Session: 37-04 Unsteady Flow Modeling

Paper Number: 81564

81564 - An Approximate Time Domain Nonlinear Harmonic Method for Analyzing Unsteady Flows With Multiple Fundamental Modes 

Axial flow turbomachines often have many blade rows and the blade counts are often different due to aeroelatsic consideration. As a consequence, the flow fields of middle blade rows are subjected to unsteady disturbances of at least two fundamental frequencies. This poses a great challenge to efficient analysis of the unsteady flows using the time domain harmonic balance method. With two or more fundamental frequencies, it is no longer viable to solve the unsteady flow equations at equally spaced time instants distributed over one of the fundamental period, as the inverse Fourier transform matrix is often ill conditioned.

Many efforts have been made in dealing with the challenge. These include the use of more time instants in an analysis, non-uniform time sampling, optimum time period, and so on. In this investigation, an approximate inverse Fourier transform matrix is constructed to alleviate the solution difficulty. Two different approximate inverse Fourier transform matrices will be proposed. The approximate inverse Fourier transform will allow separate and uniform time sampling for each fundamental frequency, leading to an approximate inverse Fourier transform matrix which is well-conditioned. Nevertheless, the proposed method will still maintain some level of coupling between unsteady flows of different frequencies. Numerical case studies will be provided to demonstrate the effectiveness of the proposed method in managing solution stability and capturing the coupling between flow components of different fundamental frequencies. The solution accuracy and efficiency of the proposed method will also be compared with those of an existing method that uses non-uniform time sampling.

Presenting Author: Dingxi Wang Northestern Polytechnical University

Presenting Author Biography: Dingxi is currently a professor and head of the department of fluid machinery at school of Power and Energy, Northwestern Polytechnical University. He obtained his Bachelor degree and Master degree in engineering at Northwestern Polytechnical University in 2002 and 2005 respectively and his PhD in computational fluid dynamics at University of Durham in 2009. He worked on turbomachinery aerodynamics and aeroelasticity as a senior engineer from July 2008 to May 2012 and a principal engineer from June 2012 to Dec 2015 at Siemens Industrial Turbomachinery Ltd in the UK. He joined Northwestern Polytechnical University in Jan 2016. He teaches undergraduate turbomachinery aerodynamics and postgraduate turbomachinery aeroelasticity. His research interest covers turbomachinery aerodynamics and aeroelasticity and related numerical methods development.

Authors:

Sen Zhang Northwestern Polytechnical University
Dingxi Wang Northestern Polytechnical University