Double-diffusive instability in core–annular pipe flow

Abstract

The instability in a pressure-driven core–annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen–Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.