Ron Barron

On the Darcy-Lapwood-Brinkman-Saffman dusty fluid flow models through porous media part I: models development

Abstract Mathematical models based on the differential equations approach are developed to describe the motion of an incompressible dusty fluid in porous media. The macroscopic governing equations are derived through the volume-averaging technique and take into account the cases of one-way and two-way interaction between the phases present. The models, based on Saffmans dusty gas model, are then subclassified to account for the different types of flow through porous media.

A new numerical approach to solve an elliptic equation

A new numerical approach to solve an elliptic partial differential equation that originates from the governing equations of steady state fluid flow and heat transfer is presented. The elliptic partial differential equation is transformed by introducing an exponential function to eliminate the convection terms in the equation. A fourth-order central differencing scheme and a second-order central differencing scheme are used to numerically solve the transformed elliptic partial differential equation. Analytical solutions of this equation are also given. Comparisons are made between the analytical solutions, the numerical results using the present schemes, and those using the four classical differencing schemes, namely, the first-order upwind scheme, hybrid scheme, power-law scheme, and exponential scheme. The comparisons illustrate that the proposed algorithm performs better than the four classical differencing schemes.

Round impinging jets with relatively large stand-off distance

Large eddy simulation and particle image velocimetry measurements have been performed to evaluate the characteristics of a turbulent impinging jet with large nozzle height-to-diameter ratio (H/D = 20). The Reynolds number considered is approximately 28 000 based on the jet exit velocity and nozzle diameter. Mean normalized centerline velocity in both the free jet and impingement regions and pressure distribution over the plate obtained from simulations and experiments show good agreement. The ring-like vortices generated due to the Kelvin-Helmholtz instabilities at the exit of the nozzle merge, break down and transform into large scale structures while traveling towards the impingement plate. A Strouhal number of 0.63 was found for the vortices generated at the exit of the nozzle. However, this parameter is reduced along the centerline towards the impingement zone. A characteristic frequency was also determined for the large scale structures impinging on the plate. The expansion, growth, tilt, and three-d...

Analysis of the Darcy-Lapwood and the Darcy-Lapwood-Brinkman models: significance of the laplacian

A numerical solution for fluid flow through a porous medium as governed by the Darcy-Lapwood model is obtained by solving the Darcy-Lapwood-Brinkman model. The failure of the Darcy-Lapwood model in describing certain flow situations is also illustrated. A solution for the flow through a porous medium overlying curved boundaries is also obtained for the Darcy-Lapwood-Brinkman equation for moderate Re, using a numerical approach to the von Mises transformation. The viscous effects incorporated in the Darcy-Lapwood-Brinkman model are important in the study of viscous fluid flow through bounded porous media in order to include the no-slip condition on solid boundaries associated with this equation, but it is shown that these viscous effects are not so important in the current study of flow through porous media over a special type of curved boundary.

Numerical simulation of cavity flows based on transformed equations

A new numerical algorithm is applied to simulate two-dimensional lid-driven cavity flows. In this new algorithm, the momentum equations are first transformed using an exponential function to eliminate the convection terms in the equations. Then a central differencing scheme is employed to discretize the transformed equations. The cavity flows studied in this work include those with non-zero velocity component in the y-direction on the upper and lower boundaries. The results for the velocity components along the geometric centerline, stream function patterns, and vorticity contours are presented and discussed. The predicted results are in excellent agreement with benchmark solutions.

On the Darcy-Lapwood-Brinkman-Saffman dusty fluid flow models through porous media part II: applications to flow into a two-dimensional sink

Abstract The differential equations governing the flow of an incompressible dusty fluid through porous media, based on the Darcy-Lapwood-Brinkman-Saffman (DLB-S) models derived in Part I are solved numerically to illustrate the deterministic nature of the models and to study the effect of introducing a small concentration of dust, by volume, on the fluid-phase characteristics. The fluid is assumed to flow through a finite porous channel into a two-dimensional line sink. Various models are treated to provide a comparison between the two-way and the different one-way interaction processes possible between the phases present. Analyses indicate that the way in which the Darcy resistance is defined is a major distinguishing factor between the models.

Submerged Hydraulic Jump Study Using DES

AbstractIn the present paper, three-dimensional, unsteady, detached eddy simulation (DES) of a submerged hydraulic jump with an inlet Froude number of 8.2 is performed. The volume of fluid (VOF) method with a high-resolution interface capturing (HRIC) scheme is used for free-surface tracking. The mean velocity and turbulence quantities including the Reynolds stresses are compared with available experimental data to validate the results. The three-dimensional nature of the flow in the developing and developed zone of the submerged hydraulic jump is evaluated by examining the coherent structures using the λ2 criteria. Additionally, proper orthogonal decomposition (POD) analysis reveals the dominance of smaller structures in the developed region of the submerged hydraulic jump. The presence of these smaller scales is directly responsible for the energy dissipation characteristic of the submerged hydraulic jump.

CFD Simulation of Boiling Heat Transfer Using OpenFOAM

An Eulerian-Eulerian two-phase flow model has been developed to simulate the boiling heat transfer phenomenon in a pipe flow. The model was implemented in the OpenFOAM source code. The code development process was divided into two sections. In the first step, an adiabatic two-phase flow model which takes into account the effect of interfacial forces was developed. In the second step, the energy equation was activated to account for non-adiabatic conditions. In order to include the boiling effect, several different subroutines which model evaporation and condensation phenomena were attached to the solver. Results of the two-phase adiabatic flow and from the boiling model are compared with available numerical and experimental data. The simulation predictions are in reasonable agreement with the experimental data and show significant improvement relative to previous numerical results, which suggests the validity of the developed model for boiling heat transfer problems.Copyright

A new numerical algorithm based on transformed equations and its applications to very low Re fluid flows

A new numerical algorithm is presented in this study to solve the partial differential equations that govern fluid flows. This new algorithm is based on first transforming the partial differential equations by introducing an exponential function to eliminate the convection terms. A fourth-order central differencing scheme and a second-order central differencing scheme are used to discretize the transformed equations. The algorithm is then applied to simulate fluid flows with exact solutions to validate this new algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. Comparisons against the exact solution are made for the results obtained using the new numerical algorithm as well as the power-law scheme. The comparisons indicate that the present fourth-order scheme performs the best and the present second-order scheme is the next most accurate.

Large Eddy Simulation of Round Impinging Jets With Large Stand-Off Distance

Large Eddy Simulation (LES) has been carried out to study the flow of a turbulent impinging jet with large nozzle height-to-diameter ratio. The dynamic Smagorinsky model was used to simulate the subgrid-scale stresses. The jet exit Reynolds number is 28,000. The study presents a detailed evaluation of the flow characteristics of an impinging jet with nozzle height of 20 diameters above the plate. Results of the mean normalized centerline velocity and wall shear stress show good agreement with previous experiments. Analysis of the flow field shows that vortical structures generated due to the Kelvin-Helmholtz instabilities in the shear flow close to the nozzle undergo break down or merging when moving towards the plate. Unlike impinging jets with small stand-off distance where the ring-like vortices keep their interconnected shape upon reaching the plate, no sign of interconnection was observed on the plate for this large stand-off distance. A large deflection of the jet axis was observed for this type of impinging jet when compared to the cases with small nozzle height-to-diameter ratios.Copyright