The Reduced-order Modelling And Control Of Mixing Layer Using Machine Learning

Mixing layer is a typical flow configuration which involves the fundamental study like coherent structures and practical problems like mixing enhancement,noise reduction,drag reduction,etc.The research on the mixing layer is of considerable engineering and theoretical interests.However,the mixing layer flow exhibits spatial-temporal multiscales with strongly nonlinearity.The numerical and experimental study will bring a large amount of data.These two aspects pose great challenges to the flow control and physical understanding of the mixing layer.This thesis conducts the reduced-order modelling and flow control study on the incompressible and supersonic mixing layer using a set of machine learning algorithms.We propose a reduced-order model based on machine learning,which can analyze the spatial modes,model and predict the dynamical behavior of the mixing layer.We propose a model-free control strategy based on machine learning,which has been successfully applied to the multi-frequency open-loop control and closed-loop control of the incompressible mixing layer.Finally,we employ the multi-frequency forcings to control the supersonic mixing layer aiming at mixing enhancement.Firstly,due to the drawback of cluster-based Markov model(CMM)on predicting the temporal evolution of a dynamical system,we propose the cluster-based network model(CNM).In CNM,the evolution of a dynamical system is modelled as transitions between the representative states.The transition motions are described by the direct transition probability matrix and the corresponding time-scales are given by the averaged transition time matrix.CNM is successfully applied to analyze the Lorenz system.The phase portrait of two wings is well resolved by 10 centroids and corresponding transitions.Five oscillating time periods are accurately predicted.We propose a machine learning control method using the linear genetic programming(LGP).The control law is formulated as a predefined structure.The determination of best control law is considered as an optimization problem minimizing the defined cost function.The best control law is searched in a pure data-driven manner aiming at the global minimum value.This method is successfully applied to the closed-loop control of three coupled oscillators.Then CMM and CNM are respectively employed to analyze an incompressible mixing layer.Only 10 centroids can identify the two events of the mixing layer: KelvinHelmholtz vortices(K-H)and vortex-pairing(VP).The dynamical evolution exhibits the cyclic motion inside K-H states and transitions between K-H and VP.CMM can accurately predict the probability distribution of each cluser.CNM can well predict the dynamical evolution with the time horizon of 100 time units.The CMM and CNM are respectively applied to a supersonic mixing layer with high Reynolds number.More complicated flow structures are well resolved and can be separated into two subsets: single/double vortex interaction(SDV)and multiple vortex interaction(MV).The evolution of flow structures and the related fluctuation energy is well revealed.The individual MV centroid carries much larger energy than that of SDV.However,the MV states are populated at a small probability and the overall energy only takes a small portion.The machine learning control is applied to an incompressible mixing layer.Aiming at mixing layer destabilization and stabilization,we conduct multi-frequency open-loop control and closed-loop control.With regards to the mixing layer destabilization,both the multi-frequency open-loop control and closed-loop control increase the fluctuation energy by a factor of 2.5.The best open-loop control law exhibits a square wave signal with two alternating duty cycles.The best closed-loop control law behaves a square wave with a fixed duty cycle.The corresponding flow structures show the advance instability and vortex-pairing nearly in the whole flow field.In the mixing layer stabilization,the best open-loop control law is a signal with double high frequencies,which can reduce the fluctuation energy by 23%.The best closed-loop control exhibits single high frequency achieving 26% reduction on the fluctuation energy.At this time,the K-H vortices appear in advance and keep their shapes without further vortex-pairing.The CNM analysis on the flow field forced by the best control laws for both mixing layer destabilization and stabilization reveal the strictly periodic motions between centroids.Inspired by the multi-frequency forcings on the mixing enhancement in the incompressible regime,we study the cavity-actuated supersonic mixing layer.Introducing a cavity in the upstream can generate self-sustained,high and multi-frequency forcings without any energy addition.The wake downstram the splitter plate is highly reduced.The mixing layer growth rate increases by 50%.The flow field presents the strict frequency-lock phenomenon with the same spectra as the cavity self-oscillation.CNM analysis indicates that multi-frequency forcings from the supersonic cavity flow significantly influence the flow structures of the centroids,correspondingly related to the wake mode and shear-layer mode of the cavity self-oscillation.Overally,introducing a cavity increases the energy fluctuation of the supersonic mixing layer by a factor of 3.27.Temporally,cavity-actuated supersonic mixing layer exhibits the periodic transition between 10 representative states accompanying the periodic energy fluctuation.In the appendices,we discuss how to determine the optimal number of the cluster.Then the CNM is applied to analyze the three-dimensional actuated turbulent boundary layer.Finally,we compare and analyze the CNM and POD.