| Autor: |
Frey, Christian, Backhaus, Jan, Ashcroft, Graham, Geiser, Georg, Winhart, Benjamin, Stueer, Heinrich |
| Zdroj: |
Journal of Turbomachinery; 20240101, Issue: Preprints p1-10, 10p |
| Abstrakt: |
In this paper, approaches to implement implicit pseudotime marching for harmonic balance are studied. We first give a motivation for using pseudotime stepping as a solution technique. It turns out that, when discretization errors are neglected, the harmonic balance solution converges to a stable periodic flow, provided that the initial solution is sufficiently close to that solution. This motivates the use of a robust implicit pseudotime marching approach. A central question is which simplifications of the residual Jacobian are appropriate in terms of the overall efficiency and robustness of the solver. As has been shown in the literature, the spectral time-derivative operator should be taken into account in the implicit system. On the other hand, the linearization of the flow residual can be simplified to a certain extent, especially if the system is solved in the frequency domain. In this paper, we show that, up to terms which scale with the amplitude of the disturbances, the linear system matrix is the sum of a scalar diagonal and a block diagonal matrix with identical blocks for each harmonic. We show that when the unsteadiness is small, the nonlinear coupling terms can be neglected in the implicit solver and the resulting special matrix structure can be exploited to massively speed up the solver. In contrast, when a strong disturbance is simulated, this simplification can lead to significant losses in robustness. Our findings are illustrated by means of the forced response analysis of a transonic compressor in off-design conditions. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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