Harmonic Solution of Unsteady Flow Around Blades with Separation

Conventional time-linearized harmonic methods using a pseudo-time-marching technique often exhibit solution divergence behavior for highly loaded conditions with flow separation. This is attributed to the growth of linear instabilities associated with small-scale limit-cycle oscillations of the base-flow state. In the present work, an alternative harmonic formulation is adopted for modeling harmonic disturbances with an intention to harness nonlinearity as a means of stabilization while achieving the same computational efficiency as a conventional time-linearized model. One unsteady complex-number harmonic solution is made equivalent to two real-number steady-flow solutions with simple source terms, whereas nonlinearity is retained in the convective fluxes of discretized flow equations. The validity and effectiveness of the method has been demonstrated in comparisons with semi-analytical results for a flat plate cascade and experimental data for low- and high-speed turbine cascades. The computational results show that the present harmonic solver is robust with much improved convergence over the conventional time-linearized model. It is shown that converged solutions can be effectively obtained using the present method for unsteady flows with large-scale separation.

[1]  Mehmet Imregun,et al.  Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids , 2001 .

[2]  T. Chen,et al.  Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach , 2001 .

[3]  G. A. Gerolymos,et al.  Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations , 2002 .

[4]  Li He,et al.  Some Modeling Issues on Trailing-Edge Vortex Shedding , 2001 .

[5]  J. J. Adamczyk,et al.  Unsteady flow in a supersonic cascade with subsonic leading-edge locus , 1978 .

[6]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

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

[8]  Frank Lane,et al.  System Mode Shapes in the Flutter of Compressor Blade Rows , 1956 .

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

[10]  Li He,et al.  Unsteady flow in oscillating turbine cascades. Part 1: Linear cascade experiment , 1998 .

[11]  Li He,et al.  Unsteady flow in oscillating turbine cascades : Part 2-Computational study , 1998 .

[12]  Howard P. Hodson,et al.  ON THE INTERPRETATION OF MEASURED PROFILE LOSSES IN UNSTEADY WAKE-TURBINE BLADE INTERACTION STUDIES , 1998 .

[13]  Li He,et al.  Computation of unsteady flows around oscillating blades using linear and nonlinear harmonic Euler methods , 1997 .

[14]  Klaus A. Hoffmann,et al.  Fundamental Equations of Fluid Mechanics , 1996 .

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

[16]  A. Jameson.  Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[17]  Jeffrey P. Thomas,et al.  Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique , 2002 .

[18]  Kenneth C. Hall,et al.  A Time-Linearized Navier–Stokes Analysis of Stall Flutter , 2000 .

[19]  Juan J. Alonso,et al.  Application of a Non-Linear Frequency Domain Solver to the Euler and Navier-Stokes Equations , 2002 .

[20]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[21]  Torsten Fransson,et al.  Viscous and Inviscid Linear/Nonlinear Calculations Versus Quasi-Three-Dimensional Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration , 1999 .

[22]  Edward M. Greitzer,et al.  Effects of Stator Pressure Field on Upstream Rotor Performance , 1999 .

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

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