A Numerical Study of Developing Free Convection Between Isothermal Vertical Plates

1991 ◽  
Vol 113 (3) ◽  
pp. 620-626 ◽  
Author(s):  
D. Naylor ◽  
J. M. Floryan ◽  
J. D. Tarasuk
Keyword(s):  
Free Convection ◽  
Numerical Study ◽  
Navier Stokes ◽  
Elliptic Solution ◽  
Inlet Flow ◽  
Number Range ◽  
Aspect Ratios ◽  
Cast Doubt ◽  
Elliptic Solutions ◽  
Energy Equations

Steady two-dimensional laminar free convection between isothermal vertical plates including entrance flow effects has been numerically investigated. The full elliptic forms of the Navier-Stokes and energy equations are solved using novel inlet flow boundary conditions. Results are presented for Prandtl number Pr = 0.7, Grashof number range 50 ≤ Grb ≤ 5×104, and channel aspect ratios of L/b = 10, 17, 24. New phenomena, such as inlet flow separation, have been observed. The results cast doubt on the validity of previous elliptic solutions. Comparisons with the approximate boundary-layer results show that a full elliptic solution is necessary to get accurate local quantities near the channel entrance.

Numerical Performances Study of Curved Photovoltaic Panel Integrated with Phase Change Material

2020 ◽  
Vol 22 (4) ◽  
pp. 1439-1452
Author(s):  
Mohamed L. Benlekkam ◽  
Driss Nehari ◽  
Habib Y. Madani
Keyword(s):  
Phase Change ◽  
Phase Change Material ◽  
Numerical Study ◽  
Numerical Data ◽  
Navier Stokes ◽  
Photovoltaic Panel ◽  
Pv Panel ◽  
Energy Equations ◽  
Solid Liquid ◽  
Change Material

AbstractThe temperature rise of photovoltaic’s cells deteriorates its conversion efficiency. The use of a phase change material (PCM) layer linked to a curved photovoltaic PV panel so-called PV-mirror to control its temperature elevation has been numerically studied. This numerical study was carried out to explore the effect of inner fins length on the thermal and electrical improvement of curved PV panel. So a numerical model of heat transfer with solid-liquid phase change has been developed to solve the Navier–Stokes and energy equations. The predicted results are validated with an available experimental and numerical data. Results shows that the use of fins improve the thermal load distribution presented on the upper front of PV/PCM system and maintained it under 42°C compared with another without fins and enhance the PV cells efficiency by more than 2%.

Numerical Study of the Effect of Inlet Constriction on Bubble Growth During Flow Boiling in Microchannels

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Vapor Bubbles ◽  
Reversed Flow ◽  
Cross Sectional ◽  
Parallel Microchannels ◽  
Energy Equations

Flow boiling through microchannels is characterized by nucleation of vapor bubbles on the channel walls and their rapid growth as they fill the entire channel cross-section. In parallel microchannels connected through a common header, formation of vapor bubbles often results in flow maldistribution that leads to reversed flow in certain channels. The reversed flow is detrimental to the heat transfer and leads to early CHF condition. One way of eliminating the reversed flow is to incorporate flow restrictions at the channel inlet. In the present numerical study, a nucleating vapor bubble placed near the restricted end of a microchannel is numerically simulated. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The results show that with no restriction the bubble moves towards the nearest channel outlet, whereas in the presence of a restriction, the bubble moves towards the distant but unrestricted end. It is proposed that channels with increasing cross-sectional area may be used to promote unidirectional growth of the vapor plugs and prevent reversed flow.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Flow Characteristics in a Three-Dimensional Rectangular Channel With a Pair of Ribs Placed Symmetrically at the Channel Walls

2000 ◽  
Author(s):  
M. Singh ◽  
P. K. Panigrahi ◽  
G. Biswas
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Energy Equations

Abstract A numerical study of rib augmented cooling of turbine blades is reported in this paper. The time-dependent velocity field around a pair of symmetrically placed ribs on the walls of a three-dimensional rectangular channel was studied by use of a modified version of Marker-And-Cell algorithm to solve the unsteady incompressible Navier-Stokes and energy equations. The flow structures are presented with the help of instantaneous velocity vector and vorticity fields, FFT and time averaged and rms values of components of velocity. The spanwise averaged Nusselt number is found to increase at the locations of reattachment. The numerical results are compared with available numerical and experimental results. The presence of ribs leads to complex flow fields with regions of flow separation before and after the ribs. Each interruption in the flow field due to the surface mounted rib enables the velocity distribution to be more homogeneous and a new boundary layer starts developing downstream of the rib. The heat transfer is primarily enhanced due to the decrease in the thermal resistance owing to the thinner boundary layers on the interrupted surfaces. Another reason for heat transfer enhancement can be attributed to the mixing induced by large-scale structures present downstream of the separation point.

Three-Dimensional Simulation of Laminar Rectangular Impinging Jets, Flow Structure, and Heat Transfer

1999 ◽  
Vol 121 (1) ◽  
pp. 50-56 ◽  
Author(s):  
I. Sezai ◽  
A. A. Mohamad
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Impinging Jets ◽  
Navier Stokes ◽  
Aspect Ratios ◽  
Laminar Jets ◽  
Nusselt Number Distribution ◽  
Dimensional Simulation ◽  
Energy Equations

The flow and heat transfer characteristics of impinging laminar jets issuing from rectangular slots of different aspect ratios have been investigated numerically through the solution of three-dimensional Navier-Stokes and energy equations in steady state. The three-dimensional simulation reveals the existence of pronounced streamwise velocity off-center peaks near the impingement plate. Furthermore, the effect of these off-center velocity peaks on the Nusselt number distribution is also investigated. Interesting three-dimensional flow structures are detected which cannot be predicted by two-dimensional simulations.

scholarly journals The effect of surface regression on the downward flame spread over a solid fuel in a quiescent ambient

2007 ◽  
Vol 11 (2) ◽  
pp. 67-86 ◽  
Author(s):  
Mohammad Ayani ◽  
Javad Esfahani ◽  
Antonio Sousa
Keyword(s):  
Solid Fuel ◽  
Flame Spread ◽  
Solid Phase ◽  
Numerical Study ◽  
Control Volume ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Gas Temperature ◽  
Arrhenius Kinetics ◽  
Energy Equations

The present work is addressed to the numerical study of the transient laminar opposed-flow flame spread over a solid fuel in a quiescent ambient. The transient governing equations - full Navier-Stokes, energy, and species (oxygen and volatiles) for the gas phase, and continuity and energy equations for the solid phase (fuel) with primitive variables are discretized in a staggered grid by a control volume approach. The second-order Arrhenius kinetics law is used to determine the rate of consumption of volatiles due to combustion, and the zero-order Arrhenius kinetics law is used to determine the rate of degradation of solid fuel. The equations for the fluid and solid phases are solved simultaneously using a segregated technique. The physical and thermo-physical properties of the fluid (air) such as density, thermal conductivity, and viscosity vary with temperature. The surface regression of the solid fuel is modeled numerically using a discrete formulation, and the effect upon the results is analyzed. The surface regression of the solid fuel as shown affects on the fuel surface and gas temperature, mass flux and velocity of volatiles on the top surface of fuel, total energy transferred to the solid phase, etc. It seems the results to be realistic. .

scholarly journals Numerical study of the coupled natural convection with surface radiation in a cylindrical annular enclosure

2020 ◽  
Vol 330 ◽  
pp. 01029
Author(s):  
Mohamed Amine MEDEBBER ◽  
Abderrahmane AISSA ◽  
Belkacem OULD SAID ◽  
Noureddine RETIEL ◽  
Mohammed EL GANAOUI
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Surface Radiation ◽  
Navier Stokes ◽  
Simpler Algorithm ◽  
Energy Equations ◽  
Volume Method ◽  
Rayleigh Numbers ◽  
Total Average

The interaction of natural convection with thermal radiation of black surfaces in a cylindrical enclosure filled with air has been numerically investigated. The steady-state continuity, Navier-Stokes and energy equations were discretized using the control volume method and solved numerically via the SIMPLER algorithm. Effects of Rayleigh number (Ra), wall emissivity (εp) and height ratio parameter (X) are studied. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The total average Nusselt number has also been discussed for valuating heat transfer through the enclosure.

Estimation of Aerodynamic Heating on Scramjet Inlets and Validation with Measurements

2021 ◽  
pp. 1-36
Author(s):  
Ram Prabhu M ◽  
Chakravarthy Balaji ◽  
Thirumalachari Sundararajan ◽  
Chacko M J
Keyword(s):  
Heat Flux ◽  
Navier Stokes ◽  
Aerodynamic Heating ◽  
Number Range ◽  
Flow Simulations ◽  
Long Duration ◽  
Standard Design ◽  
Flow Features ◽  
Flux Estimation ◽  
Energy Equations

Abstract Aerodynamic heating levels on a typical inlet configuration of a scramjet engine are estimated using both standard design correlations and numerical flow simulations. The stagnation point heat flux is estimated using the Fay and Riddell formula. Aerodynamic heating over the inclined ramps is estimated using the Van Driest method. Numerical flow simulations are carried out using a Reynolds Averaged Navier Stokes (RANS) solver coupled with energy equations and the Shear Stress Transport (SST) k-ω turbulence model. The aerodynamic heat flux estimates are validated with in-house measurements in a shock tunnel and for a scramjet flight experiment in the Mach number range 1.59 to 7.92. The emergence of a good agreement between them confirms the appropriateness of design correlations for heat flux estimation in scramjet inlets. The choice of simplification and appropriateness of design correlations to complex geometries demand critical assessment. Numerical flow simulations capture flow features and enable identification of potential augmented heating zones, which will be critical for long duration scramjet missions.

Effect of Surface Radiation on Free Convection in Vertical Cylinders Partially Annular

2018 ◽  
Vol 389 ◽  
pp. 36-49
Author(s):  
Belkacem Ould Said ◽  
Mohamed Amine Medebber ◽  
Nourddine Retiel
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Radiation Heat Transfer ◽  
Surface Radiation ◽  
Navier Stokes ◽  
Discrete Ordinates ◽  
Energy Equations ◽  
Vertical Cylinders ◽  
Rayleigh Numbers ◽  
Emissivity Coefficient

The coupled of free convection with surface radiation in an annular region of two concentric vertical cylinders filled with air has been numerically investigated. The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation (RTE). The computations have been performed for 103 ≤Ra≤ 106, with the emissivity coefficient of all the walls varying between 0 and 1. The influence of the both, Rayleigh numbers and emissivity coefficient of the wall for fixed height ratio X=0.5 on natural convection and radiation heat transfer in enclosure have been solved. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The average Nusselt number has also been discussed for different emissivity through the enclosure.

scholarly journals Numerical study of mixed convection and entropy generation in the Poiseulle-Benard channel in different angles

2010 ◽  
Vol 14 (2) ◽  
pp. 329-340 ◽  
Author(s):  
Mostafa Nourollahi ◽  
Mousa Farhadi ◽  
Kurosh Sedighi
Keyword(s):  
Nusselt Number ◽  
Entropy Generation ◽  
Numerical Study ◽  
Navier Stokes ◽  
Bejan Number ◽  
Optimum Angle ◽  
Velocity Gradients ◽  
Negative Effect ◽  
Energy Equations ◽  
Rayleigh Numbers

The issue of entropy generation and Nusselt number in Poiseuille-Benard channel flow are analyzed by solving numerically Navier-Stokes and energy equations with the use of the classic Boussinesq incompressible approximation. The Nusselt number is studied as a function of q. In addition variations of entropy generation and the Bejan number as a function of q and j are studied. The channel angle (q) and irreversibility (j) were changed from -25 to 30 and from 10-5 to 1, respectively, whereas Reynolds, Peclet, and Rayleigh numbers were fixed at Re = 10, Pe = 20/3, and Ra = 104. More over the positive and negative effect of buoyancy force on flow field, Nusselt number and entropy generation are discussed. Optimum angle for dif- ferent irreversibilities are specified by definition h as the rate of the Nusselt number to the entropy generation, the optimum angle was distinguished for different irreversibility. Results show that the Nusselt number changes very slightly and is almost constant when q changes from -10 to 10 and the Nusselt number decreases sharply when q increases from 20 to 30 or decreases from -15 to -25. Moreover it has been found that the entropy generation due to heat transfer is localized at areas where heat exchanged between the walls and the flow is maximum, while the entropy generation due to fluid friction is maximum at areas where the velocity gradients are maximum such as vortex centers. Consequently when q is decreased from -15 to -25 or is increased from 20 to 30 entropy generation for small irreversibilities decreases and increases sharply for large irreversibilities.

Sign in / Sign up

Export Citation Format

Share Document