CN103245485B - A kind of ventilated supercavitation equilibrium point catastrophe characteristics decision maker and decision method thereof - Google Patents

Abstract

The invention belongs to nonlinear kinetics and sensor detection field, be specifically related to a kind of decision maker of the determination supercavity equilibrium point catastrophe characteristics based on nonlinear dynamics theory and special decision method thereof.Ventilated supercavitation equilibrium point catastrophe characteristics decision maker, is made up of integral operation module, perturbation analysis module, sensor assembly, data acquisition module, data processing module, comparison operation module.In the process that the present invention navigates by water at supercavitating vehicle, the state that can judge residing for ventilated supercavitation more in time according to the operational configuration of sail body, Real-Time Monitoring may cause ventilated supercavitation to undergo mutation unstable sensitive parameter, once the sensitive parameter of ventilated supercavitation is close to sudden change critical parameters value, just take appropriate measures, make the sensitive parameter of ventilated supercavitation away from sudden change critical parameters value, and then ensure the stability of ventilated supercavitation, for the steady steaming of supercavitating vehicle provides basic guarantee.

Description

A kind of ventilated supercavitation equilibrium point catastrophe characteristics decision maker and decision method thereof

Technical field

The invention belongs to nonlinear kinetics and sensor detection field, be specifically related to a kind of decision maker of the determination supercavity equilibrium point catastrophe characteristics based on nonlinear dynamics theory and special decision method thereof.

Background technology

The application of supercavity technology can make under water or the frictional resistance of surface motions body significantly reduces, improve headway, but supercavitating flow is a kind of very complicated flow field problem, contain the flow phenomenon of more complicated in the fluid dynamics researchs such as unsteady flo w, compressible, phase transformation, turbulence, bring difficulty to the research of Bubble dynamics characteristic.

Research at present for complicated cavity flow characteristic mainly adopts numerical simulation and experimental study two kinds of methods, and research contents mainly concentrates on the numerical simulation of permanent Ventilated Supercavity Shape and the analytical calculation of ventilation rule and verification experimental verification.Wherein method for numerical simulation mainly adopts the flow field characteristic of the Boundary Element Method two and three dimensions supercavity in homogeneous equiulbrium flow theory and potential flow theories, the flow-disturbing problem of burbling cavitation and the new method etc. of calculating cavity form, as non-patent literature " numerical simulation study of a Ventilated Supercavity Shape stability " literary composition, be published in " Computational Mechanics journal ", a kind of computing method for calculating unsteady flo w Ventilated Supercavity Shape have been developed according to Logvinovich cavity cross section independently-inflatable principle in literary composition, and use the method to carry out numerical simulation study to Ventilated Supercavity Shape stability.Research shows: model velocity, the elasticity of gases, ventilation rate, and rate of losing heart, after fluid field pressure, model, body and cavitation device resistance coefficient all can have an impact to Ventilated Supercavity Shape stability.Dissimilar different with the impact of disturbance on bubbling crystallzation morphological stability of different modes, ventilated supercavitation shows time-lag effect and oscillating characteristic after receiving disturbance.This research method calculated amount is large, and execution cycle is long, needs the computing machine of high configuration to provide hardware condition; And experimental study method is as non-patent literature " Ventilated Supercavity Shape and stability experiment research thereof ", be published in " Harbin Engineering University's journal ", the serial experiment by carrying out in water hole in literary composition is studied Ventilated Supercavity Shape and stability thereof.Research shows, gravity is different with the ventilated supercavitation impact that pass gas process is formed on venting process, but ventilated supercavitation axis variable increases all in a non-linear manner.When gravity effect is less, under identical cavitation number, ventilated supercavitation and natural supercavitation basic simlarity in form and yardstick.Preliminary work needed for experimental study is heavy, cost is high, repeatability is poor.

Summary of the invention

The object of this invention is to provide a kind of process simple, simple operation, do not need the ventilated supercavitation equilibrium point catastrophe characteristics decision maker carrying out numerical simulation, the present invention also aims to the ventilated supercavitation equilibrium point catastrophe characteristics decision method providing this device a kind of special.

The object of the present invention is achieved like this:

Ventilated supercavitation equilibrium point catastrophe characteristics decision maker, be made up of integral operation module, perturbation analysis module, sensor assembly, data acquisition module, data processing module, comparison operation module, integral operation module carries out integral operation to existing cavity cross-sectional expansion equation, and integral operation result is inputed to perturbation analysis module; Perturbation analysis module carries out linearization process to bubbling crystallzation volume, exports the sensitive parameter collection of ventilated supercavitation equilibrium point sudden change; The sensitive parameter that sensor assembly measures bubbling crystallzation inputs to data acquisition module; The data collected are carried out A/D conversion and are inputed to data processing module by data acquisition module; Data processing module carries out filtering to the sensitive parameter obtained, stores and curve plotting; The actual measured value of the sensitive parameter collection that comparative analysis module exports perturbation analysis module and data processing module compares, and judges that ventilated supercavitation equilibrium point is undergone mutation the possibility of characteristic.

Sensor assembly comprises the pressure transducer measuring pressure and the acceleration transducer measuring movable body acceleration; Data acquisition module adopts data collecting card, and data processing module adopts single-chip microcomputer, and integral operation module adopts singlechip chip, perturbation analysis module to adopt singlechip chip, and comparison operation module adopts operational amplifier chip.

Sensitive parameter comprises pressure, movable body acceleration.

Ventilated supercavitation equilibrium point catastrophe characteristics decision method, comprises the steps:

(1) cavity cross-sectional expansion equation is set up:

$\frac{{\∂}^{2}S(\mathrm{\τ},t)}{\∂t^2}=-\frac{k_1\mathrm{\Δp}(\mathrm{\τ},t)}{\mathrm{\ρ}},x\left(t\right)-l\left(t\right)\≤\mathrm{\ξ}\≤x\left(t\right),$

$S(\mathrm{\τ},\mathrm{\τ})=\frac{\mathrm{\π}{D}_n^2}{4},\frac{\∂S(\mathrm{\τ},\mathrm{\τ})}{\∂t}=\frac{k_{1}A}{4}{D}_{n}V\sqrt{c_x}$

Δ p (τ, t)=p in formula _∞(ξ)+p ₁(t)-p _c(t), wherein τ≤t is the cross section ξ rise time; X (t) is absolute x coordinate corresponding to cavity generator current time t; p ₁t () is environmental pressure disturbance; p _ct () is pressure in cavity; p _∞(ξ) be the environmental pressure of infinite point; L (t) is cavity length; c _xfor cavity drag coefficient; k ₁=4 π/A ², A=2 is empirical constant, D _nfor cavitator diameter, V is real time kinematics body speed;

(2) integral operation is carried out to existing cavity cross-sectional expansion equation:

With initial cavity length l ₀with movable body speed V _∞as scale, nondimensionalization process is carried out to cavity cross-sectional expansion equation:

$\frac{{\∂}^{2}S(\mathrm{\τ},t)}{\∂t^2}=-\frac{k_1\mathrm{\σ}\left(t\right)}{2},t-l\left(t\right)\≤\mathrm{\τ}\≤t$

Wherein σ (t) is cavitation number, and the closure condition of cavity is:

S(t,t)=S(t-l(t),t)→0

Carry out twice integration to the cavity cross-sectional expansion equation of nondimensionalization to obtain:

$S(\mathrm{\τ},t)=\frac{k_1{\mathrm{\σ}}_0}{4}[t-\mathrm{\τ}-2\underset{\mathrm{\τ}}{\overset{t}{\∫}}(t-u)\stackrel{\‾}{\mathrm{\σ}}\left(u\right)\mathrm{du}]$

In formula σ ₀for natural cavitation number, u is integration variable,

The integral equation of contact ventilated supercavitation length and cavitation number is obtained in conjunction with cavity closure condition:

$l\left(t\right)=2\underset{t-l\left(t\right)}{\overset{t}{\∫}}(t-u)\stackrel{\‾}{\mathrm{\σ}}\left(u\right)\mathrm{du};$

(3) calculate unique equilibrium point of ventilated supercavitation, cavity volume carried out linearization process at equilibrium point place, obtain linear perturbation system and ventilated supercavitation and may to undergo mutation the parameter area of characteristic:

Cavity balanced gas quality Non-di-mensional equation is:

$\frac{d}{\mathrm{dt}}\left[(\mathrm{\β}-\stackrel{\‾}{\mathrm{\σ}}\left(t\right))Q\left(t\right)\right]=\mathrm{\β}[{\stackrel{\·}{q}}_{\mathrm{in}}-{\stackrel{\·}{q}}_{\mathrm{out}}\left(t\right)]$

Wherein β is dynamic similarity parameter, for Ventilation Rate, for time dependent disappointing speed, combine with the integral equation contacting ventilated supercavitation length and cavitation number, obtain the equilibrium point that ventilated supercavitation is unique:

$\stackrel{\‾}{\mathrm{\σ}}\left(t\right)=1,l\left(t\right)=1$

By cavity volume $Q\left(t\right)=\frac{k_1{\mathrm{\σ}}_0}{4}[-\frac{l^2\left(t\right)}{2}+\underset{t-l\left(t\right)}{\overset{t}{\∫}}{(t-u)}^2\stackrel{\‾}{\mathrm{\σ}}\left(u\right)\mathrm{du}]$ Carry out linearization process at equilibrium point place, obtain linear perturbation system:

$\left\{\begin{array}{c}{\stackrel{\·}{\mathrm{\σ}}}_1\left(t\right)=a{\mathrm{\σ}}_1\left(t\right)+b\\ i_1\left(t\right)=\frac{a{\mathrm{\σ}}_1\left(t\right)+2\mathrm{b\ϵ}{l}_1\left(t\right){\mathrm{\σ}}_1\left(t\right)+b}{2\mathrm{\ϵ}{l}_1\left(t\right)-1}\end{array}\right.$

Wherein a and b is parametric variable, and ε is dimensionless, obtains Jacobi matrix and the eigenwert of linear perturbation, judges that ventilated supercavitation may undergo mutation the parameter area of characteristic as 2.6196< β;

(4) sensitive parameter of ventilated supercavitation is measured, filtering carried out to sensitive parameter, numeric ratio comparatively calculates, store and curve plotting, the sensitive parameter of ventilated supercavitation compares with sudden change critical parameters value, judges that ventilated supercavitation is undergone mutation when sensitive parameter is greater than sudden change critical parameters value; Judge that ventilated supercavitation is not undergone mutation when sensitive parameter is less than sudden change critical parameters value.

Beneficial effect of the present invention is: in the process that the present invention navigates by water at supercavitating vehicle, the state that can judge residing for ventilated supercavitation more in time according to the operational configuration of sail body, Real-Time Monitoring may cause ventilated supercavitation to undergo mutation unstable sensitive parameter, once the sensitive parameter of ventilated supercavitation is close to sudden change critical parameters value, just take appropriate measures, make the sensitive parameter of ventilated supercavitation away from sudden change critical parameters value, and then ensure the stability of ventilated supercavitation, for the steady steaming of supercavitating vehicle provides basic guarantee.

Accompanying drawing explanation

Fig. 1 is the device composition frame chart judging ventilated supercavitation equilibrium point catastrophe characteristics;

Fig. 2 judges the method for ventilated supercavitation equilibrium point catastrophe characteristics and the workflow diagram of device.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further:

Composition frame chart of the present invention as shown in Figure 1, is made up of integral operation module, perturbation analysis module, sensor assembly, data acquisition module, data processing module and comparative analysis module.Wherein said integral operation module and the function of perturbation analysis module are realized by mcu programming; The measurement of pressure signal that sensor assembly realizes and the measurement function of acceleration signal realize multimetering by miniature patch formula pressure transducer respectively, and the acquisition of movable body linear acceleration is measured by the single-axis accelerometer ADXL190 with analog signal output; The function that data acquisition module realizes is by the collection of the A/D functional realiey simulating signal of pci data capture card and digital conversion; The integral operation function that data processing module completes and multiplication and division calculate and are realized by mcu programming; Comparison operation module is completed by mcu programming equally, and the programmable I/O pin of single-chip microcomputer receives the output of perturbation analysis module and data processing module.A kind of workflow diagram determining the device embodiment of ventilated supercavitation equilibrium point catastrophe characteristics as shown in Figure 2.

The present invention includes integral operation module, perturbation analysis module.Integral operation module is based on the mathematical model of Logvinovich cavity cross-sectional area expansion Independence Principle, obtain cavity cross-sectional expansion equation, according to the closure condition of cavity afterbody, Integral Processing is carried out to cavity cross-sectional expansion equation, obtains the integral equation of contact ventilated supercavitation length and cavitation number; Cavity volume is carried out linearization process at equilibrium point place by perturbation analysis module, obtains linear perturbation system, and ventilated supercavitation may be undergone mutation the parameter area of characteristic.Concrete steps are as follows:

A () adopts the mathematical model based on Logvinovich cavity cross-sectional area expansion Independence Principle, obtain cavity cross-sectional expansion equation

$\frac{{\&PartialD;}^{2}S(\mathrm{\&tau;},t)}{\&PartialD;t^2}=-\frac{k_1\mathrm{\&Delta;p}(\mathrm{\&tau;},t)}{\mathrm{\&rho;}},x\left(t\right)-l\left(t\right)\&le;\mathrm{\&xi;}\&le;x\left(t\right),---\left(1\right)$

$S(\mathrm{\&tau;},\mathrm{\&tau;})=\frac{\mathrm{\&pi;}{D}_n^2}{4},\frac{\&PartialD;S(\mathrm{\&tau;},\mathrm{\&tau;})}{\&PartialD;t}=\frac{k_{1}A}{4}{D}_{n}V\sqrt{c_x}$

Δ p (τ, t)=p in formula _∞(ξ)+p ₁(t)-p _c(t), wherein τ≤t is the cross section ξ rise time; X (t) is absolute x coordinate corresponding to cavity generator current time t; p ₁t () is environmental pressure disturbance; p _ct () is pressure in cavity; p _∞(ξ) be the environmental pressure of infinite point; L (t) is cavity length; c _xfor cavity drag coefficient; k ₁=4 π/A ², A=2 is empirical constant, D _nfor cavitator diameter, V is real time kinematics body speed.

With initial cavity length l ₀with movable body speed V _∞as scale, nondimensionalization process is carried out to equation (1),

$\frac{{\&PartialD;}^{2}S(\mathrm{\&tau;},t)}{\&PartialD;t^2}=-\frac{k_1\mathrm{\&sigma;}\left(t\right)}{2},t-l\left(t\right)\&le;\mathrm{\&tau;}\&le;t---\left(2\right)$

Wherein σ (t) is cavitation number, and the closure condition of cavity is

S(t,t)=S(t-l(t),t)→0(3)

In conjunction with closure condition (3), twice integration is carried out to equation (2), draws

$S(\mathrm{\&tau;},t)=\frac{k_1{\mathrm{\&sigma;}}_0}{4}[t-\mathrm{\&tau;}-2\underset{\mathrm{\&tau;}}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)\mathrm{du}]---\left(4\right)$

In formula σ ₀for natural cavitation number, u is integration variable.(4) formula is substituted into cavity closure condition (3), draws contact unknown function with the equation of l (t)

$l\left(t\right)=2\underset{t-l\left(t\right)}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)\mathrm{du}---\left(5\right)$

B the result of integral operation module combines with cavity balanced gas quality Non-di-mensional equation by (), calculate unique equilibrium point of ventilated supercavitation.

Cavity balanced gas quality Non-di-mensional equation is

$\frac{d}{\mathrm{dt}}\left[(\mathrm{\&beta;}-\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(t\right))Q\left(t\right)\right]=\mathrm{\&beta;}[{\stackrel{\&CenterDot;}{q}}_{\mathrm{in}}-{\stackrel{\&CenterDot;}{q}}_{\mathrm{out}}\left(t\right)]---\left(6\right)$

Wherein β is dynamic similarity parameter (equaling the ratio of steam cavitation number and its actual numerical value), and play an important role in calculating non-stationary cavity stream, β=1 is equivalent to natural supercavitation.When β increases, the elasticity of gases in ventilated supercavitation increases. for Ventilation Rate, for time dependent disappointing speed.Equation (5) is combined with equation (6) and is obtained the unique equilibrium point of ventilated supercavitation utilize perturbation analysis module by cavity volume $Q\left(t\right)=\frac{k_1{\mathrm{\&sigma;}}_0}{4}[-\frac{l^2\left(t\right)}{2}+\underset{t-l\left(t\right)}{\overset{t}{\&Integral;}}{(t-u)}^2\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)\mathrm{du}]$ Carry out linearization process at equilibrium point place, obtain linear perturbation system, $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_1\left(t\right)=a{\mathrm{\&sigma;}}_1\left(t\right)+b\\ i_1\left(t\right)=\frac{a{\mathrm{\&sigma;}}_1\left(t\right)+2\mathrm{b\&epsiv;}{l}_1\left(t\right){\mathrm{\&sigma;}}_1\left(t\right)+b}{2\mathrm{\&epsiv;}{l}_1\left(t\right)-1}\end{array}\right.,$ Wherein a and b is parametric variable, and ε is dimensionless, obtains Jacobi matrix and the eigenwert of system, according to Bifurcation Theory, judges that ventilated supercavitation may undergo mutation the parameter area of characteristic as 2.6196< β.

The present invention also comprises sensor assembly, data acquisition module, data processing module, comparison operation module.Sensor assembly comprises pressure sensor module and acceleration sensor module, and pressure sensor module is made up of multiple pressure transducer, exports the voltage signal p be directly proportional to pressure in cavity _{c_a}, movable body linear acceleration measured by acceleration transducer, and exports corresponding voltage signal a _a; The voltage signal p that data acquisition module adopts the A/D function Real-time Collection sensor assembly in data collecting card to export _{c_a}and acceleration signal a _aand convert them to corresponding digital signal p _{c_d}and a _d; Data processing module is completed by mcu programming, carries out integration obtain rate signal by the signal exported acceleration transducer utilize relation, p _∞for environmental pressure, obtain actual cavitation number, and then obtain β; Whether comparison operation module is completed by mcu programming equally, compare the β that data processing module exports and drop in the parameter area that perturbation analysis module obtains, to determine whether ventilated supercavitation can undergo mutation phenomenon.If β is close to critical value, by the numerical value changing β of taking the necessary measures.

Claims (4)

1. a ventilated supercavitation equilibrium point catastrophe characteristics decision maker, be made up of integral operation module, perturbation analysis module, sensor assembly, data acquisition module, data processing module, comparison operation module, it is characterized in that: integral operation module carries out integral operation to existing cavity cross-sectional expansion equation, and integral operation result is inputed to perturbation analysis module;

Described cavity cross-sectional expansion equation is:

$\frac{{\&part;}^{2}S(\mathrm{\&tau;},t)}{\&part;t^2}=-\frac{k_1\mathrm{\&Delta;}p(\mathrm{\&tau;},t)}{\mathrm{\&rho;}},x\left(t\right)-l\left(t\right)\&le;\mathrm{\&xi;}\&le;x\left(t\right),$

$S(\mathrm{\&tau;},\mathrm{\&tau;})=\frac{{\mathrm{\&pi;D}}_n^2}{4},\frac{\&part;S(\mathrm{\&tau;},\mathrm{\&tau;})}{\&part;t}=\frac{k_{1}A}{4}{D}_{n}V\sqrt{c_x}$

Δ p (τ, t)=p in formula _∞(ξ)+p ₁(t)-p _c(t), wherein τ≤t is the cross section ξ rise time; X (t) is absolute x coordinate corresponding to cavity generator current time t; p ₁t () is environmental pressure disturbance; p _ct () is pressure in cavity; p _∞(ξ) be the environmental pressure of infinite point; L (t) is cavity length; c _xfor cavity drag coefficient; k ₁=4 π/A ², A=2 is empirical constant, D _nfor cavitator diameter, V is real time kinematics body speed;

Described integral operation carried out to existing cavity cross-sectional expansion equation be:

With initial cavity length l ₀with movable body speed V _∞as scale, nondimensionalization process is carried out to cavity cross-sectional expansion equation:

$\frac{{\&part;}^{2}S(\mathrm{\&tau;},t)}{\&part;t^2}=-\frac{k_1\mathrm{\&sigma;}\left(t\right)}{2},t-l\left(t\right)\&le;\mathrm{\&tau;}\&le;t$

Wherein σ (t) is cavitation number, and the closure condition of cavity is:

S(t,t)＝S(t-l(t),t)→0

Carry out twice integration to the cavity cross-sectional expansion equation of nondimensionalization to obtain:

$S(\mathrm{\&tau;},t)=\frac{k_1{\mathrm{\&sigma;}}_0}{4}\&lsqb;t-\mathrm{\&tau;}-2\underset{\mathrm{\&tau;}}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)du\&rsqb;$

In formula σ ₀for natural cavitation number, u is integration variable,

The integral equation of contact ventilated supercavitation length and cavitation number is obtained in conjunction with cavity closure condition:

$l\left(t\right)=2\underset{t-l\left(t\right)}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)du;$

Perturbation analysis module carries out linearization process to bubbling crystallzation volume, exports the sensitive parameter collection of ventilated supercavitation equilibrium point sudden change; Cavity balanced gas quality Non-di-mensional equation is:

$\frac{d}{dt}\&lsqb;(\mathrm{\&beta;}-\stackrel{\&OverBar;}{\mathrm{\&sigma;}}(t\left)\right)Q\left(t\right)\&rsqb;=\mathrm{\&beta;}\&lsqb;{\stackrel{\&CenterDot;}{q}}_{in}-{\stackrel{\&CenterDot;}{q}}_{out}\left(t\right)\&rsqb;$

Wherein β is dynamic similarity parameter, for Ventilation Rate, for time dependent disappointing speed, combine with the integral equation contacting ventilated supercavitation length and cavitation number, obtain the equilibrium point that ventilated supercavitation is unique:

$\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(t\right)=1,l\left(t\right)=1$

By cavity volume carry out linearization process at equilibrium point place, obtain linear perturbation system:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_1\left(t\right)=a{\mathrm{\&sigma;}}_1\left(t\right)+b\\ {\stackrel{\&CenterDot;}{l}}_1\left(t\right)=\frac{{\mathrm{a\&sigma;}}_1\left(t\right)+2{\mathrm{b\&epsiv;l}}_1\left(t\right){\mathrm{\&sigma;}}_1\left(t\right)+b}{2{\mathrm{\&epsiv;l}}_1\left(t\right)-1}\end{array}\right.$

Wherein a and b is parametric variable, and ε is dimensionless, obtains Jacobi matrix and the eigenwert of linear perturbation, judges that ventilated supercavitation may undergo mutation the parameter area of characteristic as 2.6196 < β;

The sensitive parameter that sensor assembly measures bubbling crystallzation inputs to data acquisition module; The data collected are carried out A/D conversion and are inputed to data processing module by data acquisition module; Data processing module carries out filtering to the sensitive parameter obtained, stores and curve plotting; The actual measured value of the sensitive parameter collection that comparative analysis module exports perturbation analysis module and data processing module compares, and judges that ventilated supercavitation equilibrium point is undergone mutation the possibility of characteristic; Described sensitive parameter comprises pressure, movable body acceleration.

2. a kind of ventilated supercavitation equilibrium point catastrophe characteristics decision maker according to claim 1, is characterized in that: described sensor assembly comprises the pressure transducer measuring pressure and the acceleration transducer measuring movable body acceleration; Data acquisition module adopts data collecting card, and data processing module adopts single-chip microcomputer, and integral operation module adopts singlechip chip, perturbation analysis module to adopt singlechip chip, and comparison operation module adopts operational amplifier chip.

3. a ventilated supercavitation equilibrium point catastrophe characteristics decision method, is characterized in that, comprise the steps:

(1) cavity cross-sectional expansion equation is set up:

$\frac{{\&part;}^{2}S(\mathrm{\&tau;},t)}{\&part;t^2}=-\frac{k_1\mathrm{\&Delta;}p(\mathrm{\&tau;},t)}{\mathrm{\&rho;}},x\left(t\right)-l\left(t\right)\&le;\mathrm{\&xi;}\&le;x\left(t\right),$

$S(\mathrm{\&tau;},\mathrm{\&tau;})=\frac{{\mathrm{\&pi;D}}_n^2}{4},\frac{\&part;S(\mathrm{\&tau;},\mathrm{\&tau;})}{\&part;t}=\frac{k_{1}A}{4}{D}_{n}V\sqrt{c_x}$

Δ p (τ, t)=p in formula _∞(ξ)+p ₁(t)-p _c(t), wherein τ≤t is the cross section ξ rise time; X (t) is absolute x coordinate corresponding to cavity generator current time t; p ₁t () is environmental pressure disturbance; p _ct () is pressure in cavity; p _∞(ξ) be the environmental pressure of infinite point; L (t) is cavity length; c _xfor cavity drag coefficient; k ₁=4 π/A ², A=2 is empirical constant, D _nfor cavitator diameter, V is real time kinematics body speed;

(2) integral operation is carried out to existing cavity cross-sectional expansion equation:

With initial cavity length l ₀with movable body speed V _∞as scale, nondimensionalization process is carried out to cavity cross-sectional expansion equation:

$\frac{{\&part;}^{2}S(\mathrm{\&tau;},t)}{\&part;t^2}=-\frac{k_1\mathrm{\&sigma;}\left(t\right)}{2},t-1\left(t\right)\&le;\mathrm{\&tau;}\&le;t$

Wherein σ (t) is cavitation number, and the closure condition of cavity is:

S(t,t)＝S(t-l(t),t)→0

Carry out twice integration to the cavity cross-sectional expansion equation of nondimensionalization to obtain:

$S(\mathrm{\&tau;},t)=\frac{k_1{\mathrm{\&sigma;}}_0}{4}\&lsqb;t-\mathrm{\&tau;}-2\underset{\mathrm{\&tau;}}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)du\&rsqb;$

In formula σ ₀for natural cavitation number, u is integration variable,

The integral equation of contact ventilated supercavitation length and cavitation number is obtained in conjunction with cavity closure condition:

$l\left(t\right)=2\underset{t-l\left(t\right)}{\overset{t}{\&Integral;}}(t-u)\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)du;$

(3) calculate unique equilibrium point of ventilated supercavitation, cavity volume carried out linearization process at equilibrium point place, obtain linear perturbation system and ventilated supercavitation and may to undergo mutation the parameter area of characteristic:

Cavity balanced gas quality Non-di-mensional equation is:

$\frac{d}{dt}\&lsqb;(\mathrm{\&beta;}-\stackrel{\&OverBar;}{\mathrm{\&sigma;}}(t\left)\right)Q\left(t\right)\&rsqb;=\mathrm{\&beta;}\&lsqb;{\stackrel{\&CenterDot;}{q}}_{in}-{\stackrel{\&CenterDot;}{q}}_{out}\left(t\right)\&rsqb;$

Wherein β is dynamic similarity parameter, for Ventilation Rate, for time dependent disappointing speed, combine with the integral equation contacting ventilated supercavitation length and cavitation number, obtain the equilibrium point that ventilated supercavitation is unique:

$\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(t\right)=1,l\left(t\right)=1$

By cavity volume $Q\left(t\right)=\frac{k_1{\mathrm{\&sigma;}}_0}{4}\&lsqb;-\frac{l^2\left(t\right)}{2}+\underset{t-l\left(t\right)}{\overset{t}{\&Integral;}}{(t-u)}^2\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\left(u\right)du\&rsqb;$ Carry out linearization process at equilibrium point place, obtain linear perturbation system:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_1\left(t\right)=a{\mathrm{\&sigma;}}_1\left(t\right)+b\\ {\stackrel{\&CenterDot;}{l}}_1\left(t\right)=\frac{{\mathrm{a\&sigma;}}_1\left(t\right)+2{\mathrm{b\&epsiv;l}}_1\left(t\right){\mathrm{\&sigma;}}_1\left(t\right)+b}{2{\mathrm{\&epsiv;l}}_1\left(t\right)-1}\end{array}\right.$

Wherein a and b is parametric variable, and ε is dimensionless, obtains Jacobi matrix and the eigenwert of linear perturbation, judges that ventilated supercavitation may undergo mutation the parameter area of characteristic as 2.6196 < β;

(4) sensitive parameter of ventilated supercavitation is measured, filtering carried out to sensitive parameter, numeric ratio comparatively calculates, store and curve plotting, the sensitive parameter of ventilated supercavitation compares with sudden change critical parameters value, judges that ventilated supercavitation is undergone mutation when sensitive parameter is greater than sudden change critical parameters value; Judge that ventilated supercavitation is not undergone mutation when sensitive parameter is less than sudden change critical parameters value.

4. a kind of ventilated supercavitation equilibrium point catastrophe characteristics decision method according to claim 3, is characterized in that: described sensitive parameter comprises pressure, movable body acceleration.