CN109238639B - Method for calculating tail cavity radius of super cavity navigation body - Google Patents

Abstract

The invention discloses a calculation method for a cavitation bubble radius at the tail of a supercavitation navigation body. Step 1, initial conditions: parameters in the actual process are given, and some composite physical parameters are given through correlation operation; step 2, determining the expansion time of the section of the cavitation bubble at the tail part of the navigation body: according to the position of cavitation bubbles in spacex _i Time of the spread of the placet(x _i ) Equal to the cavitation device on the head of the navigation bodyx _i Time of starting movementt _k . Establishing a correlation equation and derivingt _k The expression of (1); step 3, dispersing a Lobvivich independent expansion equation: dispersing the Lobvivich independent expansion equation by using a complex Simpson formula; step 4, an iteration method: the iteration adopts a space iteration method, namely, a certain point in space is calculated from cavitation development until cavitation collapse at the position, then the calculation of the cavitation section at the next position is carried out, and the whole iteration is divided into inner layer iteration and outer layer iteration. The algorithm of the invention can accurately calculate the cavitation bubble size at the tail of the navigation body.

Description

Method for calculating tail cavity radius of super cavity navigation body

Technical Field

The invention relates to a calculation method of a cavitation radius of a super-cavitation navigation body, in particular to a calculation method of a cavitation radius of a tail part of a super-cavitation navigation body.

Background

When the supercavity navigation body moves underwater, the vacuoles formed by air and water vapor extend to the surface of the whole navigation body from the cavitator, so that the contact between the navigation body and water is blocked, and the frictional resistance is greatly reduced. The underwater supercavitation navigation body can realize torpedo penetration interception, ship damage, frogman attack and the like within a certain distance, and has very important application.

The determination of the cavitation radius of the tail of the super-cavitation-bubble navigation body is of great significance for researching the tail shooting motion of the super-cavitation-bubble navigation body, and a calculation formula of the cavitation radius of the tail of the navigation body with the cavitation number within a certain range is given based on a super-cavitation-bubble navigation body test. Kulkarni and Choi propose an elliptical cavitation semi-empirical progressive solution formula that can be calculated for a vehicle with a speed of 300-1300m/s, but with a large error. At present, most of determination methods related to the tail cavity radius of the supercavitation navigation body are semi-empirical formulas and empirical formulas, and the limitations are as follows: the calculation can be only carried out on the supercavitation navigation body with the cavitation number and the navigation speed within a certain variation range, and the navigation speed is lower. At present, no method for determining the tail cavity radius of a navigation body under high-speed navigation exists. Therefore, in order to provide a method for determining the cavitation bubble radius of the tail of the navigation body without condition limitation, the cavitation bubble radius of the tail of the navigation body is theoretically calculated through a Lobvinovich cavitation independent expansion equation based on energy conservation and an unsteady Bernoulli equation, and an accurate cavitation prediction method is provided for researching the tail shooting motion of the navigation body.

Disclosure of Invention

The invention aims to provide a calculation method of a cavitation radius of a super-cavitation navigation body, which aims to predict the cavitation radius of the tail part of the super-cavitation navigation body by means of theoretical calculation and provide an accurate calculation basis for analyzing the tail shooting motion of the navigation body.

The technical solution for realizing the invention is as follows: a method for calculating the cavitation radius of the tail part of a supercavitation navigation body comprises the following steps:

step 1, initial conditions: parameters in the actual process are given, and some composite physical parameters are given through correlation operation;

step 2, determining the expansion time of the section of the cavitation bubble at the tail part of the navigation body: according to cavitation at spatial position x_iTime t (x) of the spread of the place_i) Equal to the cavitation from x of the head of the navigation body_iAt the time t of the start of movement_k. Establishing a correlation equation and deriving t_kThe expression of (1);

step 3, dispersing a Lobvivich independent expansion equation: dispersing the Lobvivich independent expansion equation by using a complex Simpson formula;

step 4, an iteration method: the iteration adopts a space iteration method, namely, a certain point in space is calculated from cavitation development until cavitation collapse at the position, then the calculation of the cavitation section at the next position is carried out, and the whole iteration is divided into inner layer iteration and outer layer iteration.

Compared with the prior art, the invention has the following remarkable advantages: 1) the method has no condition limitations such as navigation speed, cavitation number and the like, and can calculate the cavitation cross section area of the tail part of the supercavitation navigation body 2). 3) The calculation method used by the invention has no spatial error accumulation and high calculation precision.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

Detailed Description

The invention will be further described with reference to the accompanying drawings and specific examples.

Step 1, initial conditions: setting the navigation depth h and the initial speed v of the navigation body₀Initial displacement x₀Atmospheric pressure P on the surface of the fluid₀The fluid density rho and the fluid temperature T, and searching the corresponding fluid saturated vapor pressure P at the current temperature according to the fluid temperature_vLength L of navigation body, radius R of cavitator, mass m of navigation body, gravitational acceleration g, and end time t of navigation body motion_fAnd calculating time step lengths delta T and delta T inside and outside.

From newton's second law:

integral available velocity expression:

wherein A is₀＝πR²Is the cross-sectional area of the cavitator, C_x0The vehicle speed change was calculated from the cavitation resistance coefficient of 0.82.

Step 2, determining the expansion time of the section of the cavitation bubble at the tail part of the navigation body: according to the independent expansion principle of the Lobvinovich vacuole, the expansion of the section of the vacuole is only related to the physical environment of the current position, so that the vacuole is positioned at the space position x_iTime t (x) of the spread of the place_i) Equal to the cavitation from x of the head of the navigation body_iAt the time t of the start of movement_k. There is therefore the equation:

t(x_i)＝t_k

so when the navigation body goes from x_iStarting from the position, the displacement length of the cavitator is equal to the length L of a sailing body, and x is the length_iCavitation of a siteThe section area is the section area S of the corresponding tail cavity of the navigation body_k. Thus, there is the equation:

solving the integral equation can yield t_kThe solution of (a) is:

step 3, dispersing a Lobvivich independent expansion equation: the Lobvinovich deduces a cavitation independent expansion equation based on the potential flow theory according to an energy conservation equation:

where k is a coefficient weakly dependent on the cavitation number σ ═ Δ p/(0.5 ρ v)²) Usually, k is 4 pi/(A)²) A ≈ 2 is an empirical constant.

Let τ be the moment of formation of section x, the Logvinovich vacuole expansion equation is integrated to obtain:

discretizing the upper process by using a complex Simpson formula, and enabling f to be (t-u) (p-p)_v) Then:

step 4, an iteration method: the iterative solution adopts space iteration, namely a certain point in the space is calculated from cavitation development until the cavitation at the position collapses, and then the calculation of the cavitation section at the next position is carried out, wherein the whole iteration is divided into inner layer iteration and outer layer iteration.

(1) Given navigation body movement time t_sAs an outer layer calculation stop condition, an initial time t_iWhen equal to 0, the outer step Δ t, calculate t_iThe running speed v (t) of the time-of-day vehicle_i)；

(2) Calculating the spatial position x of a navigation body_i＝x_i-1+v(t_i)Δt；

(3) Calculating t_iInitial expansion rate of time-of-flight cavitation

(4) Calculating navigation body head cavitator from x_iStarting movement L long used time t_kWith t_kAs being at a point x in space_iCalculating the sectional area of the upper cavity, namely calculating the stop condition of the inner layer;

(5) given the inner time step Δ T, calculate at (0, T)_k) In the time period, the sectional area of the cavitation bubble at the tail part of the navigation body at each moment is calculated until the inner layer is finished;

(6) and (5) repeating the steps (1) to (5) until the outer layer calculation is finished.

The following is a more detailed description with reference to examples.

Setting the navigation depth of a navigation body to be 2m, the initial speed to be 200m/s, the initial displacement to be 0m, the atmospheric pressure on the surface of the fluid to be 101325Pa and the density of the fluid to be 1000kg/m³The fluid temperature is 27 ℃, and the corresponding fluid saturated vapor pressure at the current temperature is found to be 3564Pa, the length of the navigation body is 156.8mm, the radius of the cavitator is 2.25mm, the mass of the navigation body is 0.1kg, and the gravity acceleration is 9.8m/s²The end time of the navigation body movement is 0.1s, and the internal and external calculation time step length is 10^-5s、10^-7s。

The comparison between the calculated value and the test value of the cavitation bubbles at the tail of the navigation body at different speeds is shown in table 1, so that the test value and the calculated value are better consistent, and the calculation of the cavitation bubbles at the tail of the navigation body can be accurately calculated by the algorithm.

TABLE 1 comparison of calculated values of cavitation diameter before and after disturbance of corresponding nodes with test values

。

Claims (2)

1. A method for calculating the cavitation radius of the tail part of a supercavitation navigation body is characterized by comprising the following steps:

step 1, initial conditions: setting the navigation depth h and the initial speed v of the navigation body₀Initial displacement x₀Atmospheric pressure P on the surface of the fluid₀The fluid density rho and the fluid temperature T, and searching the corresponding fluid saturated vapor pressure P at the current temperature according to the fluid temperature_vThe length L of the navigation body, the radius R of the cavitator, the mass m of the navigation body, the gravity acceleration g, the motion ending time T of the navigation body, and the internal and external calculation time step length delta T and delta T;

wherein A is₀＝πR²Is the cross-sectional area of the cavitator, C_x0Calculating the speed change of the navigation body by taking the cavitation device resistance coefficient as 0.82;

step 2, determining the expansion time of the section of the cavitation bubble at the tail part of the navigation body: cavitation at spatial position x_iTime t (x) of the spread of the place_i) Equal to the cavitation from x of the head of the navigation body_iAt the time t of the start of movement_k(ii) a When the navigation body goes from x_iStarting from the position, the displacement length of the cavitator is equal to the length L of a sailing body, and x is the length_iThe section area of the cavitation bubble at the position is the section area S of the cavitation bubble at the tail part of the corresponding navigation body_kThus, there is the equation:

step 3, dispersing a Lobvivich independent expansion equation: the Lobvinovich deduces a cavitation independent expansion equation based on the potential flow theory according to an energy conservation equation:

wherein k is coefficient, k is 4 pi/(A)²) A is an empirical constant;

discretizing the upper process by using a complex Simpson formula, and enabling f to be (t-u) (P-P)_v) Then:

D_nis the cavitator diameter;

step 4, an iteration method: the iterative solution adopts space iteration, namely a certain point in the space is calculated from cavitation development until the cavitation at the position collapses, and then the calculation of the cavitation section at the next position is carried out, wherein the whole iteration is divided into inner layer iteration and outer layer iteration.

2. The method for calculating the cavitation radius of the tail part of the super-cavitation-bubble vehicle according to claim 1, wherein the specific implementation process in the step 4 is as follows:

(1) given navigation body movement time t_sAs an outer layer calculation stop condition, an initial time t_iWhen equal to 0, the outer step Δ t, calculate t_iThe running speed v (t) of the time-of-day vehicle_i)；

(2) Calculating the spatial position x of a navigation body_i＝x_i-1+v(t_i)Δt；

(3) Calculating t_iInitial expansion rate of time-of-flight cavitation

(4) Calculating navigation body head cavitator from x_iStarting movement L long used time t_kWith t_kAs being at a point x in space_iCalculating the sectional area of the upper cavity, namely calculating the stop condition of the inner layer;

(5) given the inner time step Δ T, calculate at (0, T)_k) In the time period, the sectional area of the cavitation bubble at the tail part of the navigation body at each moment is calculated until the inner layer is finished;

(6) and (5) repeating the steps (1) to (5) until the outer layer calculation is finished.

Images