Large Eddy Simulation of Shear-Free Interaction of Homogeneous Turbulence with a Flat-Plate Cascade

In this paper we are interested in the distortion of homogeneous isotropic turbulence as it passes through a cascade of thin ∞at plates. Spatial large eddy simulation (LES) is conducted for a linear cascade composed of six plates. Because suppression of the normal component of velocity is the main mechanism of distortion, we neglect the presence of mean shear in the boundary layers and wakes, and allow slip velocity on the plate surfaces. We only enforce the zero normal velocity condition on the plates. This boundary condition treatment is motivated by rapid distortion theory (RDT) in which viscous efiects are neglected, however the present LES approach accounts for nonlinear and turbulence difiusion efiects by a sub-grid scale model. The normal Reynolds stresses and velocity spectra are analyzed ahead, within, and downstream of the cascade. Good agreement with predictions of rapid distortion theory in the region of its validity is obtained. Also, the normal Reynolds stress proflles are found to be in qualitative agreement with available experimental data.

[1]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[2]  S. Ragab,et al.  Large-eddy simulation of a mixing layer , 1991 .

[3]  D. M. Bushnell.  Body-turbulence interaction , 1984 .

[4]  William K. Blake,et al.  Turbulence Ingestion Noise, Part 2: Rotor Aeroacoustic Response to Grid-Generated Turbulence , 2002 .

[5]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[6]  D. Telionis,et al.  PARALLEL BLADE–VORTEX INTERACTION , 1998 .

[7]  Alexandre Corjon,et al.  Investigation of Ambient Turbulence Effects on Vortex Evolution using LES , 2000 .

[8]  Nigel Peake,et al.  Noise generation by the interaction between ingested turbulence and a rotating fan , 1998, Journal of Fluid Mechanics.

[9]  John Wojno,et al.  Turbulence Ingestion Noise, Part 1: Experimental Characterization of Grid-Generated Turbulence , 2002 .

[10]  P. Sagaut,et al.  LES-DNS: The Aeronautical and Defense Point of View , 1997 .

[11]  U. Piomelli,et al.  Subgrid-Scale Models for Compressible Large-Eddy Simulations , 2000, Theoretical and Computational Fluid Dynamics.

[12]  J. B. Perot,et al.  Shear-free turbulent boundary layers , 1994 .

[13]  Applications of a Fifth-Order Non-Centered Compact Scheme for Large Eddy Simulation , 2005 .

[14]  M. S. Howe.  Theory of Vortex Sound , 2002 .

[15]  Michel Roger,et al.  Effect of Angle of Attack and Airfoil Shape on Turbulence-Interaction Noise , 2005 .

[16]  Stewart A. L. Glegg,et al.  The response of a swept blade row to a three-dimensional gust , 1999 .

[17]  W. Devenport,et al.  Interaction of Large Scale Homogeneous Turbulence with a Cascade of Flat Plates , 2003 .

[18]  D. Gottlieb,et al.  The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes , 1993 .

[19]  Hafiz M. Atassi,et al.  Scattering of incident disturbances by an annular cascade in a swirling flow , 2004, Journal of Fluid Mechanics.

[20]  Miguel R. Visbal,et al.  High-Order-Accurate Methods for Complex Unsteady Subsonic Flows , 1999 .

[21]  Stephane Redonnet,et al.  Numerical simulations of fan interaction noise using a hybrid approach , 2005 .

[22]  C. Rowley,et al.  Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems , 2000 .

[23]  P. Durbin,et al.  Statistical Theory and Modeling for Turbulent Flows , 2001 .

[24]  Parviz Moin,et al.  Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence , 1995, Journal of Fluid Mechanics.

[25]  A New Characteristic Nonreflecting Boundary Condition for the Multidimensional Navier-Stokes Equations , 2005 .

[26]  Tim Colonius,et al.  MODELING ARTIFICIAL BOUNDARY CONDITIONS FOR COMPRESSIBLE FLOW , 2004 .

[27]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[28]  William J. Devenport,et al.  Leading edge noise , 2006 .

[29]  G.,et al.  TOWARD THE LARGE-EDDY SIMULATION OF COMPRESSIBLE TURBULENT FLOWS , 2022 .

[30]  Xiaolin Zhong,et al.  High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition , 1998 .

[31]  Miguel R. Visbal,et al.  On the use of higher-order finite-difference schemes on curvilinear and deforming meshes , 2002 .

[32]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[33]  J. M. R. Graham.  The effect of a two-dimensional cascade of thin streamwise plates on homogeneous turbulence , 1998 .

[34]  Jan Werner Delfs,et al.  An overlapped grid technique for high resolution CAA schemes for complex geometries , 2001 .

[35]  F. Farassat,et al.  Broadband Noise Predictions for an Airfoil in a Turbulent Stream , 2003 .

[36]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[37]  M. Carpenter,et al.  Fourth-order 2N-storage Runge-Kutta schemes , 1994 .

[38]  S. Corrsin,et al.  Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence , 1971, Journal of Fluid Mechanics.

[39]  K M Case,et al.  NUMERICAL SIMULATION OF TURBULENCE , 1973 .

[40]  M. Nallasamy,et al.  A Computational Aeroacoustic Prediction of Discrete-Frequency Rotor-Stator Interaction Noise - a Linear Theory Analysis , 2004 .

[41]  William J. Devenport,et al.  The Interaction of Large Scale Turbulence with a Cascade of Flat Plates , 2003 .

[42]  J.M.R. Graham,et al.  Acoustic effects due to turbulence passing through cascades of thin aerofoils , 1986 .

[43]  Thomas Hagstrom,et al.  Accurate Radiation Boundary Conditions for the Linearized Euler Equations in Cartesian Domains , 2002, SIAM J. Sci. Comput..

[44]  R. R. Mankbadi,et al.  Evaluation of Boundary Conditions for the Gust-Cascade Problem , 1998 .

[45]  Simulating the Interaction of a Three-Dimensional Vortex with Airfoils Using CAA , 2001 .

[46]  Hoong Thiam Toh,et al.  Large Eddy Simulation of Supersonic Twin-Jet Impingement Using a Fifth-Order WENO Scheme , 2004 .

[47]  Jan Werner Delfs,et al.  Leading edge noise studies using CAA , 1999 .

[48]  G. S. Patterson,et al.  Numerical simulation of turbulence , 1972 .

[49]  J. Larssen.  Large scale homogeneous turbulence and interactions with a flat-plate cascade , 2005 .

[50]  The Response of a Flat Plate Cascade to Incident Vortical Waves , 2006 .

[51]  A I Tolstykh.  High Accuracy Non-Centered Compact Difference Schemes for Fluid Dynamics Applications , 1994 .

[52]  Michael B. Giles,et al.  Nonreflecting boundary conditions for Euler equation calculations , 1990 .