Sage Journals: Discover world-class research

Abstract

This article presents a primitive-variable calculation procedure for a time-dependent deforming interface and its relevant conjugate viscous flows in a multi-fluid system. A deforming fluid/fluid interface boundary is explicitly tracked using a moving mesh. In order to decide the shape of the deforming interface separating two conjugate viscous flows on both sides, a ‘modified Ryskin-Leal method’ is proposed. This is combined with the ‘continuous stress method’ for interfacial velocity, previously developed by the authors, to treat the boundary conditions. The governing equations are solved by the SIMPLE method, which is implemented with high-order schemes to obtain high fidelity of interfacial transport and flow phenomena.

The calculation procedure is verified. These include fluid droplets with documented numerical results and air bubbles with experimental data. Further verifications of the algorithm are carried out by numerically studying the dynamic behaviours of a rising air bubble; these dynamic behaviours include the time-dependent rising, deformation, evolution of flow fields, and propagation of concentration field.

Keywords

fluid-fluid interface conjugate viscous flows modified Ryskin-Leal method numerical simulation

Get full access to this article

View all access options for this article.

References

Shyy

Udaykumar

H. S.

Rao

M. M.

Smith

R. W.

Computational fluid dynamics with moving boundaries, 1996 (Taylor & Francis, Philadelphia).

Hirt

C. W.

Nichols

B. D.

Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 1981, 39, 201–225.

Unverdi

S. O.

Tryggvason

A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys., 1992, 100, 25–37.

Osher

Sethian

J. A.

Fronts propagating with curvature dependent speed: Algorithm based on Halmilton-Jacobi formulations. J. Comput. Phys., 1988, 79, 12–49.

Ryskin

Leal

L. G.

Numerical solution of free-boundary problems in fluid mechanics. Part 1: The finite-difference technique. J. Fluid Mech., 1984, 148, 1–17.

Ryskin

Leal

L. G.

Numerical solution of free-boundary problems in fluid mechanics. Part 2: Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech., 1984, 148, 19–35.

Salvador

Contribution to numerical simulation of flow around a deformable bubble. PhD Thesis, ECN Universit de Nantes, 1994.

Raymond

Rosant

J. M.

A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids. Chem. Eng. Sci., 2000, 55, 943–955.

W. Z.

Yan

Y. Y.

An alternating dependent variables (ADV) method for treating slip boundary conditions of free surface flows with heat and mass transfer. Numer. Heat Transf., Part B, 2002, 41, 165–189.

10.

W. Z.

Yan

Y. Y.

A direct-predictor method for solving steady terminal shape of a gas bubble rising through a quiescent liquid. Numer. Heat Transf., Part B, 2002, 42, 55–71.

11.

Lai

Yan

Y. Y.

Gentle

C. R.

Smith

J. M.

Numerical study of conjugate steady viscous flow about and inside a spherical bubble. 12th International Heat Transfer Conference, Grenoble, France, 18–23, August 2002, pp. 581–586.

12.

Dandy

Leal

L. G.

Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers. J. Fluid Mech., 1989, 208, 161–192.

13.

Gaskell

P. H.

Lau

A. K. C.

Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Int. J. Numer. Methods Fluids, 1988, 8, 617–641.

14.

Demirdzic

Peric

Space conservation law in finite volume calculations of fluid flow. Int. J. Numer. Methods Fluids, 1988, 8, 1037–1050.

15.

Trulio

J. G.

Trigger

K. R.

Numerical solution of the one-dimensional hydrodynamic equations in an arbitrary time-dependent coordinate system. Report UCLR-6522, University of California Lawrence Radiation Laboratory, 1961.

16.

Thomas

P. D.

Lombard

C. K.

Geommetric conservation law and its application to flow computations on moving grids. AIAA J., 1979, 17, 1030–1037.

17.

Khosla

P. K.

Rubin

S. G.

A diagonal dominant second-order accurate implicit scheme. Comput. Fluids, 1974, 2, 207–209.

18.

Darwish

M. S.

Moukalled

F. H.

Normalized variable and space formulation methodology for high-resolution schemes. Numer. Heat Transf., Part B, 1994, 26, 79–96.

19.

Lai

Yan

Y. Y.

The effects of choosing dependent variables and cell-face velocities on convergence of the SIMPLE algorithm using non-orthogonal grids. Int. J. Numer. Methods Heat Fluid Flow, 2001, 11, 524–546.

20.

Lai

Yan

Y. Y.

Gentle

C. R.

A calculation procedure for conjugate viscous flows about and inside single bubbles. Numer. Heat Transf., Part B, 2003, 43, 241–265.

21.

Thompson

J. F.

Thames

F. C.

Mastin

C. W.

Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies. J. Comput. Phys., 1974, 15, 299–319.

22.

Mei

Klausner

J. F.

Lawrence

A note on the history force on a spherical bubble at finite Reynolds number. Phys. Fluids, 1994, 6, 418–420.

Calculation procedure for time-dependent deforming interfaces in multi-fluid systems

Abstract

Abstract

Keywords

Get full access to this article

References