Linearized Euler predictions of unsteady aerodynamic loads in cascades

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) flow plus an unsteady, harmonically varying, small-disturbance flow. Linear variable coefficient equations describe the small-disturbance behavior of the flow and are solved using a pseudotime time-marching Lax-Wendroff scheme. For the blade-motion problem, a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition

[1]  P. Rajan,et al.  A comparative study of three techniques for estimation of turbulence energy spectrum , 1992 .

[2]  Man Mohan Rai,et al.  Three-Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction; Part I1 - Results , 1989 .

[3]  Michael B. Giles,et al.  Calculation of Unsteady Wake/Rotor Interaction , 1987 .

[4]  Hafiz M. Atassi,et al.  Unsteady disturbances of streaming motions around bodies , 1989, Journal of Fluid Mechanics.

[5]  Kenneth C. Hall,et al.  A Reduced Order Model of Unsteady Flows in Turbomachinery , 1995 .

[6]  Howard P. Hodson,et al.  An Inviscid Blade-to-Blade Prediction of a Wake-Generated Unsteady Flow , 1985 .

[7]  Kenneth C. Hall,et al.  Deforming Grid Variational Principle for Unsteady Small Disturbance Flows in Cascades , 1993 .

[8]  Antony Jameson,et al.  Computation of unsteady transonic flows by the solution of Euler equations , 1988 .

[9]  Russ D. Rausch,et al.  Euler flutter analysis of airfoils using unstructured dynamic meshes , 1989 .

[10]  David L. Whitfield,et al.  Three-dimensional unsteady Euler solutions for propfans and counter-rotating propfans in transonic flow , 1987 .

[11]  John Batina,et al.  Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis , 1989 .

[12]  Dennis L. Huff,et al.  Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme , 1991 .

[13]  Robert Haimes,et al.  Validation of a Numerical Method for Unsteady Flow Calculations , 1993 .

[14]  K. Hall.  A deforming grid variational principle and finite element method forcomputing unsteady small disturbance flows in cascades , 1992 .

[15]  Oddvar Bendiksen,et al.  Transonic flutter analysis using the Euler equations , 1987 .

[16]  J. Batina.  UNSTEADY EULER ALGORITHM WITH UNSTRUCTURED DYNAMIC MESH FOR COMPLEX – AIRCRAFT AERODYNAMIC ANALYSIS , 1991 .

[17]  Kenneth C. Hall,et al.  Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations , 1992 .

[18]  Fernando Sisto,et al.  Numerical Computation of Nonstationary Aerodynamics of Flat Plate Cascades in Compressible Flow , 1976 .

[19]  Li He,et al.  An Euler Solution for Unsteady Flows Around Oscillating Blades , 1990 .

[20]  Joseph M. Verdon,et al.  A linearized unsteady aerodynamic analysis for transonic cascades , 1984, Journal of Fluid Mechanics.

[21]  Edward F. Crawley,et al.  Calculation of unsteady flows in turbomachinery using the linearized Euler equations , 1989 .

[22]  C. Wayne Mastin,et al.  TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies , 1977 .

[23]  N. Ron-Ho,et al.  A Multiple-Grid Scheme for Solving the Euler Equations , 1982 .

[24]  Joseph M. Verdon,et al.  Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades , 1982 .

[25]  Dana R. Lindquist,et al.  On the validity of linearized unsteady Euler equations with shock capturing , 1991 .

[26]  Derek Bradley,et al.  Turbulent burning velocities: a general correlation in terms of straining rates , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[27]  Kenneth C. Hall,et al.  EIGENANALYSIS OF UNSTEADY FLOW ABOUT AIRFOILS, CASCADES, AND WINGS , 1994 .

[28]  J. J. Adamczyk,et al.  Subsonic flow past an oscillating cascade with steady blade loading - Basic formulation , 1975 .

[29]  R. Ni.  A multiple grid scheme for solving the Euler equations , 1981 .