Adjoint algorithms for the Navier–Stokes equations in the low Mach number limit

Chandler, Gary; Juniper, Matthew P.; Nichols, Joseph W.; Schmid, Peter J.

doi:10.1016/j.jcp.2011.11.013

Cited by 47 publications

(51 citation statements)

References 42 publications

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“…A comparison of the direct and discrete approaches to compute direct and adjoint modes can be found in the recent work by Chandler et al [23]. Regarding adjoint methods for hydrodynamic stability, an overview of recent developments has been compiled by Luchini and Bottaro [24].…”

Section: Adjoint Problemmentioning

confidence: 99%

“…To quantify this overlap, the structural sensitivity [23,25] is computed, thus locating the most sensitive regions of the eigenvalue problem to localized feedback (internal changes in the system or wavemaker region). The structural sensitivity maps can be calculated using the expression S = ||qAdj|| • ||q|| with < qAdj.q >= 1> with q and q A dj as the direct and adjoint modes, where < •, • > denote the inner product defined by Equation (23) in Section 3.2, with its associated norm 11 • 11 = < •, • > 1 / 2 . The resulting sensitivity map for the NACA0012 is shown in Figure 14.…”

Section: Adjoint Analysis and Control Of The 2d Naca0012 Profile Undementioning

confidence: 99%

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Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Iorio

González

Ferrer

2014

Numerical Methods in Fluids

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SUMMARYIn this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier-Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications.The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data.In the transonic buffet case, the baseflow is computed using the Spalart-Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

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Section: Adjoint Problemmentioning

confidence: 99%

Section: Adjoint Analysis and Control Of The 2d Naca0012 Profile Undementioning

confidence: 99%

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Iorio

González

Ferrer

2014

Numerical Methods in Fluids

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“…However, we note that both continuous and discrete formulations should provide analogous results. Comparisons between discrete and continuous approaches may be found elsewhere [6,43]. In addition, we note that the stability analysis presented here does not assume any parallel or weakly parallel flow assumption as it is of global type.…”

Section: Discrete Linear Instability Analysismentioning

confidence: 99%

Sensitivity Analysis to Control the Far-Wake Unsteadiness Behind Turbines

2017

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Abstract:We explore the stability of wakes arising from 2D flow actuators based on linear momentum actuator disc theory. We use stability and sensitivity analysis (using adjoints) to show that the wake stability is controlled by the Reynolds number and the thrust force (or flow resistance) applied through the turbine. First, we report that decreasing the thrust force has a comparable stabilising effect to a decrease in Reynolds numbers (based on the turbine diameter). Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the turbines and one far downstream. Third, we show that adding a localised control force, in the regions identified by the sensitivity analysis, stabilises the wake. Particularly, locating the control forcing close to the turbines results in an enhanced stabilisation such that the wake remains steady for significantly higher Reynolds numbers or turbine thrusts. The analysis of the controlled flow fields confirms that modifying the velocity gradient close to the turbine is more efficient to stabilise the wake than controlling the wake far downstream. The analysis is performed for the first flow bifurcation (at low Reynolds numbers) which serves as a foundation of the stabilization technique but the control strategy is tested at higher Reynolds numbers in the final section of the paper, showing enhanced stability for a turbulent flow case.

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“…Sensitivity maps are provided by combining direct and adjoint modes. The importance of adjoint modes and sensitivity maps, together with the mathematical machinery required for the study of the sensitive flow regions to different parameters, has been studied by different authors [87,26,59,44,24]. In addition, these studies provide detailed reviews of the "state of the art" techniques in linear stability analysis and sensitivity analysis, addressing the relevance that the adjoint plays in the analysis of these problems, and also giving a comprehensive overview of the above-mentioned techniques and outlining the possibilities of linking sensitivity information with open/closed loop control.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Chandler et al [24] compared the discrete and the continuous approach for the low Mach number equations for a low density jet and showed that both methods provide very similar results. On the one hand, the continuous approach, for this particular case, showed a faster rate of convergence while requiring a less resolved mesh.…”

Section: Discrete Vs Continuousmentioning

confidence: 99%

Discrete linear stability and sensitivity analysis of fluid flows

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Adjoint algorithms for the Navier–Stokes equations in the low Mach number limit

Cited by 47 publications

References 42 publications

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Sensitivity Analysis to Control the Far-Wake Unsteadiness Behind Turbines

Discrete linear stability and sensitivity analysis of fluid flows

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