Deforming Grid Variational Principle for Unsteady Small Disturbance Flows in Cascades

A variational method for computing unsteady subsonic flows in turbomachinery blade rows is presented. A variational principle that describes the harmonic small disturbance behavior of the full potential equations about a nonlinear mean flow is developed. Included in this variational principle is the effect of a deforming computational grid that conforms to the motion of vibrating airfoils. Bilinear isoparametric finite elements are used to discretize the variational principle, and the resulting discretized equations are solved efficiently using lower-upper decomposition. The use of a deforming computational grid dramatically improves the accuracy of the method since no error-producing extrapolation is required to apply the upwash boundary conditions or to evaluate the unsteady pressure on the airfoil surfaces

[1]  D. S. Whitehead.  A finite element solution of unsteady two-dimensional flow in cascades , 1990 .

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

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

[4]  D. Holmes,et al.  2D Linearized Harmonic Euler Flow Analysis for Flutter and Forced Response , 1993 .

[5]  F. O. Carta,et al.  Unsteady Gapwise Periodicity of Oscillating Cascaded Airfoils , 1982 .

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

[7]  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 .

[8]  M. Lighthill.  CIX. A Technique for rendering approximate solutions to physical problems uniformly valid , 1949 .

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

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

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

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

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

[14]  Kenneth C. Hall,et al.  Calculation of Unsteady Linearized Euler Flows in Cascades Using Harmonically Deforming Grids , 1993 .

[15]  H. Bateman,et al.  IRROTATIONAL MOTION OF A COMPRESSIBLE INVISCID FLUID. , 1930, Proceedings of the National Academy of Sciences of the United States of America.

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

[17]  Torsten Fransson,et al.  Aeroelasticity in Turbomachines - Comparison of Theoretical and Experimental Cascade Results Communication , 1986 .