scholarly journals Prediction of Unsteady Natural Convection within a Square Cavity Containing an Obstacle at High Rayleigh Number Value

2015 ◽  
Vol 55 ◽  
pp. 19-26
Author(s):  
Basma Souayeh ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya ◽  
Taieb Lili
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Stokes Equations ◽  
Computer Code ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Convection Flow ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Volume Method

The present work deals with the prediction of a natural convection flow in a square cavity, partially heated by an obstacle placed at the bottom wall. The two transverse walls and the top wall of the cavity are supposed to be cold, the remaining walls are kept insulated. The main parameter of numerical investigations is the Rayleigh number (engine convection) varying from 103 to 105. When Ra is fixed at 107, the flow and thermal fields bifurcate and undergoes an unsteady behavior at critical positions. Flow patterns corresponding to the unsteady state are presented and analyzed in the current study. The simulations were conducted using a numerical approach based on the finite volume method and the projection method, which are implemented in a computer code in order to solve the Navier-Stokes equations.

Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid

1996 ◽  
Vol 316 ◽  
pp. 53-72 ◽  
Author(s):  
Bernard Zappoli ◽  
Sakir Amiroudine ◽  
Pierre Carles ◽  
Jalil Ouazzani
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Square Cavity ◽  
Piston Effect ◽  
Navier Stokes Equations ◽  
Significant Difference ◽  
Buoyancy Driven Convection ◽  
Volume Method ◽  
Very High

The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier–Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases: (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in high-speed flows provokes an overheating of the upper wall; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO2 is found, in the form of a double-roll convective structure.

scholarly journals Three-Dimensional Numerical Study of the Effect of Protective Barrier on the Dispersion of the Contaminant in a Building

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1125
Author(s):  
Chemseddine Maatki
Keyword(s):  
Rayleigh Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Vector ◽  
Volume Method ◽  
The Impact ◽  
Buoyancy Ratio

The finite volume method and potential-vorticity vector formalism in their three-dimensional form were used to numerically study the impact of an adiabatic and impermeable vertical barrier on the dispersion of a local aero-contaminant due to the double-diffusive Rayleigh–Benard convection inside a cubic container. Different governing parameters such as the Rayleigh number, buoyancy ratio and barrier height were analyzed for Le = 1.2 and Pr = 0.7, representing an air-contaminant mixture. The potential-vector-vorticity formalism in the three-dimensional form allowed the elimination of the pressure terms appearing in the Navier–Stokes equations. It was found that the heat and mass transfer as well as the effectiveness of the barrier in reducing contaminant dispersion are strongly influenced by the buoyancy ratio, the barrier size and the Rayleigh number. In addition, the barrier effectiveness is more than 70% for a height of half the building height.

scholarly journals Numerical Study of the Routes toward Chaos of Natural Convection within an Inclined Enclosure

2012 ◽  
Vol 5 (1) ◽  
pp. 105-117
Author(s):  
F. Kieno ◽  
A. Ouedraogo ◽  
O. M. Zongo ◽  
J. D. Bathiebo ◽  
B. Zeghmati
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Limit Cycle ◽  
Limit Point ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Attractor Behaviour

Two-dimensional numerical study of transient natural convection in an inclined cubic cavity filled with air using stream function-vorticity form for the Navier-Stokes equations has been carried out to explore the route toward chaos. The hot and cold vertical walls are maintained isothermal at temperature Tc and Th respectively and the other walls are adiabatic.  Two angles of inclination of the cavity 25° and 65° are considered. Transfers equations are solved using finite-difference discretization procedures. The study predicts various critical Rayleigh numbers for the two tilted angles characterizing the variation of the attractor behaviour and shows that the larger the Rayleigh number is, the more sensitive the attractor becomes to time step and meshes size. The routes toward the chaos followed by the attractor are: limit point / limit cycle / T2 torus / cycle fitted on a T2 torus / chaos / T2 torus / cycle fitted on a T2 torus / chaos when the Rayleigh number increases. The analysis confirms also the bifurcation of the attractor from a limit point to a limit cycle via an overcritical Hopf bifurcation for a Rayleigh number between 1.95x106 and 1.96x106.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i1.10709        J. Sci. Res. 5 (1), 105-117 (2013) 

scholarly journals Scale Effects on a Tip Rake Propeller Working in Open Water

2019 ◽  
Vol 7 (11) ◽  
pp. 404 ◽  
Author(s):  
Lungu
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Stokes Equations ◽  
Scale Effects ◽  
Open Water ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Conference Organization ◽  
Volume Method

The scale effect on the accuracy of a numerical simulation in ship hydrodynamics represents an important issue of the propeller numerical analysis. To grasp a better understanding on the influence of this effect, an introspection on the performances of an unconventional propeller is proposed in the present study. The paper describes an investigation of the performances of a tip rake propeller recently chosen as benchmark by the International Towing Tank Conference organization (ITTC hereafter). The numerical simulation is carried out by making use of the ISIS-CFD solver, part of the FineTM/Marine package available in the NUMECA suite. The solver is based on the finite volume method to build the spatial discretization of the governing equations. The incompressible unsteady Reynolds Averaged Navier-Stokes Equations (RANSE) are solved in a global approach. Reported solutions are compared with the experimental data provided by Schiffbau-Versuchsanstalt (SVA) Potsdam GmbH to validate the accuracy of the numerical approach. Since for the full scale the experimental data could not be possible, the ITTC’78 extrapolation method-based proposed by the SVA Potsdam has been taken as a basis for comparisons and discussions. A set of remarks will conclude the paper by providing some guidelines for further approaches in terms of the particulars of the numerics that may be further employed in similar studies.

Air Flow Turbulent Fluctuations in a Centrifugal Fan

2005 ◽  
Author(s):  
F. Z. Sierra ◽  
H. C. Lara ◽  
J. Kubiak ◽  
J. Siqueiros ◽  
J. C. Garcia ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Air Flow ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Navier Stokes Equations ◽  
Turbulent Fluctuations ◽  
Operation Conditions ◽  
Fixed Parameter ◽  
Volume Method

In this work air flow turbulent fluctuations within the volute-impeller interaction region in a centrifugal fan are analyzed. The fan is part of one group of four similar units that provide the necessary air into a steam generator, in a power plant of 70 MW capacity. A numerical approach based on the finite volume method has been employed to solve the full set of Navier-Stokes equations in 3-D. Multiple reference frame was used to simulate the circular motion of the rotor inside the volute which remained static as well as the air entrance and exit sections. The whole domain was divided into 1.350 × 106 cells. Additional terms due to centrifugal and Coriolis forces were taken into account in the computation. The turbulence was addressed using one model based on renormalized group theory, RNG. Emphasis is focused on describing the velocity field within the annulus in between the rotor and the volute and its fluctuations. One first set of results indicate that the highest velocities appear in the region close to the blades tip, but they decay immediately after entering the annular volute-impeller region. Over there, the flow develops into two zones which are well defined through dynamic and static pressure contours. The results show how the magnitude of turbulence intensity varies according to different operation conditions of the fan, taking as fixed parameter the pressure at exit. The behavior of turbulence in the radial direction for a number of flow sections, starting from the cutter at the exit of the fan are examined as well.

scholarly journals An Efficient Strategy to Deliver Understanding of Both Numerical and Practical Aspects When Using Navier-Stokes Equations to Solve Fluid Mechanics Problems

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 178 ◽  
Author(s):  
Adair ◽  
Jaeger
Keyword(s):  
Undergraduate Students ◽  
Solution Method ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Various Boundary Conditions ◽  
Volume Method

An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known ‘driven-cavity’ problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics.

Computational Simulation of Turbulent Natural Convection in a Volumetrically Heated Square Cavity

2013 ◽  
Author(s):  
Camila Braga Vieira ◽  
Bojan Niceno ◽  
Jian Su
Keyword(s):  
Natural Convection ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Oxide Material ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Turbulent Natural Convection

This work aimed to analyze the turbulent natural convection in a volumetrically heated fluid with Prandtl number equal to 0.6, representing the oxide material layer of a corium. Four turbulence models were scrutinized in order to select the most appropriate one for turbulence modeling based on Reynolds Averaged Navier-Stokes equations (RANS) of natural convection in a molten core. The turbulence models scrutinized are the standard k-ε, Shear Stress Transport (SST), low-Reynolds-k-ε (Launder-Sharma) and also an elliptic blending model ν2-f. The simulations were carried out in a square cavity with isothermal walls, for Rayleigh numbers (Ra) ranging from 109 to 1011. The numerical simulations, performed in an open-source of Computational Fluid Dynamics (CFD) - OpenFOAM (Open Field Operation and Manipulation), provided outcomes of average Nusselt number as function of Ra number, which were in a reasonable agreement with an experimental correlation and other authors’ simulations. It was also possible to observe the limitations and robustness of each model analyzed, enabling to conclude that the most adequate turbulence models for the present physical problem were SST and ν2-f.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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