A one-dimensional momentum conservation equation for a straight jet driven by an electrical field is developed. It is presented in terms of a stress component, which can be applied to any constitutive relation of fluids. The only assumption is that the fluid is incompressible. The results indicate that both the axial and radial constitutive relations are required to close the governing equations of the straight charged jet. However, when the trace of the extra stress tensor is zero, only the axial constitutive relation is required. It is also found that the second normal stress difference for the charged jet is always zero. The comparison with other developed momentum equations is made.
The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with invariants.Then the implicit differential equations solver 'ddaskr' is used to solve the ODEs and post-stabilization is executed at the end of each step.Results show the distributions of radius,linear charge density,stretching ratio and also the horizontal velocity at a time point.Meanwhile,the spiral and expanding projections to X-Y plane of the jet centerline suggest the occurring of bending instability.
Yan Liu,~(a)) and Ruojing Zhang~(b)) School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China
