the tail of the projectile, R is the radius of the cavitation bubble at the tail of the projectile, ΔR = Rr; The tail of the projectile glides and lifts F p The calculation formula is: Where r is the radius of the projectile tail, R is the radius of the cavitation bubble at the projectile tail, ΔR = Rr, ρ is the density of water, V is the velocity of the projectile center of mass, h is the wetting depth of the projectile, and the velocity of the projectile tail V is 1 =-w+q(Lx c )+V wc , L is the length of the truncated cone projectile, V wc is the cavitation lateral velocity, V 2 is the contraction velocity of the tail cavitation bubble, contraction is positive; Resultant moment at the projectile tail M p The calculation formula is: In the formula, x c is the distance from the plane of the truncated cone projectile head to the center of mass, l is the wetted length of the projectile; Friction force at the projectile tail F f The calculation formula is: In the formula, ρ is the density of water, u is the flow rate of water, S w is the wetted area, C f is the friction coefficient, Reynolds number Re = ρul / μ, μ is the viscosity coefficient of water; The component of the projectile's center of mass gravity in the projectile's body coordinate system G x and G z The calculation formula is: G x =-mgsinθ G z =-mgcosθ。 2. The method for quickly calculating the water-entry trajectory of a truncated oval projectile according to claim 1, It is characterized in that Step 1: Establish a fixed coordinate system o E x E z E and the projectile coordinate system o B x B z B , the specific method is: Fixed coordinate system origin o E Placed at the water entry point on the horizontal surface, x E The axis is parallel to the horizontal plane, z E The positive direction of the axis is perpendicular to the horizontal plane and upward; the origin of the projectile coordinate system is o B Located at the center of gravity of the projectile, x B The positive direction of the axis points to the projectile head along the projectile axis, z B The positive direction of the axis is perpendicular to x B Axial direction; x B Axis and x E The angle between the axes is the projectile attitude angle θ, located at x E The upper side of the axis is positive.

3. The method for quickly calculating the water-entry trajectory of a truncated oval projectile according to claim 1, It is characterized in that Step 2: Establish the 3DOF projectile motion equation in the projectile coordinate system. The specific method is: The 3DOF projectile motion equation in the projectile coordinate system is: Where m is the mass of the projectile, u and w are the components of the velocity of the center of mass of the projectile in the projectile coordinate system, and q is the velocity of the center of mass of the projectile in the fixed coordinate system x. E o E z E Angular velocity of the plane, G x and G z is the component of the projectile's gravity in the projectile's coordinate system, θ is the projectile's attitude angle, and F D and F L is the component of the fluid dynamics of the projectile head in the projectile body coordinate system, F f and F p is the fluid friction and gliding lift of the wetted part of the projectile tail, I y is the moment of inertia of the projectile, M c M is the resultant moment of the fluid dynamics of the projectile head on the center of mass of the projectile, p is the resultant moment of the fluid dynamics at the tail of the projectile on the center of mass of the projectile; The calculation formulas for the projectile mass center velocity, projectile attitude angle and projectile mass center coordinates in a fixed coordinate system are: V-u 2 +w 2 θ=θ 0 -qt Where V is the velocity of the projectile center of mass, θ 0 is the initial projectile attitude angle when the projectile enters the water, t is the sailing time after the projectile enters the water, (x Et , z Et ) is the coordinate of the center of mass of the projectile in the fixed coordinate system.

4. A fast calculation system for the trajectory of a truncated oval projectile entering water, It is characterized in that Based on the method for rapid calculation of the water-entry trajectory of a truncated oval projectile as described in any one of claims 1 to 3, rapid calculation of the water-entry trajectory of a truncated oval projectile is achieved.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the fast calculation method for the water entry trajectory of a truncated oval projectile is based on the fast calculation method for the water entry trajectory of a truncated oval projectile as described in any one of claims 1 to 3 to achieve fast calculation of the water entry trajectory of a truncated oval projectile.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for quickly calculating the water-entry trajectory of a truncated oval projectile based on any one of claims 1 to 3 is used to implement a quick calculation of the water-entry trajectory of a truncated oval projectile.

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