DIRECT SIMULATION OF INTERFACIAL WAVES IN A HIGH-VISCOSITY-RATIO AND AXISYMMETRICAL CORE-ANNULAR FLOW

direct numerical simulation of spatially periodic wavy core flows is c arried out under the assumption that the densities of the two fluids a re identical and that the viscosity of the oil core is so large that i t moves as a rigid solid which may nevertheless be deformed by pressur e forces in the water. The waves which develop are asymmetric with ste ep slopes in the high-pressure region at the front face of the wave cr est and shallower slopes at the low-pressure region at the lee side of the crest. The simulation gives excellent agreement with the experime nts of Pal, Chen & Joseph (1992) on up flow in vertical core flow wher e axisymmetric bamboo waves are observed. We define a threshold Reynol ds number and explore its utility; the pressure force of the water on the core relative to a fixed reference pressure is negative for Reynol ds numbers below the threshold and is positive above. The wave length increases with the hold-up ratio when the Reynolds number is smaller t han a second threshold and decreases for larger Reynolds numbers. We v erify that very high pressures are generated at stagnation points on t he wavefront. It is suggested that a positive pressure force is requir ed to levitate the core off the wall when the densities are not matche d and to centre the core when they are. A further conjecture is that t he principal features which govern wavy core flows cannot be obtained from any theory in which inertia is neglected.