A complete rotor–stator coupling method for frequency domain analysis of turbomachinery unsteady flow

Abstract The paper presents a rotor–stator coupling method for analyzing unsteady flow field within multi-blade-row turbomachines using a frequency domain method. The coupling method is called time and space mode decomposition and matching method. It is based upon coordinate transformation and Fourier transformation to extract relevant time and space modes represented by frequency of unsteadiness, nodal diameter and Fourier coefficients. Detailed procedures together with relevant formula are established to identify the matching time and space modes across an interface and calculate corresponding mode coefficients. The mode coefficients are then matched across an interface with the use of a one-dimensional non-reflective implementation. To verify the correctness and effectiveness of the proposed interface treatment, a transonic compressor was used as a test case. The unsteady flow field within it was analyzed using a time domain time marching method to obtain the results as a reference. Then various frequency domain solutions with different resolution of unsteady frequencies were performed. Comparison of amplitude of different static pressure harmonics between frequency domain solutions and the reference time domain solution was made and discussed.

[1]  Guillaume Puigt,et al.  Non-uniform time sampling for multiple-frequency harmonic balance computations , 2013, J. Comput. Phys..

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

[3]  Earl H. Dowell,et al.  Harmonic balance methods applied to computational fluid dynamics problems , 2013 .

[4]  Xinrong Su,et al.  Implicit solution of time spectral method for periodic unsteady flows , 2009 .

[5]  W. Ning,et al.  Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines , 1998 .

[6]  Li He,et al.  Nonlinear Time and Frequency Domain Methods for Multirow Aeromechanical Analysis , 2014 .

[7]  Li He,et al.  Experimental and Computational Study of Oscillating Turbine Cascade and Influence of Part-Span Shrouds , 2009 .

[8]  H. D. Li,et al.  Blade Count and Clocking Effects on Three-Bladerow Interaction in a Transonic Turbine , 2003 .

[9]  A. Jameson,et al.  Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations , 1988 .

[10]  Marc Montagnac,et al.  Block-Jacobi Implicit Algorithms for the Time Spectral Method , 2008 .

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

[12]  A. Jameson,et al.  Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique , 2007 .

[13]  Earl H. Dowell,et al.  Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors , 2008, J. Comput. Phys..

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

[15]  Kivanc Ekici,et al.  Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor , 2010 .

[16]  Xiuquan Huang,et al.  Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System , 2017 .

[17]  Guillaume Dufour,et al.  Time-domain harmonic balance method for aerodynamic and aeroelastic simulations of turbomachinery flows , 2013 .

[18]  Graham Ashcroft,et al.  A Harmonic Balance Technique for Multistage Turbomachinery Applications , 2014 .

[19]  Andrea Arnone,et al.  Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method , 1993 .

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

[21]  Kenneth C. Hall,et al.  Unsteady Simulation of a 1.5 Stage Turbine Using an Implicitly Coupled Nonlinear Harmonic Balance Method , 2012 .

[22]  Charles Hirsch,et al.  The nonlinear harmonic method: from single stage to multi-row effects , 2013 .

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

[24]  R. Wells,et al.  Blading Aerodynamics Design Optimization With Mechanical and Aeromechanical Constraints , 2006 .

[25]  A. Jameson,et al.  Turbomachinery Applications with the Time Spectral Method , 2005 .