Revisiting the Space-Time Gradient Method: A Time-clocking Perspective, High Order Difference Time Discretization and Comparison with the Harmonic Balance Method

Boqian Wang, Dingxi Wang, Mohammad Rahmati, Xiuquan Huang*

*Corresponding author for this work

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Abstract

This paper revisits the Space-Time Gradient (STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric Gauss-Seidel/Gauss-Seidel (LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-count-reduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.
Original languageEnglish
Pages (from-to)45-58
Number of pages14
JournalChinese Journal of Aeronautics
Volume35
Issue number11
Early online date6 Jun 2022
DOIs
Publication statusPublished - 1 Nov 2022

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