Numerical solution of a Newtonian jet emanating from a converging channel

Abstract

Abstract A theoretical analysis has been carried out to find the shape and final thickness of a Newtonian jet emanating from a converging channel. The gravitational force is neglected but the surface tension effect is included in the present analysis. There are four variables, i.e. the contraction ratio L , the converging angle θ, the Reynolds number Re and the capillary number Ca, that completely determine the flow field. The effects of these four variables on the motion of the jet are examined. The mathematical problem of the jet is formulated with stream function and vorticity as dependent variables. The boundary-fitted coordinate transformation method developed by Thompson et al. is adopted to map the flow geometry into a regular domain for numerical integration, and the finite difference method is applied to solve the flow equations in the transformed plane. We have found that the final thickness of the jet will reach its frozen value as L > 15. As Re > 50 , the jet contraction coefficient is very close to that of a potential Helmholtz jet. Surface tension is only important if Re is small. The jet contraction coefficients as functions of Re and θ are presented. We have also found that a vortex may exist in the converging channel if the converging angle θ > 75° .