Transition from the perfect core-annular flow in a constricted tube to unsteady – stratified, bubbling, pulsing and spray – flow regimes
Advancing the chemical engineering fundamentals
Multifase Flows - II (T2-5b)
Keywords: Core Annular flow, Flow regimes, Direct Numerical Simulation, Drops, Bubbles
Flows of two or more immiscible fluids exhibit numerous phenomena with intrinsic scientific interest and important practical applications. Such applications from the oil and plastics industries include the production of oil from the ground (flow with water or steam in porous media), its water-facilitated transportation through pipelines, its chemical transformation in packed-bed reactors (flow with gaseous reactants in porous media) and the production of bicomponent and composite plastics and layered films (flow inside and out of channels).
In this work, a Volume Tracking (VT) algorithm has been implemented for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). A constant pressure gradient sets them in motion. The surface tension force is approximated using the continuous surface force method. A boundary-fitted coordinate transformation is applied and all terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one-sided forward finite differences in time. The well-known failure of centered finite differences arises as the Reynolds number increases and leads to non-physical oscillations in the interface and failure of convergence with mesh refinement. These problems are resolved and computations with Reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third-order upwind differences using Lagrangian Polynomials. In each time step, the incompressibility condition is enforced by a transformed Poisson equation, which is linear in pressure. This equation is solved by direct LU decomposition.
The main parameters of the problem are: The Reynolds number, the Weber number, the viscosity ratio of the two fluids, the volume fraction occupied by the core fluid and various geometric characteristics of the tube. We will present a complete parametric study of the conditions under which the stratified (trickling) flow is stable or turns into pulsing, bubbling or spray flow. For example, we have shown that decreasing the volume fraction of the core fluid results in transitions from stratified flow to the pulsing and bubbling flow regimes in which the core fluid becomes discontinuous and the size of generated bubbles strongly depends on this volume fraction. The transition from the trickling flow to the spray regime occurs as the effect of the surface tension fades. We will present a sequence of figures that demonstrate the formation of small ripples which then grow to fingers of the annular more viscous fluid pointing towards the less viscous one. Due to the inertia of the core fluid these fingers are torn off the main body of the annular fluid and thus, they create drops of the annular fluid inside the continuous stream of the core fluid. The spray regime arises also when the core fluid is the more viscous one, but in this case the fingers are pointing towards the annular fluid.
References
1. Kouris, Ch., & Tsamopoulos, J., Core-Annular flow in a periodically constricted circular tube, I. Steady state, linear stability and energy analysis, J. Fluid Mech., 432, 31-68 (2001)
2. Kouris, Ch., & Tsamopoulos, J., Core-Annular flow in a periodically constricted circular tube, II. Dynamics, J. Fluid Mech., 432, 31-68 (2002)
3. Zacharioudaki, M., Kouris, Ch., Dimakopoulos, Y., & Tsamopoulos, J., A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate trasformation and 3rd order upwinding, submitted for publication to J. Comp. Physics
Presented Monday 17, 15:40 to 16:00, in session Multifase Flows - II (T2-5b).
