Pitching moment analysis method suitable for underwater movement of supercavitation projectile

Abstract

The invention discloses a pitching moment analysis method suitable for underwater movement of a supercavitation projectile. The method comprises the steps that the movement speed, the movement posture, the projectile body stress and the wetting condition of the supercavitation projectile are obtained; pitching moment coefficients of the projectile in water and water vapor are obtained according to the motion parameter interpolation; calculating the pitching moment of the projectile generated by the gas in the cavitation bubble according to the motion parameter and the pitching moment coefficient; calculating the pitching moment of the projectile generated by water according to the motion parameter and the pitching moment coefficient; the tail beat force generated when the supercavitation projectile generates tail beat is obtained, and the pitching moment generated by the tail beat force is calculated; and calculating the total pitching moment of the supercavitation projectile on the basis of the pitching moment generated by the gas, the pitching moment generated by the water and the pitching moment generated by the tail beat force. According to the calculation method, the wetting length and wetting area of the tail beat of the supercavitation projectile can be accurately calculated, the total pitching moment of the supercavitation projectile moving in water can be accurately and conveniently solved, and the research cost is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of projectiles and arrows, and in particular relates to a pitch moment analysis method suitable for a supercavitation projectile moving in water. Background Art

[0002] When a supercavitating projectile moves underwater, the pitching moment will affect the motion characteristics of the projectile, and then affect the motion law of the supercavitating projectile and the performance of the supercavitating projectile weapon. Therefore, the analysis of the pitching moment plays an important role in the design and verification of the projectile. When the motion of a supercavitating projectile in water is disturbed, a tail slap phenomenon will occur, and parameters such as the tail slap force and the angle of attack will show quasi-periodic oscillation characteristics. In order to analyze the pitching moment characteristics of a supercavitating projectile, it is necessary to analyze the dynamic torque of each part of the projectile during the tail slap process.

[0003] When a supercavitating projectile moves in water, the projectile is wrapped by the cavitation and is subject to an aerodynamic torque. At present, the aerodynamic torque of the projectile is usually solved with the help of aerodynamic coefficients; when a supercavitating projectile has a tail slap, it will get wet and be subject to a tail slap force, which will produce a pitching moment on the projectile. The wetted part will move relative to the water and will be subject to a hydrodynamic torque. The process of a supercavitating projectile moving in water is an unsteady motion involving vapor-liquid two-phase flow. Due to the limited volume structure of the cavitation, as well as the level of experiments and tests, it is difficult to obtain the hydrodynamic force, tail slap force and wetting conditions of the supercavitating projectile through experiments. Summary of the invention

[0004] The purpose of the present invention is to provide a pitch moment analysis method suitable for supercavitation projectile moving in water, and to analyze the dynamic moments of various parts of the projectile during the tail slapping process.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A method for analyzing the pitching moment of a supercavitating projectile moving in water is used to calculate the total pitching moment M of a supercavitating projectile moving in water by the following formula: z :

[0007] M z =M z气 +M z水 +M z拍

[0008]

[0009] M z水 =m z水 q 水 S 沾湿 L 沾湿

[0010] M z拍=F y L o sin|α|+F x L o cos|α|

[0011] Among them, M z气 is the pitch moment of the projectile caused by the water vapor in the cavitation bubble, M z水 is the pitching moment of the projectile caused by the water, M z拍 is the pitching moment generated by the tail beat force; is the derivative of the aerodynamic pitch moment coefficient with respect to the angle of attack, α is the projectile angle of attack; S is the cross-sectional area of ​​the projectile, L is the projectile length, q 气 is the flow field dynamic pressure, several m z水 is the pitch moment coefficient of the supercavitating projectile in water, S 沾湿 is the wetted area when the projectile tail hits, L 沾湿 is the wet length of the projectile tail when hitting, q 水 is the water dynamic pressure, F x and F y are the components of the tail force in the x-axis and y-axis directions, L o The tail force acting point O 拍 The axial distance from the center of mass of the projectile. The x-axis is parallel to the speed of the projectile and in the opposite direction. The y-axis is perpendicular to the x-axis in the longitudinal symmetry plane of the projectile.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) A method for calculating the wetted length and wetted area of ​​the tail of a supercavitating projectile is proposed, which provides a strong support for the torque analysis of the tail process;

[0014] (2) A method for analyzing the pitch moment of a supercavitating projectile moving in water is proposed. It can provide relatively accurate torque input for the tail-beat motion of the projectile and realize the motion stability analysis of the supercavitating projectile and the theoretical solution of its underwater trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a step diagram of an implementation method of the pitching moment analysis method for a supercavitating projectile moving in water according to the present invention.

[0016] Figure 2 Schematic diagram of the wetting condition of the tail of a supercavitating projectile moving underwater.

[0017] Figure 3 Schematic diagram for solving the wetted area of ​​the tail of a supercavitating projectile.

[0018] Figure 4 Schematic diagram for solving the tail force of a supercavitating projectile.

[0019] Figure 5 Schematic diagram of another situation where the tail of a supercavitating projectile gets wet while moving underwater.

[0020] Figure 6 Schematic diagram of the supercavitating projectile when it is not wetted. DETAILED DESCRIPTION

[0021] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0022] Figure 2 The schematic diagram of a supercavitating projectile hitting the upper cavitation wall during tail slap is shown. In this case, the projectile moves in the gas inside the cavitation bubble and is subject to the aerodynamic pitch moment from the gas; when a supercavitating projectile moves in water, tail slapping occurs, and when the tail slaps, it comes into contact with the water and is subject to the hydrodynamic moment; when the projectile tail slaps, it is subject to the tail slap force, so the projectile is subject to a tail slap moment. Therefore, when calculating the total pitch moment to which a supercavitating projectile is subject, the above moments should be calculated separately first.

[0023] The present invention proposes a pitch moment analysis method suitable for supercavitation projectiles moving in water, such as Figure 1 As shown, it mainly includes:

[0024] Step S1: obtaining the moving speed of the supercavitating projectile, the projectile attack angle, the tail slap force exerted on the projectile, the projectile tail slap depth, the wetted length and the wetted area;

[0025] Through experiments, the motion of supercavitating projectiles was captured by high-speed cameras, and the velocity V and the angle of attack α of the projectile were obtained. The positional relationship between the cavitation and the projectile and the wetting position of the projectile were captured by high-speed cameras, and the tail-beat depth h of the projectile and the axial distance L between the tail-beat force application point and the center of mass were obtained. o The tail shot depth h can also be obtained by taking a high-speed camera to obtain the cavity diameter R at the tail of the projectile. c , which is indirectly obtained with the help of geometric relationships in subsequent calculations. Figure 2 The rectangular coordinate system is established as shown in the figure. The origin of the coordinate coincides with the center of mass O of the projectile. The x-axis is parallel to the projectile's velocity and in the opposite direction. The y-axis is perpendicular to the x-axis in the longitudinal symmetry plane of the projectile. The components F of the tail force of the supercavitating projectile on the x-axis and y-axis are obtained by calculation. x and F y , wetted area S 沾湿 , wetted length L 沾湿 In addition, the cross-sectional area S and length L of the cylindrical section of the projectile's warhead should be obtained as the reference area and reference length for calculating the aerodynamic pitching moment, respectively, and the gas density and humidity and liquid density in the projectile's motion environment should be obtained as a reference for finding the pitching moment coefficient.

[0026] Figure 3The calculation method of the wetted area of ​​a supercavitating projectile during tail stroke is shown. Since the curvature of the cavitation at the wetted position is small, the cavitation-water interface is simplified to a straight line when analyzing the wetting situation. As shown in the figure, when the tail stroke depth is h, the wetted length is:

[0027]

[0028] The radius of the supercavitation projectile is R. Take a microelement dl at a distance l from the intersection of the wetted and unwetted points. The maximum length d of the wetted cross section at this point and the angle θ of half of the central angle of the arc length of the wetted area can be expressed as:

[0029] d=ltanα (2)

[0030]

[0031] The above α is the projectile attack angle, and D is the projectile diameter.

[0032] The calculation formula for the wetted area at the microelement dl is:

[0033]

[0034] Integrating equation (4) yields the wetted area:

[0035]

[0036] Figure 4 The solution method of the tail slap force is shown. The maximum depth of the tail slap of a supercavitating projectile is h, which affects the fluid boundary layer with a thickness of λh (where λ is an empirical coefficient less than 1). According to the conservation of momentum, the components of the projectile tail slap force on the x-axis and y-axis are as follows:

[0037] F x =ρ 水 S 层 V 2 (1-cosα) (6)

[0038] F y =ρ 水 S 层 V 2 sinα (7)

[0039] The F x and F y is the component of the tail force on the x-axis and y-axis, S 层 =λhD is the characteristic area of ​​the fluid boundary layer that the projectile tail is immersed in when hitting, ρ 水 is the density of water, and V is the velocity of the projectile. The maximum depth of the tail shot can be obtained experimentally or solved with the help of the following geometric relationship:

[0040]

[0041] Where R c is the radius of the cavitation bubble at the tail of the projectile, and L is the length of the projectile.

[0042] When the tail force is substituted into the calculation, the positive and negative should be distinguished, such as Figure 2 The projectile hits the upper cavitation wall, where the tail force component F x and F y All should be taken as positive values ​​for calculation; Figure 5 The projectile hits the lower cavitation wall, F x Take positive value, F y Substitute negative values ​​into calculations.

[0043] Step S2: obtaining the derivative of the pitch moment coefficient of the projectile in water and the pitch moment coefficient in water vapor with respect to the angle of attack by interpolation according to the motion parameters;

[0044] The pitch moment coefficient table is a table related to the projectile shape and flow field conditions. The table contains some speeds or Mach numbers and the corresponding pitch moment coefficients. The corresponding pitch moment coefficient can be obtained according to the projectile speed or the local Mach number. The specific method of this step is: select the corresponding pitch moment coefficient table according to the type of projectile, the humidity of the motion environment, and the density of water vapor and water. Look up the table according to the projectile movement speed obtained above. If the speed is the same as a speed value in the table, the corresponding coefficient can be directly obtained; if the projectile movement speed is not in the table, the pitch moment coefficient is interpolated according to the similar speed value. Through the above operation, the derivative of the pitch moment coefficient of the supercavitating projectile in water vapor with respect to the angle of attack should be obtained at this step. and the pitch moment coefficient m of the supercavitating projectile in water z水 .

[0045] Step S3: Calculate the pitching moment M generated by the water vapor in the cavitation according to the motion parameters and the derivative of the pitching moment coefficient in the water vapor with respect to the angle of attack. z气 ;

[0046] The derivative of the pitch moment coefficient of a supercavitating projectile in water vapor with respect to the angle of attack is obtained Substitute and calculate the pitching moment M caused by the gas in the cavitation bubble z气 The projectile moves in the gas in the cavitation bubble, and only a small part of it is wetted. Therefore, when calculating the aerodynamic pitching moment, it can be approximately regarded as moving completely in water vapor. The projectile used is an axisymmetric body and is approximately in steady-state motion at each moment. Therefore, the pitching moment coefficient term can be expressed by the angle of attack and the derivative of the pitching moment coefficient with respect to the angle of attack. At this time, the pitching moment generated by the gas is as follows:

[0047]

[0048] in is the derivative of the aerodynamic pitch moment coefficient with respect to the angle of attack, obtained by the aforementioned table lookup; α is the projectile angle of attack; S is the cross-sectional area of ​​the cylindrical section of the projectile warhead; L is the projectile length; q 气 is the flow field dynamic pressure, which can be expressed as:

[0049]

[0050] Where V is the velocity of the projectile, ρ 气 is the density of the gas inside the cavity.

[0051] The above aerodynamic pitching moment M z气 is the moment about the center of mass O of the supercavitating projectile.

[0052] Step S4: Calculate the pitching moment M generated by the projectile in the water according to the motion parameters and the pitching moment coefficient z水 ;

[0053] The obtained pitch moment coefficient m of the supercavitating projectile in water is z水 Substitute it and calculate the pitching moment M caused by the wet part of the projectile during its movement in water. z水 When the supercavitating projectile is wet, the dynamic torque is:

[0054] M z水 =m z水 q 水 S 沾湿 L 沾湿 (11)

[0055] Where S 沾湿 is the wetted area when the projectile tail hits, L 沾湿 is the wetted length of the projectile tail when it hits, which can be solved by the above equations (1) and (5) respectively. Since only a small part of the supercavitating projectile tail is in contact with water when it hits, equation (11) is based on the wetted area S 沾湿 As a reference area, take the wetted length L 沾湿 As a reference length. 水 is the water area dynamic pressure, which can be expressed as:

[0056]

[0057] where ρ 水 is the density of water.

[0058] There are moments during the tail stroke when supercavitating projectiles do not get wet, e.g. Figure 6 When the projectile is not wetted, the dynamic torque generated by the water is zero, that is:

[0059] M z水 =0 (13)

[0060] The above hydrodynamic pitching moment M z水 is the moment about the center of mass O of the supercavitating projectile.

[0061] Step S5: Obtain the tail force of the supercavitating projectile when it is tail-striking, and calculate the pitch moment M generated by the tail force z拍 ;

[0062] When a supercavitating projectile is tail-slapped, it will be subjected to a tail-slap force. It is necessary to calculate and solve the tail-slap force of the supercavitating projectile, and calculate the moment on the center of mass of the projectile generated by the tail-slap force based on the geometric relationship. The pitch moment caused by the tail-slap force is:

[0063] M z拍 =F y L o sin|α|+F x L o cos|α| (14)

[0064] Among them, F x and F y is the x- and y-axis components of the tail force, L o The tail force acting point O 拍 is the axial distance from the projectile's center of mass O, and α is the projectile's angle of attack.

[0065] The above angle of attack is only used to calculate the geometric relationship between the length of the tail slap force point from the center of mass of the projectile and the force arm of the tail slap force. Therefore, the angle of attack α is taken as an absolute value in equation (14). The tail slap force obtained by equations (6) and (7) is F x and F y , when the tail force is substituted into the calculation, the positive and negative directions should be distinguished, such as Figure 2 The projectile hits the upper cavitation wall, and the tail force component F x and F y are all taken as positive values; Figure 5 The projectile hits the lower cavitation wall, and the tail force F x Take a positive value, F y The pitch moment generated by the tail force of the supercavitation projectile can be obtained through the above calculation.

[0066] When the projectile does not hit the cavitation bubble, the schematic diagram is as follows Figure 6 As shown, the projectile is not subjected to the tail force, and the pitch moment generated by the tail force is zero, that is:

[0067] M z拍 =0 (15)

[0068] According to the above formula, the pitching moment M z拍 is the moment about the center of mass O of the supercavitating projectile.

[0069] The pitching moment calculated above includes the pitching moment M generated by the gas in the cavitation bubble. z气 , the pitching moment M generated by water z水 and the pitch moment M generated by the tail force z拍 The three pitching moments are all moments relative to the center of mass of the supercavitating projectile, so they can be added together to obtain the total pitching moment. The positive and negative moments should be distinguished during calculation.

[0070] Step S6: The pitch moment M generated by the gas z气 , the pitching moment M generated by water z水 and the pitching moment M generated by the tail force z拍 Based on this, the total pitching moment M of the supercavitating projectile is calculated. z .

[0071] The total pitching moment on a supercavitating projectile moving in water is:

[0072] M z =M z气 +M z水 +M z拍 (16)

[0073] The above implementation method can be used to solve the pitch moment that the supercavitating projectile is subjected to at any time when moving underwater.

[0074] Obviously, the above embodiments of the present invention are only examples to clearly illustrate the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A method for analyzing the pitching moment of a supercavitating projectile moving in water, characterized in that: The total pitching moment M of the supercavitating projectile moving in water is calculated by the following formula: z : M z =M z气 +M z水 +M z拍 M z水 =m z水 q 水 S 沾湿 L 沾湿 M z拍 =F y L o sin|α|+F x L o cos|α| Among them, M z气 is the pitch moment of the projectile caused by the water vapor in the cavitation bubble, M z水 is the pitching moment of the projectile caused by the water, M z拍 is the pitching moment generated by the tail beat force; is the derivative of the aerodynamic pitch moment coefficient with respect to the angle of attack, α is the projectile angle of attack; S is the cross-sectional area of ​​the projectile, L is the projectile length, q 气 is the flow field dynamic pressure, several m z水 is the pitch moment coefficient of the supercavitating projectile in water, S 沾湿 is the wetted area when the projectile tail hits, L 沾湿 is the wet length of the projectile tail when hitting, q 水 is the water dynamic pressure, F x and F y are the components of the tail force in the x-axis and y-axis directions, L o is the tail-beat force acting point O 拍 The axial distance from the center of mass of the projectile. The x-axis is parallel to the speed of the projectile and in the opposite direction. The y-axis is perpendicular to the x-axis in the longitudinal symmetry plane of the projectile.

2. The pitching moment analysis method for supercavitation projectiles moving in water according to claim 1 is characterized in that: in: F x =ρ 水 S 层 V 2 (1-cosα) F y =ρ 水 S 层 V 2 Sinai ρ 水 is the density of water, V is the speed of the projectile, S 层 It is the characteristic area of ​​the fluid boundary layer that the projectile tail is immersed in when it hits.

3. The pitching moment analysis method for supercavitation projectiles moving in water according to claim 1 is characterized in that: The calculation method of the wetted area when the projectile tail hits is: Take a microelement dl at a distance l from the intersection of wetted and unwetted points. The maximum length d of the wetted cross section and the half angle θ of the arc length of the wetted area at this point can be expressed as: d = ltanα The calculation formula for the wetted area at the microelement dl is: Integrating the above formula gives the wetted area: Where h is the maximum tail slap depth of a supercavitating projectile and D is the projectile diameter.

4. The pitch moment analysis method for supercavitation projectile in water according to claim 1, characterized in that: in Where h is the maximum tail slap depth of a supercavitating projectile.

5. The pitching moment analysis method for supercavitation projectiles moving in water according to claim 3 is characterized in that: in: Where R c is the radius of the cavitation bubble at the tail of the projectile, L is the length of the projectile, and D is the diameter of the projectile.

6. The pitch moment analysis method for supercavitation projectile in water according to claim 1, characterized in that: in: where ρ 水 is the density of water and V is the velocity of the projectile.

7. The pitch moment analysis method for supercavitation projectile in water according to claim 1, characterized in that: When the projectile hits the upper cavitation wall, the tail force component F x and F y should be taken as positive values ​​for calculation; when the projectile hits the lower cavitation wall, F x Take positive value, F y Substitute negative values ​​into calculations.

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