Stability And Control Of Plane Poiseuille Flow At Post Critical Reynolds Number / Ahmed Gamal Kamel Mohammed ; Supervised Mohammed Khalil Ibrahim

Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Aerospace Engineering

In this work, a stability study for plane Poiseuille flow was presented by solving Orr-Sommerfeld equation. Some previous researches for flow stability and control were also presented. A solver was developed for simulating the flow field by solving Navier-Stokes equations using direct numerical simulations. The solver was validated by comparing our results for some fundamental problems with some the published results before implementing the direct numerical simulation solver. Also, a solver for Orr-Sommerfeld equation was developed and validated with the published results. The critical Reynold{u2019}s number and wavenumber was calculated and presented in this work for the plane Poiseuille flow. The direct numerical simulation solver was developed by combining the previous solvers in order to simulate the flow transition from laminar to turbulent. The validation for the direct numerical simulation solver was presented by comparing the results with Orr-Sommerfeld solution. A model-based controller for stabilizing the plane Poiseuille flow was presented using suction and blowing technique on through slots along the walls of the channel in order to regain the laminar state for the flow field. The controller was tested for different values of Reynolds numbers and wavenumbers within the critical and post critical stability regimes for the plane Poiseuille flow

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