Abstract
In this contribution laminar to turbulent transition is studied in a pressure gradient driven flow confined between Taylor cylinders. The outer cylinder is assumed rotating and the inner cylinder is under translational motion. In this respect, a mathematical model describing the physics of flow dynamics is presented and implemented using MATLAB. Spectral collocation approach is used to calculate the eigenvalues which predict the critical stability parameter value. The critical parameters at which the laminar to turbulent transition just starts are calculated. The neutral stability diagrams are obtained for various physical situations characterizing the limit points of damping and growth of the wave disturbances. It is observed that an increase in the swirl and translation allows the transition to start later than the classical case. However, increase in the gap width allows the transition to appear earlier than the classical case. A change in the Tollmien Schlichting mechanism is seen with the change in swirl, translation and gap width of the two cylinders. Moreover, the linear stability analysis discussed here provides a basis for the nonlinear stability analysis with the help of adjoints calculated and presented.
Highlights
Transition is a very important and fascinating mechanism in fluid mechanics
The free body diagram of the neutral stability curve is shown in Fig. 2 where Rec is the critical Reynolds number which accounts for the onset of transition from laminar to turbulence
We study the linear stability characteristics of a pressure gradient driven flow confined between two cylinders with the rotation of outer cylinder and translation of inner cylinder
Summary
Transition is a very important and fascinating mechanism in fluid mechanics. It is a change in the vortical state which can be understood as distribution of vorticity in the flow field. In the presence of different set of forces (from thermal origin and due to system rotation as a hole), a flow may undergo transition. It is attempted to unveil a relationship between the equations for the weakly linear evolution of disturbances inducing transition according to the nonlinear stability theory of Stewartson and Stuart.. It is attempted to unveil a relationship between the equations for the weakly linear evolution of disturbances inducing transition according to the nonlinear stability theory of Stewartson and Stuart.2 In this respect, a laminar to turbulent transition is studied and discussed for the flow confined within the Taylor cylinders with the rotation of outer cylinder, whereas inner one is being translated only.
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