Nonlinear Modeling And Coherent Structure Analysis Method For Unsteady Flow Control

The improvement of the load of fans or compressors is an effective approach to developing a high thrust–weight ratio of aircraft engines.Moreover,a flow control technique is effective in overcoming the problem of flow separation caused by a high load.Unsteady flow control methods have received extensive attention in recent years given the low energy consumption required to achieve the same flow control performance.However,the mechanism of unsteady flow control remains unclear,thereby restricting its further development and application.To address this problem,in this study,a nonlinear model of unsteady flow control is established,and a spatio–temporal analysis method of coherent structures is developed.The mechanism of unsteady flow control is studied on the basis of the abovementioned approaches.In addition,a passive 3D unsteady flow control method is proposed for an air-driven ducted fan.This study mainly includes the following aspects:1)The theoretical basis of the unclear mechanism and imperfect reduced-order model of the unsteady flow control is initially discussed.A forced Duffing–Van der Pol two-equation nonlinear reduced-order model for unsteady flow control is established on the basis of 2D incompressible N–S equation,Stuart vortex row,and S–L theory.The selection of initial conditions and independent parameters of the model is discussed,and two indices,namely,maximum Lyapunov exponent and degree of entrainment,are introduced to evaluate the overall characteristics of the model.The chaotic motion described by the model without external excitation is then analyzed,and four phenomena under external excitations,namely,frequency dependence,threshold effect,location dependence,and synchronization effect,are addressed.Furthermore,the mechanism of unsteady flow control reflected by the model is discussed.2)A spatio–temporal DMD method is developed considering the shortcomings of existing analysis methods for coherent structures and on the basis of element rearrangement,block matrix,and re-decomposition techniques.This method,which is suitable for fully developed flow analysis,can be used to extract the streamwise spatial information of coherent structures and extend the information acquisition dimensions for unsteady flow fields.Moreover,the validity and applicability of this method are verified on the basis of a typical spatio–temporal function and an unsteady shear flow field.Moreover,the perturbation POD and SVD-based DMD methods are introduced to analyze the energy transfer of the flow field under control and solve the problem in which the rank deficient matrix cannot be decomposed,respectively.3)A study on the numerical and experimental data of pulsed jet flow control in a curved diffuser shows that appropriate control parameters of a pulsed jet can “accomplish a great task with minimal effort through clever maneuvers.” In addition,the frequency dependence,threshold effect,location dependence,and synchronization effect in the nonlinear reduced-order model occur in the actual flow field,thereby demonstrating the validity of the model.A unified mechanism framework composed of three main mechanisms,which relate to the advantages and unique phenomena of unsteady flow controls,are interpreted on the basis of the coherent structure analysis and the nonlinear reduced-order model.4)The air-driven ducted fan propulsion system is analyzed conceptually and thermodynamically.Then,an air-driven ducted fan is preliminarily designed,and its demand for highly efficient flow control methods is explained.Furthermore,for the air-driven highly loaded ducted fan,a passive 3D unsteady jet flow control method of strong engineering practicality is proposed.Its advantages,design method of the main parameters,and adaptivity under an off-design condition are analyzed or explained.On the basis of a simplified plane cascade,the corresponding numerical simulation and experiment are conducted to verify the validity and feasibility of the 3D unsteady jet flow control preliminarily.Finally,the potential and mechanism of the 3D unsteady jet flow control,which utilizes spanwise and streamwise vortices,are discussed.