UNSTEADY SIMULATION OF A 1.5 STAGE TURBINE USING AN IMPLICITLY COUPLED NONLINEAR HARMONIC BALANCE METHOD
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The harmonic balance method implemented within STARCCM+
is a mixed frequency/time domain computational fluid dynamic
technique, which enables the efficient calculation of timeperiodic
flows. The unsteady solution is stored at a small number
of fixed time levels over one temporal period of the unsteady flow
in a single blade passage in each blade row; thus the solution
is periodic by construction. The individual time levels are coupled
to one another through a spectral operator representing the
time derivative term in the Navier-Stokes equation, and at the
boundaries of the computational domain through the application
of periodic and nonreflecting boundary conditions. The blade
rows are connected to one another via a small number of fluid
dynamic spinning modes characterized by nodal diameter and
frequency. This periodic solution is driven to the correct solution
using conventional (steady) CFD acceleration techniques, and
thus is computationally efficient. Upon convergence, the time
level solutions are Fourier transformed to obtain spatially varying
Fourier coefficients of the flow variables. We find that a small
number of time levels (or, equivalently, Fourier coefficients) are
adequate to model even strongly nonlinear flows. Consequently,
the method provides an unsteady solution at a computational
cost significantly lower than traditional unsteady time marching
methods.
The implementation of this nonlinear harmonic balance
method within STAR-CCM+ allows for the simulation of multiple
blade rows. This capability is demonstrated and validated
using a 1.5 stage cold flow axial turbine developed by the University
of Aachen. Results produced using the harmonic balance
method are compared to conventional time domain simulations
using STAR-CCM+, and are also compared to published experimental
data. It is shown that the harmonic balance method is
able to accurately model the unsteady flow structures at a computational
cost significantly lower than unsteady time domain
simulation.

Author Name: 
Chad H. Custer
Jonathan M. Weiss
Venkataramanan Subramanian
Author Company: 
CD-adapco
Products: 
Conference Location: 
Copenhagen
Conference Proceeding PDF: 
Conference Date: 
Thursday, June 11, 2015
Conference Name: 
ASME Turbo