Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique

Arathi K. Gopinath*, Edwin van der Weide, Juan J. Alonso, Antony Jameson, Kivanc Ekici, Kenneth C. Hall

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

88 Citations (Scopus)


In this paper, we propose an extension of the Harmonic Balance method for three-dimensional, unsteady, multi-stage turbomachinery problems modeled by the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. This time-domain algorithm simulates the true geometry of the turbomachine (with the exact blade counts) using only one blade passage per blade row, thus leading to drastic savings in both CPU and memory requirements. Modified periodic boundary conditions are applied on the upper and lower boundaries of the single passage in order to account for the lack of a common periodic interval for each blade row. The solution algorithm allows each blade row to resolve a specified set of frequencies in order to obtain the desired computation accuracy; typically, a blade row resolves only the blade passing frequencies of its neighbors. Since every blade row is setup to resolve different frequencies the actual Harmonic Balance solution in each of these blade rows is obtained at different instances in time or time levels. The interaction between blade rows occurs through sliding mesh interfaces in physical time. Space and time interpolation are carried out at these interfaces and can, if not properly treated, introduce aliasing errors that can lead to instabilities. With appropriate resolution of the time interpolation, all instabilities are eliminated. This new procedure is demonstrated using both two-and three dimensional test cases and can be shown to significantly reduce the cost of multi-stage simulations while capturing the dominant unsteadiness in the problem.

Original languageEnglish
Title of host publication45th AIAA Aerospace Sciences Meeting, Reno, Nevada, 8-11 January 2007
Subtitle of host publicationCollection of Technical Papers
PublisherAmerican Institute of Aeronautics and Astronautics
Number of pages20
ISBN (Electronic)978-1-62410-012-3
ISBN (Print)978-1-56347-890-1
Publication statusPublished - 3 Jul 2007
Externally publishedYes
Event45th AIAA Aerospace Sciences Meeting 2007 - Reno, United States
Duration: 8 Jan 200711 Jan 2007
Conference number: 45


Conference45th AIAA Aerospace Sciences Meeting 2007
Country/TerritoryUnited States

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