A method for analyzing the pitching moment of a supercavitating projectile moving in water

Abstract

The present invention discloses a method for analyzing the pitching moment of a supercavitating projectile moving in water, comprising the following steps: obtaining the velocity, motion posture, force on the projectile, and wetting conditions of the supercavitating projectile; interpolating the pitching moment coefficients of the projectile in water and water vapor based on the motion parameters; calculating the pitching moment of the projectile generated by the gas in the cavitation cavity based on the motion parameters and the pitching moment coefficients; calculating the pitching moment of the projectile generated by the water based on the motion parameters and the pitching moment coefficients; obtaining the tail-slap force of the supercavitating projectile when it is tail-slapping, and calculating the pitching moment generated by the tail-slap force; and calculating the total pitching moment of the supercavitating projectile based on the pitching moment generated by the gas, the pitching moment generated by the water, and the pitching moment generated by the tail-slap force. The present invention proposes a method for accurately calculating the wetted length and wetted area of ​​the supercavitating projectile's tail-slap, which can accurately and conveniently solve the total pitching moment of a supercavitating projectile moving in water, thereby reducing research costs.

Description

Technical Field

[0001] The present invention belongs to the technical field of projectiles and arrows, and in particular relates to a pitching moment analysis method applicable to a supercavitating projectile moving in water. Background Art

[0002] During underwater motion, the pitching moment of a supercavitating projectile affects its kinematic characteristics, thus affecting both its motion and the weapon's performance. Therefore, analyzing this pitching moment plays a crucial role in projectile design and calibration. When a supercavitating projectile's underwater motion is disturbed, it experiences tail slap, with parameters such as the tail slap force and angle of attack exhibiting quasi-periodic oscillations. To analyze the pitching moment characteristics of a supercavitating projectile, it is necessary to analyze the various dynamic moments experienced during the tail slap.

[0003] When a supercavitating projectile moves through water, it is enveloped by the cavitation bubble and subjected to an aerodynamic torque. Currently, the aerodynamic torque of a projectile is typically calculated using aerodynamic coefficients. During tail stroke, the supercavitating projectile becomes wetted and subjected to a tail stroke force, which generates a pitching moment on the projectile. The wetted portion moves relative to the water, subjecting it to a hydrodynamic torque. The motion of a supercavitating projectile in water is an unsteady motion involving vapor-liquid two-phase flow. Due to the limited volume of the cavitation bubble and the limited experimental and testing capabilities, experimentally determining the hydrodynamic forces, tail stroke forces, and wetting conditions experienced by a supercavitating projectile is challenging. Summary of the Invention

[0004] The purpose of the present invention is to provide a pitching moment analysis method suitable for supercavitating projectiles moving in water, and to analyze the dynamic moments of each part of the projectile during the tail slapping process.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] A method for analyzing the pitching moment of a supercavitating projectile in water is used to calculate the total pitching moment M of a supercavitating projectile in water using 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 pitching moment of the projectile caused by the water vapor in the cavitation, M z水 is the pitching moment of the projectile caused by the water, M z拍 is the pitching moment generated by the tailbeat force; is the derivative of the aerodynamic pitching moment coefficient with respect to the angle of attack, α is the projectile angle of attack; S is the projectile cross-sectional area, L is the projectile length, q 气 is the flow field dynamic pressure, several m z水 is the pitching moment coefficient of the supercavitating projectile in water, S 沾湿 is the area wetted by the tail of the projectile, L 沾湿 is the length of the projectile tail when it is wet, q 水 is the dynamic pressure of the water area, F x and F y are the components of the tail force in the x-axis and y-axis directions, L o The tail-beat force point O 拍 The axial distance from the center of mass of the projectile, the x-axis is parallel to the projectile's velocity and in the opposite direction, and 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 strong support for the torque analysis of the tail.

[0014] (2) A method for analyzing the pitching moment of a supercavitating projectile in water is proposed, which 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 present invention for analyzing the pitching moment of a supercavitating projectile moving in water.

[0016] Figure 2 Schematic diagram of the tail wetting 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 a supercavitating projectile when it is not wetted. DETAILED DESCRIPTION

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0022] Figure 2 A schematic diagram shows a supercavitating projectile striking the upper cavitation wall during tail slap. In this scenario, the projectile, moving within the gas within the cavitation, experiences an aerodynamic pitching moment from the gas. When a supercavitating projectile moves through water, tail slapping occurs, and during this process, it comes into contact with the water, subjecting it to a hydrodynamic moment. During tail slapping, the projectile experiences a tail slap force, resulting in a tail slapping moment. Therefore, when calculating the total pitching moment experienced by a supercavitating projectile, these moments must be calculated separately.

[0023] The present invention proposes a method for analyzing the pitching moment of a supercavitating projectile in water. Figure 1 As shown, it mainly includes:

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

[0025] By conducting experiments, the motion of supercavitating projectiles was captured using a high-speed camera, and the projectile velocity V and projectile attack angle α were obtained. The positional relationship between the cavitation bubble and the projectile, as well as the projectile's wetting position, were captured using a high-speed camera, and the projectile's tail slap depth h and the axial distance L between the tail slap 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 cavitation diameter R at the tail of the projectile. c , which is obtained indirectly 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. The gas density, humidity, and liquid density of the projectile's motion environment should be obtained as a reference for finding the pitching moment coefficient.

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

[0027]

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

[0029] d=ltan|α| (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 infinitesimal point dl is:

[0033]

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

[0035]

[0036] Figure 4 The solution for the tail slap force is demonstrated. The maximum tail slap depth of a supercavitating projectile is h, affecting a fluid boundary layer with a thickness of λh (where λ is an empirical coefficient less than 1). Based on the conservation of momentum, the components of the projectile's tail slap force on the x and y axes 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 tailbeat force on the x-axis and y-axis, S 层 =λhD is the characteristic area of ​​the fluid boundary layer immersed in the projectile tail during the stroke, ρ 水 is the density of water, and V is the velocity of the projectile. The maximum depth of the tail slap can be obtained experimentally or solved using 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: interpolating the motion parameters to obtain the pitching moment coefficient of the projectile in water and the derivative of the pitching moment coefficient in water vapor with respect to the angle of attack;

[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 coefficients can be obtained according to the projectile speed or the local Mach number. The specific method of this step is: according to the type of projectile, the humidity of the motion environment, the density of water vapor and water, select the corresponding pitch moment coefficient table. According to the projectile motion speed obtained above, the table is looked up. If the speed is the same as a speed value in the table, the corresponding coefficient can be directly obtained; if the projectile motion speed is not in the table, the pitch moment coefficient is obtained by interpolation based on the similar speed value. Through the above operations, 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 pitching 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 pitching moment coefficient of the 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 within the cavitation bubble, with only a small portion being wetted. Therefore, when calculating the aerodynamic pitching moment, it can be approximately considered to be moving entirely within water vapor. The projectile is axisymmetric and approximately in steady-state motion at each moment. Therefore, the pitching moment coefficient term can be expressed as the angle of attack and the derivative of the pitching moment coefficient with respect to the angle of attack. The pitching moment generated by the gas in this case is as follows:

[0047]

[0048] in is the derivative of the aerodynamic pitching moment coefficient with respect to the angle of attack, obtained by the aforementioned table lookup; α is the projectile's angle of attack; S is the cross-sectional area of ​​the cylindrical section of the projectile's warhead; L is the projectile's 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 based on the motion parameters and the pitching moment coefficient z水 ;

[0053] The obtained pitching moment coefficient m of the supercavitating projectile in water is z水 Substitute and calculate the pitching moment M caused by the wet part of the projectile during its movement in water. z水 When a 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] Among them S 沾湿 is the area wetted by the tail of the projectile, L 沾湿 is the wetted length of the projectile when it hits the tail, which can be solved by the above equations (1) and (5) respectively. Since only a small part of the supercavitating projectile is in contact with water when it hits the tail, equation (11) uses the wetted area S 沾湿 As a reference area, the wetted length L 沾湿 As a reference length. 水 is the water 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 the supercavitating projectile does 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 during tail slapping and calculate the pitching moment M generated by the tail slapping force z拍 ;

[0062] When a supercavitating projectile is tail-slapping, it is subject to a tail-slapping force. It is necessary to calculate the tail-slapping force of the supercavitating projectile and calculate the moment on the center of mass of the projectile generated by the tail-slapping force based on the geometric relationship. The pitching moment caused by the tail-slapping 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 component of the tail force in the x-axis and y-axis directions, L o The tail-beat force 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 As shown, 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 above calculation can be used to obtain the pitching moment generated by the tail force of the supercavitating projectile.

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

[0067] M z拍 =0 (15)

[0068] The pitching moment M calculated according to the above formula 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 pitching 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 the calculation.

[0070] Step S6: The pitching 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, calculate the total pitching moment M of the supercavitating projectile 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-mentioned implementation method can be used to solve the pitching moment that a supercavitating projectile is subjected to at any moment when it moves 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 field, other different forms of changes or modifications can be made based on 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 scope of protection of the present invention.

Claims

1. A method for analyzing the pitching moment of a supercavitating projectile in water, characterized in that: The total pitching moment M of the supercavitating projectile 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 pitching moment of the projectile caused by the water vapor in the cavitation, M z水 is the pitching moment of the projectile caused by the water, M z拍 is the pitching moment generated by the tailbeat force; is the derivative of the aerodynamic pitching moment coefficient with respect to the angle of attack, α is the projectile angle of attack; S is the projectile cross-sectional area, L is the projectile length, q 气 is the flow field dynamic pressure, several m z水 is the pitching moment coefficient of the supercavitating projectile in water, S 沾湿 is the area wetted by the tail of the projectile, L 沾湿 is the length of the projectile tail when it is wet, q 水 is the dynamic pressure of the water area, F x and F y are the components of the tail force in the x-axis and y-axis directions, L o The tail-beat force point O 拍 The axial distance from the center of mass of the projectile, the x-axis is parallel to the velocity of the projectile and in the opposite direction, and the y-axis is perpendicular to the x-axis in the longitudinal symmetry plane of the projectile; 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 the wetted and unwetted points. The maximum wetted length d of the cross section at this point and the half angle θ of the central angle of the circle subtended by the arc length of the wetted area are expressed as follows: d=ltan|α| D is the projectile diameter; The calculation formula for the wetted area at the infinitesimal point dl is: Integrating the above formula gives the wetted area: Where h is the maximum tail slap depth of a supercavitating projectile; Where h is the maximum tail slap depth of the supercavitating projectile, R c is the radius of the cavitation bubble at the tail of the projectile.

2. The method for analyzing the pitching moment of a supercavitating projectile in water according to claim 1, 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 hitting.

3. The method for analyzing the pitching moment of a supercavitating 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.

4. The method for analyzing the pitching moment of a supercavitating 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 All 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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