Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique

A harmonic balance technique for modeling unsteady nonlinear e ows in turbomachinery is presented. The analysis exploits the fact that many unsteady e ows of interest in turbomachinery are periodic in time. Thus, the unsteady e ow conservation variables may be represented by a Fourier series in time with spatially varying coefe cients. This assumption leads to a harmonic balance form of the Euler or Navier ‐Stokes equations, which, in turn, can be solved efe ciently as a steady problem using conventional computational e uid dynamic (CFD) methods, including pseudotime time marching with local time stepping and multigrid acceleration. Thus, the method is computationally efe cient, at least one to two orders of…

• CM
  Carnegie Mellon University
• GR
  Glenn Research Center