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) 

Numerical Study of Wave Slamming on an Oscillating Flap

2014 ◽  
Author(s):  
Yanji Wei ◽  
Alan Henry ◽  
Olivier Kimmoun ◽  
Frederic Dias
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Wave Slamming ◽  
Volume Method

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flap-type wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

Three-dimensional natural convection in a box: a numerical study

1977 ◽  
Vol 83 (1) ◽  
pp. 1-31 ◽  
Author(s):  
G. D. Mallinson ◽  
G. De Vahl Davis
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Inertial Interaction ◽  
Longitudinal Temperature

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

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.

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 natural convection in a square cavity under non-boussinesq conditions

2016 ◽  
Vol 20 (5) ◽  
pp. 1509-1517 ◽  
Author(s):  
Saber Hamimid ◽  
Messaoud Guellal ◽  
Madiha Bouafia
Keyword(s):  
Natural Convection ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Numerical Study ◽  
Transport Coefficients ◽  
Boussinesq Approximation ◽  
Numerical Code ◽  
Navier Stokes ◽  
Large Temperature ◽  
Navier Stokes Equations

Natural convection in a differentially heated cavity has been carried out under large temperature gradient. The study has been performed by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the Low Mach Number approximation. The LMN model constitutes an important numerical problem for low speed flows. It is based on the filtering of acoustic waves from the complete Navier-Stokes equations. Various simulations were conducted including constant or variable transport coefficients and both small and large temperature differences. A comparison between an incompressible code based on the Boussinesq approximation and the LMN compressible code shows that the incompressible model is not sufficient to simulate natural convective flow for large temperature differences.

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.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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