A hydrofoil stability prediction method based on a hydrodynamic reduced-order model

Abstract

The application discloses a hydrofoil stability prediction method based on a water power reduced-order model, and belongs to the technical field of shipbuilding industry and fluid machinery. The application establishes a continuous state space water power reduced-order model through signal training, parameter identification, state transformation and bilinear transformation, calculates the matrix eigenvalue of the model, and judges the stability of a flow field in combination with a flow field stability criterion. The application obtains a mass matrix, a stiffness matrix and a structure motion equation considering the additional mass effect of water by performing three-dimensional modeling, finite element analysis and Theodorsen theory calculation on a reference hydrofoil, and establishes a continuous state space parameterized structure reduced-order model. The application couples the water power reduced-order model and the parameterized structure reduced-order model to establish a parameterized hydroelastic fluid-structure coupling reduced-order model, and improves the stability prediction precision and efficiency of the hydrofoil in combination with the matrix eigenvalue of the parameterized hydroelastic fluid-structure coupling reduced-order model and a hydroelastic fluid-structure coupling system stability criterion. The application can analyze the change rule of the instability boundary of the hydroelastic fluid-structure coupling system with a mass ratio, and solves related engineering technical problems such as hydrofoil optimization application.

Description

TECHNICAL FIELD

[0001] The present application relates to a water wing stability prediction method based on a water power reduced order model, belonging to the shipbuilding industry and fluid machinery technical field. BACKGROUND

[0002] Hydraulic machinery as an important energy equipment, in water power development, water transfer across the basin, urban drainage, agricultural irrigation and petroleum industry, chemical industry, aerospace engineering, ocean engineering, environmental engineering and many other fields related to the development of national economy and national security have a wide range of applications. With the development of material science, elastic materials begin to be widely used in hydraulic machinery to reduce the weight of equipment and improve the operating efficiency. Compared with traditional metal materials, elastic structure is easy to cause deformation and vibration under extreme mechanical environment such as complex vortex system and unsteady cavitation flow, making the study of water elasticity response more complex. Especially when the lock-in phenomenon occurs, it is often accompanied by rapid and severe structural vibration divergence, and the structural amplitude increases, which leads to structural instability and failure, and further affects the stability of the equipment operation, and even destroys the whole system.

[0003] At present, although the CFD / CSD fluid-structure coupling numerical calculation method can better reflect the time domain and frequency domain characteristics of unsteady turbulent structure and its induced structural vibration response, the requirement of more refined turbulent structure capture and more accurate water power prediction significantly increases the time and space complexity of calculation. At the same time, for the lock-in instability of complex water elasticity system, there is a lack of accurate prediction, and the reduced order model based on limited CFD simulation data can describe the main characteristics of high-order cavitation turbulent flow system, which provides a new opportunity for predicting the stability of complex water-elastic fluid-structure coupling system. SUMMARY

[0004] In order to solve the problems of large computational complexity and low prediction accuracy of hydrofoil stability in existing fluid-structure coupling algorithms, the main purpose of the present invention is to provide a hydrofoil stability prediction method based on a hydrodynamic reduction model. A continuous state-space hydrodynamic reduction model is established through signal training, parameter identification, state transformation, and bilinear transformation. The stability of the flow field is judged by calculating its matrix eigenvalues ​​and combining it with the flow field stability criterion, thereby improving the prediction efficiency of the hydrofoil flow field stability. By performing three-dimensional modeling, finite element analysis, and Theodorsen theory calculation on the reference hydrofoil, the mass matrix, stiffness matrix, and structural motion equation considering the added mass effect of water are obtained, and then a continuous state-space parameterized structural reduction model is established through state transformation. The continuous state-space hydrodynamic reduction model and the continuous state-space parameterized structural reduction model are coupled to establish a parameterized hydroelastic fluid-structure coupling reduction model, and a hydroelastic fluid-structure coupling system stability criterion is constructed. The matrix eigenvalues ​​of the parameterized hydroelastic fluid-structure coupling reduction model and the hydroelastic fluid-solid coupling system stability criterion are combined to improve the prediction accuracy and efficiency of the hydroelastic fluid-solid coupling system stability. The present invention can use the relative mass ratio as a variable to analyze the variation law of the instability boundary of the hydroelastic fluid-solid coupling system with the mass ratio, optimize and improve the hydrofoil design, avoid the damage to the hydrofoil structure when the frequency locking phenomenon of the hydrofoil fluid-solid coupling system occurs, and extend the service life of the hydrofoil components.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a method for predicting the stability of a hydrofoil based on a hydrodynamic reduced-order model, comprising the following steps:

[0007] Step 1: Collect the structural displacement input signal of the reference hydrofoil, use the hydrodynamic response as the output, perform signal training and parameter identification, and establish the discrete difference equation of the ARX model.

[0008] Step 2: Based on the discrete difference equations of the ARX model established in step 1, a continuous state-space hydrodynamic reduction model is established through state transformation and bilinear transformation.

[0009] Step 3: Calculate the eigenvalues ​​of the continuous state-space hydrodynamic reduction model matrix, construct the flow field stability criterion, and judge the stability of the flow field according to the positive or negative real part of the eigenvalue, thereby improving the prediction efficiency of the reference hydrofoil flow field stability.

[0010] Step 4: By performing three-dimensional modeling, finite element analysis and Theodorsen theory calculation on the reference hydrofoil, the mass matrix, stiffness matrix and structural motion equation of the hydrofoil considering the added mass effect of water are obtained.

[0011] Step 5: Based on the structural motion equation considering the added mass effect of water obtained in step 4, a continuous state space parameterized structural reduced order model is further established through state transformation.

[0012] Step 6: The continuous state space hydrodynamic reduced order model obtained in step 2 and the continuous state space parameterized structural reduced order model obtained in step 5 are coupled to establish a parameterized hydroelastic fluid-structure coupling reduced order model.

[0013] Step 7: The eigenvalues of the parameterized hydroelastic fluid-structure coupling reduced order model matrix are calculated to construct a stability criterion for the hydroelastic fluid-structure coupling system. According to the sign of the real part of the eigenvalues of the parameterized hydroelastic fluid-structure coupling reduced order model matrix and the stability criterion for the fluid-structure coupling system, the prediction accuracy and efficiency of the stability of the fluid-structure coupling system are improved.

[0014] Step 8: Taking the relative mass ratio as a variable, the variation law of the instability boundary of the hydroelastic fluid-structure coupling system with the mass ratio is analyzed efficiently and accurately by obtaining the eigenvalue trajectory diagram of the fluid-structure coupling system model of the hydrofoil with different relative mass ratios, the hydrofoil design is optimized and improved to avoid the destruction of the hydrofoil structure when the fluid-structure coupling system of the hydrofoil locks frequency, and the service life of the hydrofoil component is prolonged.

[0015] As a preferred, in the step 1, the discrete difference equation of the ARX model is obtained as follows

[0016]

[0017] wherein ξ is the input signal, f a is the output quantity. A i and B i are the coefficient matrices obtained after training and identification, and na and nb are the delay orders of the input and output quantities, respectively.

[0018] As a preferred, in the step 2, the continuous state space hydrodynamic reduced order model is established through state transformation and bilinear transformation as follows

[0019]

[0020] wherein g a is the state variable of the continuous state space of the hydrodynamic reduced order model, ξ is the input of the state space, f a is the output of the state space, t is the t-th time, A a , B a , C a , D a are the parameters of the continuous state space of the hydrodynamic reduced order model.

[0021] As a preferred, in the step 3, the stability criterion for the flow field of the reference hydrofoil model is given as follows

[0022]

[0023] Preferably, in step 4, the mass matrix, stiffness matrix and structural motion equation of the hydrofoil considering the added mass effect of water are obtained by performing three-dimensional modeling, finite element analysis and Theodorsen theory calculation on the reference hydrofoil, and the implementation method is as follows:

[0024] First, based on the 3D modeling software, a reference hydrofoil model is established to obtain the generalized mass matrix and stiffness matrix as follows

[0025]

[0026] Among them, m, S θ , I θ , K h , K θ are the mass of the hydrofoil per unit span, the mass moment of static mass about the rigid center, the mass moment of inertia about the rigid center, the bending stiffness and the torsional stiffness respectively.

[0027] Then the additional mass matrix and additional stiffness matrix calculated based on Theodorsen theory are given as follows

[0028]

[0029] Where U is the incoming flow velocity, ρ f is the density of water, a and b are the distance from the elastic axis of the hydrofoil to the midpoint of the chord and the half-chord length of the hydrofoil, respectively. k = ωb / U is the reduction frequency, and ω is the natural frequency of the system. C(k) is the Theodorsen function.

[0030] Ignoring the response amplitude, the damping matrix is ​​set to 0. By combining with the generalized mass matrix and stiffness matrix, the mass matrix and stiffness matrix considering the added mass effect of water are obtained, and then the structural motion equation is obtained as follows:

[0031]

[0032] in ξ represents the generalized acceleration and displacement of the structure, F CFD Indicates external force.

[0033] As an advantage, in step 5, a continuous state space parameterized structure reduction model is established by state transformation, as follows

[0034]

[0035] Among them, g s are the state variables in the continuous state space of the parameterized structural reduction model, ξ is the input of the state space, f a is the output of the state space, t is the t-th time, A s , B s , C s , D s are the continuous state space parameters of the parameterized structural reduced order model, respectively:

[0036]

[0037] where 0 is a square matrix, I represents the unit matrix, q is the dynamic pressure. fs , K fs are the mass matrix and the stiffness matrix of the parameterized structural reduced order model considering the added mass effect of water, respectively, as follows

[0038]

[0039] where μ = m / ρ f πb 2 is the mass ratio of the hydrofoil, a, b, c are the distance from the elastic axis of the hydrofoil to the midpoint of the chord, the half chord length, and the chord length, respectively, x θ , r θ , ω θ , ω h are the dimensionless distance with the center of gravity behind the center of stiffness, the dimensionless turning radius of the hydrofoil to the center of stiffness, the first order natural frequency of the hydrofoil, and the second order natural frequency of the hydrofoil, respectively.

[0040] As preferred, in step 6, the parameterized hydro-elastic fluid-structure interaction reduced order model is established, as follows

[0041]

[0042] where the subscripts a and s represent the fluid and the structure, respectively, t is the t-th time step, x a is the state variable of the state space of the hydrodynamic reduced order model, x s is the state variable of the state space of the parameterized structural reduced order model; A a , B a , C a , D a are the continuous state space parameters of the hydrodynamic reduced order model; A s , B s , C s are the continuous state space parameters of the parameterized structural reduced order model.

[0043] As preferred, in step 7, the stability criterion of the parameterized hydro-elastic fluid-structure interaction system is given, as follows

[0044]

[0045] Advantages:

[0046] 1. The water wing stability prediction method based on the water power reduced order model discloses a three-dimensional modeling of a reference water wing, finite element analysis and Theodorsen theory calculation, obtains the water wing mass matrix, stiffness matrix and structure motion equation considering the additional mass effect of water, and further establishes a continuous state space parameterized structure reduced order model.

[0047] 2. The water wing stability prediction method based on the water power reduced order model establishes a continuous state space water power reduced order model through signal training, parameter identification, state transformation and bilinear transformation, analyzes the matrix eigenvalues and combines the flow field stability criterion to judge the stability of the flow field, and further improves the prediction efficiency of the flow field stability.

[0048] 3. The water wing stability prediction method based on the water power reduced order model can take the relative mass ratio as a variable to analyze the change rule of the water elastic fluid coupling system instability boundary with the mass ratio, optimize and improve the water wing design, avoid the water wing structure damage when the water wing fluid coupling system lock frequency phenomenon occurs, and prolong the service life of the water wing component. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a flow chart of the water wing stability prediction method based on the water power reduced order model.

[0050] Figure 2 is a comparison of the water power coefficients obtained by CFD calculation and the ARX reduced order model, wherein: Figure 2 (a) is the lift coefficient, Figure 2 (b) is the moment coefficient.

[0051] Figure 3is the matrix eigenvalue analysis based on the water dynamic reduced order model.

[0052] Figure 4 is the matrix eigenvalue analysis based on the water dynamic reduced order model.

[0053] Figure 5 is the model eigenvalue root trajectory of the hydro-elastic coupling system of different relative mass ratio hydrofoils. DETAILED DESCRIPTION

[0054] For the purpose of better illustrating the object and advantages of the present application, the embodiments of the present application are described in detail below in conjunction with the accompanying drawings and specific examples.

[0055] As shown in the figure, the hydrofoil stability prediction method based on the water dynamic reduced order model disclosed in the embodiment is implemented as follows: Figure 1 Step 1, collect the structural displacement input signal of the reference hydrofoil, take the water dynamic response as the output, perform signal training and parameter identification, and establish the discrete difference equation of the ARX model.

[0056] Firstly, take the “3211” signal as the input signal, including the bending deformation h and the torsional deformation θ of the reference hydrofoil, take the water dynamic response calculated based on ANSYS CFX as the output signal, including the lift coefficient C l and the moment coefficient C m , and establish the ARX discrete difference equation through signal training and parameter identification.

[0057]

[0058]

[0059] wherein ξ is the bending deformation h and the torsional deformation θ of the reference hydrofoil, f a is the corresponding lift coefficient C l and the moment coefficient C m . A i and B i are the coefficient matrices to be identified, and na and nb are the delay orders of the input and output quantities respectively.

[0060] Step 2, establish the continuous state space water dynamic reduced order model through state transformation and bilinear transformation.

[0061] Firstly, define the state vector x a (k)=[y a (k-1),....,y a (k-na),u(k-1),....,u(k-nb+1)] T convert the ARX discrete difference equation into the state space equation under discrete time. ​

[0062]

[0063] Among them, x a is the state variable in the discrete time state space, are the parameters of the state space in discrete time.

[0064] Through bilinear transformation, the discrete-time state-space equation is transformed into a continuous-time state-space equation, and the corresponding continuous-time state-space hydrodynamic reduced-order model is established.

[0065]

[0066] Among them, g a are the state variables in the continuous state space of the hydrodynamic reduced-order model, ξ is the input of the state space, f a is the output of the state space, t is the tth moment, A a 、B a 、C a 、D a are the continuous state space parameters of the hydrodynamic reduced-order model.

[0067] Step 3: Calculate the matrix A in the continuous state space hydrodynamic reduction model a The eigenvalue of is used to construct the flow field stability criterion, and the flow field stability is determined according to the positive or negative real part of the eigenvalue.

[0068] When the matrix A a When there is an eigenvalue with a real part greater than 0, the flow field is unstable; when the matrix A a When the real parts of the eigenvalues ​​are all less than 0, the flow field is stable.

[0069] Step 4: By performing three-dimensional modeling, finite element analysis and Theodorsen theory calculation on the reference hydrofoil, the mass matrix, stiffness matrix and structural motion equation of the hydrofoil considering the added mass effect of water are obtained.

[0070] First, based on the Solidworks 3D modeling software, a reference hydrofoil structure model is established to obtain the unit span hydrofoil mass and the mass moment of inertia of the hydrofoil to the rigid center, and then the generalized mass matrix and stiffness matrix of the model are obtained as follows:

[0071]

[0072] Among them, m, S θ , I θ , K h , K θ are the mass of the hydrofoil per unit span, the mass moment of static mass about the rigid center, the mass moment of inertia about the rigid center, the bending stiffness and the torsional stiffness respectively.

[0073] Based on Theodorsen theory, the added mass matrix and added stiffness matrix considering the effect of fluid added mass are calculated as follows

[0074]

[0075] where U is the incoming flow velocity, p f is the density of water, a, b are the distance from the elastic axis of hydrofoil to the midpoint of chord and the half chord length of hydrofoil respectively, k = ωb / U is the reduced frequency, ω is the natural frequency of the system. C(k) is the Theodorsen function, which considers the lift loss caused by wake through Hankel equation H(k),

[0076]

[0077] Without considering the response amplitude, the damping matrix is set to 0. By combining with the generalized mass matrix and stiffness matrix, the mass matrix and stiffness matrix considering the effect of water added mass are obtained, and then the structural motion equation is obtained as follows

[0078]

[0079] where, ξ、 are the bending and torsional deformation and acceleration of the hydrofoil, F CFD represents the lift and moment on the hydrofoil.

[0080] Step 5, based on the structural motion equation considering the effect of water added mass, a continuous state space parameterized structural reduced order model is established.

[0081] By defining the state vector the discrete state parameterized structural reduced order model is converted into a continuous state space parameterized structural reduced order model as follows

[0082]

[0083] where, g s is the state variable of the continuous state space of the parameterized structural reduced order model, ξ is the input of the state space, including the bending and torsional deformation and acceleration of the hydrofoil, f a is the output of the state space, including the lift coefficient and moment coefficient of the hydrofoil, t is the t time, A s , B s , C s , D s are the continuous state space parameters of the parameterized structural reduced order model, respectively

[0084]

[0085] where 0 is a square matrix, I is an identity matrix, q = 1 / πμr θ 2 M is the dynamic pressure. fs , K fs are the mass matrix and the stiffness matrix of the parameterized structural reduced-order model considering the added mass effect of water, respectively, as follows

[0086]

[0087] where μ = m / ρ f πb 2 is the mass ratio of the hydrofoil, a, b, c are the distance from the elastic axis of the hydrofoil to the midpoint of the chord, the half chord length, and the chord length, respectively, x θ , r θ , ω θ , ω h are the dimensionless distance from the center of gravity of the hydrofoil to the center of stiffness, the dimensionless turning radius to the center of stiffness, the first-order natural frequency, and the second-order natural frequency of the hydrofoil, respectively.

[0088] Step 6, coupling the continuous state space hydrodynamic reduced-order model and the continuous state space parameterized structural reduced-order model to obtain a continuous state space parameterized hydroelastic fluid-structure interaction reduced-order model.

[0089]

[0090] where the subscripts a and s represent the fluid and the structure, respectively, t is the t-th time step, x a is the state variable of the continuous state space of the hydrodynamic reduced-order model, x s is the state variable of the continuous state space of the parameterized structural reduced-order model; A a , B a , C a , D a are the continuous state space parameters of the hydrodynamic reduced-order model; A s , B s , C s are the continuous state space parameters of the parameterized structural reduced-order model, where only the matrices A s and B s change with the change of the structural characteristics.

[0091] Step 7, calculating the eigenvalues of the parameterized hydroelastic fluid-structure interaction reduced-order model matrix to construct a stability criterion for the hydroelastic fluid-structure interaction system. According to the stability criterion for the fluid-structure interaction system and the positive and negative of the real part of the eigenvalues of the parameterized hydroelastic fluid-structure interaction reduced-order model matrix, the stability of the fluid-structure interaction system is determined.

[0092] When the matrix A ae has an eigenvalue with a real part greater than 0, the hydroelastic fluid-structure interaction system is unstable; when the matrix Aae When the real parts of the eigenvalues ​​of are all less than 0, the hydroelastic fluid-solid coupling system is stable.

[0093] Step 8: Using the relative mass ratio as a variable, by obtaining the characteristic root locus diagram of the fluid-structure coupling system model for hydrofoils with different relative mass ratios, the variation law of the instability boundary of the hydroelastic fluid-structure coupling system with the mass ratio is analyzed, and the hydrofoil design is optimized to avoid structural damage when the frequency locking phenomenon of the hydrofoil fluid-structure coupling system occurs, thereby extending the service life of the hydrofoil components.

[0094] Taking the NACA0009 composite hydrofoil for propeller as a verification reference, the instability frequency of the hydrofoil when frequency locking occurs at an incoming flow velocity of 11 m / s is calculated. Figure 2 The comparison between the hydrodynamic coefficients identified by the continuous state-space hydrodynamic reduction model based on the ARX model and the CFD simulation results shows that the lift coefficient and moment coefficient are very consistent, which verifies the effectiveness of the hydrodynamic reduction model. Figure 3 is the eigenvalue of the hydrodynamic reduced-order model matrix when the frequency locking phenomenon occurs, and the real parts are all negative, indicating that the hydrofoil flow field is stable when the frequency locking phenomenon occurs. Figure 4 is the matrix eigenvalue of the parameterized hydroelastic fluid-structure coupling reduced-order model when the hydrofoil mode n = 18. In the interval where the real part is positive, there is a pair of conjugate eigenvalues, indicating that the fluid-structure coupling system is unstable at this time and is caused by structural modal instability. Figure 5 For the fluid-structure coupling system of hydrofoils with different relative mass ratios, the matrix eigenvalues ​​of the hydroelastic fluid-structure coupling reduced-order model are calculated. That is, hydrofoils with real parts greater than 0 will experience structural instability in an operating environment with an incoming flow velocity of 11 m / s. Therefore, these mass ratio parameters should be avoided as much as possible when designing hydrofoils.

[0095] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting hydrofoil stability based on a hydrodynamic reduced-order model, characterized by: The following steps are included: Step 1: Collect the structural displacement input signal of the reference hydrofoil, use the hydrodynamic response as the output, perform signal training and parameter identification, and establish the discrete difference equation of the ARX model; Step 2: Based on the discrete difference equations of the ARX model established in step 1, a continuous state-space hydrodynamic reduction model is established through state transformation and bilinear transformation; Step 3: Calculate the eigenvalues ​​of the continuous state-space hydrodynamic reduction model matrix, construct the flow field stability criterion, and judge the stability of the flow field based on the positive or negative real part of the eigenvalue, thereby improving the prediction efficiency of the reference hydrofoil flow field stability. Step 4: By performing 3D modeling, finite element analysis, and Theodorsen theory calculation on the reference hydrofoil, the mass matrix, stiffness matrix, and structural motion equations of the hydrofoil considering the added mass effect of water are obtained; Step 5: Based on the structural motion equations considering the added mass effect of water obtained in step 4, a continuous state space parameterized structural reduced-order model is established through state transformation; Step 6: Couple the continuous state-space hydrodynamic reduced-order model obtained in step 2 and the continuous state-space parameterized structural reduced-order model obtained in step 5 to establish a parameterized hydroelastic fluid-structure coupled reduced-order model; Step 7: Calculate the eigenvalues ​​of the parameterized hydroelastic fluid-structure coupling reduced-order model matrix and construct a stability criterion for the hydroelastic fluid-structure coupling system. Improve the prediction accuracy and efficiency of the fluid-structure coupling system stability based on the positive and negative real parts of the eigenvalues ​​of the parameterized hydroelastic fluid-structure coupling reduced-order model matrix and the stability criterion of the fluid-structure coupling system.

2. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 1, wherein: The method further includes step 8, which uses the relative mass ratio as a variable, obtains characteristic root locus diagrams of the fluid-structure coupling system model of hydrofoils with different relative mass ratios, and efficiently and accurately analyzes the variation law of the instability boundary of the hydroelastic fluid-structure coupling system with the mass ratio, optimizes and improves the hydrofoil design, avoids damage to the hydrofoil structure when the frequency locking phenomenon of the hydrofoil fluid-structure coupling system occurs, and extends the service life of the hydrofoil components.

3. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 1 or 2, characterized in that: In step 1, the discrete difference equation of the ARX model is obtained as follows Where ξ is the input signal, f a is the output; A i and B i is the coefficient matrix obtained by identification after training, na and nb are the delay orders of input and output respectively.

4. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 3, wherein: In step 2, a continuous state space hydrodynamic reduction model is established through state transformation and bilinear transformation, as follows Among them, g a are the state variables in the continuous state space of the hydrodynamic reduced-order model, ξ is the input of the state space, f a is the output of the state space, t is the tth moment, A a 、B a 、C a 、D a are the continuous state space parameters of the hydrodynamic reduced-order model.

5. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 4, characterized in that: In step 3, the stability criterion of the flow field of the reference hydrofoil model is given as follows:

6. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 5, characterized in that: In step 4, the mass matrix, stiffness matrix and structural motion equation of the hydrofoil considering the added mass effect of water are obtained by performing three-dimensional modeling, finite element analysis and Theodorsen theory calculation on the reference hydrofoil. The implementation method is as follows: First, based on the 3D modeling software, a reference hydrofoil model is established to obtain the generalized mass matrix and stiffness matrix as follows Among them, m, S θ , I θ , K h , K θ are the mass of the hydrofoil per unit span, the mass moment of static force about the rigid center, the mass moment of inertia about the rigid center, the bending stiffness and the torsional stiffness respectively; Then the additional mass matrix and additional stiffness matrix calculated based on Theodorsen theory are given as follows Where U is the incoming flow velocity, ρ f is the density of water, a and b are the distance from the elastic axis of the hydrofoil to the midpoint of the chord and the half-chord length of the hydrofoil, respectively, k = ωb / U is the reduction frequency, ω is the natural frequency of the system; C(k) is the Theodorsen function; Ignoring the response amplitude, the damping matrix is ​​set to 0. By combining it with the generalized mass matrix and stiffness matrix, the mass matrix and stiffness matrix considering the added mass effect of water are obtained, and then the structural motion equation is obtained as follows: in ξ represents the generalized acceleration and displacement of the structure, F CFD Indicates external force.

7. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 6, wherein: In step 5, a continuous state space parameterized structure reduction model is established through state transformation, as follows Among them, g s are the state variables in the continuous state space of the parameterized structural reduction model, ξ is the input of the state space, f a is the output of the state space, t is the tth moment, A s 、B s 、C s 、D s are the continuous state space parameters of the parameterized structural reduction model, which are: Among them, 0 is a square matrix, I represents the unit matrix, q is the dynamic pressure; M fs , K fs are the mass matrix and stiffness matrix of the parameterized structural reduction model considering the added mass effect of water, as follows where μ = m / ρ f πb 2 is the mass ratio of the hydrofoil, a, b, and c are the distance from the elastic axis of the hydrofoil to the midpoint of the chord, the half-chord length, and the chord length, respectively. θ 、r θ 、ω θ 、ω h They are the dimensionless distance of the center of gravity behind the rigid center, the dimensionless radius of gyration of the hydrofoil to the rigid center, the first-order natural frequency of the hydrofoil, and the second-order natural frequency of the hydrofoil.

8. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 7, characterized in that: In step 6, a parameterized hydroelastic fluid-solid coupling reduced-order model is established as follows: where the subscripts a and s represent the fluid and structure respectively, t is the tth time step, and x a is the state variable in the state space of the hydrodynamic reduced-order model, x s is the state variable of the state space of the parameterized structural reduction model; A a 、B a 、C a 、D a is the continuous state space parameter of the hydrodynamic reduced-order model; A s 、B s 、C s are the continuous state-space parameters of the parameterized structural reduced-order model.

9. The method for predicting hydrofoil stability based on a hydrodynamic reduced-order model according to claim 8, characterized in that: In step 7, the stability criterion of the parameterized hydroelastic fluid-solid coupling system is given as follows:

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