| The temporal evolution of an initially laminar two-fluid channel flow is investigated using linear stability analysis and direct numerical simulation. The stability of a two-fluid shear flow is encountered in numerous situations, including water wave generation by wind, atomization of fuels, aircraft deicing and nuclear reactor cooling. The application of particular interest in this study is liquefying hybrid combustion, for which the two-fluid channel flow is used as a model problem to characterize the relevant mixing and entrainment mechanisms. The two fluids are miscible with dissimilar densities and viscosities. The thickness of one of the fluid layers is much smaller than that of the other, with the denser and more viscous fluid comprising the thin layer.;Linear stability analysis is used to identify possibly unstable modes in the two-fluid configuration. The analysis is considered for two different situations. In one case, the fluid density and viscosity change discontinuously across a sharp interface, while in the other, the fluids are separated by a finite thickness transition layer, over which the fluid properties vary continuously. In the sharp interface limit, the linear stability is governed by an Orr-Sommerfeld equation in each fluid layer, coupled by boundary conditions at the interface. A numerical solution of the system of equations is performed using a Chebyshev spectral collocation method. In the case where the fluids are separated by a finite thickness transition zone, an Orr-Sommerfeld-type equation is solved with the compound matrix method.;The non-linear stages of the flow evolution are investigated by direct numerical simulation. In a temporal simulation, two of the three spatial dimensions are periodic. Fourier spectral discretization is used in these dimensions, while a compact finite difference scheme is utilized in the non-periodic direction. The time advancement is performed by a projection method with a third order Adams-Bashforth-Moulton predictor-corrector scheme. Initial conditions for the DNS are supplied by the linear stability analysis.;Linear stability analysis indicates that the thickness of the transition zone between the fluids has a significant impact on the amplification of the two least stable modes present in the two-fluid channel flow. Compared to the sharp interface limit, one of the modes is damped and the other one is either amplified or damped depending on the Reynolds number. Two dissimilar entrainment mechanisms are observed in the DNS calculations, corresponding to these two modes. One results in significantly more entrainment and mixing between the two fluids. This mechanism exhibits a greater degree of vorticity generation, particularly due to the baroclinic effect. |
