The Parametrized Reduced Order Modeling For Unsteady Flows Based On Proper Orthogonal Decomposition

Computational fluid dynamics(CFD)method is the main tool for researchers to analyze complex flows in depth.However,with the complexity and refinement of the research object,it often takes a lot of time and computational resources to use traditional CFD simulation,especially in parameter optimization,flows control and other research designs,which requires multiple simulations in the parameter domain.Therefore,the reduced order modeling for complex flows has gradually become a research hotspot in the fields of mechanics,machinery and other engineering technologies.Unsteady aerodynamic force is the main external excitation of the blade to high circumferential fatigue damage.However,due to the complex flow in the aero-engine,with the coexistence of multiple nonlinear factors,multi-physics field coupling and other characteristics,it is difficult to carry out efficient and accurate flow analysis and simulation calculations.The development of efficient and accurate reduced-order methods for solving large-scale flow problems can help achieve in-depth analysis and prediction of complex transient flow problems.In this paper,parametrized reduced order models(PROMs)for parametric transient flows is investigated.Based on the POD method,an in-depth theoretical study is conducted to address the limitations of its existing applications.Based on the concept of separation of spatial,temporal,and parametric variables,new PROMs are proposed to improve the prediction stability and modeling efficiency.The main research contents and results are as follows:Latin hypercube sampling(LHS)is used to design the parameter domain of the flow field,and its corresponding numerical solutions are obtained by CFD.All these solutions integrate a database for feature extraction of the flow problems.For the global time reduced bases solution problem of the large-scale flow field,a Sub-block POD(SBP)basis solution strategy is proposed to achieve the solution on a limited computing platform.To improve stability of PROMs,this paper proposes a reduced method based on the independent solution of POD space-time bases(IST-ROM).This method captures the spatial and temporal characteristics of flows in the form of POD reduced bases,and characterizes the influence of parameters on the flows in the form of reduced coefficients.The global spatial bases is obtained directly by the POD method,while the global temporal base is obtained by the SBP method.The mapping relationship between the parameters and the reduced order coefficients is constructed by gaussian process regression(GPR).According to the prediction results,IST-ROM has a very high prediction accuracy,with the field average prediction error controlled at less than 4% and the maximum error on the field controlled at about 10%.Although the SBP method makes it possible to solve the global temporal bases for large scale complex flows,the efficiency is still limited.In this paper,we also propose the idea of data reduction based on the combination of discrete Fourier transform(DFT)and POD methods.Firstly,the spatial features of the flow field are captured in the form of POD bases,and then the temporal features are captured in the form of trigonometric bases on the low-order data.Finally,the mapping relationship between the parameters and the reduced order coefficients is obtained by artificial neural networks(ANN)algorithm.Thus the modeling efficiency of POD-DFT-ANN-ROM(PDA-ROM)is improved by orders of magnitude compared with that of IST-ROM.According to the prediction results,the field average prediction error of PDA-ROM is reduced below 8%,and the maximum error on the field is about 20%,which is slightly worse than that of IST-ROM.This paper proposes a PROM of transient flow field with POD spatio-temporal bases recursive solution(PST-ROM)that combines the advantages of both methods.PST first obtains the global spatial bases by the POD method,and then uses the POD method again to obtain the temporal bases on the reduced-order data.The spatio-temporal bases are all in the form of POD bases to ensure the high accuracy of feature capture,while the recursive solution idea avoids the difficulty of solving the high-dimensional global temporal bases.Finally,the relationship between the flow parameters and the reduced coefficients is established by GPR.According to the validation results of the algorithm,PST-ROM has similar prediction accuracy as IST-ROM and similar modeling efficiency as PDA-ROM.