Optimization design method of conical cavitator for supercavitation projectile

Abstract

The invention discloses an optimization design method of a conical cavitator for a supercavitation projectile. The optimization design method comprises the following steps: step 1, defining an operation condition and calculating a cavitation number; step 2, establishing a mathematical model of the supercavity contour; step 3, establishing a mathematical model of total projectile resistance; 4, establishing a mathematical model of hydrodynamic characteristics of the cavitator; 5, constructing a constraint optimization problem, and formalizing the design problem into a constrained mathematical optimization problem; 6, solving an optimization problem, solving the constraint optimization problem through a numerical algorithm, and obtaining a group of optimal design parameters capable of enabling the total resistance to be minimum, namely, the optimal cavitator diameter and the optimal full cone angle; according to the invention, the minimization of the total hydrodynamic resistance can be realized, and meanwhile, the generated supercavitation can be ensured to completely wrap the projectile.

Description

Technical Field

[0001] This invention belongs to the field of underwater high-speed vehicle design, and in particular, it is an optimized design method for a conical cavitation device used in supercavitating projectiles. Background Technology

[0002] Supercavitation technology creates a giant bubble (cavitation bubble) on the surface of a high-speed underwater vehicle, isolating the vehicle from the high-density water medium and thus greatly reducing drag. The cavitation unit, a key component installed at the bow of the vehicle, directly determines the shape and size of the cavitation bubble through its geometry, and also constitutes the primary source of drag for the vehicle.

[0003] In existing technologies, cavitation device (Cavitation Device) designs (such as disc-shaped or conical) often focus on ensuring the generation of sufficiently large cavitation bubbles to envelop the entire projectile. However, this typically results in the use of large or blunt-shaped cavitation devices, which themselves generate significant pressure drag. This design approach lacks a systematic, quantifiable process to balance the conflicting objectives of "generating sufficiently large cavitation bubbles" and "minimizing self-drag." Specifically, for a projectile of a given length and diameter, under specific operating speeds and water depths, precisely selecting the cavitation device's diameter and cone angle to minimize total drag while ensuring complete envelopment of the projectile remains an unresolved technical challenge. Existing designs largely rely on experience or optimization for single objectives, failing to provide a globally optimal solution for specific operating conditions.

[0004] Therefore, there is an urgent need in this field for a systematic, physical model-based optimization design method to scientifically determine the optimal geometric parameters of the conical cavitation device, so as to minimize the total drag of the projectile while satisfying the constraint of complete supercavitation encapsulation. Summary of the Invention

[0005] The purpose of this invention is to provide an optimized design method for a conical cavitation device for supercavitating projectiles, so as to minimize the total hydrodynamic drag while ensuring that the generated supercavitation can completely envelop the projectile.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] An optimization design method for a conical cavitation generator used in supercavitating projectiles, employing the following optimization function for iterative solution:

[0008]

[0009] The constraint equation is:

[0010]

[0011] The iterative solution process is as follows:

[0012] (1) Determine the full cone angle of the cavitation unit The search range and search step size;

[0013] (2) The i-th full cone angle starting from the minimum full cone angle:

[0014] 1) Using the constraint equations, solve inversely to find the minimum cavitation diameter required to satisfy the enclosed conditions;

[0015] 2) Substitute the minimum cavitation diameter and the i-th full cone angle into the optimization function to calculate the total drag of the projectile in a fully supercavitated state. ;

[0016] (3) The full cone angle is increased from the minimum value to the maximum value according to the search step size. Repeat process (2) to collect the total resistance corresponding to all full cone angles. Draw the total resistance The curve that varies with the full cone angle;

[0017] (4) The x-coordinate corresponding to the lowest point of the curve is the optimal full cone angle. The optimal full cone angle Substituting the constraints into the equation, we obtain the optimal cavitation diameter;

[0018] in The density of water, The steady-state velocity of the projectile. The diameter of the bottom of the cavitation cone. The dimensionless cavitation number represents the projectile's operating environment. The correction coefficient for fitting the cone angle of the experimental cavitation diameter. The cone angle fitting correction coefficient is given by denoted as L, where L is the projectile body length. This represents the cavitation drag coefficient.

[0019] The significant advantages of this invention compared to existing technologies are:

[0020] (1) A physical model-based optimization design method is provided, which unifies the two objectives of "ensuring complete encapsulation of supercavitation" and "minimizing cavitation resistance" in a mathematical model, thus overcoming the blindness of traditional empirical design methods;

[0021] (2) By introducing the cone angle correction coefficient and drag coefficient of the cone cavitation device through experiments, the cavitation theory model is corrected, which more realistically reflects the cavitation morphology and drag characteristics and improves the reliability of the design;

[0022] (3) By adopting the constraint boundary transformation into a single variable search strategy, the solution complexity of the optimization problem is reduced, which facilitates engineering implementation and rapid iteration. Attached Figure Description

[0023] Figure 1 This is a structural schematic diagram of the supercavitating projectile and its key parameters as described in this invention.

[0024] Figure 2 This is a flowchart of the optimization design method described in this invention.

[0025] Figure 3 This is a schematic diagram showing the variation of total resistance with cavitation cone angle according to an embodiment of the present invention, illustrating the existence of an optimal solution. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0027] Reference Figure 1 A supercavitating projectile 0 has a body 1 with a total length of L and a body diameter of D. A conical cavitator 2 is mounted on the projectile's nose, and the diameter of the bottom of the cone of the cavitator 2 is [missing information]. The full cone angle is During high-speed flight, the cavitation device 2 generates a supercavitation bubble 3 around the projectile, the profile of which is determined by a function. describe.

[0028] The optimization design method of the present invention has the following process: Figure 2 As shown, the specific steps are as follows:

[0029] Step 1: Define operating conditions and calculate cavitation numbers

[0030] Determine the steady-state velocity of the projectile. and underwater depth Environmental parameters, such as the dimensionless cavitation number of the operating environment, are then used to calculate these parameters. The calculation formula is as follows:

[0031]

[0032] in Standard atmospheric pressure The density of water, It is the acceleration due to gravity. This is the saturated vapor pressure of water. This refers to the projectile's velocity.

[0033] Step 2: Establish a mathematical model of the supercavitation profile

[0034] Based on the Logvinovich independent expansion principle with cone angle correction and its semi-empirical formula, the profile of the closed stage of a supercavitation 3-cavitation bubble can be approximated as an ellipsoid. When 60° ≤ ≤160°, its maximum radius and length It can be estimated using the following formula:

[0035]

[0036]

[0037] in The correction coefficient for fitting the cone angle of the experimental cavitation diameter. The cone angle fitting correction coefficient for the cavitation length is... , .

[0038] Therefore, the cavitation radius With axial distance (The origin is the center of the bottom surface of the cavitation cone.) The axis is along the projectile axis. The relationship between the positive axis and the direction of the projectile cavitation device towards the tail is as follows. for:

[0039]

[0040] Step 3: Establish a mathematical model for the total drag of the projectile.

[0041] Establish the total drag of the projectile in a fully supercavitated state. The mathematical model assumes that the total resistance mainly comes from the pressure resistance of the cavitation device itself, and expresses it as the diameter of the cavitation device. cavitation drag coefficient The density of water and running speed function .

[0042] In a fully enclosed supercavitated state, the total drag of the projectile... It is approximately equal to the resistance of cavitation 2 itself. That is:

[0043]

[0044] Step 4: Establish a mathematical model of the hydrodynamic characteristics of the cavitation device.

[0045] Establish cavitation drag coefficient Its geometry (full cone angle) ) and operating conditions (cavitation number) The functional relationship between () and (). Based on Logvinovich's independent expansion principle and empirical formula, the drag coefficient of the conical cavitation device is (). Its expression is:

[0046]

[0047] in This is the second-order correction factor for the cone angle of the drag coefficient. .

[0048] Step 5: Construct the constrained optimization problem

[0049] The design problem is formalized as a constrained mathematical optimization problem:

[0050] ●Optimization objective: Minimize total resistance .

[0051] ●Design variable: Cavitation diameter and full cone angle .

[0052] ●Constraints: At the tail of the projectile ( The cavitation radius must be greater than or equal to the projectile radius, i.e. .

[0053] Step Six: Solve the optimization problem

[0054] The above constrained optimization problem is solved using numerical algorithms to obtain a set of values ​​that minimizes the total resistance. The minimum optimal design parameter, i.e., the optimal cavitation diameter. and optimal full cone angle .

[0055] The specific method is as follows:

[0056] Integrating the above models, we obtain a model based on... and This is a bivariate constrained optimization problem with variables. Based on physical insights, the optimal solution must lie on the constraint boundary, meaning the cavitation bubble exactly encloses the entire projectile. Therefore, the constraints can be simplified to the equation: Combining the above equations, we have:

[0057]

[0058] Using this constraint, a variable (e.g.) can be analytically or numerically defined. ) represents another variable ( The function of ) Substituting this relationship into the total resistance objective function, the original problem can be transformed into a single-variable optimization problem, with the optimization function as follows:

[0059]

[0060] Numerical algorithms are used to solve this single-variable optimization problem. Specifically, at a preset cone angle... Within the range ( The iterative search is performed as follows:

[0061] (1). Determine the search interval for the full cone angle β. and search step size Δβ; These correspond to the minimum and maximum values ​​of the full cone angle β, respectively;

[0062] (2) For the i-th full cone angle β i (from start):

[0063] 1) Using the constraint equation (7), the minimum cavitation diameter required to satisfy the enclosure condition is solved by inverse solution. ;

[0064] 2) The obtained and β i Substituting into the total drag formula (8), the total drag of the projectile is calculated. ;

[0065] (3)β i from Increasing Δβ accordingly until Repeat process 2 to collect all full cone angles β i Corresponding total projectile drag Draw the total drag of the projectile. The curve showing the variation of the full cone angle β, as shown below. Figure 3 As shown;

[0066] (4) Find on the curve The minimum point is 4, and the corresponding full cone angle β value is the optimal full cone angle β*. The optimal full cone angle... Substituting the constraint equation (7) from step six, we obtain the optimal cavitation diameter Dc*.

[0067] Through the above process, the two-parameter optimization problem is transformed into a single-parameter traversal, ultimately outputting the optimal design parameters. This is the result that the present invention aims to determine. A conical cavitation device manufactured using this set of parameters can achieve a given ( Under the condition of ), for parameter ( The projectile provides complete supercavitation while minimizing hydrodynamic drag.

Claims

1. A method for optimizing the design of a conical cavitation generator for supercavitating projectiles, characterized in that, The following optimization function is used for iterative solution: The constraint equation is: The iterative solution process is as follows: (1) Determine the full cone angle of the cavitation unit The search range and search step size; (2) The i-th full cone angle starting from the minimum full cone angle: 1) Using the constraint equations, solve inversely to find the minimum cavitation diameter required to satisfy the enclosed conditions; 2) Substitute the minimum cavitation diameter and the i-th full cone angle into the optimization function to calculate the total drag of the projectile in a fully supercavitated state. ; (3) The full cone angle is increased from the minimum value to the maximum value according to the search step size. Repeat process (2) to collect the total resistance corresponding to all full cone angles. Draw the total resistance The curve that varies with the full cone angle; (4) The x-coordinate corresponding to the lowest point of the curve is the optimal full cone angle. The optimal full cone angle Substituting the constraints into the equation, we obtain the optimal cavitation diameter; in The density of water, The steady-state velocity of the projectile. The diameter of the bottom of the cavitation cone. The dimensionless cavitation number represents the projectile's operating environment. The correction coefficient for fitting the cone angle of the experimental cavitation diameter. The cone angle fitting correction coefficient is given by denoted as L, where L is the projectile body length. This represents the cavitation drag coefficient.

2. The method for optimizing the design of a conical cavitation device for a supercavitating projectile according to claim 1, characterized in that, cavitation drag coefficient for: in This is the second-order correction factor for the cone angle of the drag coefficient.

3. The method for optimizing the design of a conical cavitation device for a supercavitating projectile according to claim 1 or 2, characterized in that, Dimensionless cavitation number of the projectile's operating environment for: in Standard atmospheric pressure underwater depth It is the acceleration due to gravity. This is the saturated vapor pressure of water.

4. The method for optimizing the design of a conical cavitation device for a supercavitating projectile according to claim 1, characterized in that, Full cone angle of cavitation The value range is 60°≤ ≤160°.

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