Structured Input-Output Analysis of Compressible Plane Couette Flow

Bhattacharjee, Diganta; Mushtaq, Talha; Seiler, Peter; Hemati, Maziar S.

doi:10.2514/6.2023-1984

Cited by 5 publications

(5 citation statements)

References 20 publications

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“…Applications of this framework to wider parameter regimes and flow configurations such as compressible flows [53] are directions of ongoing work. Extracting corresponding optimal forcing and response mode shapes [41] are expected to provide insights for flow control applications.…”

Section: Optimal Perturbation Structurementioning

confidence: 99%

A structured input-output approach to characterizing optimal perturbations in wall-bounded shear flows

Liu¹,

Sheng²,

Rath³

et al. 2023

Preprint

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This work builds upon recent work exploiting the notion of structured singular values to capture nonlinear interactions in the analysis of wallbounded shear flows. In this context, the structured uncertainty can be interpreted in terms of the flow structures most likely to be amplified (the optimal perturbations). Here we further analyze these perturbations through a problem reformulation that decomposes this uncertainty into three components associated with the streamwise, wall-normal and spanwise velocity correlations. We then demonstrate that the structural features of these correlations are consistent with nonlinear optimal perturbations and results from secondary stability analysis associated with streamwise streaks. These results indicate the potential of structured input-output analysis for gaining insight into both linear and nonlinear behavior that can be used to inform sensing and control strategies for transitional wall-bounded shear flows.

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Section: Optimal Perturbation Structurementioning

confidence: 99%

A structured input-output approach to characterizing optimal perturbations in wall-bounded shear flows

Liu¹,

Sheng²,

Rath³

et al. 2023

Preprint

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show abstract

“…Recently, SSV has emerged as a means of performing a structured input-output analysis of transitional shear flows to study instability mechanisms. [14][15][16][17] However, Liu et al [14][15][16] utilize MATLAB's Robust Control Toolbox, which does not allow for repeated full-blocks. The only cases handled by MATLAB are nonrepeated, complex full-blocks and the repeated (real or complex) scalars.…”

Section: Introductionmentioning

confidence: 99%

“…This repeated structure naturally arises in fluid dynamics and other convective systems. Recently, SSV has emerged as a means of performing a structured input‐output analysis of transitional shear flows to study instability mechanisms 14–17 . However, Liu et al 14–16 utilize MATLAB's Robust Control Toolbox, which does not allow for repeated full‐blocks.…”

Section: Introductionmentioning

confidence: 99%

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Structured singular value of a repeated complex full‐block uncertainty

Mushtaq,

Bhattacharjee,

Seiler

et al. 2024

Intl J Robust & Nonlinear

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The structured singular value (SSV), or , is used to assess the robust stability and performance of an uncertain linear time‐invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full‐blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full‐blocks. This specific class of uncertainty is relevant for the input‐output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full‐blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full‐blocks. The upper bound can be formulated as a semi‐definite program (SDP), which we solve using a standard interior‐point method to compute optimal scaling matrices associated with the repeated full‐blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full‐block structure.

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