MATEC Web Conf.
Volume 286, 201914th Congress of Mechanics (CMM2019)
|Number of page(s)||3|
|Section||Fluid Mechanics, Rheology, Modeling, Instabilities and Transition|
|Published online||14 August 2019|
Transient energy growth of channel flow with cross-flow
Laboratory of Mechanics, Faculty of Sciences Ain-Chock, University Hassan II-Casablanca, Morocco.
The effect of a uniform cross flow (injection/ suction) on the transient energy growth of a plane Poiseuille flow is investigated. Non-modal linear stability analysis is carried out to determine the two-dimensional optimal perturbations for maximum growth. The linearized Navier-Stockes equations are reduced to a modified Orr Sommerfeld equation that is solved numerically using a Chebychev collocation spectral method. Our study is focused on the response to external excitations and initial conditions by examining the energy growth function G(t) and the pseudo-spectrum. Results show that, the transient energy of the optimal perturbation grows rapidly at short times and decline slowly at long times when the cross-flow rate is low or strong. In addition, the maximum energy growth is very pronounced in low injection rate than that of the strong one. For the intermediate cross-flow rate, the transient energy growth of the perturbation, is only possible at the long times with a very high-energy gain. Analysis of the pseudo-spectrum show that the non-normal character of the modified Orr-Sommerfeld operator tends to a high sensitivity of pseudo-spectra structures.
Key words: Cross flow / Non-modal linear stability / Poiseuille flow / Spectral method / Transient energy growth.
© The Authors, published by EDP Sciences, 2019
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