G.J.F. Smit

Modelling of non-Newtonian purely viscous flow through isotropic high porosity synthetic foams

Abstract A unified modelling theory for the prediction of the pressure drop of non-Newtonian purely viscous flow through isotropic high porosity synthetic foams is proposed. The model is derived by volumetrically averaging the equations of motion over an arbitrary two-phase system of stationary solids and a traversing fluid. Closure is obtained by using a formerly introduced rectangular representation of the pore space morphology. The shear rate dependency of the viscosity is incorporated through the shear stress in terms of the power-law model. The proposed model, which is based purely on physical principles with no artificial adjusting parameters, is compared to other predictive models in terms of friction factor as a function of the Reynolds number. Predicted pressure drop results are also compared to published experimental results to verify the validity of the model.

Pressure drop prediction of power law fluid through granular media

Abstract A unified modelling theory for the prediction of the pressure drop of power law flow through granular media is evaluated against experimental data. The proposed model, for which the only changeable parameters are the porosity, microstructure length scale and the fluid properties, provides a satisfactory representation of the data for a relative large range Reynolds numbers.

Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid

Models that are used for the simulation of two-phase flows in coastal dynamics make extensive use of empirical data. The main focus of this investigation is to develop models for specific aspects of two-phase flows that are based on physical principles in order to reduce the use of such data. In this study several existing empirically based drag force models are discussed. The motion of spherical or near-spherical solid particles through a Newtonian fluid is investigated and a new method for closure of the drag force, using a Representative Unit Cell is discussed and compared to the existing models as well as to experimental data. The various drag models were also evaluated by numerical simulations, using an in-house developed program based on an adaptation of the SIMPLE procedure.

An analytical pore-scale, shear stress model for purely viscous non-Newtonian fluids traversing porous media

An analytical model for incompressible, generalized Newtonian fluids traversing granular porous media is proposed. This model is based on the volume averaging of the governing equations. Interstitial quantities are obtained through means of a pore‐scale model. For flow through porous media in the Darcy regime, the fluid‐solid interaction term is written in terms of the interstitial wall shear stress which is a function of the average interstitial channel velocities. The wall shear stress is obtained by assuming fully developed flow in the interstitial channels. Approximations are made in order to obtain explicit expressions for the wall shear stress. The final analytical expressions obtained for predicting the flow through porous media can easily be implemented numerically and allow for a wide variety of practical implementations.

Evaluation of shear stresses of generalized Newtonian fluids in pore scale closure models

A new analytical expression for the gradient of the intrinsic phase average of the pressure in terms of the wall shear stresses is proposed. This expression is obtained by volume averaging of the governing equations and closure by means of the two dimensional RUC model (a pore‐scale model for the analysis of fluid traversing a porous medium). One is the model for generalized Newtonian fluids traversing porous media and the other for fluid flowing through a two dimensional porous medium of which the interstitial channel widths may differ in size. The shear stresses in the interstitial channels of the RUC are evaluated by means of numerical simulations and compared to the fully developed velocity profile assumed in the RUC model.

On Particle‐Particle Interaction Forces for Dilute Systems

Particle‐particle interaction forces due to simple shear motion of particles relative to each other are investigated. The particle‐particle interaction force originates from the force balance equations derived for a single particle and extended to the group. A closed form is obtained using a combined collision sphere and REV approach. Rewriting in terms of a particle viscosity and rate of strain yields an expression which is similar to that proposed by [1].

Two Phase Flow Modelling for Low Concentration Spherical Particle Motion Through a Newtonian Fluid

Current models used for the simulation of two‐phase flows in coastal dynamics make extensive use of empirical data. The main focus of this investigation is to develop models for specific aspects of two‐phase flows that are based on physical principles in order to reduce the use of such data. In this study several existing empirically based drag force models are discussed. The motion of spherical or near‐spherical solid particles through a Newtonian fluid is investigated and a new method for the closure of the drag force, using a Representative Unit Cell is discussed and compared to the existing models as well as experimental data. The various drag models were also evaluated by numerical simulations, using an in‐house developed program based on an adaptation of the SIMPLE procedure.

Modelling Procedure For Prediction Of FlowThrough Porous Materials

Recent advances in a unified modelling theory, developed to quantify pressure gradients in homogeneous porous media, are discussed. The framework of the analytic modelling procedure is presented as well as the manner of inclusion of problem dependent specifications such as morphology, length scale, tortuosity and anisotropy of the porous medium microstructure and also the fluid rheology and interstitial Reynolds number.