J.P. Du Plessis

Pressure drop modelling in cellular metallic foams

Abstract A theoretical model is presented for the prediction of pressure drop in a Newtonian fluid flowing through highly porous, isotropic metallic foams. The model is based on a rigorous assumption of piece-wise plane Poiseuille flow and a simplistic geometrical model, and shows promise to accurately predict the hydrodynamic conditions in both the Darcy and Forchheimer regimes, without a priori knowledge of the flow behaviour of the particular metallic foam.

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.

Heat transfer correlation for thermally developing laminar flow in a smooth tube with a twisted-tape insert

Abstract A new method of correlating heat transfer characteristics is presented for the case of thermally developing laminar flow in a smooth tube with a twisted-tape insert. The tube is considered to be at a constant temperature axially and peripherally and the tape is fully adiabatic. The correlating method is based on numerical results for the case on an infinitely thin tape and the finite tape thickness is incorporated through the definition of effective flow parameters. A complete step-by-step procedure for the implementation of the final correlative equation is presented.

Friction factor prediction for fully developed laminar twisted-tape flow

Abstract Friction factor characteristics are necessary for the evaluation of the efficiency of heat transfer enhancement by means of a twisted-tape insert in a smooth tube. Effective flow parameters are introduced to facilitate the correlation of friction factor data in such cases. A utility chart from which the friction factor-Reynolds number product for twisted-tape flow may be predicted, is presented in graphical form. Results from a parametric numerical study on laminar, constant property twisted-tape flow are provided and also presented graphically. These results are used to construct a correlative expression from which friction factor characteristics for laminar flow may be obtained. The finite thickness of the tape is taken into consideration.

On Closure Modelling Of Volume AveragedEquations For Flow Through Two-dimensionalArrays Of Squares

The closure of volume averaged equations for creep flow through two-dimensional arrays of squares is discussed. Use is made of a representative unit cell for the approximation of the stresses at fluid-solid interfaces and the resulting equations are applicable to fluid discharge through regular arrays or isotropic ensembles of squares. Subdivision of the pore space into volumes where different physical effects predominate, forms an important framework for the assumptions of the analyticalmodel.Thisalso leadsto thedefinitionofa streamlinetortuosityin terms of the said sub-volumes. Numerical prediction of the flow within a representative unit cell was carried out to determine the accuracy of the analytical model. The result is a simplistic deterministic model for the prediction of creep flow through arrays of squares which forms the lower Reynolds number limit for a more general model.

A Two-Equation Model for Heat Conduction in Porous Media I Theory

A two-equation model is presented which describes the conservation of heat in each phase of a porous medium in which diffusion is the predominant means of heat transfer, and of which the phases are not in thermal equilibrium with each other. The model is derived using the method of local volume averaging. This formulation, together with the introduction of characteristic temperature distributions, yields the definition of an effective and a coupled thermal conductivity tensor.

Saturated crossflow through a two-dimensional porous medium

Abstract Momentum transport equations for laminar incompressible Newtonian flow through a two-dimensional porous medium are derived. The modelling is based on volume averaging concept. A rectangular representation of fluid-solid interfaces renders the transport equations applicable over the entire porosity range from zero through unity. Non-linear effects in the velocity-pressure gradient relationship are introduced through consideration of flow development along solid surfaces within the porous medium. The results are also applicable to crossflow through a bundle of parallel but arbitrarily scattered tubes.

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.

On tortuosity and areosity tensors for porous media

An average streamwise channel velocity is proposed as a more accurate representation of the actual intrapore velocity than the intrinsic phase average velocity. A relationship is derived between the average streamwise channel velocity and the interstitial velocity and superficial velocity. New definitions of tortuosity and areosity as second-order tensors are proposed for porous media in general. Novel names, semantically in line with the respective physical meanings, are proposed for these quantities. The definitions produce results which conform with several other published results and are applicable to anisotropic media in general.

REFORMULATION OF THE SIMPLEN DISCRETIZATION SCHEME TO ACCOMMODATE NONCENTRALIZED INTERFACES

The SIMPLEN discretization scheme based on a nonstaggered orthogonal grid is derived from an extension of the original power-law scheme. A revised interface interpolation equation, which no longer requires the interfaces to be located centrally between nodes, is presented. The expression for the orthogonal interface convection-diffusion flux is reformulated and the associated pressure correction factor is provided. The adopted formulation allows boundary control volumes to be treated essentially as internal control volumes and leads to an update of the power-law approximation to improve its accuracy. The extended method is applied to two test cases of laminar incompressible flow.