Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition

Abstract The approach of proper orthogonal decomposition (POD) has been extensively adopted for fluid dynamics in fixed geometries. This technique is examined here for fluid flow with moving boundaries; in the context of cavitating and phase change flows, and fluid–membrane interaction. The purpose is to assess the capability of POD in extracting the salient features and offering a compact representation to the CFD solutions associated with boundary movement. The cavitating flow simulations are investigated to distill the effect of turbulence modeling, between the Launder–Spalding and a filter-based turbulence models. The lower-order eigenmodes of the flow field, for both turbulence models, show different flow structures and global parameters between higher and lower cavitation numbers. The effect of multi-timescales produced by the filter-based turbulence model is discerned by POD analysis. For 3-D, membrane wing flows, very few POD modes seem sufficient for accurate representation of the velocity field. However, reduced-order analysis of the aerodynamic performance, which is strongly dictated by pressure, may be coarsened by moving membrane dynamics. The flow with fusion is further considered for its solid–liquid phase front propagation. While few modes can sufficiently construct the flow field for the later interval of the flow, a larger number of POD modes are required to provide the flow scales for the initial part of the phase change process.

[1]  Wei Shyy,et al.  Filter-based unsteady RANS computations , 2004 .

[2]  Wei Shyy,et al.  Accurate Time-Dependent Computations and Reduced-Order Modeling for Multiphase Flows , 2004 .

[3]  Anuradha M. Annaswamy,et al.  Active closed-loop control of supersonic impinging jet flows using POD models , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[4]  R. Murray,et al.  On the choice of norm for modeling compressible flow dynamics at reduced-order using the POD , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  R. D. Prabhu,et al.  The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows , 2001 .

[6]  W. Shyy,et al.  A Pressure-Based Method for Turbulent Cavitating Flow Computations , 2001 .

[7]  Wei Shyy,et al.  Membrane wing aerodynamics for micro air vehicles , 2003 .

[8]  W. Shyy,et al.  Impact of Turbulence and Compressibility Modeling on Three-Dimensional Cavitating Flow Computations , 2003 .

[9]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[10]  Yongsheng Lian,et al.  Proper Orthogonal Decomposition for Three-Dimensional Membrane Wing Aerodynamics , 2003 .

[11]  A. Günther,et al.  Structure of the temperature field in a flow over heated waves , 2002 .

[12]  Wei Shyy,et al.  Interfacial dynamics‐based modelling of turbulent cavitating flows, Part‐1: Model development and steady‐state computations , 2004 .

[13]  W. Shyy,et al.  Interfacial dynamics‐based modelling of turbulent cavitating flows, Part‐2: Time‐dependent computations , 2004 .

[14]  Julio Soria,et al.  Particle image velocimetry measurements of a backward-facing step flow , 2002 .

[15]  Joel Delville,et al.  Pressure velocity coupling in a subsonic round jet , 2000 .

[16]  Roi Gurka,et al.  Vorticity characterization in a turbulent boundary layer using PIV and POD analysis , 2001 .

[17]  Paul G. A. Cizmas,et al.  Proper Orthogonal Decomposition of Turbine Rotor-Stator Interaction , 2003 .

[18]  John L. Lumley,et al.  Low-dimensional models for flows with density fluctuations , 1997 .

[19]  Remi Manceau,et al.  Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model , 2001, Journal of Fluid Mechanics.

[20]  Ekkehard W. Sachs,et al.  Managing POD models by optimization methods , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[21]  David J. Lucia,et al.  Domain Decomposition for Reduced-Order Modeling of a Flow with Moving Shocks , 2002 .

[22]  Bérengère Podvin,et al.  On the adequacy of the ten-dimensional model for the wall layer , 2001 .

[23]  Wei Shyy,et al.  Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows , 2002 .

[24]  M. Michard,et al.  Flow analysis of two-dimensional pulsed jets by particle image velocimetry , 2001 .

[25]  Jean-Paul Bonnet,et al.  Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition , 1999, Journal of Fluid Mechanics.

[26]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[27]  S. Arunajatesan,et al.  Development of low dimensional models for control of compressible flows , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..