scholarly journals INSTABILITY OF THE RAYLEIGH-BENARD CONVECTION FOR INCLINED LOWER WALL WITH TEMPERATURE VARIATION

2016 ◽  
Vol 14 (2) ◽  
pp. 179
Author(s):  
Sadoon Ayed ◽  
Gradimir Ilić ◽  
Predrag Živković ◽  
Mića Vukić ◽  
Mladen Tomić
Keyword(s):  
Temperature Variation ◽  
Wave Number ◽  
Lower Plate ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Time Period ◽  
The Mean ◽  
Convective Cells ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper deals with an analysis of a two-dimensional viscous fluid flow between the two parallel plates inclined with respect to the horizontal plane, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period after which it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, there is a longitudinal sinusoidal temperature variation imposed on the mean temperature. We have investigated the wave number and amplitude influence of this variation on the subcritical stability and the onset of the Rayleigh-Bénard convective cells, by direct numerical simulation of 2D Navier-Stokes and energy equation.

scholarly journals Rayleigh-Bénard convection instability in the presence of temperature variation at the lower wall

2012 ◽  
Vol 16 (suppl. 2) ◽  
pp. 281-294
Author(s):  
Milos Jovanovic ◽  
Dragan Zivkovic ◽  
Jelena Nikodijevic
Keyword(s):  
Temperature Variation ◽  
Wave Number ◽  
Lower Plate ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Time Period ◽  
The Stability ◽  
Convective Cells ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper analyzes the two-dimensional viscous fluid flow between two parallel plates, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period, and afterwards it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, and there is longitudinal sinusoidal temperature variation imposed on the mean temperature. We investigate the wave number and amplitude influence of this variation on the stability of Rayleigh-Benard convective cells, by direct numerical simulation of 2-D Navier-Stokes and energy equation.

scholarly journals Bounds for convection between rough boundaries

2016 ◽  
Vol 804 ◽  
pp. 370-386 ◽  
Author(s):  
David Goluskin ◽  
Charles R. Doering
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Temperature Difference ◽  
Upper Bound ◽  
Bottom Boundary ◽  
Leading Term ◽  
The Mean ◽  
Rough Boundaries ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We consider Rayleigh–Bénard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background method to derive an upper bound on the mean heat flux across the layer for all admissible boundary geometries. This flux, normalized by the temperature difference between the boundaries, can grow with the Rayleigh number ($Ra$) no faster than $O(Ra^{1/2})$ as $Ra\rightarrow \infty$. Our analysis yields a family of similar bounds, depending on how various estimates are tuned, but every version depends explicitly on the boundary geometry. In one version the coefficient of the $O(Ra^{1/2})$ leading term is $0.242+2.925\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$, where $\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$ is the mean squared magnitude of the boundary height gradients. Application to a particular geometry is illustrated for sinusoidal boundaries.

scholarly journals Convection due to an unstable density difference across a permeable membrane

2008 ◽  
Vol 609 ◽  
pp. 139-170 ◽  
Author(s):  
BABURAJ A. PUTHENVEETTIL ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Large Scale ◽  
Dendritic Structure ◽  
Membrane Dynamics ◽  
Diffusion Regime ◽  
Permeable Membrane ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Mean ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study natural convection driven by unstable concentration differences of sodium chloride (NaCl) across a horizontal permeable membrane at Rayleigh numbers (Ra) of 1010 to 1011 and Schmidt number (Sc)=600. A layer of brine lies over a layer of distilled water, separated by the membrane, in square-cross-section tanks. The membrane is permeable enough to allow a small flow across it at higher driving potentials. Based on the predominant mode of transport across the membrane, three regimes of convection, namely an advection regime, a diffusion regime and a combined regime, are identified. The near-membrane flow in all the regimes consists of sheet plumes formed from the unstable layers of fluid near the membrane. In the advection regime observed at higher concentration differences (ΔC) across the membrane, there is a slow overturning through-flow across the membrane; the transport across the membrane occurs mostly by advection. This phenomenology explains the observed Nub~Ra2/Sc scaling of the Nusselt number. The planforms of sheet plumes near the membrane show a dendritic structure due to the combined influence of the mean shear due to the large-scale flow and the entrainment flow of the adjacent plumes. The near-membrane dynamics show initiation, elongation and merger of plumes; a movie is available with the online version of the paper. Increase in Ra results in a larger number of closely and regularly spaced sheet plumes. The mean plume spacing in the advection regime $\overline{\lambda}_b$, is larger than the mean plume spacing in Rayleigh–Bénard convection ($\overline{\lambda}$), and shows a different Ra-dependence. The plume spacings in the advection regime (λb) show a common log-normal probability density function at all Ra. We propose a phenomenology which predicts $\overline{\lambda}_b$ ~ $\sqrt{Z_w Z_{V_i}}$, where Zw and $Z_{V_i}$ are, respectively, the near-wall length scales in Rayleigh–Bénard convection (RBC) and due to the advection velocity. In the combined regime, which occurs at intermediate values of ΔC, the flux scales as (ΔC/2)4/3. At lower driving potentials, in the diffusion regime, the flux scaling is similar to that in turbulent RBC.

scholarly journals Horizontal Wave Number Dependence of Type II Solutions in Rayleigh?Benard Convection with Hexagonal Planform

1984 ◽  
Vol 37 (5) ◽  
pp. 531 ◽  
Author(s):  
JM Lopez ◽  
JO Murphy
Keyword(s):  
Vertical Component ◽  
Wave Number ◽  
Type I ◽  
Type Ii ◽  
Horizontal Wave ◽  
Convection Problem ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Cyclonic Type

The horizontal wave number dependence of the hexagonal planform solutions for the RayleighBenard convection problem, which have a nonzero vertical component of vorticity (type II solutions), has been established. Over the range of wave numbers which support cellular convection, comparisons between the thermal transport characteristics of these cyclonic type solutions and those traditionally obtained from nonlinear investigations of the single horizontal mode equations (type I solutions) have been made. From the numerical results obtained, it is found that the cell aspect ratio which maximizes the heat flux of type II solutions is larger than that for type I solutions, at quivalent parameter values, and that the value of the horizontal wave number giving maximum Nusselt number for type II solutions increases with Rayleigh number and decreases with Prandtl number.

Evaluating the Effect of Number of Spans on Heat Transfer in Greenhouses

2019 ◽  
Author(s):  
S. Kruger ◽  
L. Pretorius
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Fluid Dynamic ◽  
Cfd Model ◽  
Transfer Velocity ◽  
Nusselt Number Distribution ◽  
Convective Cells ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract The present study concerns convective flows in the empty volume above the plant canopy in a confined greenhouse. The purpose of this paper is to numerically investigate the effect of the number of spans on the convective heat transfer in closed greenhouses. The initial greenhouse CFD model cavity is validated against experimental results found in the literature. Thermal convection is induced by heating the bottom of the cavity. The numerical model is then modified to represent two-l greenhouse cavities with different numbers of spans. The computational fluid dynamic (CFD) software is then used to analyze mainly the natural convective heat transfer, velocity and temperature distributions for the single span greenhouse, as well as multi-span greenhouses (containing two and three spans). The greenhouse CFD model floor is heated, and the walls are adiabatic, corresponding to Rayleigh-Bénard convection. A mesh sensitivity analysis was conducted to determine a suitable size for the mesh. Results show that adding additional spans to the initial single-span cavity has a pronounced effect on the Nusselt-number distribution on the floor of the cavity. The temperature and velocity distributions were also significantly influenced. The four-span cavity showed three convective cells instead of four as for the lowest Rayleigh number.

Numerical Study of Effect of Polymer Additives on Heat Transport in Turbulent Rayleigh- Bénard Convection

2012 ◽  
Vol 472-475 ◽  
pp. 1283-1288 ◽  
Author(s):  
Chen Hui Zheng ◽  
Chang Feng Li ◽  
Hua Hong Jiang
Keyword(s):  
Heat Transport ◽  
Large Scale ◽  
Numerical Study ◽  
Navier Stokes ◽  
Polymer Additive ◽  
Bénard Convection ◽  
Turbulence Regime ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this study, the Reynolds-Averaged-Navier-Stokes (RANS) model combined with the Cross Viscosity Equation is used, applied to the soft turbulence regime (Ra =5×105~4×107) and hard turbulence regime (Ra>4×107) of Rayleigh-Bénard convection (RBC). The relation curves between heat transport (Nusselt number) and other parameters, as well as flow pattern changes of RBC are obtained for the cases with different Rayleigh number and concentration of the polymer additive. The simulations show that the presence of polymer additive can lead to an enhancement of the heat transfer with larger effect in the hard turbulence regime than those in the soft turbulence regime. It is also shown that in the soft turbulence regime the reversal cycles are shorter than in hard turbulence regime. The symmetric vortices in the diagonal corner of enclosed space shrink and the velocities of large-scale circulation (LSC) increase accordingly.

scholarly journals Large-scale mean patterns in turbulent convection

2015 ◽  
Vol 776 ◽  
pp. 96-108 ◽  
Author(s):  
Mohammad S. Emran ◽  
Jörg Schumacher
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

Large-scale patterns, which are well-known from the spiral defect chaos (SDC) regime of thermal convection at Rayleigh numbers $\mathit{Ra}<10^{4}$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh–Bénard convection in extended cylindrical cells with an aspect ratio ${\it\Gamma}=50$ and $\mathit{Ra}>10^{5}$. They are revealed when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $\mathit{Ra}_{\ast }$, that describes the convection of the mean patterns, is indeed in the SDC range. The turbulent Prandtl numbers are smaller than one, with $0.2\leqslant \mathit{Pr}_{\ast }\leqslant 0.4$ for Prandtl numbers $0.7\leqslant \mathit{Pr}\leqslant 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude sidewall forcing when the level of turbulent fluctuations in the flow is sufficiently high.

scholarly journals Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli

2019 ◽  
Vol 29 (1) ◽  
pp. 251-279 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Bingham Fluids ◽  
Bingham Model ◽  
Content Type ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Mean ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Purpose This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition. Design/methodology/approach The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions. Originality value Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ ri/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 104 ≤ Ra ≤ 105 for the CWHF configuration.

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