Ashraf Balabel¹,

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.4, pp. 283-301, 2012, DOI:10.3970/cmes.2012.089.283

Abstract This paper presents a novel numerical method for solving the twophase flow problems with moving interfaces in either laminar or turbulent flow regimes. The developed numerical method is based on the solution of the Reynolds- Averaged Navier Stokes equations in both phases separately with appropriate boundary conditions located at the interface separating the two fluids. The solution algorithm is performed on a regular and structured two-dimensional computational grid using the control volume approach. The complex shapes as well as the geometrical quantities of the interface are determined via the level set method. The numerical method is firstly validated against the… More >

Yongsheng An¹, Xiaodong Wu¹, Deli Gao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.2, pp. 123-142, 2012, DOI:10.3970/cmes.2012.089.123

Abstract The accuracy of numerical simulation of a two-phase (oil and water) flow in a fractured horizontal well depends greatly upon the types of grids used in the computation. Cartesian grids have been widely used in recent years, but they have some disadvantages in describing complex structural wells, such as fractured horizontal wells. For example, Cartesian grids are not efficient in describing the main wellbores and the fractures of fractured horizontal wells, and the results can frequently suffer from grid orientation effects, even though a grid-refinement is often introduced to enhance the adaptability of a Cartesian grid. The PEBI (Perpendicular Bisector)… More >

Qin Lou¹, Zhaoli Guo^1,2, Chuguang Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 175-188, 2011, DOI:10.3970/cmes.2011.076.175

Abstract Due to the mesoscopic and kinetic nature, the lattice Boltzmann equation (LBE) method has become an efficient and powerful tool for modeling and simulating interfacial dynamics of multi-phase flows. In this work we discuss several fundamental properties of two-phase LBE models. Particularly, the effects of force discretization, spurious currents in the vicinity of interfaces, and checkerboard effects with the underlying lattices, are investigated. More >

K. Ibrahim¹, W.A. El-Askary^1,2, A. Balabel¹, I.M. Sakr¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 79-104, 2012, DOI:10.3970/cmes.2012.085.079

Abstract In the present paper, a numerical code has been developed with different turbulence models aiming at simulating turbulent bubbly flows in vertical circular pipes. The mass and momentum conservation equations are used to describe the motion of both phases (water/air). Because of the averaging process additional models are needed for the inter-phase momentum transfer and turbulence quantities for closure. The continuous phase (water) turbulence is represented using different turbulence models namely: two-equation k-ε, extended k-ε and shear-stress transport (SST) k-ω turbulence models which contains additional term to account for the effect of the dispersed phase (air) on the continuous phase… More >

Ashraf Balabel

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 599-638, 2012, DOI:10.3970/cmes.2012.083.599

Abstract In the present paper, a new generalized level set numerical method based on the Fast Marching Method is developed for predicting the moving interface thermo-fluid dynamics in turbulent free surface flows. The numerical method is devoted to predict the turbulent interfacial dynamics resulting from either aerodynamic force or thermocapillary effects. The unsteady Reynolds averaged Navier-Stokes equations (RANS) and energy equation are coupled with the level set method and solved separately in each phase using the finite volume method on a non-staggered grid system. The application of the fast marching technique enables the fast as well as the accurate transport of… More >

J. Bonilla¹, L.J. Yebra¹, S. Dormido²

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.1, pp. 13-38, 2010, DOI:10.3970/cmes.2010.067.013

Abstract This paper presents and discusses a mean densities method applied to a steam-water two-phase flow mathematical model which uses a finite volume method and a staggered grid for discretizing a rigid volume in control volumes, where the thermodynamic properties are calculated. This method is based on the concepts of uniform pressure among all the control volumes and mean density in each control volume, allowing smooth thermodynamic properties, hence avoiding discontinuity at phase boundaries. This method wipes out the chattering problem due to the continuous and differentiable modelling of density and its partial derivatives, which leads to faster simulations and increases… More >

S. Aland¹, J. Lowengrub², A. Voigt¹

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 77-108, 2010, DOI:10.3970/cmes.2010.057.077

Abstract We present a new method for simulating two-phase flows in complex geometries, taking into account contact lines separating immiscible incompressible components. We combine the diffuse domain method for solving PDEs in complex geometries with the diffuse-interface (phase-field) method for simulating multiphase flows. In this approach, the complex geometry is described implicitly by introducing a new phase-field variable, which is a smooth approximation of the characteristic function of the complex domain. The fluid and component concentration equations are reformulated and solved in larger regular domain with the boundary conditions being implicitly modeled using source terms. The method is straightforward to implement… More >

Hossein M. Shodja^1,2,3, Alireza Hashemian^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 17-34, 2008, DOI:10.3970/cmes.2008.032.017

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations (ODEs). Subsequently, Gear's method is… More >

F. Bierbrauer, S.-P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 1-22, 2007, DOI:10.3970/cmes.2007.019.001

Abstract Recently the use of the one-field formulation in the numerical solution of the Navier-Stokes equations for two-phase incompressible flow has become a very attractive approach in CFD (computational fluid dynamics). While the presence of material discontinuities across fluid interfaces presents some difficulty, it is their combination with a non-solenoidal discontinuous initial velocity field, commonly occurring in the mathematical formulation, that has provided the greatest hindrance in the numerical solution. This paper presents three analytical solutions, the Bounded Creeping Flow, Solenoidal and Conserved Solenoidal Solutions, which are both continuous, incompressible, retain as much of the original mathematical formulation as possible and… More >

T. Uchiyama¹

FDMP-Fluid Dynamics & Materials Processing, Vol.7, No.4, pp. 371-388, 2011, DOI:10.3970/fdmp.2011.007.371

Abstract This study proposes a three-dimensional grid-free method to simulate particle-laden gas flows. It is based on a vortex method. The flow region is not resolved into computational grids, but the gas vorticity field is discretized by vortex elements. The behavior of the vortex element and the particle motion are simultaneously calculated by using the Lagrangian approach. Eight cubic cells are locally allocated around each particle to compute the effect of the particle motion on the gas flow. In each cell, the change in the vorticity due to the particle is calculated, and it is considered by generating a vortex element… More >