Analytical and level-set method based numerical study on oil–water smooth/wavy stratified-flow in an inclined plane-channel

Level-set method based transient 2D simulation of developing oil–water smooth-stratified (SS) and wavy-stratified (WS) flow in a horizontal and inclined plane-channel is done; for various inlet-velocity (uin), inlet-interface-height (Hin), inclination-angle (θ), reduced surface-tension (σ ⩽ σow) and reduced gravity (g ⩽ ge). At the certain critical value of the governing parameters, SS to WS flow transition is captured, analyzed and reasoned. Increase in uin, Hin and θ and a decrease in σow and ge are found to destabilize the SS flow. For fully-developed SS flow, a detailed analytical solution of interface-height, maximum axial-velocity, its transverse location, pressure-gradient and wall-shear stress is proposed for an inclined channel; an excellent agreement between the present analytical and numerical results is also reported. The SS flow analytical-results are also compared with the time-averaged WS flow numerical-results (near the channel-outlet), to understand the reasons for flow-transition. Flow development is studied with the help of axial variation of interface-height and maximum (over the cross-section of the channel) axial velocity; time-averaged for WS flow. Furthermore, the variation of development-length for SS flow and WS flow is studied. Finally, stretching of interface-area due to onset of WS flow is presented with the help of interfacial-area-concentration. Its calculation directly from the Dirac-delta function of the level set method is a novel-contribution.

► Effect of velocity and interface-height at inlet, reduced surface-tension & gravity is studied.
► Smooth to wavy stratified flow transition is captured, analyzed and reasoned.
► A detailed analytical solution for fully-developed smooth-stratified flow is proposed.
► Calculation of interfacial-area-concentration for level set method is proposed.