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Volume 30, Issue 5
Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow

Ankita Mittal, Bajrang Sharma & Sharath S. Girimaji

Commun. Comput. Phys., 30 (2021), pp. 1323-1345.

Published online: 2021-10

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  • Abstract

The fundamental nature of flow instability in wall bounded flows changes with Mach number. The objectives of this study are two-fold, (i) compute the instability modes in high Mach number Poiseuille flows using linear stability analysis (LSA) and, (ii) perform direct numerical simulations (DNS) of the instability development using a solver based on gas kinetic method (GKM) for the purpose of code validation by comparison against LSA results. The LSA and DNS are performed for the case of Poiseuille flow over a range of Mach numbers – from moderately supersonic to hypersonic speeds. First, LSA is employed to identify the most unstable mode over the range of Mach numbers. We then perform two sets of GKM-DNS to corroborate the LSA results over the Mach number range. In the first set of simulations, the background field is initially perturbed with the most unstable mode identified by LSA and the evolution is monitored. It is shown that GKM-DNS accurately captures the exponential growth in kinetic energy for all Mach numbers. The second set of GKM-DNS simulations is performed by superposing the background pressure field with random initial perturbations. After an initial transient period, the modes predicted by LSA dominate the DNS flow field evolution. The wave-vector and mode shapes of the dominant instability are well replicated by GKM-DNS at each Mach number. These insights in the linear regime of high speed Poiseuille flow and validation of GKM are important for understanding and simulating wall bounded flows.

  • AMS Subject Headings

76F06, 76K05, 76N99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1323, author = {Mittal , AnkitaSharma , Bajrang and Girimaji , Sharath S.}, title = {Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1323--1345}, abstract = {

The fundamental nature of flow instability in wall bounded flows changes with Mach number. The objectives of this study are two-fold, (i) compute the instability modes in high Mach number Poiseuille flows using linear stability analysis (LSA) and, (ii) perform direct numerical simulations (DNS) of the instability development using a solver based on gas kinetic method (GKM) for the purpose of code validation by comparison against LSA results. The LSA and DNS are performed for the case of Poiseuille flow over a range of Mach numbers – from moderately supersonic to hypersonic speeds. First, LSA is employed to identify the most unstable mode over the range of Mach numbers. We then perform two sets of GKM-DNS to corroborate the LSA results over the Mach number range. In the first set of simulations, the background field is initially perturbed with the most unstable mode identified by LSA and the evolution is monitored. It is shown that GKM-DNS accurately captures the exponential growth in kinetic energy for all Mach numbers. The second set of GKM-DNS simulations is performed by superposing the background pressure field with random initial perturbations. After an initial transient period, the modes predicted by LSA dominate the DNS flow field evolution. The wave-vector and mode shapes of the dominant instability are well replicated by GKM-DNS at each Mach number. These insights in the linear regime of high speed Poiseuille flow and validation of GKM are important for understanding and simulating wall bounded flows.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0053}, url = {http://global-sci.org/intro/article_detail/cicp/19931.html} }
TY - JOUR T1 - Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow AU - Mittal , Ankita AU - Sharma , Bajrang AU - Girimaji , Sharath S. JO - Communications in Computational Physics VL - 5 SP - 1323 EP - 1345 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2021-0053 UR - https://global-sci.org/intro/article_detail/cicp/19931.html KW - Gas kinetic method, compressible linear stability theory, hypersonic flows. AB -

The fundamental nature of flow instability in wall bounded flows changes with Mach number. The objectives of this study are two-fold, (i) compute the instability modes in high Mach number Poiseuille flows using linear stability analysis (LSA) and, (ii) perform direct numerical simulations (DNS) of the instability development using a solver based on gas kinetic method (GKM) for the purpose of code validation by comparison against LSA results. The LSA and DNS are performed for the case of Poiseuille flow over a range of Mach numbers – from moderately supersonic to hypersonic speeds. First, LSA is employed to identify the most unstable mode over the range of Mach numbers. We then perform two sets of GKM-DNS to corroborate the LSA results over the Mach number range. In the first set of simulations, the background field is initially perturbed with the most unstable mode identified by LSA and the evolution is monitored. It is shown that GKM-DNS accurately captures the exponential growth in kinetic energy for all Mach numbers. The second set of GKM-DNS simulations is performed by superposing the background pressure field with random initial perturbations. After an initial transient period, the modes predicted by LSA dominate the DNS flow field evolution. The wave-vector and mode shapes of the dominant instability are well replicated by GKM-DNS at each Mach number. These insights in the linear regime of high speed Poiseuille flow and validation of GKM are important for understanding and simulating wall bounded flows.

Ankita Mittal, Bajrang Sharma & Sharath S. Girimaji. (2021). Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow. Communications in Computational Physics. 30 (5). 1323-1345. doi:10.4208/cicp.OA-2021-0053
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