Simulation of Free Convection in a Porous Enclosure Using the One-Temperature Approach

2014 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Paulo H. S. Carvalho
Keyword(s):  
Nusselt Number ◽  
Control Volume ◽  
Simple Algorithm ◽  
Fluid Phase ◽  
Solid Material ◽  
Solid Matrix ◽  
Thermal Conductivity Ratio ◽  
Turbulent Regime ◽  
Algebraic Equations ◽  
The One

This article investigates the influence of porosity and thermal conductivity ratio on the Nusselt number in a heated vertical cavity. Heat transfer modeling across the enclosure assumed the hypothesis of thermal equilibrium between the solid matrix and the fluid phase. Transport equations were discretized using the control-volume method and the system of algebraic equations was relaxed via the SIMPLE algorithm. Results showed that, when using the one temperature model under the turbulent regime, the cavity Nusselt number is reduced for higher values of the ratio ks/kf as well as when the material porosity is increased. In both cases, conduction through the solid material overwhelms convection across the medium.

Turbulent Double-Diffusive Free Convection in a Porous Square Cavity Simulated With the Two Temperature Approach

2016 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Paulo H. S. Carvalho
Keyword(s):  
Solid Phase ◽  
Control Volume ◽  
Chemical Species ◽  
Simple Algorithm ◽  
Fluid Phase ◽  
Solid Matrix ◽  
Thermal Conductivity Ratio ◽  
Algebraic Equations ◽  
Square Cavity ◽  
Volume Method

This work investigates the influence of thermal conductivity ratio on energy and mass transport across a porous square cavity. Modeling of heat transfer from side to side of the enclosure assumed the hypothesis of thermal non-equilibrium between the solid matrix and the fluid phase. Transport equations were discretized using the control-volume method and the system of algebraic equations obtained was relaxed via the SIMPLE algorithm. Results showed that Shw, mass flux of chemical species and heat flux in the solid phase are strongly dependent of ks/kf, significantly increasing their values as such ratio increases.

Effect of Thermal Conductivity Ratio on Laminar Double-Diffusive Free Convection in a Porous Cavity

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Paulo H. S. Carvalho ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Free Convection ◽  
Thermal Equilibrium ◽  
Control Volume ◽  
Simple Algorithm ◽  
Thermal Conductivity Ratio ◽  
Control Volume Method ◽  
Algebraic Equations ◽  
Square Cavity ◽  
Volume Method ◽  
Double Diffusive

This work presents a study on double-diffusive free convection in a porous square cavity using the thermal equilibrium model. Transport equations are discretized using the control-volume method, and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effect of ks/kf on average Nusselt and Sherwood values was investigated. Results show that increasing ks/kf affects Nuw and Shw boosting mass transfer at the expense of reducing overall heat transport across the enclosure.

A Thermo-Mechanical Model for a Counterflow Biomass Gasifier

2014 ◽  
Vol 354 ◽  
pp. 227-235
Author(s):  
Marcelo J.S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Control Volume ◽  
Simple Algorithm ◽  
Thermal Capacity ◽  
Macroscopic Model ◽  
Algebraic Equations ◽  
Medium Permeability ◽  
Mechanical Approach ◽  
Volume Method

This article presents a thermo-mechanical approach to investigate heat transfer between solid and fluid phases in a model gasifier. A two-temperature equation approach is applied in addition to a macroscopic model for laminar flow through a porous moving bed. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effects on inter-phase heat transfer due to variation of medium permeability, thermal conductivity and thermal capacity are analyzed. Results indicate that for smaller medium permeabilities, as well as for higher solid-to-fluid thermal capacity and thermal conductivity ratios, enhancement of heat transfer between phases is observed.

Use of Foam-Like Materials to Enhance Heat Transfer From Surfaces Subjected to Impinging Jets

2009 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Cleges Fischer
Keyword(s):  
Thermal Conductivity ◽  
Porous Layer ◽  
Control Volume ◽  
Simple Algorithm ◽  
Impinging Jets ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
System Pressure ◽  
Volume Method ◽  
Range Of Values

In this paper, numerical simulation of a jet impinging against a flat plane covered with a layer of a porous material is presented. The plate is kept at a temperature higher than that of the incoming fluid. Macroscopic transport equations are obtained based on a volume average concept. Discretization of such governing equations is accomplished by means of the control volume method applied with a boundary-fitted nonorthogonal coordinate system. Pressure-velocity coupling is treated with the use of the SIMPLE algorithm. Parameters such as permeability, thickness of the porous layer and thermal conductivity ratio are varied in order to analyze their effects on the local distribution of Nu. Results indicate that inclusion of a porous layer decreases the peak in Nu avoiding excessive heating or cooling at the stagnation point. Also found was that the integral heat flux from the wall is enhanced for certain range of values of layer thickness, porosity, and thermal conductivity ratio.

scholarly journals Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

10.29007/31n4 ◽  
2018 ◽  
Author(s):  
Luca Cozzolino ◽  
Raffaele Castaldo ◽  
Luigi Cimorelli ◽  
Renata Della Morte ◽  
Veronica Pepe ◽  
...  
Keyword(s):  
Shallow Water ◽  
Riemann Problem ◽  
Shallow Water Equations ◽  
Initial Conditions ◽  
Numerical Models ◽  
Control Volume ◽  
Fluid Phase ◽  
Problem Solution ◽  
The One ◽  
Solid Obstacles

The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.

scholarly journals A detailed analysis of flow and heat transfer characteristics under a turbulent intermittent jet impingement on a concave surface

2021 ◽  
pp. 334-334
Author(s):  
Ali Hajimohammadi ◽  
Mehran Zargarabadi ◽  
Javad Mohammadpour
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Average Nusselt Number ◽  
Computational Study ◽  
Control Volume ◽  
Simple Algorithm ◽  
Jet Impingement ◽  
Concave Surface ◽  
Flow And Heat Transfer

A computational study is carried out of the three-dimensional flow field and heat transfer under a turbulent intermittent circular jet impingement on a concave surface. The control-volume procedure with the SIMPLE algorithm is employed to solve the unsteady RANS (use full form) equations. The RNG k-? model is implemented to simulate turbulence due to its success in predicting similar flows. The numerical results are validated by comparing them with the experimental data. The effects of jet Reynolds number and oscillation frequency on the flow and heat transfer are evaluated. The profiles of instantaneous and time-averaged Nusselt numbers exhibit different trends in axial (x) and circumferential (s) directions. It is found that increasing frequency from 50 to 200 Hz results in considerable time-averaged Nusselt number enhancement in both axial and curvature directions. The intermittent jet at a frequency of 200 Hz enhances the total average Nusselt number by 51.4%, 40%, and 33.7% compared to the steady jet values at jet Reynolds numbers of 10000, 23000, and 40000, respectively. In addition, a correlation for the average Nusselt number is proposed depending on the Reynolds number and the Strouhal number.

scholarly journals An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

Direct numerical simulation of a turbulent jet impinging on a heated wall

2015 ◽  
Vol 764 ◽  
pp. 362-394 ◽  
Author(s):  
T. Dairay ◽  
V. Fortuné ◽  
E. Lamballais ◽  
L.-E. Brizzi
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Nusselt Number ◽  
Direct Numerical Simulation ◽  
Temperature Fields ◽  
Heated Wall ◽  
Small Scale ◽  
Turbulent Regime ◽  
High Heat Transfer ◽  
Radial Evolution

AbstractDirect numerical simulation (DNS) of an impinging jet flow with a nozzle-to-plate distance of two jet diameters and a Reynolds number of 10 000 is carried out at high spatial resolution using high-order numerical methods. The flow configuration is designed to enable the development of a fully turbulent regime with the appearance of a well-marked secondary maximum in the radial distribution of the mean heat transfer. The velocity and temperature statistics are validated with documented experiments. The DNS database is then analysed focusing on the role of unsteady processes to explain the spatial distribution of the heat transfer coefficient at the wall. A phenomenological scenario is proposed on the basis of instantaneous flow visualisations in order to explain the non-monotonic radial evolution of the Nusselt number in the stagnation region. This scenario is then assessed by analysing the wall temperature and the wall shear stress distributions and also through the use of conditional averaging of velocity and temperature fields. On one hand, the heat transfer is primarily driven by the large-scale toroidal primary and secondary vortices emitted periodically. On the other hand, these vortices are subjected to azimuthal distortions associated with the production of radially elongated structures at small scale. These distortions are responsible for the appearance of very high heat transfer zones organised as cold fluid spots on the heated wall. These cold spots are shaped by the radial structures through a filament propagation of the heat transfer. The analysis of probability density functions shows that these strong events are highly intermittent in time and space while contributing essentially to the secondary peak observed in the radial evolution of the Nusselt number.

scholarly journals Study of convection heat transfer enhancement inside lid driven cavity utilizing fins and nanofluid

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2431-2442
Author(s):  
Arash Lavasani ◽  
Mousa Farhadi ◽  
Darzi Rabienataj
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Richardson Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Convection Flow ◽  
Driven Cavity ◽  
Ratio Change ◽  
Hot Surface

In the present study, the effect of suspension of nanoparticle on mixed convection flow is investigated numerically in lid driven cavity with fins on its hot surface. Study is carried out for Richardson numbers ranging from 0.1 to 10, fin(s) height ratio change from 0.05 to 0.15 and volume fraction of nanoparticles from 0 to 0.03, respectively. The thermal conductivity ratio (kfin/kf) is equal to 330 and Grashof number is assumed to be constant (104) so that the Richardson numbers changes with Reynolds number. Results show that the heat transfer enhances by using nanofluid for all studied Richardson numbers. Adding fins on hot wall has different effects on heat transfer depend to Richardson number and height of fins. Use of low height fin in flow with high Richardson number enhances the heat transfer rate while by increasing the height of fin the heat transfer reduces even lower than it for pure fluid. The overall enhancement in Nusselt number by adding 3% nanoparticles and 3 fins is 54% at Ri=10. They cause reduction of Nusselt Number by 25% at Ri=0.1. Higher fins decrease the heat transfer due to blocking fluid at corners of fins.

scholarly journals A Simple Algorithm for Finding a Non-negative Basic Solution of a System of Linear Algebraic Equations

2021 ◽  
Vol 28 (3) ◽  
pp. 234-237
Author(s):  
Gleb D. Stepanov
Keyword(s):  
Simplex Method ◽  
Gaussian Elimination ◽  
Simple Algorithm ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Linear Programming Problems ◽  
Two Stages ◽  
Computational Resources

This article describes an algorithm for obtaining a non-negative basic solution of a system of linear algebraic equations. This problem, which undoubtedly has an independent interest, in particular, is the most time-consuming part of the famous simplex method for solving linear programming problems.Unlike the artificial basis Orden’s method used in the classical simplex method, the proposed algorithm does not attract artificial variables and economically consumes computational resources.The algorithm consists of two stages, each of which is based on Gaussian exceptions. The first stage coincides with the main part of the Gaussian complete exclusion method, in which the matrix of the system is reduced to the form with an identity submatrix. The second stage is an iterative cycle, at each of the iterations of which, according to some rules, a resolving element is selected, and then a Gaussian elimination step is performed, preserving the matrix structure obtained at the first stage. The cycle ends either when the absence of non-negative solutions is established, or when one of them is found.Two rules for choosing a resolving element are given. The more primitive of them allows for ambiguity of choice and does not exclude looping (but in very rare cases). Use of the second rule ensures that there is no looping.

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