Application of the TVD scheme to the nonlinear instability analysis of a capillary jet

Abstract

In the past, when either the perturbation-type method or direct-simulation approach was used to analyse capillary jets, the governing equations, which are parabolic in time and elliptic in space, were simplified or linearized. In the present study, the convective derivative term and a full, nonlinear form of the capillary pressure term are retained in the governing equations to investigate nonlinear effects on the break-up of capillary jets. In this work, the TVD (i.e. total variation diminishing) scheme with flux-vector splitting is applied to obtain the solutions of the system of nonlinear equations in a matrix form. Numerical results show that the present nonlinear model predicts longer jet break-up lengths and slower growth rates for capillary jets than the previous linear model does. Comparing with other measurements from past literatures, the nonlinear results are consistent with the experimental data and appear more accurate than the linear analysis. In the past, the classic perturbation-type analyses assumed constant growth rates for the fundamental and all harmonic components. By contrast, the present model is able to capture the local features of growth rates, which are not spatially and temporally constant. Copyright © 2006 John Wiley & Sons, Ltd.