Research on liquid sloshing characteristics in irregular tank and equivalent dynamic modeling method

Abstract

The application relates to a method for researching liquid sloshing characteristics and equivalent dynamics modeling of a special-shaped storage tank, and belongs to the technical field of novel powered aircrafts. Specifically, the method comprises the following steps: establishing an equivalent dynamics model of propellant sloshing of the special-shaped storage tank; on the basis of the NS equation, coupling the established equivalent dynamics model of propellant sloshing of the special-shaped storage tank to establish a high-precision gas-liquid two-phase flow numerical calculation framework under a severe sloshing working condition; performing grid division on the special-shaped storage tank, importing the established numerical framework to perform boundary condition setting and numerical calculation, and performing gas-liquid distribution, gas content rate and stress analysis under full flight working conditions; and finally, based on the analysis results, a sloshing parameter theoretical model of the special-shaped storage tank is established. The method assists in the design and optimization of the special-shaped storage tank of the novel powered aircraft, and saves test cost and time.

Description

Technical Field

[0001] This invention relates to a method for studying the liquid sloshing characteristics in an irregularly shaped tank and for modeling equivalent dynamics, belonging to the field of new powered aircraft technology. Background Technology

[0002] The fuel tanks of the novel powered aircraft are primarily responsible for providing the propulsion system with fuel to ensure stable combustion. The sloshing characteristics and parameters of the liquid fuel within the tanks have a significant impact. During engine start-up, high-intensity maneuvers, return turns, and landing, the liquid sloshing within the tanks is violent and complex, sometimes resulting in liquid rollover, leading to air entrapment at the ejector pump inlet and engine malfunction. Furthermore, the novel powered aircraft's fuel tanks are irregularly shaped, resulting in complex liquid sloshing characteristics during flight. Their equivalent dynamic modeling is difficult to represent, posing challenges to flight attitude control and seriously affecting the aircraft's structural safety. While domestic and international research has conducted equivalent dynamic modeling studies on the sloshing characteristics of typical fuel tanks under specific conditions, there is limited research on the large-scale liquid sloshing characteristics under conditions of drastic overload changes, and no equivalent dynamic models or studies on the sloshing characteristics throughout the entire flight process have been found for irregularly shaped fuel tanks. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for studying the liquid sloshing characteristics in irregularly shaped tanks and modeling equivalent dynamics, so as to assist in the design and optimization of irregularly shaped tanks for new powered aircraft and save experimental costs and time.

[0004] The technical solution of this invention is: a method for studying the liquid sloshing characteristics in an irregularly shaped storage tank and for equivalent dynamic modeling, comprising:

[0005] Establish an equivalent dynamic model of propellant sloshing in irregularly shaped tanks;

[0006] Based on the Navier-Stokes equations, an equivalent dynamic model of propellant sloshing in irregularly shaped tanks is coupled to obtain a two-phase dynamic model of propellant gas-liquid flow.

[0007] The irregularly shaped tank was meshed and imported into the established propellant gas-liquid two-phase flow dynamics model for boundary condition setting and numerical calculation to obtain the liquid level change characteristics during the overload process.

[0008] Based on the liquid level change characteristics obtained during the overload change process, the gas-liquid distribution, gas content and stress under all flight conditions are analyzed, and the gas-liquid distribution, gas content and stress change characteristics under the conditions are calculated.

[0009] Based on the gas-liquid distribution and the characteristics of gas content and stress variation under operating conditions, a theoretical model of the swaying parameters of an irregularly shaped storage tank is constructed.

[0010] The establishment of the equivalent dynamic model of propellant sloshing in the irregularly shaped tank includes:

[0011] Assuming the z-axis is opposite to the direction of gravity, and the x-axis is coplanar with the liquid sloshing velocity vector v0 and the gravitational acceleration g, we obtain the equivalent dynamic model of propellant sloshing in the irregularly shaped tank, as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] Among them, l n m is the length of the massless pendulum arm in the nth mode; n z is the sway mass of the nth mode; n Let m be the swaying mass. n The position of the wobbling along the Z-axis; For the volume mode of the nth order mode; f n The natural frequency of the nth mode; the area partition S f For the free surface of the liquid, S w The portion of the liquid's outer surface that contacts the storage tank; ξ n ρ is the eigenvector matrix of the nth mode; f Let be the density of the liquid; r be the position vector of the liquid's center of mass in the inertial frame; m0 be the rigid mass, which is considered not to participate in the sloshing; Z0 be the position of the rigid mass m0 along the Z-axis; m i Zc is the swaying mass; Zc is the swaying mass m. i Position on the Z-axis; m is the mass of the liquid;

[0018] Considering the effect of surface tension, a torsion spring with a natural frequency f is added to the equivalent dynamic model. n The equality condition is expressed as:

[0019]

[0020] In the formula: k n Let be the stiffness coefficient of the torsion spring. B is the Bond number, g is the acceleration due to gravity, R0 is the characteristic dimension of the tank, σ is the surface tension coefficient of the liquid at the free surface, and ρ f The density of the liquid.

[0021] Based on the Navier-Stokes equations, a propellant sloshing equivalent dynamic model is coupled to obtain a propellant gas-liquid two-phase flow dynamic model, including:

[0022] For the equivalent dynamic model of propellant sloshing in irregularly shaped tanks, the liquid volume fraction control equation is solved, and the gas-liquid interface is constructed using the geometric reconstruction method to obtain the propellant gas-liquid two-phase flow dynamic model.

[0023] The propellant gas-liquid two-phase flow dynamics model was modified using the coupled VOF method and the Level-set method, and the Heaviside function was adopted. Smooth the fluid properties at the gas-liquid interface.

[0024] The governing equation for liquid volume fraction is expressed as follows:

[0025]

[0026] Where α is the volume fraction of the liquid propellant, and t and U represent time and velocity, respectively.

[0027] The UI constructor for the Level Set method is:

[0028]

[0029] In the formula: d(x,t) is the minimum distance from node x to the phase interface, and this characteristic distance d(x,t) requires the surface tension of the liquid.

[0030] Fluid properties are expressed as:

[0031]

[0032] in, This is a Heaviside function used to smooth the fluid properties γ at the interface. The subscript g represents the gas phase, l represents the liquid phase, and m represents the gas-liquid mixture.

[0033] When the propellant tank experiences strong nonlinear flow, including complex large curvature backflow and flow stall, during the liquid sloshing process under severe overload conditions throughout the flight, or when there is transitional flow on the tank wall, the WALE wall adaptive eddy viscosity model in the LES method is used to solve the problem and obtain the propellant gas-liquid two-phase flow dynamics model.

[0034] The process of meshing the irregularly shaped tank and importing it into the established propellant gas-liquid two-phase flow dynamics model for boundary condition setting and numerical calculation to obtain the liquid level change characteristics during overload changes includes:

[0035] An octree partitioning method for three-dimensional structures is adopted, dividing the structure into eight identical sub-mesh;

[0036] All boundaries of the irregularly shaped storage tank are set as non-slip walls, and liquid is filled into the irregularly shaped storage tank according to the initial filling amount at the time.

[0037] Set the time step; before calculating each point of interest, calculate the current liquid mass and the steady-state value of the liquid's steady-state distribution characteristics under overload, and then change the overload to obtain the liquid level change characteristics during the overload change process.

[0038] The calculations obtained for the gas-liquid distribution, gas content, and stress variation characteristics at the operating conditions include: dividing the entire flight process into three segments based on the overload variation characteristics: normal overload turning, normal overload reduction, and normal overload sudden drop; identifying the operating point with more drastic liquid level changes based on the liquid level change characteristics during the overload change process, and obtaining the gas-liquid distribution, gas content, and stress variation characteristics at the operating conditions; the more drastic changes refer to liquid level fluctuations exceeding 20% ​​during the overload change process.

[0039] Based on the gas-liquid distribution, gas content, and stress variation characteristics under operating conditions, a theoretical model for the sloshing parameters of an irregularly shaped storage tank is established. This includes: expressing the liquid sloshing frequency, the distance from the center of mass of the sloshing liquid to the liquid surface, the lateral displacement of the sloshing mass, and the liquid relative to the sloshing mass using theoretical equations based on the gas-liquid distribution, gas content, and stress variation characteristics under operating conditions, thus obtaining the theoretical model for the sloshing parameters of the irregularly shaped storage tank.

[0040] Liquid sloshing frequency:

[0041]

[0042] Distance from the center of mass of the liquid to the liquid surface during sloshing:

[0043]

[0044] The linear limit displacement value Y of liquid sloshing when the sloshing angle is θ:

[0045]

[0046] Relative sloshing mass of liquid:

[0047]

[0048] Where: h is the liquid height, R is half the liquid surface span, C1R is the equivalent radius after correction by the correction factor C1, and g is the acceleration. Let m1 be the relative sloshing mass, m be the liquid sloshing mass, m be the total mass of the liquid in the tank, and ξ1 be the root of the first derivative of the Bessel function of the first kind.

[0049] The advantages of this invention compared to the prior art are:

[0050] 1. This invention discloses a method for studying the liquid sloshing characteristics in an irregularly shaped tank and for modeling equivalent dynamics. It studies the sloshing characteristics of liquid propellant in an irregularly shaped tank in a novel powered aircraft under different flight attitudes, and realizes the equivalent dynamics modeling of liquid propellant sloshing.

[0051] 2. The present invention discloses a method for studying the liquid sloshing characteristics in an irregularly shaped tank and an equivalent dynamic modeling method. Based on a high-precision numerical calculation framework for tank propellant sloshing and two-phase flow using a gas-liquid two-phase flow model and a dynamic fluid-structure interaction model, the present invention conducts multiphase fluid-structure interaction numerical calculations and simulations for different sloshing conditions of the tank.

[0052] 3. This invention discloses a method for studying the liquid sloshing characteristics and equivalent dynamic modeling within an irregularly shaped tank. Through coupled calculations of the flow field and structural field, it can accurately predict the gas-liquid distribution and forces within the tank under all flight conditions. Compared to experimental research methods, this method saves a significant amount of time and resources.

[0053] 4. This invention discloses a method for studying the liquid sloshing characteristics in an irregularly shaped propellant tank and for equivalent dynamic modeling, obtaining typical characteristic parameters such as the sloshing frequency and sloshing mass of the propellant throughout the entire flight process. Based on the numerical analysis results, theoretical equations are used to express the characteristic parameters of the tank's sloshing characteristics. This method assists in the design and optimization of irregularly shaped propellant tanks for novel powered aircraft, saving experimental costs and time. Attached Figure Description

[0054] Figure 1 This invention discloses a flowchart of a method for studying the sloshing characteristics of liquid in an irregularly shaped storage tank and modeling its equivalent dynamics.

[0055] Figure 2 This is the representation of the propellant sloshing equivalent mechanical model of the present invention;

[0056] Figure 3 This is a schematic diagram of the adaptive mesh structure of the present invention. Detailed Implementation

[0057] like Figure 1 As shown, this invention provides a method for studying the liquid sloshing characteristics and equivalent dynamic modeling of an irregularly shaped propellant tank. First, an equivalent dynamic model of propellant sloshing in the irregularly shaped tank is established. Simultaneously, a high-precision numerical calculation method for gas-liquid two-phase flow under severe sloshing conditions is developed, employing adaptive dynamic meshing for refinement and optimization, and boundary conditions are set. Based on this, gas-liquid distribution, gas content, and stress analysis are performed under all flight conditions, and a theoretical model of the sloshing parameters of the irregularly shaped tank is established.

[0058] Step 1: Establish an equivalent dynamic model of propellant sloshing in irregularly shaped tanks

[0059] In a complete description of the swaying problem, the functions to be solved are the velocity potential function and the wave height function. By separating the time variable from this unsteady scalar function, the functions to be solved can be expressed as a linear combination based on the swaying mode eigenvectors, and the combination coefficients are called mode functions.

[0060] For irregularly shaped tanks with complex boundaries, they can be abstracted into a classical scalar field problem, and solved quickly and conveniently using the finite element method. An elastic body composed of three-dimensional orthotropic materials is constructed, and modal analysis is used to quickly obtain the natural frequencies of each swaying mode and the corresponding surface mode shapes. Under translational excitation, the volume modal function b... n (t) and surface mode function a i The following relationship exists between (t):

[0061]

[0062] Combining the basic formulas of swaying modes, the discrete form of the dynamic boundary conditions at the free surface can be obtained as follows:

[0063]

[0064] In the formula, v0 represents the sloshing velocity vector of the liquid; each parameter is expressed in integral form of the sloshing mode eigenvector:

[0065]

[0066] The momentum K of the nth-order mode generated by the liquid sloshing in the tank l and angular momentum H l for:

[0067]

[0068]

[0069] In the formula: n w r is the fluid rotational velocity vector. n Let be the position vector of the liquid center of mass in the inertial frame for the nth mode; the equivalent mechanical model of the liquid sloshing in the tank is represented in the form of a spring-mass or pendulum, such as... Figure 2 As shown in the formula above, the dynamic response of a liquid system can be considered as the effect of the superposition of sloshing modes.

[0070] For the above equivalent mechanical model, its dynamic elements include natural frequencies and modal masses. The dynamic equivalence principle of the model for liquid sloshing is that the natural frequencies, response forces, and response torques are constant. Assuming that the z-axis is opposite to the direction of gravity and the x-axis is coplanar with v0 and g, the expressions for the parameters of the equivalent mechanical model can be obtained as follows:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Among them, l n m is the length of the massless pendulum arm in the nth mode; n z is the sway mass of the nth mode; n Let m be the swaying mass. n The position of the wobbling along the Z-axis; For the volume mode of the nth order mode; f n The natural frequency of the nth mode; the area partition S f For the free surface of the liquid, S w The portion of the liquid's outer surface that contacts the storage tank; ξ n ρ is the eigenvector matrix of the nth mode; f Let be the density of the liquid; r be the position vector of the liquid's center of mass in the inertial frame; m0 be the rigid mass, which is considered not to participate in the sloshing; Z0 be the position of the rigid mass m0 along the Z-axis; m i Zc is the swaying mass; Zc is the swaying mass m. i Position on the Z-axis; m is the mass of the liquid;

[0077] Considering the influence of surface tension, a torsion spring similar to that of the swing arm can be added to the equivalent dynamic model. The condition for their equal frequencies is expressed as follows:

[0078]

[0079] In the formula: k n Let be the stiffness coefficient of the torsion spring. B is the Bond number, g is the acceleration due to gravity, R0 is the characteristic dimension of the tank, σ is the surface tension coefficient of the liquid at the free surface, and ρ f The density of the liquid.

[0080] Step 2: Establish a high-precision numerical calculation framework for gas-liquid two-phase flow under severe shaking conditions.

[0081] This example builds a high-precision interface capture method based on an existing VOF two-phase flow model and coupled with the Level-set method. Furthermore, it establishes a numerical calculation model for gas-liquid two-phase flow in tanks with large-scale fractured interfaces by correcting the wetting angle between the gas-liquid interface and the solid wall based on the stress balance of the two-phase interface.

[0082] For the established modified model governing equations, the convection equations for the volume fraction are solved, and the gas-liquid interface is constructed using a geometric reconstruction method. The governing equation for the liquid volume fraction can be expressed as:

[0083]

[0084] Where: α is the volume fraction of the liquid propellant, t and U represent time and velocity, respectively; the mixing velocity of the two-phase medium is solved by the momentum equation:

[0085]

[0086]

[0087] Where: fluid properties are solved by the mixing density formula μ m =αμ l +(1-α)μ g , ρ=αρ l +(1-α)ρ g ρ m =αρ l +(1-α)ρ g , ρ is the surface tension, and the surface tension coefficient σ is a function of the wetting angle, where k is the surface curvature. m ρ is the density of the gas-liquid mixture. l ρ is the density of the liquid phase. g The density of the gas phase is μ. m For gas-liquid two-phase hybrid viscosity, μ l The dynamic viscosity of the liquid phase is μ. g The gas phase dynamic viscosity;

[0088] To construct a clearer gas-liquid interface, the propellant two-phase flow model is modified by coupling the VOF method and the Level-Set method. The interface constructor of the Level-Set method is as follows:

[0089]

[0090] In the formula: d(x,t) is the minimum distance from node x to the phase interface. This characteristic distance d(x,t) is introduced into the surface tension f in the momentum equation. bz =σκ(d)nδ to more accurately describe the effect of surface tension of the liquid medium on the deformation of the interphase interface. Furthermore, considering the discontinuity of fluid physical properties at the interface between different phases, the Heaviside function is used to ensure the stability of the numerical calculation. Smoothing of fluid properties γ (density, viscosity, etc.) within a small range at the interface. Fluid properties can be uniformly described as:

[0091]

[0092] Wherein, the subscript g represents the gas phase, l represents the liquid phase, and m represents a gas-liquid mixture;

[0093] In the CLSVOF method, the entire computational domain is solved as a whole. The function can then be represented as:

[0094]

[0095] h represents the liquid height. To address the complex high-curvature backflow and flow stall during the liquid sloshing process in the aircraft tank throughout the flight and under severe overload conditions, as well as the transitional flow that may exist on the tank wall, the WALE wall adaptive eddy viscosity model in the LES method is used for solution.

[0096] Step 3: Setting the mesh boundary conditions for numerical calculation under all flight conditions

[0097] Step 3.1: Due to the complex structure of the storage tank, the interface morphology at the microstructures within the tank is difficult to predict accurately. Considering the large macroscopic scale of the computational domain, an adaptive dynamic mesh is used for densification and optimization at the interface. An octree partitioning method for three-dimensional structures is adopted, dividing the mesh into eight identical sub-mesh according to a specific direction. If only one partitioning is performed, it is considered first-order; if the sub-mesh is partitioned again, it is considered second-order, and so on. Figure 3 Schematic diagrams of the mesh structure of the dynamic adaptive mesh in two-dimensional and three-dimensional cases are given.

[0098] Step 3.2: During the calculation process, all boundaries of the tank are set as non-slip walls, and liquid is filled into the tank according to the initial filling amount.

[0099] Step 3.3, the time step set in the numerical solution process of this example is 1e. -2 s. At the same time, before each operating condition calculation begins, the stable value of the previous operating condition under the current mass is calculated first, and then the overload is changed to observe the change of liquid level under the overload change operating condition.

[0100] Step 4: Gas-liquid distribution, gas content, and stress analysis under all flight conditions

[0101] Based on the characteristics of overload variation, this calculation divides the entire flight process into three segments. Based on the numerical calculation results, the operating points where the liquid level changes drastically are identified, and the operating conditions with the most severe liquid level sloshing corresponding to each stage are listed.

[0102] Step 5: Establish a theoretical model for the swaying parameters of irregularly shaped storage tanks

[0103] Based on the numerical analysis results, the characteristic parameters of the tank swaying characteristics are expressed by theoretical equations.

[0104] The frequency of liquid sloshing is:

[0105]

[0106] The distance from the center of mass of the liquid to the liquid surface during sloshing is:

[0107]

[0108] The linear limit displacement value Y of liquid sloshing, when the sloshing angle is 10° (determined according to the formula in the book; if it is uncertain, it is also related to the amplitude of the sloshing, then it is not a constant), represents the lateral displacement of the sloshing mass as follows:

[0109]

[0110] The relative sloshing mass of the liquid is:

[0111]

[0112] Where: h is the liquid height, R is half the liquid surface span, C1R is the equivalent radius corrected by coefficient C1, and g is the acceleration. Let m1 be the relative sloshing mass, m be the liquid sloshing mass, and m be the total mass of the liquid in the tank. ξ1 is the root value of the first derivative of the Bessel function of the first kind, taken as 1.8412.

[0113] For a smooth tank without anti-sloshing devices, the results of resonance attenuation tests on sloshing damping show that the liquid sloshing damping ratio is constant under a given filling condition, independent of the sloshing wave height, and satisfies the similarity criterion:

[0114]

[0115] Where: ν is the kinematic viscosity coefficient of the liquid, C is a constant related to the liquid level in the tank, and C2 is a correction coefficient considering the shape of the tank in this study.

[0116] The function of C was obtained by fitting according to the literature. The relationship between C and x = h / R was obtained by fitting an exponential function as follows:

[0117] C=a*exp(b*x)+c*exp(d*x) (23)

[0118] For a*, take 36.52, for b*, take -12.03, for c*, take 1.672, and for d*, take -0.2769.

[0119] This example demonstrates a method for studying the liquid sloshing characteristics within an irregularly shaped propellant tank and establishing an equivalent dynamic model. It achieves equivalent dynamic theoretical modeling and numerical calculation of liquid propellant sloshing, obtaining typical characteristic parameters such as sloshing frequency and sloshing mass throughout the entire flight process. Based on the analysis results and theoretical model, it assists in the design and optimization of irregularly shaped propellant tanks for novel powered aircraft, saving experimental costs and time.

[0120] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention based on the above-disclosed technical content without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for studying the liquid sloshing characteristics in an irregularly shaped storage tank and modeling its equivalent dynamics, characterized in that, include: Establish an equivalent dynamic model of propellant sloshing in irregularly shaped tanks; Based on the Navier-Stokes equations, an equivalent dynamic model of propellant sloshing in irregularly shaped tanks is coupled to obtain a two-phase dynamic model of propellant gas-liquid flow. The irregularly shaped tank was meshed and imported into the established propellant gas-liquid two-phase flow dynamics model for boundary condition setting and numerical calculation to obtain the liquid level change characteristics during the overload process. Based on the liquid level change characteristics obtained during the overload change process, the gas-liquid distribution, gas content and stress under all flight conditions are analyzed, and the gas-liquid distribution, gas content and stress change characteristics under the conditions are calculated. Based on the gas-liquid distribution and gas content and force variation characteristics under working conditions, theoretical equations are used to express the liquid sloshing frequency, the distance from the center of mass of the sloshing liquid to the liquid surface, the lateral displacement of the sloshing mass, and the liquid relative to the sloshing mass, so as to obtain a theoretical model of the sloshing parameters of the irregular tank. The establishment of the equivalent dynamic model of propellant sloshing in the irregularly shaped tank includes: set up The axis is opposite to the direction of gravity. Axis and liquid sloshing velocity vector Gravitational acceleration Coplanarity yields an equivalent dynamic model of propellant sloshing in irregularly shaped tanks, specifically: in ， For the first n The length of the massless swing arm in the first mode; For the first n The wobbling mass of the first mode; For shaking mass The position of the wobbling along the Z-axis; For the first n Volume modes of order modes; For the first n Natural frequencies of first-order modes; area partitioning S f For the free surface of the liquid, S w The portion of the liquid's outer surface that comes into contact with the storage tank; For the first n The eigenvector matrix of the first mode; The density of the liquid; r Let be the position vector of the liquid's center of mass in the inertial frame; m 0 represents rigid mass, which is considered not to participate in the swaying. Z 0 represents rigid mass. m The position of 0 on the Z-axis; Zc is the swaying mass. Position on the Z-axis; Considering the effect of surface tension, a torsion spring is added to the equivalent dynamic model along with the swing arm, whose natural frequency is... The equality condition is expressed as: In the formula: Let be the stiffness coefficient of the torsion spring. , B for Bond number, g It is the acceleration due to gravity. R 0 represents the characteristic dimension of the storage tank. σ The surface tension coefficient of the liquid at the free surface. The density of the liquid; Based on the Navier-Stokes equations, a propellant sloshing equivalent dynamic model is coupled to obtain a propellant gas-liquid two-phase flow dynamic model, including: For the equivalent dynamic model of propellant sloshing in irregularly shaped tanks, the liquid volume fraction control equation is solved, and the gas-liquid interface is constructed using the geometric reconstruction method to obtain the propellant gas-liquid two-phase flow dynamic model. The propellant gas-liquid two-phase flow dynamics model was modified using the coupled VOF method and the Level-set method, and the Heaviside function was adopted. H ( φ Smooth the fluid properties at the gas-liquid interface; The process of meshing the irregularly shaped tank and importing it into the established propellant gas-liquid two-phase flow dynamics model for boundary condition setting and numerical calculation to obtain the liquid level change characteristics during overload changes includes: An octree partitioning method for three-dimensional structures is adopted, dividing the structure into eight identical sub-mesh; All boundaries of the irregularly shaped storage tank are set as non-slip walls, and liquid is filled into the irregularly shaped storage tank according to the initial filling amount at the time. Set the time step; before calculating each point of interest, calculate the current liquid mass and the steady-state value of the liquid's steady-state distribution characteristics under overload, and then change the overload to obtain the liquid level change characteristics during the overload change process.

2. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, The governing equation for liquid volume fraction is expressed as follows: in: This refers to the volume fraction of the liquid propellant. t and U They represent time and speed, respectively.

3. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, The UI constructor for the Level Set method is: In the formula: d(x, t) is the minimum distance from node x to the phase interface, and this characteristic distance d(x, t) requires the surface tension of the liquid.

4. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, Fluid properties are expressed as: Where H(φ) is the Heaviside function, used to smooth the fluid property γ at the interface, and the subscripts are used to represent the interface properties. g Represents the gas phase. l Represents the liquid phase. m It represents a gas-liquid mixture.

5. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, When the propellant tank experiences strong nonlinear flow, including complex large curvature backflow and flow stall, during the liquid sloshing process under severe overload conditions throughout the flight, or when there is transitional flow on the tank wall, the WALE wall adaptive eddy viscosity model in the LES method is used to solve the problem and obtain the propellant gas-liquid two-phase flow dynamics model.

6. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, The calculations obtained for the gas-liquid distribution, gas content, and stress variation characteristics at the operating conditions include: dividing the entire flight process into three segments based on the overload variation characteristics: normal overload turning, normal overload reduction, and normal overload sudden drop; identifying the operating point where the liquid level changes drastically during the overload variation process based on the liquid level variation characteristics; and obtaining the gas-liquid distribution, gas content, and stress variation characteristics at the operating conditions based on the liquid level variation characteristics. The term "drastic" refers to a liquid level fluctuation range exceeding 20% ​​during the overload variation process.

7. The method for studying the liquid sloshing characteristics and equivalent dynamic modeling in an irregularly shaped storage tank according to claim 1, characterized in that, The theoretical equations expressing the liquid sloshing frequency, the distance from the center of mass of the sloshing liquid to the liquid surface, the lateral displacement of the sloshing mass, and the liquid relative to the sloshing mass are derived based on the gas-liquid distribution and gas content and stress variation characteristics under operating conditions. This yields a theoretical model of the sloshing parameters for the irregularly shaped tank, including: Liquid sloshing frequency: Distance from the center of mass of the liquid to the liquid surface during sloshing: Linear limit displacement value of liquid sloshing When the swing angle is θ: Relative sloshing mass of liquid: in: For liquid height, It is half the span of the liquid surface. To pass the correction coefficient The corrected equivalent radius, For acceleration, For relative swaying mass, Let the mass of the liquid be the mass of the sloshing. The total mass of the liquid in the tank. is the root value of the first derivative of the Bessel function of the first kind.

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