Raad I. Issa

Solution of the implicitly discretised reacting flow equations by operator-splitting

Abstract A non-iterative method for handling the coupling of the implicitly discretised time-dependent fluid flow equations is described. The method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations. The main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step, with the split sets of equations being amenable to solution by standard techniques. At each time-step, the procedure yields solutions which approximate the exact solution of the difference equations. The accuracy of this splitting procedure is assessed for a linearised form of the discretised equations, and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time-step size. By virtue of this, it is possible to dispense with iteration, thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods. This is verified in a companion paper which presents results of computations carried out using the method.

Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model

Abstract A mechanistic approach to the prediction of hydrodynamic slug initiation, growth and subsequent development into continuous slug flow in pipelines is presented. The approach is based on the numerical solution of the one-dimensional transient two-fluid model equations. The advantage of this approach is that the flow field is allowed to develop naturally from any given initial conditions as part of the transient calculation; the slugs evolve automatically as a product of the computed flow development. The need for the many phenomenological models for flow regime transition, formation of slugs and their dynamics can thus be minimized. It is shown that when the two-fluid model is invoked within the confines of the conditions under which it is mathematically well-posed, it is capable of capturing the growth of instabilities in stratified flow leading to the generation of slugs. The computed rates of growth of such instabilities compare well with the values obtained from Kelvin–Helmholtz analyses. Simulations are then carried out for a large number of pipe configurations and flow conditions that lead to slug flow. These include horizontal, inclined and V-section pipes. The results of computations for slug characteristics are compared with data obtained from the literature and it is found that the agreement is remarkable given the simplicity of the one-dimensional model.

Numerical prediction of phase separation in two-phase flow through T-junctions

The paper presents a predictive numerical method which solves the full, three-dimensional, two-fluid model equations for dispersed two-phase flow by control-volume discretization. The methodology incorporates general coordinates, indirect-addressing for easy mapping of non-rectangular domains and is based on the use of non-staggered meshes. Turbulence is modelled either by the standard k—e turbulence model or by an extension of that model which accounts for void-fraction fluctuations. The method is applied to air-water bubbly flow in a rectangular cross-section T-junction for which experimental data is available. Comparisons of the predictions with measured velocities and phase separation ratios show good agreement. Contours of the volume-fraction reveal the presence of a pocket of high gas concentration at the entrance to the side arm, similar to that actually found in experiments. The effects of interfacial drag model, turbulence model and bubble diameter on the predictions are also investigated.

An improved PISO algorithm for the computation of buoyancy-driven flows

A numerical procedure for the calculation of buoyancy-driven flows using the finite-volume approach is presented. It is based on an extension of the operator-splitting procedure PISO of Issa [1] to the specific case in which the coupling between velocity/pressure and temperature is important, as is the case in problems involving free-convection flows. A comparison of the proposed procedure with a standard iterative method shows improvement both in terms of computing speed (a factor of 2.1 to 4.1) and robustness.A numerical procedure for the calculation of buoyancy-driven flows using the finite-volume approach is presented. It is based on an extension of the operator-splitting procedure PISO of Issa [1] to the specific case in which the coupling between velocity/pressure and temperature is important, as is the case in problems involving free-convection flows. A comparison of the proposed procedure with a standard iterative method shows improvement both in terms of computing speed (a factor of 2.1 to 4.1) and robustness.

A numerical model of slug flow in vertical tubes

Abstract This paper presents a numerical method for the determination of the flow field structure in slug flow in vertical tubes. The method is based on the ensemble averaged transport equations governing the flow of the liquid around the Taylor bubble and in the slug, which together comprise one slug unit. Turbulence is accounted for by the k -ϵ model. An iterative scheme is used to compute the shape and velocity of the Taylor bubble simultaneously with the flow field; the conditions which are taken to determine these quantities are uniform bubble pressure and smoothness of the bubble nose. The equations are discretised using a finite volume technique on a block structured, non-orthogonal mesh which conforms to the flow domain boundary. The predicted velocities of a single Taylor bubble rising in both stagnant and moving liquid agree very well with experimental data. For a train of Taylor bubbles in periodic slug flow, the computed bubble rise velocity and pressure gradient agree well with the data provided that account is taken of the presence of dispersed gas in the liquid slug.

Pressure-Based Compressible Calculation Method Utilizing Total Variation Diminishing Schemes

A pressure-based implicit procedure to solve the Euler and Navier-Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is described. The boundedness criteria for this procedure are determined from total variation diminishing (TVD) schemes, which are based on characteristic variables and are applied to the fluxes of the convected quantities, including mass flow rate. The procedure incorporates the κ-e eddy-viscosity turbulence model. The algorithm is first tested for inviscid flows at different Mach numbers ranging from subsonic to supersonic on a bump in a channel geometry, where the results are compared with other existing numerical solutions. The method is then validated against experiment and another numerical solution for the case of turbulent transonic flow through a gas turbine rotor blade cascade for which wind-tunnel experimental data exist

Modelling of annular flow through pipes and T-junctions

Abstract This paper describes a computational model for the prediction of isothermal annular two-phase flow in vertical and horizontal intersecting pipes and presents the results of its application to predict phase separation in a horizontal T-junction. The method is based on computational fluid dynamics techniques (CFD) to compute the dispersed core flow simultaneously with the flow of the liquid film along the walls. The core is represented as a dispersed two-phase mixture in which the droplets are tracked using a Lagrangian technique; the wall liquid film is modelled as a thin boundary layer. Full account is made of the interaction between the wall-film and the droplet flow in the core through mass and momentum transfer mechanisms. The method has already been validated against experimental data for fully developed annular flow in vertical and horizontal pipes; there, the predicted film thickness was found to be in satisfactory agreement with data obtained from the literature. The method is now applied to the phenomenon of phase separation occurring in T-junctions where it is found that the predictions for phase split agree quite well with measurements from an independent experiment for a range of phase split ratios. The predictions for wall-film thickness also exhibit similar trends to the data but do not quite match the locations where wall-film thickness peaks occur.

A method for particle location and field interpolation on complex, three-dimensional computational meshes

Abstract A method for locating particles within arbitrary three-dimensional computational meshes is described. It is based on an iterative procedure which uses transformed coordinates defined by iso-parametric functions. The method also enables one to interpolate field values from the mesh nodes to the particle position. Example applications demonstrate how effective the method is. For very distorted computational cells special practices have to be introduced in order to keep the number of iterations to a minimum.

Review of Applicability of the One‐dimensional Two‐fluid Model to the Prediction of Wave Growth and Slug Evolution in Horizontal Pipes

The paper reviews recently made advances in the application of the two‐fluid model to the numerical simulation of wave growth and ensuing development of slug flow in horizontal pipes. Results from the well‐established linear stability analysis of the governing equations are examined first. Such analyses show that under certain conditions, perturbations in stratified flow can grow into waves that may eventually develop into slugs; this has been verified by numerical computations. These computations can be followed through the growth phase of the waves to the evolution of continuous trains of slugs; this technique is called “slug capturing.” Such a capability provides a powerful tool for predicting slug flow and its characteristics like slug length and frequency in an automatic manner. This technique has been validated extensively against measurements and was found to give remarkably good agreement for slug characteristics. An interesting and remarkable finding is the ability of the model to predict the sta...

Applicability of the Momentum‐Flux‐Parameter Closure for the Two‐Fluid Model to Slug Flow

This paper investigates the use of the momentum flux closure relationship, with the aim of obtaining a well‐posed set of equations for the transient one‐dimensional two‐fluid model in the slug flow regime. The inclusion of the momentum flux parameters for the gas and liquid phases takes into account the effect of velocity profiles in the one‐dimensional area‐averaged equations. It is found that the new model is well‐posed only for certain values of the coefficient. However, the values necessary to ensure well‐posedness are much higher than is deemed to be physically plausible; also the slug flow properties predicted are at variance with experimental data.