On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods

2001 ◽  
Vol 123 (4) ◽  
pp. 941-947 ◽  
Author(s):  
Marcos H. J. Pedras ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Turbulent Flow ◽  
Porous Structure ◽  
Volume Averaging ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Periodic Cell ◽  
Initial Work ◽  
Adjusted Model

Many engineering and environmental system analyses can benefit from appropriate modeling of turbulent flow in porous media. Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, ε, a macroscopic model was proposed for such media (IJHMT, 44(6), 1081-1093, 2001). In that initial work, the medium was simulated as an infinite array of cylindrical rods. As an outcome of the volume averaging process, additional terms appeared in the equations for k and ε. These terms were here adjusted assuming now the porous structure to be modeled as an array of elliptic rods instead. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low Reynolds formulation, in the periodic cell composing the medium. Different porosity and Reynolds numbers were investigated. The fine turbulence structure of the flow was computed and integral parameters were presented. The adjusted model constant was compared to similar results for square and cylindrical rods. It is expected that the contribution herein provide some insight to modelers devoted to the analysis of engineering and a environmental systems characterized by a porous structure saturated by a fluid flowing in turbulent regime.

scholarly journals MACROSCOPIC TURBULENCE MODEL ADJUSTMENT FOR A POROUS MEDIUM MODELED AS AN INFINITE ARRAY OF TRANSVERSALLY-DISPLACED ELLIPTIC RODS

2003 ◽  
Vol 2 (2) ◽  
Author(s):  
M. H. J. Pedras ◽  
M. J. S. De Lemos
Keyword(s):  
Volume Averaging ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Governing Equations ◽  
Periodic Cell ◽  
Aspect Ratios ◽  
Infinite Array ◽  
Model Adjustment ◽  
High Reynolds ◽  
Adjusted Model

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, , a macroscopic model was proposed for flow in porous media (Pedras and de Lemos, IJHMT 44 (6) 2001). As an outcome of the volume averaging process, additional terms appeared in the equations for k and . These terms were here adjusted assuming the porous structure to be modeled as an infinity array of transversal elliptic rods. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low and high Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios were investigated. The adjusted model was compared against others types of rods found in the literature, showing similar results.

A General Macroscopic Model for Turbulent Flow in Porous Media

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Nima F. Jouybari ◽  
Mehdi Maerefat ◽  
T. Staffan Lundström ◽  
Majid E. Nimvari ◽  
Zahra Gholami
Keyword(s):  
Porous Media ◽  
Turbulent Flow ◽  
Present Model ◽  
Flow Characteristics ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Solid Matrix ◽  
Turbulent Regime ◽  
Rod Bundles ◽  
Capillary Model

The present study deals with the generalization of a macroscopic turbulence model in porous media using a capillary model. The additional source terms associated with the production and dissipation of turbulent kinetic energy due to the presence of solid matrix are calculated using the capillary model. The present model does not require any prior pore scale simulation of turbulent flow in a specific porous geometry in order to close the macroscopic turbulence equations. Validation of the results in packed beds, periodic arrangement of square cylinders, synthetic foams, and longitudinal flows such as pipes, channels, and rod bundles against available data in the literature reveals the ability of the present model in predicting turbulent flow characteristics in different types of porous media. Transition to the fully turbulent regime in porous media and different approaches to treat this phenomenon are also discussed in the present study. Finally, the general model is modified so that it can be applied to lower Reynolds numbers below the range of fully turbulent regime in porous media.

scholarly journals MACROSCOPIC TURBULENCE MODEL ADJUSTMENT FOR A POROUS MEDIUM MODELED AS AN INFINITE ARRAY OF TRANSVERSALLY-DISPLACED ELLIPTIC RODS

2003 ◽  
Vol 2 (2) ◽  
pp. 73
Author(s):  
M. H. J. Pedras ◽  
M. J. S. De Lemos
Keyword(s):  
Dissipation Rate ◽  
Infinite Medium ◽  
Macroscopic Model ◽  
Governing Equations ◽  
Periodic Cell ◽  
Aspect Ratios ◽  
Infinite Array ◽  
Model Adjustment ◽  
High Reynolds ◽  
Adjusted Model

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, , a macroscopic model was proposed for flow in porous media (Pedras and de Lemos, IJHMT 44 (6) 2001). As an outcome of the volume averaging process, additional terms appeared in the equations for k and . These terms were here adjusted assuming the porous structure to be modeled as an infinity array of transversal elliptic rods. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low and high Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios were investigated. The adjusted model was compared against others types of rods found in the literature, showing similar results.

scholarly journals Symmetry breaking of turbulent flow in porous media composed of periodically arranged solid obstacles

2021 ◽  
Vol 929 ◽  
Author(s):  
Vishal Srikanth ◽  
Ching-Wei Huang ◽  
Timothy S. Su ◽  
Andrey V. Kuznetsov
Keyword(s):  
Numerical Simulation ◽  
Porous Medium ◽  
Porous Media ◽  
Symmetry Breaking ◽  
Turbulent Flow ◽  
Vortex Shedding ◽  
Flow Instability ◽  
Flow In Porous Media ◽  
Turbulent Regime ◽  
Solid Obstacles

The focus of this paper is a numerical simulation study of the flow dynamics in a periodic porous medium to analyse the physics of a symmetry-breaking phenomenon, which causes a deviation in the direction of the macroscale flow from that of the applied pressure gradient. The phenomenon is prominent in the range of porosity from 0.43 to 0.72 for circular solid obstacles. It is the result of the flow instabilities formed when the surface forces on the solid obstacles compete with the inertial force of the fluid flow in the turbulent regime. We report the origin and mechanism of the symmetry-breaking phenomenon in periodic porous media. Large-eddy simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct numerical simulation is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget and (2) two- and three-dimensional flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape and Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid-obstacle geometries. In the macroscale, the principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry breaking in porous media involves unresolved flow physics that should be taken into consideration while modelling flow inhomogeneity in the macroscale.

scholarly journals Incompressible variable-density turbulence in an external acceleration field

2017 ◽  
Vol 827 ◽  
pp. 506-535 ◽  
Author(s):  
Ilana Gat ◽  
Georgios Matheou ◽  
Daniel Chung ◽  
Paul E. Dimotakis
Keyword(s):  
Growth Rate ◽  
Turbulent Flow ◽  
Shear Layers ◽  
Variable Density ◽  
Fluid Composition ◽  
Turbulent Regime ◽  
Low Density ◽  
Acceleration Field ◽  
Density Ratios ◽  
Mixed Fluid

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

Investigating the entropy generation around an airfoil in turbulent flow

2020 ◽  
Vol 92 (7) ◽  
pp. 1001-1017
Author(s):  
Mohammad Reza Saffarian ◽  
Farzad Jamaati ◽  
Amin Mohammadi ◽  
Fatemeh Gholami Malekabad ◽  
Kasra Ayoubi Ayoubloo
Keyword(s):  
Mach Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Entropy Generation ◽  
Turbulent Regime ◽  
Content Type ◽  
Sst Turbulence Model ◽  
Effects Of Temperature ◽  
Energy Equations ◽  
Naca 0012

Purpose This study aims to evaluate the amount of entropy generation around the NACA 0012 airfoil. This study takes place in four angles of attack of 0°, 5°, 10° and 16° and turbulent regime. Also, the variation in the amount of generated entropy by the changes in temperature and Mach number is investigated. Design/methodology/approach The governing equations are solved using computational fluid dynamics techniques. The continuity, momentum and energy equations and the equations of the SST k-ω turbulence model are solved. The entropy generation at different angles of attack is calculated and compared. The effect of various parameters in the generation of entropy is presented. Findings Results show that the major part of the entropy generation is at the tip of the airfoil. Also, increasing the angle of attack will increase the entropy generation. Also, results show that with increasing the temperature of air colliding with the airfoil, the production of entropy decreases. Originality/value Entropy generation is investigated in the NACA 0012 airfoil at various angles of attack and turbulent flow using the SST turbulence model. Also, the effects of temperature and Mach number on the entropy generation are investigated.

Effects of Roughness on Turbulent Flow in Microchannels and Minichannels

2008 ◽  
Author(s):  
Timothy P. Brackbill ◽  
Satish G. Kandlikar
Keyword(s):  
Experimental Study ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Roughness Parameter ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Roughness Elements ◽  
Moody Diagram

The effect of roughness ranging from smooth to 24% relative roughness on laminar flow has been examined in previous works by the authors. It was shown that using a constricted parameter, εFP, the laminar results were predicted well in the roughened channels ([1],[2],[3]). For the turbulent regime, Kandlikar et al. [1] proposed a modified Moody diagram by using the same set of constricted parameters, and using the modification of the Colebrook equation. A new roughness parameter εFP was shown to accurately portray the roughness effects encountered in laminar flow. In addition, a thorough look at defining surface roughness was given in Young et al. [4]. In this paper, the experimental study has been extended to cover the effects of different roughness features on pressure drop in turbulent flow and to verify the validity of the new parameter set in representing the resulting roughness effects. The range of relative roughness covered is from smooth to 10.38% relative roughness, with Reynolds numbers up to 15,000. It was found that using the same constricted parameters some unique characteristics were noted for turbulent flow over sawtooth roughness elements.

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