CN113821996B - Novel rapid calculation method for high-speed entry trajectory of projectile - Google Patents
Novel rapid calculation method for high-speed entry trajectory of projectile Download PDFInfo
- Publication number
- CN113821996B CN113821996B CN202110792349.3A CN202110792349A CN113821996B CN 113821996 B CN113821996 B CN 113821996B CN 202110792349 A CN202110792349 A CN 202110792349A CN 113821996 B CN113821996 B CN 113821996B
- Authority
- CN
- China
- Prior art keywords
- cavitation
- projectile
- speed
- coordinate system
- section
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000004364 calculation method Methods 0.000 title claims abstract description 20
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 70
- 238000000034 method Methods 0.000 claims abstract description 38
- 238000009736 wetting Methods 0.000 claims abstract description 16
- 239000012530 fluid Substances 0.000 claims description 12
- 230000005484 gravity Effects 0.000 claims description 9
- 238000006073 displacement reaction Methods 0.000 claims description 7
- 229920001971 elastomer Polymers 0.000 claims description 7
- 239000000806 elastomer Substances 0.000 claims description 7
- CLOMYZFHNHFSIQ-UHFFFAOYSA-N clonixin Chemical compound CC1=C(Cl)C=CC=C1NC1=NC=CC=C1C(O)=O CLOMYZFHNHFSIQ-UHFFFAOYSA-N 0.000 claims description 3
- 230000000149 penetrating effect Effects 0.000 claims description 3
- 230000000007 visual effect Effects 0.000 claims 2
- 230000003446 memory effect Effects 0.000 abstract description 2
- 238000004088 simulation Methods 0.000 description 8
- 238000005516 engineering process Methods 0.000 description 6
- 238000011160 research Methods 0.000 description 5
- 238000010009 beating Methods 0.000 description 2
- 239000007788 liquid Substances 0.000 description 2
- 230000035515 penetration Effects 0.000 description 2
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/08—Fluids
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Fluid Mechanics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Computing Systems (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- Algebra (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Aerodynamic Tests, Hydrodynamic Tests, Wind Tunnels, And Water Tanks (AREA)
Abstract
The invention discloses a novel rapid calculation model for a high-speed projectile water inlet trajectory, which is based on the independent expansion principle of cavitation, considers the memory effect of cavitation, realizes accurate calculation of cavitation form and hydrodynamic force in the high-speed projectile water inlet process by establishing a novel cavitation form algorithm and a wetting characteristic algorithm, and realizes rapid calculation of the movement posture and the trajectory of a revolving body in the high-speed projectile water inlet process. The method can effectively calculate the generation, development, closure and other processes of the bubble shape in the high-speed water entering process of the projectile, and accurately calculate the hydrodynamic force and the movement gesture in the running process of the projectile. The invention can provide a quick and effective calculation method for researching the high-speed water entry trajectory of the projectile and the stability design of the projectile.
Description
Technical Field
The invention relates to a novel rapid calculation method for high-speed entry trajectory of a projectile, and belongs to the technical field of cross-medium weapon launching.
Background
The water inlet problem is an important field of hydrodynamic research, and has wide application prospect in natural disciplines and engineering technologies, wherein high-speed water inlet is a focus in recent years. The high-speed water-entering process of the projectile involves complex physical processes such as water-entering impact, liquid level breaking, fluid-solid coupling and the like, and has strong nonlinearity and transient property. When the projectile enters water at high speed, water entering cavitation bubbles are generated by the head part, the projectile body is wrapped in the cavity, and the resistance is reduced. Because the projectile can be disturbed when the water is filled, the projectile can swing in the cavitation, and the tail beating phenomenon occurs, so that the trajectory is changed. The high-speed water-entering bullet head, the water-entering angle, the speed and the like can greatly change the trajectory. Therefore, the key of the high-speed water entry technology of the projectile is to find out the influence factors of the structural characteristics of the projectile on the cavitation characteristic and the ballistic characteristic of the high-speed water entry, so as to quantify the structure of the projectile.
The projectile has a certain longitudinal plane rotation angular velocity under the influence of disturbance and water surface impact force at the initial stage of entering water. When the water surface and the direction of the projectile form an included angle, the water surface at the lower side of the projectile expands along radial cavitation, and the upper side of the projectile is free from the constraint of lateral water pressure, so that liquid surface splashing can be formed, surface closure cannot be formed, and the curvatures of the upper surface and the lower surface of the cavitation are inconsistent. After entering water, the projectile swings in the cavitation bubbles, and the attitude angle of the projectile also changes. When the tail of the projectile penetrates into the wall of the cavity, the tail of the projectile generates sliding lifting force to prevent the rotation of the projectile. As the depth of penetration of the tail of the projectile into the wall of the cavity increases, the kinetic energy of the projectile's rotation is dissipated and the pitch angle of the projectile reaches a critical point when the projectile reaches its maximum penetration depth. The wetted portion of the tail of the projectile is then subjected to radially high velocity fluid to rapidly push the projectile out of the cavity wall in the opposite rotational direction. During this process, the attitude angle of the projectile will change significantly, peaking. And too large a projectile attitude angle can reduce projectile stability and bend the trajectory. Therefore, the cavitation form, fluid power and trajectory of the emergent bullet after entering water at high speed are accurately calculated, the influence of the structural change of the projectile on the trajectory characteristic is found, theoretical basis is provided for optimizing the bullet shape, and the projectile structure with good stability is designed.
The current research method for high-speed water entry mainly comprises the steps of researching cavitation morphology, movement posture and displacement of the projectile after high-speed water entry through experimental observation and numerical simulation and through a high-speed shooting technology in the document Shallow angle water entry of ballistic projectiles, and finding that the length-diameter ratio of the projectile has an influence on ballistic stability. The document Experimental investigation on trajectory stability of high-speed water entry projectiles researches the ballistic characteristics of different high-speed projectiles after water entering through high-speed photography, and determines the influence of the projectile head type and the water entering speed on the stability of the high-speed water entering ballistic. The literature of the study of high-speed inclined water entry of a supercavitation projectile with a small water entry angle researches the ballistic stability of the high-speed projectile with a small angle through a high-speed photographic technology, and the sideslip angle is found to influence the stability of the high-speed water entry projectile. The literature of the study on cavitation and hydrodynamic characteristics of vertical water entry of high-speed projectile is used for researching cavitation form and hydrodynamic characteristics of vertical water entry of supersonic projectile through numerical simulation. Numerical simulation of the high-speed oblique water entry process of the projectile researches the influence of the initial attack angle of the projectile on the water entry trajectory through numerical simulation.
In the above-mentioned documents, the high-speed water entry trajectory is studied, and in the experimental aspect, the high-speed water entry process of the projectile is observed at a certain angle at a fixed position above the water surface by a high-speed photography technique, and the ballistic characteristics are analyzed by experimentally recording images and experimental results. In the numerical simulation aspect, cavitation characteristics and ballistic characteristics of the water inlet trajectory are mainly researched through differential equation iteration. However, experimental observation is limited by the test technology, so that only a limited field of view can be observed, and the change of the attitude angle of the projectile, the hydrodynamic force, the tail beating effect and the like cannot be observed. The numerical simulation is required to select a proper physical model and large-scale grid calculation to obtain effective precision, each calculation is under a single working condition, a large amount of calculation force and time are consumed, and cavitation characteristics, ballistic characteristics and the like of a high-speed water inlet process cannot be calculated efficiently and rapidly.
Disclosure of Invention
The invention solves the problems that: the method overcomes the limitations of the existing high-speed water entry trajectory experiment observation technology and the low calculation efficiency of numerical simulation, and provides a rapid calculation method of the high-speed water entry trajectory of the projectile. The invention provides a novel rapid calculation method for high-speed projectile entry trajectory of a projectile based on the independent expansion principle of cavitation and considering the memory effect of cavitation. The calculation method can effectively calculate cavitation characteristics, hydrodynamic force, trajectory and the like of the projectile in the high-speed water entering process, and provides a high-efficiency and accurate technical method for researching the cavitation characteristics and trajectory characteristics of the projectile in the high-speed water entering process.
The technical scheme of the invention is as follows:
(1) Build as shown in FIG. 1, build a fixed coordinate system (o E x E z E ) And an elastomer coordinate system (o B x B z B ). Fixed coordinate system origin o E Is placed at the water inlet point x of the horizontal plane E The axis being parallel to the horizontal plane, z E The axial direction is vertical and the horizontal surface is upward. Projectile coordinate system origin o B Is positioned at the center of gravity of the revolving body, x B The positive direction of the shaft points to the head of the revolution body along the axis of the revolution body, z B Vertical x of positive axis direction B In the axial direction. X is x B Axis and x E The included angle of the shaft is the pitch angle of the revolving bodyθ, at x E The upper side of the shaft is positive.
(2) Establishing a 3DOF motion equation of the projectile in an projectile body coordinate system, and solving the velocity component, attitude angle and displacement of the projectile body by combining initial conditions:
wherein m is the mass of the revolution body, I y Is the rotational inertia of the revolution body, u and w are the components of the mass center speed of the revolution body in an elastomer coordinate system, q is the mass center speed of the revolution body in x E o E z E Angular velocity of rotation of plane G x And G z F is the component of the weight of the revolution body in the projectile body coordinate system D And F L F is the component of the rotor head hydrodynamic force in the body coordinate system f And F p Friction force and sliding lifting force of fluid of wet part at tail part of revolving body, M c Is the resultant moment of the hydrodynamic force of the head of the revolution body to the mass center of the revolution body, M p Is the resultant moment of the fluid power at the tail of the revolving body to the mass center of the revolving body.
(3) The 1 st cavitation section generated at the moment of entering the projectile is numbered, and so on. According to the mass center speed of the outgoing projectile solved in the step (2), the radius of a newly-generated cavity section and a generated cavity section of the outgoing projectile head can be solved:
wherein τ i And t is the navigation time of the rotator after water entering, wherein the time is the moment when the ith cavitation section is formed. R is R c (t,τ i ) For the cavitation radius of the ith cavitation section at time t, R n Is the radius of the round section of the revolving body head. N is an empirical factor, taken as 1.4.C (C) d0 The drag coefficient of the disk cavitation device when the cavitation number is 0 is taken as 0.83.V (τ) i ) Sum sigma (tau) i ) Is a revolution body tau i Centroid velocity and cavitation number at time.
(4) The whole movement process of the water-entering cavitation bubbles can be regarded as an independent expansion process of each section of the cavitation bubbles according to a certain rule. In the longitudinal plane, the shape of the cavitation bubbles may be defined by the upper and lower apices of the respective cavitation bubble sections. In a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
upper vertex:
the following vertices:
wherein x is Ei And z Ei Is the coordinates of the cavitation vertex in a fixed coordinate system, x Eoi And z Eoi Is the coordinates of the mass point of the revolution body in a fixed coordinate system, θ (τ i ) Is a revolution body tau i Pitch angle, x of moment gyrorotor c Is the distance from the head of the revolution body to the position of the gravity center.
(5) The head of the revolving body after high-speed water entering can be regarded as a disc cavitation device, and the fluid power can be calculated as follows:
F L ＝0
M c ＝0
in the cavitation device characteristic areaCavitation device angle of attack->
(6) Converting the cavitation coordinate under the fixed coordinate system of the step (4) into the coordinate under the projectile body coordinate system, converting the cavitation coordinate under the fixed coordinate system into the coordinate under the projectile body coordinate system, uniformly slicing the revolving body into a limited cross section under the projectile body coordinate system, and sequentially calculating the wetting depth of each section of the revolving body penetrating into the cavitation wall surface from the tail part number, wherein the first section of the tail part is used as the wetting depth h of the revolving body, and when the wetting depth is 0, calculating the distance between the section of the revolving body and the section of the tail part of the revolving body to be used as the wetting length l of the revolving body, and calculating the wetting area S of the revolving body w Approximately sector-shaped, can be calculated by a sector area formula.
(7) Sliding lift force F of tail part of revolving body p Can be calculated as follows:
wherein R is the radius of the tail of the revolving body, deltaR=R-R, R is the cavitation radius of the tail of the revolving body, and V 1 ＝-w+q(L-x c )+V wc L is the length of the revolution body, V wc Is the transverse velocity of cavitation bubbles, V 2 The tail cavitation shrinkage speed is positive.
The tail part of the revolving body has the following resultant moment:
(8) Friction force F of tail part of revolving body f Can be calculated as follows:
in the formula, the Reynolds number R e Rhol/μ, μ is the dynamic viscosity of water, which is 1.01X10 at 20 ° - 3 Pa.s, wetted area S w Can be calculated as follows:
(9) Component G of projectile centroid gravity in projectile coordinate system x And G z The method comprises the following steps:
G x ＝-mgsinθ
G z ＝-mgcosθ
(10) And (3) bringing the external force of the projectile calculated in the steps (5), (6), (7), (8) and (9) into the equation of motion in the step (2), and setting the time step to perform time-marching solution through the Euler method.
(11) And (3) visualizing the result of the step (4) to obtain a high-speed water entering cavitation form, initializing the results calculated in the steps (5), (6), (7) and (8) to obtain a hydrodynamic force change curve in the high-speed water entering process, and visualizing the result solved in the step (2) to obtain a centroid speed, an angular speed, displacement and motion gesture change curve in the high-speed water entering process of the projectile.
Compared with the prior art, the invention has the advantages that:
(1) Compared with limitations caused by experimental observation, the technical method provided by the invention can more comprehensively obtain some details of high-speed water entering of the projectile.
(2) The calculation period of the relative numerical simulation is long, and the technical method provided by the invention can be used for quickly calculating under the condition of ensuring the effectiveness and the accuracy.
Drawings
FIG. 1 is a fixed coordinate system and an elastomeric coordinate system established in accordance with the present invention.
Figure 2 shows a cross section of the individual cavitation bubbles during high speed entry of the projectile into water.
Figure 3 shows the head hydrodynamic forces during high speed entry of the projectile into water.
Figure 4 shows tail hydrodynamic forces during high speed entry of the projectile.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings, comprising the steps of:
(1) As shown in fig. 1, a fixed coordinate system (o E x E z E ) And an elastomer coordinate system (o B x B z B ). Fixed coordinate system origin o E Is placed at the water inlet point x of the horizontal plane E The axis being parallel to the horizontal plane, z E The axial direction is vertical and the horizontal surface is upward. Projectile coordinate system origin o B Is positioned at the center of gravity of the revolving body, x B The positive direction of the shaft points to the head of the revolution body along the axis of the revolution body, z B Vertical x of positive axis direction B In the axial direction. X is x B Axis and x E The included angle of the axes is the pitching angle theta of the revolving body and is positioned at x E The upper side of the shaft is positive.
(2) Establishing a 3DOF motion equation of the projectile in an projectile body coordinate system, and solving the velocity component, attitude angle and displacement of the projectile body by combining initial conditions:
wherein m is the mass of the revolution body, I y Is the rotational inertia of the revolution body, u and w are the components of the mass center speed of the revolution body in an elastomer coordinate system, q is the mass center speed of the revolution body in x E o E z E Angular velocity of rotation of plane G x And G z F is the component of the weight of the revolution body in the projectile body coordinate system D And F L F is the component of the rotor head hydrodynamic force in the body coordinate system f And F p Friction force and sliding lifting force of fluid of wet part at tail part of revolving body, M c For the hydrodynamic pair revolution of the head of the revolution bodyMoment of mass center of mass, M p Is the resultant moment of the fluid power at the tail of the revolving body to the mass center of the revolving body.
(3) As in fig. 2, the 1 st cavitation cross section generated at the moment of entry of the projectile into water is numbered, and so on. According to the mass center speed of the outgoing projectile solved in the step (2), the radius of a newly-generated cavity section and a generated cavity section of the outgoing projectile head can be solved:
wherein τ i And t is the navigation time of the rotator after water entering, wherein the time is the moment when the ith cavitation section is formed. R is R c (t,τ i ) For the cavitation radius of the ith cavitation section at time t, R n Is the radius of the round section of the revolving body head. N is an empirical factor, taken as 1.4.C (C) d0 The drag coefficient of the disk cavitation device when the cavitation number is 0 is taken as 0.83.V (τ) i ) Sum sigma (tau) i ) Is a revolution body tau i Centroid velocity and cavitation number at time.
(4) As shown in fig. 2, the whole movement process of the water-entering cavitation bubbles can be regarded as an independent expansion process of each section of the cavitation bubbles according to a certain rule. In the longitudinal plane, the shape of the cavitation bubbles may be defined by the upper and lower apices of the respective cavitation bubble sections. In a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
upper vertex:
the following vertices:
wherein x is Ei And z Ei Is the coordinates of the cavitation vertex in a fixed coordinate system, x Eoi And z Eoi Is the coordinates of the mass point of the revolution body in a fixed coordinate system, θ (τ i ) Is a revolution body tau i Pitch angle, x of moment gyrorotor c For the head to the gravity center position of the revolution bodyIs a distance of (3).
(5) As shown in fig. 3, the head of the revolution body after high-speed water entering can be regarded as a disk cavitation device, and the fluid power can be calculated as follows:
F L ＝0
M c ＝0
in the cavitation device characteristic areaCavitation device angle of attack->
(6) Referring to fig. 4, the coordinates of the cavities in the fixed coordinate system of step (4) are converted into the coordinates in the elastic body coordinate system, the coordinates of the cavities in the fixed coordinate system are converted into the coordinates in the elastic body coordinate system, the rotation body is equally sliced into a limited number of sections in the elastic body coordinate system, the wetting depth of each rotation body section penetrating into the cavity wall surface is sequentially calculated from the tail part number, wherein the first section of the tail part is used as the wetting depth h of the rotation body, when the wetting depth is 0, the distance between the rotation body section and the section of the tail part of the rotation body is calculated as the wetting length l of the rotation body, and the wetting area S of the rotation body is calculated w Approximately sector-shaped, can be calculated by a sector area formula.
(7) Sliding lift force F of tail part of revolving body p Can be calculated as follows:
wherein R is the radius of the tail of the revolving body, deltaR=R-R, R is the cavitation radius of the tail of the revolving body, and V 1 ＝-w+q(L-x c )+V wc L is the length of the revolution body, V wc Is the transverse velocity of cavitation bubbles, V 2 The tail cavitation shrinkage speed is positive.
The tail part of the revolving body has the following resultant moment:
(8) Friction force F of tail part of revolving body f Can be calculated as follows:
in the formula, the Reynolds number R e Rhol/μ, μ is the dynamic viscosity of water, which is 1.01X10 at 20 ° - 3 Pa.s, wetted area S w Can be calculated as follows:
(9) Component G of projectile centroid gravity in projectile coordinate system x And G z The method comprises the following steps:
G x ＝-mg sinθ
G z ＝-mg cosθ
(10) And (3) bringing the external force of the projectile calculated in the steps (5), (6), (7), (8) and (9) into the equation of motion in the step (2), and setting the time step to perform time-marching solution through the Euler method.
(11) And (3) visualizing the result of the step (4) to obtain a high-speed water entering cavitation form, initializing the results calculated in the steps (5), (6), (7) and (8) to obtain a hydrodynamic force change curve in the high-speed water entering process, and visualizing the result solved in the step (2) to obtain a centroid speed, an angular speed, displacement and motion gesture change curve in the high-speed water entering process of the projectile.
The foregoing is considered to be within the scope of the invention, and is not described in detail herein.
Claims (5)
1. A novel rapid calculation method for high-speed entry trajectory of a projectile is characterized by comprising the following steps: comprising
Step one, a fixed coordinate system (o E x E z E ) And an elastomer coordinate system (o B x B z B )；
Step two, establishing an elastomer coordinate system (o B x B z B ) The following three-degree-of-freedom motion equation is used for solving the velocity component, attitude angle and displacement of the projectile by combining initial conditions:
wherein m is the mass of the revolution body, I y Is the rotational inertia of the revolution body, u and w are the components of the mass center speed of the revolution body in an elastomer coordinate system, q is the mass center speed of the revolution body in x E o E z E Angular velocity of rotation of plane G x And G z F is the component of the weight of the revolution body in the projectile body coordinate system D And F L F is the component of the rotor head hydrodynamic force in the body coordinate system f And F p Friction force and sliding lifting force of fluid of wet part at tail part of revolving body, M c Is the resultant moment of the hydrodynamic force of the head of the revolution body to the mass center of the revolution body, M p The torque of the fluid power at the tail of the revolving body to the mass center of the revolving body;
step three, the 1 st cavitation interface number generated when the projectile enters water is sequentially analogized, and the newly generated cavitation section of the head part of the emergent projectile and the radius of the generated cavitation section are solved;
step four, regarding the whole movement process of the water-entering cavitation bubbles as an independent expansion process of each section of the cavitation bubbles according to a rule, wherein the process is realized by defining the vertex coordinates of each cavitation bubble section in a longitudinal plane;
step five, calculating the external force of the emergent bullet to be substituted into the motion equation in the step two, and setting a time step length to perform time propulsion solution through an Euler method;
and step six, obtaining a visual result, wherein the visual result comprises a high-speed water entering cavitation form, a fluid dynamic change curve, a centroid speed, an angular speed, displacement and motion gesture change curve.
2. The novel rapid calculation method for high-speed water entry trajectory of projectile according to claim 1, wherein: in the first step, the origin o of the fixed coordinate system E Is placed at the water inlet point x of the horizontal plane E The axis being parallel to the horizontal plane, z E The axial direction is vertical to the horizontal surface upwards;
projectile coordinate system origin o B Is positioned at the center of gravity of the revolving body, x B The positive direction of the shaft points to the head of the revolution body along the axis of the revolution body, z B Vertical x of positive axis direction B Axially; x is x B Axis and x E The included angle of the axes is the pitching angle theta of the revolving body and is positioned at x E The upper side of the shaft is positive.
3. The novel rapid calculation method for high-speed water entry trajectory of projectile according to claim 1, wherein: in the third step, according to the mass center speed of the outgoing projectile solved in the second step, the newly-generated cavitation cross section of the outgoing projectile head and the radius of the generated cavitation cross section can be solved:
wherein τ i The time t is the navigation time of the rotator after water entering, and is the time of forming the ith cavitation section; r is R c (t，τ i ) For the cavitation radius of the ith cavitation section at time t, R n The radius of the circular section of the revolving body head is the radius; n is an empirical coefficient taken as1.4；C d0 The resistance coefficient of the disk cavitation device when the cavitation number is 0 is 0.83; v (τ) i ) Sum sigma (tau) i ) Is a revolution body tau i Centroid velocity and cavitation number at time.
4. The novel rapid calculation method for high-speed water entry trajectory of projectile according to claim 1, wherein: in the fourth step, in the longitudinal plane, the outline of the cavitation bubbles can be determined by the upper and lower vertexes of the section of each cavitation bubble; in a fixed coordinate system, the vertex coordinates of each cavitation section in the longitudinal plane can be calculated as follows:
upper vertex:
the following vertices:
wherein x is Ei And z Ei Is the coordinates of the cavitation vertex in a fixed coordinate system, x Eoi And z Eoi Is the coordinates of the mass point of the revolution body in a fixed coordinate system, θ (τ i ) Is a revolution body tau i Pitch angle, x of moment gyrorotor c Is the distance from the head of the revolution body to the position of the gravity center.
5. The novel rapid calculation method for high-speed water entry trajectory of projectile according to claim 4, wherein: the projectile external force comprises F D ，F L ，M c ，F p ，M p ，G x And G z The respective solving process is as follows:
the head of the revolving body after high-speed water entering can be regarded as a disc cavitation device, and the fluid power can be calculated as follows:
F L ＝0
M c ＝0
in the cavitation device characteristic areaCavitation device angle of attack->
Converting the cavitation coordinate under the fixed coordinate system into the coordinate under the projectile body coordinate system, uniformly slicing the revolving body into a limited cross section under the projectile body coordinate system, and sequentially calculating the wetting depth of each section of the revolving body penetrating into the cavitation wall surface from the tail part number, wherein the first section of the tail part is used as the wetting depth h of the revolving body, and when the wetting depth is 0, calculating the distance between the section of the revolving body and the section of the tail part of the revolving body as the wetting length l of the revolving body, and the wetting area S of the revolving body w The approximate sector shape can be calculated by a sector area formula;
sliding lift force F of tail part of revolving body p Can be calculated as follows:
wherein R is the radius of the tail of the revolving body, deltaR=R-R, R is the cavitation radius of the tail of the revolving body, and V 1 ＝-w+q(L-x c )+V wc L is the length of the revolution body, V wc Is the transverse velocity of cavitation bubbles, V 2 The shrinkage speed of tail cavitation bubbles is positive;
the tail part of the revolving body has the following resultant moment:
friction force F of tail part of revolving body f Can be calculated as follows:
in the formula, the Reynolds number R e Mu is the dynamic viscosity of water, which is 1.01X10 at 20 ° -3 Pa.s, wetted area S w Can be calculated as follows:
component G of projectile centroid gravity in projectile coordinate system x And G z The method comprises the following steps:
G x ＝-mg sinθ
G z ＝-mg cosθ。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110792349.3A CN113821996B (en) | 2021-07-14 | 2021-07-14 | Novel rapid calculation method for high-speed entry trajectory of projectile |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110792349.3A CN113821996B (en) | 2021-07-14 | 2021-07-14 | Novel rapid calculation method for high-speed entry trajectory of projectile |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113821996A CN113821996A (en) | 2021-12-21 |
| CN113821996B true CN113821996B (en) | 2024-01-30 |
Family
ID=78912655
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110792349.3A Active CN113821996B (en) | 2021-07-14 | 2021-07-14 | Novel rapid calculation method for high-speed entry trajectory of projectile |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113821996B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114818540B (en) * | 2022-04-28 | 2023-03-24 | 哈尔滨工业大学 | Construction method of non-torpedo-shaped navigation body high-speed water-entering trajectory prediction model |
| CN114840999B (en) * | 2022-04-28 | 2023-03-14 | 哈尔滨工业大学 | Method for constructing large slenderness ratio revolving body water-entering vacuole evolution model |
| CN114839988B (en) * | 2022-04-28 | 2023-05-26 | 哈尔滨工业大学 | Protective tail cover separation time sequence control method during high-speed water entry of navigation body |
| CN115562271B (en) * | 2022-10-10 | 2023-09-15 | 哈尔滨工业大学 | Open loop control method suitable for high-speed water inlet |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020128461A1 (en) * | 2018-12-19 | 2020-06-25 | Bae Systems Plc | Munitions and projectiles |
| CN112149362A (en) * | 2020-07-08 | 2020-12-29 | 北京电子工程总体研究所 | Method for judging motion stability of supercavitation navigation body |
| CN112325713A (en) * | 2019-12-24 | 2021-02-05 | 北京理工大学 | Analysis method for pneumatic nonlinear angular motion characteristics of double spinning bombs |
| CN112985188A (en) * | 2021-01-27 | 2021-06-18 | 西北工业大学 | Variable-structure cavitation device with water-entering load-reducing function |
-
2021
- 2021-07-14 CN CN202110792349.3A patent/CN113821996B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020128461A1 (en) * | 2018-12-19 | 2020-06-25 | Bae Systems Plc | Munitions and projectiles |
| CN112325713A (en) * | 2019-12-24 | 2021-02-05 | 北京理工大学 | Analysis method for pneumatic nonlinear angular motion characteristics of double spinning bombs |
| CN112149362A (en) * | 2020-07-08 | 2020-12-29 | 北京电子工程总体研究所 | Method for judging motion stability of supercavitation navigation body |
| CN112985188A (en) * | 2021-01-27 | 2021-06-18 | 西北工业大学 | Variable-structure cavitation device with water-entering load-reducing function |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113821996A (en) | 2021-12-21 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN113821996B (en) | Novel rapid calculation method for high-speed entry trajectory of projectile | |
| US10698980B2 (en) | Methods for constructing surfaces for optimizing fluid flow | |
| Weber et al. | Lift, drag, and cavitation onset on rudders with leading-edge tubercles | |
| CN111709151A (en) | Method for creating ship rapid mathematical model | |
| Hand et al. | An aerodynamic modelling methodology for an offshore floating vertical axis wind turbine | |
| Lu et al. | Research on the interference characteristics of successively launched underwater projectiles | |
| Young | Hydroelastic behavior of flexible composite propellers in wake inflow | |
| Feng et al. | The effects of caudal fin deformation on the hydrodynamics of thunniform swimming under self-propulsion | |
| Ma et al. | Effect of pressure-equalizing film on hydrodynamic characteristics and trajectory stability of an underwater vehicle with injection through one or two rows of venting holes | |
| Fan et al. | Modeling for active fin stabilizers at zero speed | |
| Leble et al. | A coupled floating offshore wind turbine analysis with high-fidelity methods | |
| Naser et al. | The influence of concave pectoral fin morphology in the performance of labriform swimming robot | |
| CN117521556B (en) | Submarine attitude prediction method under influence of internal solitary waves | |
| Kabir et al. | Numerical assessment of the backward facing step for NACA 0015 airfoil using computational fluid dynamics | |
| Satrio et al. | Effects of the distance ratio of circular flow disturbance on vertical-axis turbine performance: An experimental and numerical study | |
| Yang et al. | Water-exit process modeling and added-mass calculation of the submarine-launched missile | |
| Arabgolarcheh et al. | Development of an actuator line model for simulation of floating offshore wind turbines | |
| Morgoch et al. | Sprint canoe blade hydrodynamics-modeling and on-water measurement | |
| Wang et al. | Modeling and simulation of tethered undersea kites | |
| CN114547989A (en) | Method and system for rapidly calculating water-entering trajectory of truncated-egg-shaped projectile | |
| Wang et al. | Propulsive performance analysis of underwater flapping multi-foil | |
| Rostami et al. | Simulation of fluttering and autorotation motion of vertically hinged flat plate | |
| Netzband et al. | A fully coupled simulation method for floating offshore wind turbine dynamics using a boundary element method in time domain | |
| EP2713045A1 (en) | Rotating blade body for turbines using the magnus effect with rotation axis of the turbine parallel to the direction of the fluid | |
| Li et al. | Numerical and theoretical investigation on three-dimensional trajectory characteristics of skipping stones |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |