Research And Application Of Proper Orthogonal Decomposition Method For Rotating Flow Field

The rotating flow phenomenon is a very important physical movement form in modern scientific research and engineering practical application.It is closely related to research fields such as aircraft propulsion system,energy conversion system,biological blood rheology cycle and earth climate ecological structure.However,the traditional computational fluid dynamics(CFD)will severely limit the efficiency of numerical calculations and the lack of further analysis of the rotating flow phenomenon,especially in such large-scale analysis of the field of optimization calculations and the vortex structure of the rotating flow field.Therefore,while ensuring the validity of the calculation,how to promote the depth and efficiency of the CFD analysis of the rotating flow has become an urgent problem.This paper uses the advantage of proper orthogonal decomposition(POD)method with efficient and hierarchical to propose the calculation forms of main flow mode,flow low-order reconstruction and prediction for important physical parameters of rotating flow field.On this basis,the POD algorithm for the extended non-time parametric dimension is further proposed.Finally,based on the Gappy-POD method,an approximation algorithm for iterative optimization of the rotating flow field is also proposed.It provides such favorable support for a more comprehensive understanding of the physical mechanisms and the application of POD methods in complex rotational flows.The main research contents of this paper are as follows:(1)Based on the POD-Sirovich method,a POD flow modal correlation algorithm for important physical parameters of the rotating flow field is proposed.Combined with the time-domain discrete FFT algorithm,the numerical calculation form of the spectral transformation of the POD time coefficient of the flow parameters related to the rotating flow field is given.The realization process of POD modal correlation analysis of rotating flow field is also given and verified by a case.Then,using the full-order numerical results corresponding to the fully developed rotational flow in the corresponding coordinate system of the specified example,the flow modality,essential information content characteristics and time-frequency characteristics of the relevant parameters are analyzed.(2)Based on the POD modal and time coefficient correlation algorithm,a high-precision low-order reconstruction method and implementation process describing the global and feature points of the rotational flow are given,and the reconstruction deviation is quantitatively described.The global and local deviation of reconstruction using different modal orders are studied by numerical example.(3)The cubic spline interpolation method is used to give a quantitative description method of POD high-precision low-order prediction form and prediction deviation of rotating flow.The example shows that the accuracy of flow field prediction based on POD method is higher than that based on linear interpolation.For example,in the prediction of the radial velocity field,the maximum deviation value of the tip-to-loop region of the linear interpolation method is about 2.2% higher than that POD prediction of the first 3 orders,and there is an order of magnitude difference for such highest deviation level of the first 15 orders.(4)Based on the POD conventional algorithm,an improved POD algorithm for the extended non-temporal parameter dimension in rotating flow is proposed.The flow modality,correlation coefficient and flow reconstruction,prediction and corresponding deviation analysis of the extended algorithm,as well as such implementation process,are given.For the complex three-dimensional flow,an equivalent reduced subsample based on the feature surface is proposed,which can greatly reduce the computational complexity of the corresponding complex CFD numerical model.Finally,the algorithm is used to calculate and analyze the complex rotating flow of the 3D wake of the new wind turbine impeller.(5)Using the Gappy-POD method of system missing data approximation and repair,the algorithm of iterative optimization design for rotating flow field is proposed.The formation of such snapshot space of the rotating flow field and the corresponding iteration based on Gappy-POD method,as well as the implementation process,are given.Finally,the algorithm is verified and analyzed by a simplified example of the rotating wheel hub flow field.The research work shows that the POD modal,reconstruction and predictive analysis algorithms proposed in this paper,as well as the extended POD algorithm for non-time parametric dimension and the Gappy-POD design optimization algorithm for rotating flow field are all reasonable and effective.These series of algorithms not only can improve the efficiency of large-scale numerical calculations in rotational flow analysis and the implementation of related optimization designs,but also helps to further analyze and understand complex rotational flow problems.Thus,it can provide a theoretical reference for the analysis and application of rotating flow in related engineering practice.