Method for obtaining autonomous propulsion performance of flexible deformable body based on resistance correction surface element method

Abstract

The invention provides a method for acquiring autonomous propulsion performance of a flexible deformable body based on a resistance correction surface element method. The method comprises the following steps: (1) determining physical characteristics and initial parameters of the flexible deformable body and initial conditions and flow parameters of fluid; (2) carrying out direct numerical simulation on the flexible deformable body by using a classical surface element method to obtain the fluid pressure intensity borne by the object surface; (3) calculating resistance compensation applied to the center of mass of the flexible deformation body through an equivalent resistance model; (4) calculating the autonomous forward swimming speed when the flexible deformable body stably swims through the balance of the pressure and the equivalent resistance borne by the flexible deformable body in the swimming process; and (5) obtaining the hydrodynamic power and efficiency of the flexible deformable body according to the stress and the cruise speed of each part of the flexible deformable body. According to the method, the rapidity and convenience of the surface element method in calculating the fluid-solid coupling problem can be kept, and meanwhile, the error of the classical surface element method in practical application is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bionic machines, and particularly to a method for obtaining the autonomous propulsion performance of a flexible deformable body based on a modified panel method for drag. Background Art

[0002] Designing high-speed and efficient flexible deformable bodies (such as bionic robotic fish) can significantly improve the propulsion efficiency and energy utilization rate, and is more concealed and adaptable compared to traditional propeller drives. It can not only reveal the propulsion mechanism of fish, but also has wide applications in the fields of underwater robots, environmental monitoring, etc., providing new technical support for underwater engineering; in order to save construction costs, it is necessary to roughly evaluate the performance of the flexible deformable body before actual production. Traditional numerical methods usually use the immersed boundary method or the dynamic mesh method for calculation, but the former is applicable to too small a range of Reynolds numbers, and the latter requires a long calculation time.

[0003] In summary, it is necessary to further innovate the existing technology. Summary of the Invention

[0004] In view of the technical problems in the above background art, the present invention proposes a method for obtaining the autonomous propulsion performance of a flexible deformable body based on a modified panel method for drag. By using the coefficient and formula determined according to the drag scaling relationship, and combining the pressure calculated by the classical panel method, the swimming performance of the flexible deformable body is finally calculated, providing a reliable basis for the preliminary design and iteration of the flexible deformable body (such as bionic robotic fish).

[0005] To solve the above technical problems, a method for obtaining the autonomous propulsion performance of a flexible deformable body based on a modified panel method for drag provided by the present invention includes the following steps:

[0006] (1) Determine the physical characteristics and initial parameters of the flexible deformable body, as well as the initial conditions and flow parameters of the fluid;

[0007] (2) Use the classical panel method to perform direct numerical simulation of the flexible deformable body to obtain the fluid pressure on the object surface;

[0008] (3) Calculate the drag compensation applied to the centroid of the flexible deformable body through an equivalent drag model;

[0009] (4) Calculate the autonomous forward swimming speed of the flexible deformable body when it swims stably through the balance of the pressure and equivalent drag received by the flexible deformable body during swimming;

[0010] (5) Obtain the hydrodynamic power and efficiency of the flexible deformable body according to the forces on each part of the flexible deformable body and the swimming speed.

[0011] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method, wherein: the physical properties of the flexible deformable body in step (1) include the density, shape, size, width, and height of the flexible deformable body distributed along the body length.

[0012] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method, wherein the specific process of directly numerically simulating the flexible deformable body using the classical panel method in step (2) is as follows:

[0013] (2.1) Construct an initial geometric model;

[0014] (2.2) Determine the midline deformation mode of the flexible deformable body;

[0015] (2.3) Establish a coupling model between the fluid domain and the solid domain;

[0016] (2.4) Solve the flow field in the fluid domain and the force conditions of the flexible deformable body.

[0017] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method, wherein the midline deformation mode of the flexible deformable body in step (2.2) includes the function of the midline position of the flexible deformable body changing with time:

[0018]

[0019] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method, wherein the specific process of establishing a coupling model between the fluid domain and the solid domain in step (2.3) is as follows:

[0020] (2.3.1) Construct the motion equation of the fluid domain

[0021] The motion equation of the fluid domain includes the inviscid momentum equation and the continuity equation. At this time, the inviscid momentum equation can be reduced to the Laplace equation:

[0022] The inviscid momentum equation is as follows:

[0023]

[0024] In the above formula, u is the fluid velocity vector, t is the time, ρ f is the fluid density, and p is the pressure;

[0025] The continuity equation is as follows:

[0026]

[0027] (2.3.2) Construct the motion equation of the solid domain

[0028] The motion equations of the solid domain are jointly determined by the momentum equation and the angular momentum equation:

[0029] The momentum equation is:

[0030] The angular momentum equation is:

[0031] In the above equations, V is the volume of the flexible deformable body; ρ is the density of the flexible deformable body; ∫ρdV is the integral of the density of the flexible deformable body with respect to the volume of the flexible deformable body, which is the mass m of the flexible deformable body; F is the resultant external force exerted by the fluid on the solid; I is the moment of inertia of the flexible deformable body about the center of mass; Ω is the angular velocity vector of the flexible deformable body rotating about the center of mass; M is the resultant external torque exerted by the fluid on the solid.

[0032] The method for obtaining the self-propulsion performance of the flexible deformable body based on the drag-corrected panel method, wherein the specific process of solving the flow field in the fluid domain and the force condition of the flexible deformable body in step (2.4) is as follows:

[0033] (2.4.1) Initialize the physical parameters of the fluid domain, the physical parameters and deformation parameters of the solid domain;

[0034] (2.4.2) Predict the position of the flexible deformable body

[0035] Predict the acceleration a of the flexible deformable body using the Newton iteration idea G , and the angular acceleration α of the flexible deformable body G , and combining the velocity and angular velocity at the previous moment and the midline deformation of the flexible deformable body at the current moment, the predicted position of the flexible deformable body can be obtained;

[0036] (2.4.3) Calculate the velocity field and pressure field of the fluid domain

[0037] Using the predicted position of the flexible deformable body as the boundary condition, solve the velocity field and pressure field of the fluid domain using the motion equations of the fluid domain;

[0038] (2.4.4) Calculate the acting force and acting torque on the solid boundary

[0039] Calculate the resultant pressure force T on the solid boundary p And combine the resultant drag force D applied to the center of mass by the equivalent drag model to calculate the resultant external force F and resultant external torque M on the flexible deformable body;

[0040]

[0041] In the above equations, S is the area of the flexible deformable body, and n is the surface direction vector of the flexible deformable body;

[0042] (2.4.5) Calculation of the overall motion

[0043] According to the calculated resultant external force \(F\) and resultant external torque \(M\), calculate the corresponding acceleration \(a\) of the flexible deformable body G , and the angular acceleration \(\alpha\) of the flexible deformable body G Angular acceleration:

[0044]

[0045] (2.4.6) Update the fluid domain and the solid domain

[0046] Update the velocity field of the fluid domain and the position and velocity of the flexible deformable body through the motion equations of the fluid domain and the motion equations of the solid domain;

[0047] (2.4.7) Iterative calculation

[0048] Repeat the above steps (2.4.2)-(2.4.6) for iterative calculation of the time step until the predetermined simulation time or convergence condition is reached.

[0049] The method for obtaining the self-propulsion performance of a flexible deformable body based on the drag-corrected panel method, wherein the equivalent drag model in the step (3) has its coefficients and form determined by the CFD method, and the coefficients of the equivalent drag model are related to the shape of the flexible deformable body and the deformation mode of the centerline. The form of the equivalent drag model is as shown in the following formula:

[0050]

[0051] In the above formula, \(D\) x is the equivalent drag in the \(x\)-direction applied to the center of mass, and the resultant drag force \(D = D\) x \(\cdot\mathbf{e}\) x , \(\mathbf{e}\) x refers to the unit vector in the \(x\)-direction; \(f\) is the swimming frequency; \(A\) tail is the tail-beating amplitude; \(u\) c is the self-propulsion speed of the flexible deformable body forward; \(\lambda\) is the wavelength of the flexible deformable body; \(L\) is the body length of the flexible deformable body; \(F\) B is the shape correction factor based on the empirical formula; \(\xi\) λ is a parameter determined by CFD calculation related to the outer shape of the flexible deformable body, the centerline deformation mode, and the wavelength; \(d\) 1 , \(d\) 2 is a parameter determined by CFD calculation related to the outer shape of the flexible deformable body and the centerline deformation mode; \(Re\) is the Reynolds number of the dimensionless number, and its expression is: Determined by the fluid density \(\rho\) f , the body length \(L\) of the flexible deformable body, the swimming frequency \(f\), and the hydrodynamic viscosity \(\mu\) f of the fluid

[0052] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method. In this method, during the swimming process of the flexible deformable body in step (4), it is under the combined action of pressure and equivalent resistance. The pressure is calculated by the classical panel method, and the equivalent resistance is calculated by the equivalent resistance model. When the average values of the pressure and the equivalent resistance in one cycle are equal, it is considered that stable swimming has been achieved:

[0053]

[0054] In the above formula, represents the average pressure force within one cycle and acts as the thrust force; represents the average resistance within one cycle;

[0055] The autonomous forward swimming speed of the flexible deformable body during stable swimming is obtained through the thrust-resistance balance equation. If the thrust is greater than the resistance, the fish accelerates; if the thrust is less than the resistance, the fish decelerates.

[0056] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method. In step (5), the swimming speed of the flexible deformable body in the stable state is defined as the average speed within one cycle The period-averaged hydrodynamic power to be calculated includes two parts: one is the power required for the pressure on the body surface, and the other is the negative work done by the equivalent resistance; the efficiency of the flexible deformable body is defined by referring to the index in biomechanics that measures the energy consumption per unit distance, that is, the ratio of power to the product of the mass and swimming speed of the flexible deformable body:

[0057]

[0058] In the above formula, V represents the surface velocity vector of the flexible deformable body; D is the resultant resistance force applied to the center of mass; u c is the autonomous forward swimming speed vector.

[0059] Adopting the above technical solution, the present invention has the following beneficial effects:

[0060] The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method of the present invention can quickly calculate the pressure and resistance received by the flexible deformable body (such as: biomimetic robotic fish) through numerical simulation, and then determine the swimming performance such as the swimming speed, providing an important reference basis for the preliminary design and rapid iteration of the flexible deformable body, and is used to guide the design of high-speed and efficient flexible deformable body models and the setting of motion parameters. This corrected panel method has high calculation efficiency and is applicable to the case of high Reynolds number (~10^4). Compared with traditional computational fluid dynamics (CFD) methods, such as the finite element or finite volume-based solution methods, it has a faster calculation speed and can significantly reduce the calculation cost; compared with methods such as the immersed boundary method, it can be applied to a wider range of Reynolds numbers.

[0061] The present invention is optimized for self-propelled flexible deformable bodies, capable of accurately capturing the dynamic behavior of flexible deformable bodies in a flow field and achieving an in-depth analysis of the propulsion mechanism. In addition, the present invention can efficiently calculate the pressure distribution and drag characteristics of flexible deformable bodies under different swimming modes, thereby accurately predicting the propulsion efficiency, energy consumption, and flow field influence, providing theoretical support for the design of flexible deformable body propulsion systems. At the same time, the present invention is also applicable to a special case where the flexible wavelength tends to infinity, namely a rigid structure.

[0062] Compared with the prior art, the present invention has obvious advantages in terms of calculation efficiency, application scope, and engineering application value: on the one hand, its high-efficiency calculation characteristics make it suitable for rapid iterative optimization, which can significantly shorten the R & D cycle of flexible deformable bodies; on the other hand, the ability to apply to high Reynolds number flows expands the applicable scenarios of the method, enabling it to analyze a wider range of biomimetic swimming problems. Based on the method of the present invention, the design of biomimetic underwater robots can be further optimized, the propulsion efficiency can be improved, the energy consumption can be reduced, and their adaptability in complex hydrodynamic environments can be enhanced, providing important theoretical and technical support for the development of high-efficiency underwater robot technology. Description of the Drawings

[0063] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0064] Figure 1 It is a flowchart of the method for obtaining the self-propulsion performance of a flexible deformable body based on the drag-corrected panel method of the present invention

[0065] Figure 2 It is a numerical simulation flowchart of the modified panel method involved in the method for obtaining the self-propulsion performance of a flexible deformable body based on the drag-corrected panel method of the present invention;

[0066] Figure 3 It is a schematic diagram of the initial geometric model of the robotic fish involved in the method for obtaining the self-propulsion performance of a flexible deformable body based on the drag-corrected panel method of the present invention;

[0067] Figure 4 It is a schematic diagram of the midline deformation of the robotic fish involved in the method for obtaining the self-propulsion performance of a flexible deformable body based on the drag-corrected panel method of the present invention. Detailed Embodiments

[0068] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0069] The present invention will be further explained below in conjunction with specific implementation manners.

[0070] As Figure 1 shown, a method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method provided in this embodiment includes the following steps:

[0071] S100. Determine the physical characteristics and initial parameters of the flexible deformable body, as well as the initial conditions and flow parameters of the fluid;

[0072] First, determine the physical characteristics of the flexible deformable body, including the density, shape, size, and width and height distributed along the body length of the flexible deformable body; these parameters will be used to construct the initial geometric model of the flexible deformable body;

[0073] ρ: density of the flexible deformable body (kg / m 3 );

[0074] L: body length of the flexible deformable body (m);

[0075] w(x): width distributed along the body length (m);

[0076] h(x): height distributed along the body length (m);

[0077] S200. Use the corrected panel method to perform direct numerical simulation of the flexible deformable body to obtain the fluid pressure on the object surface. The steps are as follows:

[0078] S201. Construct the initial geometric model;

[0079] S202. Determine the midline deformation form of the flexible deformable body

[0080] The model should determine the pre-set time-varying midline deformation mode along the body length of the flexible deformable body as its propulsion mode; the midline deformation mode of the flexible deformable body includes the function of the midline position of the flexible deformable body changing with time:

[0081]

[0082] S203. Establish a coupling model between the fluid domain and the solid domain

[0083] In the calculation process based on the modified panel method, the coupled calculation of the fluid domain and the solid domain is the key part; this process involves transferring the motion of the solid boundary to the fluid domain, influencing the motion of the flexible deformable body through the reaction force of the fluid domain, and applying an equivalent resistance model at the center of mass of the solid to correct the lack of viscosity in the panel method.

[0084] S2031. Construct the motion equation of the fluid domain

[0085] The motion equation of the fluid domain includes the inviscid momentum equation and the continuity equation. At this time, the inviscid momentum equation can be degenerated into the Laplace equation:

[0086] The inviscid momentum equation is as follows:

[0087]

[0088] In the above formula, u is the fluid velocity vector, t is the time, ρ f is the fluid density, and p is the pressure;

[0089] The continuity equation is as follows:

[0090]

[0091] S2032. Construct the motion equation of the solid domain

[0092] The motion equation of the solid domain is jointly determined by the momentum equation and the angular momentum equation:

[0093] The momentum equation is:

[0094] The angular momentum equation is:

[0095] In the above formula, V is the volume of the flexible deformable body; ρ is the density of the flexible deformable body; ∫ρdV is the integral of the density of the flexible deformable body with respect to the volume of the flexible deformable body, which is the mass m of the flexible deformable body; F is the resultant external force of the fluid acting on the solid; I is the moment of inertia of the flexible deformable body relative to the center of mass; Ω is the angular velocity vector of the flexible deformable body rotating around the center of mass; M is the resultant external torque of the fluid acting on the solid.

[0096] S204. Solve the flow field in the fluid domain and the force condition of the flexible deformable body, as Figure 2 shown, including the following steps:

[0097] S2041. Initialize the physical parameters of the fluid domain, and initialize the physical parameters and deformation parameters of the solid domain;

[0098] S2042. Predict the position of the flexible deformable body

[0099] Use the Newton iteration idea to guess the acceleration a of the flexible deformable bodyG , and the angular acceleration α of the α flexible deformable body G , and combining the velocity, angular velocity at the previous moment and the deformation of the center line of the flexible deformable body at the current moment, the predicted position of the flexible deformable body can be obtained;

[0100] S2043. Calculate the velocity field and pressure field of the fluid domain

[0101] Using the predicted position of the flexible deformable body as the boundary condition, solve the velocity field and pressure field of the fluid domain using the motion equation of the fluid domain;

[0102] S2044. Calculate the acting force and acting moment on the solid boundary

[0103] Calculate the resultant pressure force T on the solid boundary p And combining the resultant drag force D applied on the center of mass by the equivalent drag force model, calculate the resultant external force F and resultant external moment M acting on the flexible deformable body:

[0104]

[0105] In the above formula, S is the area of the flexible deformable body, and n is the surface direction vector of the flexible deformable body;

[0106] And combining the equivalent drag force model to calculate the resultant external force F and resultant external moment M acting on the flexible deformable body;

[0107] S2045. Calculation of overall motion

[0108] Calculate the corresponding acceleration a of the flexible deformable body according to the calculated resultant external force F and resultant external moment M G , and the angular acceleration α of the α flexible deformable body G Angular acceleration:

[0109]

[0110] S2046. Update the fluid domain and solid domain

[0111] Through the motion equation of the fluid domain and the motion equation of the solid domain, update the velocity field of the fluid domain and the position and velocity of the flexible deformable body;

[0112] S2047. Iterative calculation

[0113] Repeat the above steps S2042 - S2046 to perform iterative calculation of the time step until the predetermined simulation time or convergence condition is reached.

[0114] The following combines specific examples to numerically calculate and solve the flow field in the fluid domain and the force condition of the flexible deformable body:

[0115] Assume the initial conditions of the flexible deformable body are as follows:

[0116] The density ρ of the flexible deformable body is 1000 kg / m 3 ;

[0117] The length L of the flexible deformable body is 1 m;

[0118] The deformation form of the center line is

[0119] The tail-swing amplitude A tail = A(1) = 0.1 m;

[0120] The deformation wavelength λ is 1 m;

[0121] The swimming frequency f is 1 Hz;

[0122] The density ρ of the fluid f = 1000 kg / m 3 ;

[0123] The Reynolds number Re is 50000;

[0124] Initialize the parameters of the fluid domain and the flexible deformable body:

[0125] ① Calculate the initial fluid velocity field:

[0126] u(t = 0) = 0;

[0127] ② Use the Newton iteration idea to predict the (angular) acceleration a G , α G of the flexible deformable body and calculate the new position; where Newton's Iteration is a numerical method for solving the nonlinear equation f(x) = 0, and its idea is based on the local linearization of the function; the core step is to use the tangent line at the current point to approximate the zero point of the function and gradually approximate the exact solution through iteration:

[0128]

[0129] u c (t) = u c (t - Δt) + a G Δt, Ω = Ω(t - Δt) + α G Δt;

[0130]

[0131] ③ According to the predicted new position, use the classical panel method to calculate the potential flow function φ and solve the Laplace equation:

[0132]

[0133] ④ Calculate the pressure on the solid boundary and give the drag correction:

[0134]

[0135] ⑤ Calculate the resultant force T of the hydrodynamic pressure on the flexible deformable body according to the pressure distribution p , the hydrodynamic moment M and the equivalent drag D, and calculate the corresponding overall motion:

[0136]

[0137] ⑥ Update the fluid domain and the solid domain:

[0138] Through repeated iteration of the above steps, the coupled calculation of the fluid domain and the solid domain is realized until the convergence condition or the predetermined simulation time is reached.

[0139]

[0140] Calculate the velocity and force of the flexible deformable body at different times through numerical simulation in order to compare the swimming performance of different designs.

[0141] S300. Calculate the drag compensation applied to the centroid of the flexible deformable body through the equivalent drag model;

[0142] The coefficients and form of the equivalent drag model are determined by the CFD method, which involves the dimensionless number Reynolds number Re. The form is as follows: The coefficients are related to the shape of the flexible deformable body and the deformation mode of the center line. The form of the equivalent drag model is as shown in the following formula:

[0143]

[0144] In the above formula, D x is the equivalent drag in the x direction applied to the centroid, and the resultant drag D applied by the equivalent drag model to the centroid is D x ·e x , e x refers to the unit vector in the x direction; f is the swimming frequency; A tail is the tail swing amplitude; u c is the self-propelled forward swimming speed of the flexible deformable body; λ is the wavelength of the flexible deformable body; L is the body length of the flexible deformable body; F B is the shape correction factor based on the empirical formula; ξ λ is the parameter determined by CFD calculation related to the outer shape of the flexible deformable body, the center line deformation mode and the wavelength; d 1 , d 2 is the parameter determined by CFD calculation related to the outer shape of the flexible deformable body and the center line deformation mode; Re is the Reynolds number of the dimensionless number, and its expression is: The fluid density ρf The body length L of the flexible deformable body, the swimming frequency f, and the hydrodynamic viscosity μ f are determined.

[0145] S400. Calculate the self-propelled forward swimming speed of the flexible deformable body when it swims stably through the balance between the pressure and the equivalent resistance suffered by the flexible deformable body during the swimming process;

[0146] During the swimming process, the flexible deformable body is under the combined action of pressure and equivalent resistance. The pressure is calculated by the classical panel method, and the equivalent resistance is calculated by the equivalent resistance model. When the average values of the pressure and the equivalent resistance in one period are equal, it is considered that stable swimming has been achieved:

[0147]

[0148] In the above formula, represents the average pressure force within one period and acts as a thrust force; represents the average resistance within one period;

[0149] The self-propelled forward swimming speed of the flexible deformable body when it swims stably is obtained through the thrust-resistance balance equation. If the thrust is greater than the resistance, the fish accelerates; if the thrust is less than the resistance, the fish decelerates.

[0150] S500. Obtain the hydrodynamic power and efficiency of the flexible deformable body according to the forces on each part of the flexible deformable body and the swimming speed.

[0151] The swimming speed of the flexible deformable body is defined as the average speed within one period in the stable state The period-averaged hydrodynamic power to be calculated includes two parts: one is the power required for the pressure on the body surface, and the other is the negative work done by the equivalent resistance; the efficiency of the flexible deformable body can be defined by referring to the index in biomechanics that measures the energy consumption per unit distance - the Cost of Transport (COT), that is, the ratio of the power to the product of the mass of the flexible deformable body and the swimming speed:

[0152]

[0153] Among them, F p is the distributed pressure force suffered by the flexible deformable body; V is the surface velocity vector of the flexible deformable body; D is the equivalent resistance applied to the center of mass; u c is the self-propelled forward swimming speed vector.

[0154] The following takes the robotic fish as the flexible deformable body to analyze the basis for the form of the equivalent resistance model and the determination of the coefficients:

[0155] The classical panel method is a simplified model for the idealized conditions of inviscid fluids. However, in practical applications, although robotic fish usually move at relatively high swimming speeds, with a relatively large Reynolds number and inertial forces dominant, the viscous effects cannot be ignored. Such effects are mainly reflected in the boundary layer effect and the influence of overall viscous drag. Therefore, it is necessary to correct it by establishing an equivalent resistance model. The formula of this model is based on a comprehensive consideration of various factors, including the main dimensionless numbers that control the flow field characteristics, the swimming form and shape characteristics of the robotic fish, as well as the classical resistance empirical formula, and its effectiveness is verified through CFD simulations.

[0156] The main dimensionless numbers that control the flow field characteristics:

[0157] The Reynolds number, is a key dimensionless parameter that controls the main characteristics of the Navier-Stokes equations and represents the ratio of inertial forces to viscous forces. On the other hand, the Strouhal number, is often used to describe the wake structure and represents the ratio of unsteady forces to inertial forces. Since the swimming speed of the robotic fish fluctuates during movement, the average swimming speed U is replaced by the instantaneous swimming speed u c . The resistance suffered during swimming is mainly related to the above two dimensionless numbers.

[0158] Influence of the swimming form and shape characteristics of the robotic fish:

[0159] During actual swimming, the different forms of the shape and midline deformation of the robotic fish will affect the magnitude of the resistance suffered. This influence is reflected in the parameters d 1 , d 2 as well as ξ λ . The specific values need to be determined in advance by combining CFD simulations, such as the dynamic mesh method.

[0160] Classical resistance empirical formula

[0161] In engineering practice, predecessors summarized the empirical formula form of the resistance suffered by streamlined objects in fluids through experimental studies. Here, such resistance is regarded as closely related to the shape and denoted as F B , and its specific influencing factors are mainly determined by the geometric characteristics of the flexible deformable body.

[0162] CFD simulation verification

[0163] The effectiveness of the correction effect is calculated and verified by the CFD method for typical shapes and fluctuation forms to ensure the applicability of the resistance correction model.

[0164] Appendix Figure 3The initial geometric shape of the robotic fish is shown. Mark the center line of the robotic fish, and the length of the center line is called the length of the robotic fish. A three-dimensional coordinate system is established for representation, where the X, Y, and Z axes represent the horizontal and vertical directions respectively. The dimension along the body length in the Y direction is called the width, and the dimension along the body length in the Z direction is called the height.

[0165] Appendix Figure 4 The detailed description shows that the overall form is controlled by The maximum positive distance that A(x) can reach at the tail within one period is called the tail-beat amplitude; where λ is the deformation wavelength and f is the swimming frequency.

[0166] This embodiment can achieve a rapid simulation of the dynamic characteristics of the robotic fish during forward swimming, thereby calculating the swimming performance under different designs, and providing a reliable basis for its swimming performance and further optimization under different conditions.

[0167] The present invention numerically simulates and calculates the pressure received by the flexible deformable body through the classical panel method, combines with a correction model to obtain the equivalent resistance applied to the center of mass, and calculates the forward swimming speed of the flexible deformable body after force balance, so as to quickly obtain the swimming performance of the bionic robotic fish at medium and high Reynolds numbers.

[0168] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for obtaining the autonomous propulsion performance of a flexible deformable body based on a resistance-corrected panel method, characterized in that: The following steps are involved: (1) Determine the physical properties and initial parameters of the flexible deformable body, as well as the initial conditions and flow parameters of the fluid; (2) Use the classical panel method to perform direct numerical simulation of the flexible deformable body to obtain the fluid pressure on the surface of the object; (3) Calculate the resistance compensation applied to the center of mass of the flexible deformable body through the equivalent resistance model; (4) Calculate the autonomous forward swimming speed of the flexible deformable body during stable swimming by balancing the pressure and equivalent resistance of the flexible deformable body during swimming; (5) Based on the forces acting on each part of the flexible deformable body and the swimming speed, the hydrodynamic power and efficiency of the flexible deformable body are obtained.

2. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method according to claim 1, characterized in that: The physical properties of the flexible deformable body in step (1) include the density, shape, size, and width and height of the flexible deformable body distributed along the length of the body.

3. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method according to claim 1, characterized in that: The specific process of using the classical panel method to perform direct numerical simulation of the flexible deformable body in step (2) is as follows: (2.1) Constructing the initial geometric model; (2.2) Determine the midline deformation mode of the flexible deformable body; (2.3) Establish a coupling model between fluid domain and solid domain; (2.4) Solve the flow field in the fluid domain and the stress conditions of the flexible deformable body.

4. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance-corrected panel method according to claim 3 is characterized in that: The midline deformation mode of the flexible deformable body in the step (2.2) includes a function of the midline position of the flexible deformable body changing with time:

5. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance modified panel method according to claim 3, characterized in that: The specific process of establishing the coupling model of the fluid domain and the solid domain in the step (2.3) is as follows: (2.3.1) Constructing the equation of motion of the fluid domain The equations of motion in the fluid domain include the inviscid momentum equation and the continuity equation. At this time, the inviscid momentum equation can be degenerated into the Laplace equation: The inviscid momentum equation is as follows: In the above formula, u is the fluid velocity vector, t is the time, and ρ f is the fluid density, p is the pressure; The continuity equation is as follows: ▽·u＝0； (2.3.2) Constructing the equation of motion for the solid domain The equation of motion for the solid domain is determined by the momentum equation and the angular momentum equation: The momentum equation is: The angular momentum equation is: In the above formula, V is the volume of the flexible deformable body; ρ is the density of the flexible deformable body; ∫ρdV is the integral of the density of the flexible deformable body with respect to the volume of the flexible deformable body, which is the mass m of the flexible deformable body; F is the resultant external force of the fluid on the solid; I is the moment of inertia of the flexible deformable body relative to the center of mass; Ω is the angular velocity vector of the flexible deformable body rotating around the center of mass; M is the resultant external torque of the fluid on the solid.

6. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance modified panel method according to claim 5, characterized in that: The specific process of solving the flow field in the fluid domain and the force conditions of the flexible deformable body in the step (2.4) is as follows: (2.4.1) Initialize the physical parameters of the fluid domain, and initialize the physical parameters and deformation parameters of the solid domain; (2.4.2) Predicting the position of the flexible deformable body Using Newton's iterative idea to predict the acceleration a of a flexible deformable body G , and the angular acceleration α of the flexible deformable body G , and combined with the velocity and angular velocity of the previous moment and the midline deformation of the flexible deformable body at the current moment, the predicted position of the flexible deformable body can be obtained; (2.4.3) Calculate the velocity field and pressure field of the fluid domain The velocity field and the pressure field of the fluid domain are solved using the motion equation of the fluid domain according to the predicted position of the flexible deformable body as a boundary condition; (2.4.4) Calculate the forces and moments acting on the solid boundary Calculate the resultant pressure force T on the solid boundary p And the resultant external force F and the resultant external moment M on the flexible deformable body are calculated by combining the resultant resistance force D applied on the center of mass by the equivalent resistance model; In the above formula, S is the area of ​​the flexible deformable body, and n is the direction vector of the surface of the flexible deformable body; (2.4.5) Calculation of overall motion According to the calculated total external force F and total external moment M, the corresponding acceleration a of the flexible deformable body is obtained. G , and the angular acceleration α of the flexible deformable body G Angular acceleration: (2.4.6) Update the fluid domain and solid domain Update the velocity field of the fluid domain and the position and velocity of the flexible deformable body through the motion equation of the fluid domain and the motion equation of the solid domain; (2.4.7) Iterative calculation Repeat the above steps (2.4.2)-(2.4.6) and perform iterative calculation of the time step until the predetermined simulation time or convergence condition is reached.

7. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance modified panel method according to claim 1, characterized in that: The equivalent resistance model in step (3) is determined by the CFD method to determine its coefficients and form. The coefficients of the equivalent resistance model are related to the shape of the flexible deformable body and the deformation mode of the center line. The form of the equivalent resistance model is shown in the following formula: In the above formula, D x is the equivalent resistance in the x direction applied to the center of mass, and the resistance force D applied by the equivalent resistance model to the center of mass is D x ·e x , e x refers to the unit vector in the x direction; f is the wandering frequency; A tail is the tail swing amplitude; u c is the autonomous forward swimming speed of the flexible deformable body; λ is the wavelength of the flexible deformable body; L is the length of the flexible deformable body; F B is the shape correction factor based on the empirical formula; ξ λ is a parameter determined by CFD calculation related to the shape of the flexible deformable body, the midline deformation mode and the wavelength; d1, d2 are parameters determined by CFD calculation related to the shape of the flexible deformable body and the midline deformation mode; Re is the dimensionless Reynolds number, and its expression is: From the fluid density ρ f , the length of the flexible deformable body L, the swimming frequency f and the fluid dynamic viscosity μ f Sure.

8. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance modified panel method according to claim 7, characterized in that: The flexible deformable body in step (4) is subjected to the combined effects of pressure and equivalent resistance during the swimming process. The pressure is calculated by the classical panel method, and the equivalent resistance is calculated by the equivalent resistance model. When the average values ​​of the pressure and the equivalent resistance in one cycle are equal, it is considered that stable swimming is achieved: In the above formula, Represents the average pressure force in a cycle, which plays a thrust role; Represents the average resistance in a period; The autonomous forward swimming speed of the flexible deformable body during stable swimming is obtained through the thrust-drag balance equation. If the thrust is greater than the drag, the fish accelerates, and if the thrust is less than the drag, the fish decelerates.

9. The method for obtaining the autonomous propulsion performance of a flexible deformable body based on the resistance modified panel method according to claim 1, characterized in that: The swimming speed of the flexible deformable body in the step (5) is defined as the average speed within one cycle in a stable state. The cycle average hydrodynamic power to be calculated It includes two parts: one is the power required by the surface pressure of the body, and the other is the negative work done by the equivalent resistance. The efficiency of the flexible deformable body is defined by referring to the index of energy consumption per unit distance in biomechanics, that is, the ratio of power to the product of the mass of the flexible deformable body and the swimming speed: In the above formula, V represents the surface velocity vector of the flexible deformable body; D is the resultant drag force applied to the center of mass; u c is the autonomous forward swimming velocity vector.

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