Transient energy growth of channel flow with cross-flow

Benyza, J.; Lamine, M.; Hifdi, Ahmed

doi:10.1051/matecconf/201928607008

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…It can be seen that when R v increases, the peak value G P increases firstly, attains a maximum value at R v ≈ 5 and then decreases continuously back to 1. It should be noted that G P is larger than the value at R v = 0 when R v < 17.9 (see the dashed line in figure 3(b)) and this maximum energy growth is more pronounced at low values of R v than that with strong crossflow, consistent with the conclusion by Benyza et al (2019), although they only considered the case of two-dimensional perturbation with β = 0. Further, peak wave number α P increases continuously with increasing R v , peak wave number β P drops firstly with increasing R v and later increases.…”

Section: Optimal Perturbations and Their Transient Growthsupporting

confidence: 84%

Optimal perturbations in viscous channel flow with crossflow

Chen¹,

Huang²,

Zhang³

2021

Fluid Dyn. Res.

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This work is devoted to the studies of optimal perturbation and its transient growth characteristics in the Poiseuille flow with Reynolds number R = 1000 and with crossflow. The crossflow Reynolds number R v , based on the uniform velocity in the negative normal direction, is varied from 0 to 200. The numerical result shows that the crossflow enhances the transient growth for three-dimensional disturbance case when R v < 17.9 . Seen from the contours of optimal energy growth in the wave number plane, the optimal perturbation that corresponds to the peak value of optimal growth becomes oblique perturbation, when crossflow is introduced. The corresponding streamwise wave number α P increases continuously with increasing R v , while spanwise wave number β P drops firstly with increasing R v and later increases. The comparison of exponential growth and transient growth is performed. It is observed that exponential growth becomes profound and even predominant over transient growth after a short period when the crossflow is sufficiently strong. Moreover, the mechanism of transient growth is discussed and it is found that the uniform crossflow can not cause transient growth in the absence of shear in basic flow. With increasing R v , the Orr mechanism becomes more and more important relative to lift-up mechanism for the transient growth of optimal perturbation.

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Section: Optimal Perturbations and Their Transient Growthsupporting

confidence: 84%

Optimal perturbations in viscous channel flow with crossflow

Chen¹,

Huang²,

Zhang³

2021

Fluid Dyn. Res.

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Optimal Transient Energy Growth of Two-Dimensional Perturbation in a Magnetohydrodynamic Plane Poiseuille Flow of Casson Fluid

Basavaraj,

Shivaraj Kumar

2023

Journal of Fluids Engineering

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The study investigates the influence of the Casson fluid parameter and the spanwise uniform magnetic field on the onset of instability against infinitesimal disturbances in an electrically conducting fluid flow between two parallel non-conducting rigid plates. The 4th-order linearized disturbance equation governing stability is solved using the spectral collocation method with Chebyshev-based polynomials. The aim is to analyze in detail the effect of the parameters involved in the problem using both modal and non-modal linear stability analysis. The modal analysis provides accurate values of the critical Reynolds number, critical wave number, and critical wave speed, denoted as critical triplets (αc, Rc, cc). Additionally, it examines the eigen-spectrum, growth rate curves, and neutral stability curves. On the other hand, the non-modal analysis investigates the transient energy growth G(t) of two-dimensional optimal perturbations, the pseudo-spectrum of the non-normal Orr-Sommerfeld (O-S) operator (L), and the regions of stability, instability, and potential instability of the fluid flow system. The extensive examination of both long-term behavior through modal analysis and short-term behavior through nonmodal analysis reveals that the Hartmann number acts as a stabilizing agent, delaying the onset of instability. Conversely, the Casson parameter acts as a destabilizing agent, advancing the onset of instability. The results obtained here are verified to be in good agreement with the existing literature in the absence of the Casson fluid flow parameter.

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Minimization of Peak Effect in the Free Motion of Linear Systems with Restricted Control

Dudarenko

Vunder

Melnikov

et al. 2023

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A peak effect minimization problem in the free motion of linear systems is considered in the paper. The paper proposes an iterative procedure for the peak effect minimization using a combination of the recently proposed gramian-based approach and the theory of using the condition number of an eigenvectors matrix for the upper bound estimations of the system state processes. Minimization of control costs is based on the analysis of the singular value decomposition of a gramian of control costs, followed by the formation of major and minor estimations of the gramian. Minimization of peak effect in the trajectories of free movement of systems is carried out by minimizing the condition number of the eigenvectors matrix of the matrix of a stable closed-loop system, while the state matrix with the desired eigenvalues and eigenvectors is designed with the generalized modal control. The development of an iterative algorithm for the peak effect minimization in the trajectories of linear systems under any non-zero initial conditions with restricted control is based on an aggregated index. The index takes into account both the estimate of the gramian of control costs and the condition number of the eigenvectors matrix of the stable closed-loop system. Minimization of the aggregated index makes it possible to ensure minimal deviations in the trajectories of free movement of systems of the considered class. The procedure is applied to a system of two satellites with restricted control, where peak effects in satellites relative trajectories are minimized. Two cases of peak affect minimization are considered. In the first case, the peak effect minimization in the trajectories of free movement of satellites is carried out only by minimizing the gramian of control costs. In the second case, the peak effect minimization is realized using the developed algorithm. The results illustrate the efficiency of the procedure and indicate the decrease of the peak effect for the satellites relative trajectories.

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Transient energy growth of channel flow with cross-flow

Cited by 3 publications

References 6 publications

Optimal perturbations in viscous channel flow with crossflow

Optimal perturbations in viscous channel flow with crossflow

Optimal Transient Energy Growth of Two-Dimensional Perturbation in a Magnetohydrodynamic Plane Poiseuille Flow of Casson Fluid

Minimization of Peak Effect in the Free Motion of Linear Systems with Restricted Control

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