CN117113725B - Energy obtaining analysis method of parameter pendulum type wave energy device - Google Patents
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Abstract
The invention belongs to the technical field of wave energy power generation, and relates to a method for analyzing the energy of a parameter pendulum type wave energy device, which comprises the following steps: constructing a hydrodynamic numerical model; simulating the motion time response of the floating body under the regular wave, calculating the response amplitude and the respective degree phase difference of the floating body through a hydrodynamic force numerical model, and interpolating the calculation result; solving a pendulum dynamics equation to obtain response distribution of the pendulum dynamics equation in a parameter space, optimizing pendulum energy acquisition in a traversing load mode, and calculating distribution of pendulum optimal energy acquisition in a wave parameter space; and adjusting parameters to realize iterative optimization of device design parameters. The analysis method provided by the invention can support the rough optimization of the pendulum wave energy device under the condition of large-scale wave parameter combination, help researchers to quickly evaluate the energy obtaining potential of the device, lock the main area of the device energy obtaining on the parameter space, effectively reduce the workload of the subsequent hydrodynamic force numerical simulation and physical model experiment, and accelerate the iteration speed of device research and development and optimization.
Description
Technical Field
The invention belongs to the technical field of wave energy power generation, and particularly relates to an energy acquisition analysis method of a parameter pendulum type wave energy device.
Background
The parameter pendulum type wave energy device mainly comprises a pendulum body, a floating body and a mooring device, wherein the pendulum body is hinged inside the floating body and can perform relative horizontal rotation motion with the floating body around a rotating shaft, and the floating body is connected with a seabed through catenary mooring. When the floating body moves in multiple degrees of freedom under the combined action of mooring and waves, the pendulum body moves in an oscillating or rotating mode from the balance position, and the capture of wave energy is achieved. The main energy obtaining mechanism is packaged in the floating body, does not contact with seawater, is not directly acted by wave force, has safe and reliable structure, can adapt to severe sea conditions, effectively prolongs the power generation time, and has advantages in application.
The main energy obtaining mechanism of the parameter pendulum type wave energy device is a pendulum body packaged in the floating body, and the energy obtaining mode of the parameter pendulum type wave energy device is different from that of a common wave energy device. The response of the pendulum body is jointly influenced by the motion of the floating body and the gravity, the response of the pendulum body has a certain random characteristic, and compared with a common wave energy device, the pendulum body of the parameter pendulum type wave energy device often needs to be excited for a long time to observe a stable motion state, namely, the numerical simulation cost of the device is higher. Moreover, wave energy devices generally only work normally in a limited range of wave conditions, and how to identify and determine their working intervals and tune the equipment according to the target sea area wave distribution is an important ring in the optimization work of the devices. For the wave energy device with a plurality of energy obtaining mechanisms directly contacted with the water body, the working interval of the wave energy device can be judged and regulated according to the resonance period of the floating body; for a parameter pendulum wave energy device, the resonance period of a pendulum body is closely related to the attitude angle of a floating body, the resonance state and the working range of the pendulum body are difficult to carry out qualitative judgment by theoretical means, and a large number of numerical simulations are needed as the basis. In addition, the performance of the parameter pendulum type wave energy device is influenced by various factors, including mooring system design parameters, multi-degree-of-freedom floating body design parameters, pendulum body design parameters and the like, so that the simulation workload of the device in the energy obtaining optimization process is huge, and the optimization cost of the device is high.
Jiang et al (System analysis and experimental investigation of a pendulum-based wave energy converter, OCEAN ENGINEERING, 277, 114300) have conducted related studies on such devices (parametric pendulum wave energy devices as shown in fig. 4), constructed pendulum dynamics equations based on the principle of energy capture of parametric pendulum wave energy devices, and proposed the concept of rapid assessment of pendulum energy capture based on pendulum dynamics equations, the energy capture assessment concept being as follows:
when the pendulum mass is small enough, its response cannot significantly affect the motion of the float, and can be analyzed as an independent system. The motion response of a hydrodynamic model formed by floating bodies and mooring under different wave heights and period combinations is calculated through hydrodynamic software, and the hydrodynamic calculation result is expanded through linear interpolation means. And taking the simulated floating body response data as input conditions of a pendulum body dynamics equation, calculating motion response of the pendulum body under forced excitation, obtaining the motion response and the distribution of energy acquisition on a parameter space formed by wave height and period, and realizing the evaluation of energy acquisition potential of the device.
The energy obtaining evaluation concept does not propose an optimization method of the system, and ignores partial details in the established numerical model, such as the phase relation of each degree of freedom response of the floating body, and the like, simplifies the excitation condition, and has certain defects.
Disclosure of Invention
The invention aims to solve the problems of imperfect excitation conditions, inaccurate calculation results and unclear device optimization flow of a pendulum response numerical model in the existing evaluation method, and provides a method for analyzing the energy of a parameter pendulum type wave energy device, which is a development and improvement of an energy acquisition evaluation conception of the existing parameter pendulum type wave energy device, and establishes a pendulum response numerical model with higher precision by considering complete excitation conditions and respective phase relation based on the existing swinging dynamics equation; and a specific operation method aiming at the pendulum body system energy acquisition evaluation is provided, and an analytic expression with higher calculation efficiency is provided at the same time as an auxiliary method for further accelerating the efficiency of device optimization iteration.
The technical scheme of the invention is as follows:
the energy obtaining analysis method of the parameter pendulum type wave energy device is characterized by comprising the following steps of:
constructing a hydrodynamic numerical model of a device with the coupling of the multi-degree-of-freedom floating body and the catenary mooring system;
simulating the motion time-course response of the floating body under the regular waves by referring to the period and wave height distribution of the target sea area thrown by the wave energy device, calculating the response amplitude and the respective degree phase difference of the floating body through a hydrodynamic force numerical model, and interpolating the calculation result;
calculating and interpolating by using a hydrodynamic numerical model to obtain response amplitude, phase difference and corresponding wave period data, solving a pendulum dynamics equation (a main control equation of the pendulum response numerical model), calculating motion time course response of the pendulum under different wave height and period combinations, obtaining distribution of pendulum response on a wave parameter space formed by the wave height and period, optimizing pendulum energy in a traversing load mode, and calculating distribution of pendulum optimal energy on the wave parameter space;
and analyzing the response distribution and the energy obtaining distribution calculation result, and adjusting the mooring plane arrangement, the mooring design parameter, the floating body design parameter and the pendulum body design parameter of the device to realize iterative optimization of the device design parameter.
Further, the method further comprises the steps of analyzing response distribution of the pendulum body in no-load state, wherein damping tends to be zero in no-load state, and obtaining an approximate analytical formula of a pendulum body dynamics equation through a perturbation method, wherein the approximate analytical formula is as follows:wherein, the method comprises the steps of, wherein,is any small amount introduced by the perturbation method,a linear term is represented and is used to represent,the first order term is represented by a first order term,representing a second order term; introduction of parametersDefining the applicable boundary of the approximate analytical formula:wherein, the method comprises the steps of, wherein,the angular velocity of the pendulum body in one period is relatively extremely poor,at the maximum value of the angular velocity,as a minimum value of the angular velocity,is the average value of the angular velocity;
in no-load calculation, the results of the numerical solution and the analytic solution are compared to finishAnd (3) the calibration of the system can be carried out by using an analytic solution to carry out no-load response calculation.
Further, the hydrodynamic numerical model is constructed using hydrodynamic calculation software including, but not limited to, WEC-Sim, openFOAM, AQWA, FLOW-3D.
Further, the response amplitude is interpolated, including wave height direction interpolation and periodic direction interpolation, and the processing mode of the wave height direction interpolation is as follows: selecting two data points with the same period, taking the wave height as weight, and carrying out linear interpolation on the response amplitude of any point between the two data points;
the processing mode of the periodic direction interpolation is as follows: and selecting two data points with the same wave height, and linearly interpolating the response amplitude of any point between the two data points by taking the period distance as the weight.
Further, when the phase difference data is interpolated, the interpolation is carried out only in the period direction, and the wave height direction is regarded as a constant value; the processing mode of the interpolation of the period direction is as follows: the phase difference of any point between two data points is linearly interpolated by taking the period distance as the weight.
Further, when the wave energy device is excited by wind waves to generate multi-degree-of-freedom motion at sea, the relative motion between the pendulum body and the floating body is expressed as the following pendulum body motionMechanical equation:wherein,、andis the angular displacement, angular velocity and angular acceleration of the pendulum motion,lis the distance between the mass center of the pendulum body and the rotating shaft,Mis the mass of the pendulum body, the weight of the pendulum body,Jfor the moment of inertia of the pendulum about the centre of mass,for the moment of inertia of the pendulum about the rotation axis,bfor the linear damping to which the pendulum motion is subjected,is the bow-swing acceleration of the floating body,andcorresponding to the components of the acceleration of four degrees of freedom of pitching, swaying, rolling and swaying of the floating body in the motion plane of the pendulum body,andthe gravitational acceleration is two components of the plane of pendulum motion.
Further, when the response amplitude, the phase difference and the corresponding wave period data obtained by hydrodynamic force calculation and interpolation are utilized, a floating body multi-degree-of-freedom motion time sequence with any duration can be constructed, and the time sequence of parameters required by a pendulum dynamics equation can be calculated according to the time sequence, wherein the time sequence comprises，，，Andand solving a pendulum dynamics equation (a master control equation of a pendulum response numerical model) by a fourth-order Dragon-Gregory tower method.
The invention has the beneficial effects that:
the analysis method provided by the invention has the advantages that the calculation speed is far higher than that of the traditional hydrodynamic simulation mode, the coarse optimization of the parameter pendulum type wave energy device under the condition of large-range wave parameter combination can be supported, researchers are helped to quickly evaluate the energy obtaining potential of the device, and the main area of the device in the parameter space is locked, so that the workload of the subsequent hydrodynamic numerical simulation and physical model experiment is effectively reduced.
According to the method, the floating body response time sequence with any duration can be reconstructed through an interpolation algorithm and a reconstruction method of the hydrodynamic force simulation result, so that the simulation duration in the calculation of the floating body hydrodynamic force value is further reduced; in addition, the invention also discloses an analytical solution of the pendulum dynamics equation, so that the response distribution of the pendulum in no-load is estimated, the calculation speed is far higher than that of a pendulum response numerical model, and the analytical solution is used as a supplement of a device energy obtaining rapid estimation and optimization method, so that the optimization efficiency can be further improved.
The invention is beneficial to quickly evaluating the optimization effect of the design parameters of the device, and traverses the design parameter combination of the device with low cost, thereby accelerating the research and development of the device and the iteration speed of optimization.
Drawings
FIG. 1 is a technical roadmap of the method for energy capture analysis of a parametric pendulum wave energy device of the present invention;
FIG. 2 is a comparative analysis example of a numerical solution and an analytical solution boundary provided by the present invention;
FIG. 3 is a schematic diagram of six degrees of freedom motion;
fig. 4 is a schematic structural diagram of a parametric pendulum wave energy device in the prior art.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For a further understanding of the present invention, reference will now be made to the drawings and examples.
As shown in fig. 1, the invention provides a method for analyzing the energy of a parameter pendulum wave energy device, which comprises the following steps:
1. device hydrodynamic force calculation
The parameter pendulum type wave energy device mainly comprises a pendulum body, a multi-degree-of-freedom floating body and a catenary mooring system, wherein hydrodynamic response of the device is mainly determined by the multi-degree-of-freedom floating body and the catenary mooring system.
When the wave energy device is excited by waves to generate multi-degree-of-freedom motion at sea, the relative motion between the pendulum body and the floating body can be expressed as:(1) In the method, in the process of the invention,、andis the angular displacement, angular velocity and angular acceleration of the pendulum motion,lis the distance between the mass center of the pendulum body and the rotating shaft,Mis the mass of the pendulum body, the weight of the pendulum body,Jfor the moment of inertia of the pendulum about the centre of mass,for the moment of inertia of the pendulum about the rotation axis,bfor the linear damping to which the pendulum motion is subjected,is the bow-swing acceleration of the floating body,andcorresponding to the components of the acceleration of four degrees of freedom of pitching, swaying, rolling and swaying of the floating body in the motion plane of the pendulum body,andthe gravitational acceleration is two components of the plane of pendulum motion. As shown in fig. 3, a six-degree-of-freedom motion schematic diagram is commonly used in ocean engineering.
Wherein the component of the gravitational acceleration in the plane of motion of the pendulumAndthe method is calculated by adopting the following formula:(2) In the method, in the process of the invention,andis the angular displacement of pitch and roll;
if the mass center of the floating body is positioned on the rotating shaft of the pendulum bodyAndthe method is calculated by adopting the following formula:(3) In the method, in the process of the invention,andthe heave acceleration and the heave acceleration of the floating body are respectively,andthe pitch angular acceleration and the roll angular acceleration of the floating body are respectively,drepresents the vertical distance between the floating body centroid and the pendulum body rotation plane, when the rotation plane is higher than the floating body centroid,dpositive values.
The pendulum dynamics equation (1)) is the master equation of the pendulum response numerical model, and the parameters reflecting the excitation of the floating body are in the equation，，，Andeach parameter is calculated indirectly from a time-course sequence of each degree of freedom response of the float (wherein,andcalculated by the formula (2),andcalculated by the formula (3), the last termIs the second differential of the yaw displacement). In other words, after the time-course sequence of each degree of freedom response of the floating body is obtained by hydrodynamic numerical calculation, the time-course sequence of the above five parameters can be further obtained, and after the necessary parameters are obtained, the calculation of the pendulum dynamics equation (formula (1)) can be performed.
And establishing a device hydrodynamic numerical model of coupling the multi-degree-of-freedom floating body and the catenary mooring system in hydrodynamic force calculation software (WEC-Sim, openFOAM, AQWA, FLOW-3D and the like). The main parameters of modeling include mass properties and shape dimensions of the floating body, mooring radius, mooring chain length, mooring water depth, and mooring chain mass properties of the catenary mooring system, etc. The wave distribution (the distribution range of the period and the wave height) of the target sea area thrown by the reference wave energy device simulates the motion time-course response of the floating body under the regular wave.
Under regular wave excitation, the time course of the motion of the floating body is a sine curve with the motion period consistent with the wave period, and the main parameters forming the sine curve are response amplitude, angular frequency and phase. Wherein the angular frequency corresponds to the wave period. Furthermore, the response of the float body to each degree of freedom under the combined action of the wave and mooring has a phase difference. Therefore, the hydrodynamic force calculation result will save the corresponding response amplitude data and phase difference data for each wave element.
Because of the limitation of calculation cost, hydrodynamic calculation cannot cover all wave height and period combinations in a target sea area, response amplitude data and phase difference data obtained by hydrodynamic calculation are needed to be interpolated, the interpolation generally comprises two directions of wave height and period, and the specific processing mode is as follows:
(1) Interpolation in wave height direction: selecting two data points with the same period, marking the two data points as data point A and data point B for convenience of description, wherein the period of the data point A obtained by hydrodynamic force numerical calculation is the same as that of the data point B but the wave height is different, and linear interpolation is carried out on the response amplitude of any point between the A and the B by taking the wave height as a weight; (2) periodic direction interpolation: two data points with the same wave height are selected, and are marked as data point A and data point C for convenience of description, the wave heights of the data point A and the data point C obtained by hydrodynamic force numerical calculation are the same but the periods are different, and at the moment, the response amplitude of any point between the A and the C is linearly interpolated by taking the distance of the period as the weight. The phase difference data is processed in a similar manner to the response amplitude, but is interpolated only in the periodic direction, and the wave height direction is regarded as a constant value.
2. Device energy harvesting optimization
The response amplitude, the phase difference and the corresponding wave period data obtained through hydrodynamic force calculation and interpolation can be used for constructing a floating body multi-degree-of-freedom motion time sequence with any duration. According to the obtained multi-degree-of-freedom motion time sequence of the floating body, calculating a time sequence of input parameters required by a pendulum dynamics equation:，，，and. And solving a pendulum dynamics equation (namely formula (1)) through a fourth-order Dragon-Gregory tower method to obtain a time-course sequence of pendulum motion and output power, and calculating motion response and energy obtaining conditions of the pendulum under different wave height and period combinations to obtain distribution of the pendulum on a parameter space formed by the wave height and the period. Analyzing the calculation results of response distribution and energy obtaining distribution, adjusting the mooring plane arrangement, mooring design parameters, floating body design parameters and pendulum body design parameters of the device, and realizing the design of the deviceIterative optimization of parameters.
The numerical simulation method based on the pendulum dynamics equation is applicable to no matter the pendulum is in an empty or loaded state.
In the unloaded state, the pendulum is not damped and cannot capture energy. The simulation result in the state cannot intuitively reflect the power generation potential of the pendulum body through the energy obtaining condition, but can be used as a reference of the system performance of the pendulum body in the initial period of device optimization, for example, the pendulum body with poor response in the no-load state does not need to carry out further load calculation and energy obtaining analysis.
When the pendulum system is empty (damping goes to zero), an approximate resolution of the pendulum dynamics equation is obtained by perturbation method, expressed as follows:wherein,is any small amount introduced by perturbation method, and linear term in the formulaFirst order itemSecond order termThe expression of (2) is as follows: in the above-mentioned method, the step of,andangular frequency corresponding to wave periodwTimely and convenientInter-sequencetThe conversion relation of (2) is as follows: ，，，，，is the phase difference between the respective degree of freedom response and the direction of heave, wherein。Is a constant in the linear term, expressed as follows:wherein,；；；；；；；；
，，，，，is the magnitude of the respective degree of response.
The analytic solution is a display expression, and the pendulum rotation angle can be calculated by substituting the time sequenceθIs a time-course sequence of (a) and (b). The length of the input time series typically requires only 1 wave period. Since the above analytical solution assumes that the pendulum is in pure rotational response under all wave conditions, which is not realistic, it is necessary to introduce a suitable boundary for the parametric specification analytical solution:(5) For a calculation result at a certain wave height and period,is a pendulum body in a periodThe angular velocity is relatively very poor. The pure rotational response of the pendulum has boundaries (upper and lower) in the parameter space, which can be defined byExpressed, FIG. 2 illustrates the comparison of a numerical solution with an analytical solution boundary, wherein the scatter points in the figure are pendulum response distributions identified by a Monte Carlo method calculation for a pendulum response numerical model, the triangular scatter point area is a pure rotation area obtained by the numerical solution, and the two black boundaries are obtained by twoThe resolution solution boundary identified by the value, i.e., the range of pure rotational motion identified by the resolution solution. The lower side edge corresponds to the figureIs the boundary between the pure rotation state and the static state of the pendulum body, and the upper side edge corresponds toIs the boundary between the motion states with larger response potential such as pure rotation and chaotic motion. If only the pendulum response range is evaluated, only the following needs to be consideredThe lower bound takes a value.
In the scene of no-load calculation, the pure rotation boundary corresponds toThe value is not changed obviously due to the change of the design parameters of the device, and only the results of numerical solution and analytic solution are compared to finishAnd (3) calibration (rotation boundary analysis) can use analytic solution to perform no-load response calculation. Compared with the implicit expression of a numerical simulation method and the requirement of simulation time length of thousands of seconds, the analysis method is used for displaying the expression and only calculating one wave period, and the efficiency is higher. This method replaces the numerical solution method in the early stages of device optimization toAnd the response distribution of the pendulum body when in no-load is evaluated with higher efficiency, so that the optimization iteration speed is improved.
The method is an analysis method based on pendulum dynamics equation, and is only suitable for pendulum under no-load state.
And calculating the motion response and the energy obtaining condition of the pendulum body under different wave heights and period combinations by combining the two methods, and obtaining the response distribution (such as average angular velocity) of the pendulum body. Optimizing the energy obtaining of the pendulum body in a traversing load mode, and calculating the energy obtaining distribution of the pendulum body on a parameter space formed by wave height and period.
The foregoing description is only a preferred embodiment of the present invention and is not intended to limit the present invention, but although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the technical solutions described in the foregoing embodiments, or that equivalents may be substituted for part of the technical features thereof. Any modification, equivalent replacement, variation, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The energy obtaining analysis method of the parameter pendulum type wave energy device is characterized by comprising the following steps of:
constructing a hydrodynamic numerical model of a device with the coupling of the multi-degree-of-freedom floating body and the catenary mooring system;
simulating the motion time-course response of the floating body under the regular waves according to the period and wave height distribution of the target sea area thrown by the wave energy device, calculating the response amplitude and the respective degree phase difference of the floating body through a hydrodynamic force numerical model, and interpolating the calculation result;
when the wave energy device is excited by wind and waves to generate multi-degree-of-freedom motion at sea, the relative motion between the pendulum body and the floating body is expressed as a pendulum body dynamics equation as follows:
wherein, theta,And->Is the angular displacement, angular velocity and angular acceleration of the pendulum motion, l is the distance between the pendulum mass center and the rotation axis, M is the pendulum mass, J is the moment of inertia of the pendulum about the mass center, (Ml) 2 +J) is the moment of inertia of the pendulum about the axis of rotation, b is the linear damping to which the pendulum motion is subjected, +.>Is the bow acceleration of the floating body, the gram x And jowar (r) y Two components of gravity acceleration in the plane of pendulum motion; a, a x And a y Using the formula->Calculated, where->And->The heave acceleration and the heave acceleration of the floating body, respectively,/->And->Respectively the pitch angular acceleration and the roll angular acceleration of the floating body, d represents the vertical distance between the mass center of the floating body and the rotating plane of the pendulum body, and d is a positive value when the rotating plane is higher than the mass center of the floating body;
calculating and interpolating by using a hydrodynamic numerical model to obtain response amplitude, phase difference and corresponding wave period data, solving a pendulum dynamics equation, calculating motion time response of the pendulum under different wave heights and period combinations, obtaining distribution of pendulum response on a wave parameter space formed by the wave heights and the periods, optimizing pendulum energy acquisition in a traversing load mode, and calculating distribution of pendulum optimal energy acquisition on the wave parameter space;
and analyzing the response distribution and the energy obtaining distribution calculation result, and adjusting the mooring plane arrangement, the mooring design parameter, the floating body design parameter and the pendulum body design parameter of the device to realize iterative optimization of the device design parameter.
2. The method of claim 1, further comprising the step of analyzing the response profile of the pendulum at no load, wherein the damping tends to zero at no load, and wherein the approximate analytical formula of the pendulum dynamics equation is obtained by perturbation method as follows:
θ＝θ 0 +εθ 1 +ε 2 θ 2 ，
where ε is any small amount introduced by perturbation method, θ 0 Represents a linear term, θ 1 Represents first order term, θ 2 Representing a second order term;
introduction of parameter R av Defining the applicable boundary of the approximate analytical formula:
wherein R is av The angular velocity of the pendulum body in one period is relatively extremely poor,is the maximum value of angular velocity +.>Is the minimum value of the angular velocity, +.>Is the average value of the angular velocity;
at idle loadWhen calculating, comparing the results of the numerical solution and the analytic solution to finish R av And (3) the calibration of the system can be carried out by using an analytic solution to carry out no-load response calculation.
3. The method of claim 1, wherein the hydrodynamic numerical model is constructed using hydrodynamic computing software including, but not limited to WEC-Sim, openFOAM, AQWA, FLOW-3D.
4. The method of claim 1, wherein the response amplitude is interpolated by a wave height direction interpolation and a period direction interpolation, wherein the wave height direction interpolation is performed by: selecting two data points with the same period, taking the wave height as weight, and carrying out linear interpolation on the response amplitude of any point between the two data points;
the processing mode of the periodic direction interpolation is as follows: and selecting two data points with the same wave height, and linearly interpolating the response amplitude of any point between the two data points by taking the period distance as the weight.
5. The method according to claim 1, wherein the interpolation of the data of the phase difference is performed only in the period direction, and the wave height direction is regarded as a constant value; the processing mode of the interpolation of the period direction is as follows: the phase difference of any point between two data points is linearly interpolated by taking the period distance as the weight.
6. The method of claim 1, wherein when the response amplitude, the phase difference and the corresponding wave period data obtained by hydrodynamic calculation and interpolation are utilized, a floating body multi-degree-of-freedom motion time sequence with any duration can be constructed, and the time sequence of parameters required by a pendulum dynamics equation is calculated according to the time sequence, wherein the time sequence comprises x ，ɡ y ，a x ，a y Andsolving pendulum dynamics through a fourth-order Dragon-Gregory tower methodEquation (d).
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