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Computation of the Evolution of Tollmien–Schlichting Waves Based on Global Stability Analysis

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Abstract

A computational methodology is presented for calculating the spatial evolution of Tollmien–Schlichting (T–S) waves and their amplitude growth-rate factor in substantially nonparallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier–Stokes (N–S) equations. Three stages of this methodology (obtaining a stationary solution, as well as carrying out a global stability analysis and its postprocessing) are described, and the results are presented of its validation based on the comparison of the results of calculating the characteristics of T–S waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to nonparallel flows.

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Funding

This study was supported by the Russian Science Foundation (grant no. 22-11-00041). All the calculations were performed on the high-performance Tornado cluster of Peter the Great St. Petersburg Polytechnic University (http://www.spbstu.ru).

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    K. V. Belyaev, A. V. Garbaruk, V. D. Golubkov & M. Kh. Strelets

Authors
  1. K. V. Belyaev
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  2. A. V. Garbaruk
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  3. V. D. Golubkov
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  4. M. Kh. Strelets
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Correspondence to M. Kh. Strelets.

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Belyaev, K.V., Garbaruk, A.V., Golubkov, V.D. et al. Computation of the Evolution of Tollmien–Schlichting Waves Based on Global Stability Analysis. Math Models Comput Simul 16, 29–38 (2024). https://doi.org/10.1134/S2070048224010034

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  • DOI: https://doi.org/10.1134/S2070048224010034

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