Nonlinear Stability Analysis of Thin Film Flow from a Liquid Jet Impinging on a Circular Concentric Disk

Abstract

AbstractThe paper investigates the stability of thin film flow from a liquid jet impinging on a circular concentric disk using a long-wave perturbation method to solve for the generalized nonlinear kinematic equations of free film interface. To begin with a normal mode approach is employed to obtain the linear stability solution for the film flow. In the linear stability solutions only subcritical region can be resolved. In other words, no solution of supercritical region can be obtained in linear domain. Furthermore, the role that the forces of gravitation and surface tension play in the flow is nothing but to stabilize the system. To further investigate the realistic impinging jet flow stability conditions, the weak nonlinear dynamics of a film flow is studied by using the method of multiple scales. Various subcritical nonlinear behaviors expressed in terms of absolute stability, conditional stability and explosive instability can be characterized by solving the Ginzburg-Landau equation. It is found that the jet flow will become relatively unstable for an increasing Reynolds number, a relative smaller distance from the center of the impinging jet on the disk and a smaller diameter of the exit jet. It is also concluded that the flow will always stay in a subcritical instability region if the characteristic diameter of the potential core at nozzle exit is less than 0.01mm for the numerical conditions given in this paper. In such a case when the amplitude of external flow disturbance is smaller than the threshold amplitude a stable jet flow can be ensured.