A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell

2015 ◽  
Vol 766 ◽  
pp. 172-201 ◽  
Author(s):  
Bérengère Podvin ◽  
Anne Sergent
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Intermittent Flow ◽  
Three Dimensional Model ◽  
Interaction Coefficients ◽  
Large Scale Circulation ◽  
Vertical Heat Flux ◽  
Rayleigh Benard ◽  
Stable Flow

AbstractWe consider the numerical simulation of Rayleigh–Bénard convection in a 2D square cell filled with water ($\mathit{Pr}=4.3$) at a turbulent Rayleigh number of $\mathit{Ra}=5\times 10^{7}$. We focus on the structures and dynamics of the large-scale intermittent flow. Two quasi-stable flow patterns are identified: one consists of a main diagonal roll with two corner rolls; and the other of two horizontally stacked rolls. These stable flow structures are associated with two types of events, which involve corner flow growth and pattern rotation: reversals, when the main roll rapidly switches signs; and cessations, when it disappears for longer periods. Proper orthogonal decomposition (POD) is applied independently to the velocity field and to the temperature field. In both cases, three principal modes were identified: a single-roll, large-scale circulation; a quadrupolar flow; and a double-roll, symmetry-breaking mode. The large-scale circulation is the kinetic mode with the highest energy. The most energetic temperature mode is associated with the mean temperature and corresponds to a velocity field of quadrupolar nature. The vertical heat flux is concentrated in these two modes. The reversal process is characterized by sharp fluctuations in the amplitudes of all modes. Analysis of the interaction coefficients between the spatial modes leads us to propose a three-dimensional model, based on the interaction of the large-scale circulation, the quadrupolar flow and horizontal rolls. The main dynamics and time scales of reversals and cessations are reproduced by the model in the presence of noise.

scholarly journals Boundary layer structure in turbulent Rayleigh–Bénard convection

2012 ◽  
Vol 706 ◽  
pp. 5-33 ◽  
Author(s):  
Nan Shi ◽  
Mohammad S. Emran ◽  
Jörg Schumacher
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Large Scale ◽  
Three Dimensional ◽  
Large Scale Circulation ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe structure of the boundary layers in turbulent Rayleigh–Bénard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at aspect ratio one for Rayleigh numbers of $\mathit{Ra}= 3\ensuremath{\times} 1{0}^{9} $ and $3\ensuremath{\times} 1{0}^{10} $ at fixed Prandtl number $\mathit{Pr}= 0. 7$. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of Prandtl–Blasius–Pohlhausen theory. Deviations decrease when a dynamical rescaling of the data with an instantaneously defined boundary layer thickness is performed and the analysis plane is aligned with the instantaneous direction of the large-scale circulation in the closed cell. Our numerical results demonstrate that important assumptions of existing classical laminar boundary layer theories for forced and natural convection are violated, such as the strict two-dimensionality of the dynamics or the steadiness of the fluid motion. The boundary layer dynamics consists of two essential local dynamical building blocks, a plume detachment and a post-plume phase. The former is associated with larger variations of the instantaneous thickness of velocity and temperature boundary layer and a fully three-dimensional local flow. The post-plume dynamics is connected with the large-scale circulation in the cell that penetrates the boundary region from above. The mean turbulence profiles taken in localized sections of the boundary layer for each dynamical phase are also compared with solutions of perturbation expansions of the boundary layer equations of forced or natural convection towards mixed convection. Our analysis of both boundary layers shows that the near-wall dynamics combines elements of forced Blasius-type and natural convection.

scholarly journals Koopman analysis of the long-term evolution in a turbulent convection cell

2018 ◽  
Vol 847 ◽  
pp. 735-767 ◽  
Author(s):  
Dimitrios Giannakis ◽  
Anastasiya Kolchinskaya ◽  
Dmitry Krasnov ◽  
Jörg Schumacher
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Galerkin Approximation ◽  
Three Dimensional ◽  
Free Fall ◽  
Convection Cell ◽  
Long Time ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh–Bénard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine learning is employed here to represent a regularized generator of the unitary Koopman group in the sense of a Galerkin approximation. The resulting Koopman eigenfunctions can be grouped into subsets in accordance with the discrete symmetries in a cubic box. In particular, a projection of the velocity field onto the first group of eigenfunctions reveals the four stable large-scale circulation (LSC) states in the convection cell. We recapture the preferential circulation rolls in diagonal corners and the short-term switching through roll states parallel to the side faces which have also been seen in other simulations and experiments. The diagonal macroscopic flow states can last as long as 1000 convective free-fall time units. In addition, we find that specific pairs of Koopman eigenfunctions in the secondary subset obey enhanced oscillatory fluctuations for particular stable diagonal states of the LSC. The corresponding velocity-field structures, such as corner vortices and swirls in the midplane, are also discussed via spatiotemporal reconstructions.

Unravelling the large-scale circulation modes in turbulent Rayleigh–Bénard convection

2021 ◽  
Author(s):  
Susanne Horn ◽  
Peter J. Schmid ◽  
Jonathan M. Aurnou
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mean Flow ◽  
Large Scale Circulation ◽  
Convective Systems ◽  
Aspect Ratios ◽  
Mode Decomposition ◽  
Coherent Flow Structure

Abstract The large-scale circulation (LSC) is the most fundamental turbulent coherent flow structure in Rayleigh-B\'enard convection. Further, LSCs provide the foundation upon which superstructures, the largest observable features in convective systems, are formed. In confined cylindrical geometries with diameter-to-height aspect ratios of Γ ≅ 1, LSC dynamics are known to be governed by a quasi-two-dimensional, coupled horizontal sloshing and torsional (ST) oscillatory mode. In contrast, in Γ ≥ √2 cylinders, a three-dimensional jump rope vortex (JRV) motion dominates the LSC dynamics. Here, we use dynamic mode decomposition (DMD) on direct numerical simulation data of liquid metal to show that both types of modes co-exist in Γ = 1 and Γ = 2 cylinders but with opposite dynamical importance. Furthermore, with this analysis, we demonstrate that ST oscillations originate from a tilted elliptical mean flow superposed with a symmetric higher order mode, which is connected to the four rolls in the plane perpendicular to the LSC in Γ = 1 tanks.

scholarly journals Coronal ejections from convective spherical shell dynamos

2011 ◽  
Vol 7 (S286) ◽  
pp. 154-158 ◽  
Author(s):  
J. Warnecke ◽  
P. J. Käpylä ◽  
M. J. Mantere ◽  
A. Brandenburg
Keyword(s):  
Magnetic Field ◽  
Spherical Shell ◽  
Large Scale ◽  
Convection Zone ◽  
Three Dimensional ◽  
Simplified Model ◽  
Spherical Coordinates ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Large Scale Magnetic Field

AbstractWe present a three-dimensional model of rotating convection combined with a simplified model of a corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field which is sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.

Modeling of Solids and Gas Mixing Effects in Large-Scale CFB Combustors

2003 ◽  
Author(s):  
Karsten Luecke ◽  
Ernst-Ulrich Hartge ◽  
Joachim Werther
Keyword(s):  
Combustion Chamber ◽  
Residence Time ◽  
Large Scale ◽  
Control Volume ◽  
Combustion Process ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Cross Sectional ◽  
Fuel Feed ◽  
Cross Section Area

In a CFB combustor the reacting solids are locally fed into the combustion chamber. These reactants have to be dispersed across the reactor’s cross-sectional area. Since the rate of mixing is limited this leads to a mal-distribution of the reactants and to locally varying reaction conditions. In order to describe the influence of mixing a three-dimensional model of the combustion chamber is suggested here. The model is divided into three sub-topics. First, the flow structure in terms of local gas and solids velocities and solids volume concentrations is described. Second, mixing of the solids and the gas phase has to be quantified by defining dispersion coefficients, and finally the combustion process itself, i.e. the reaction kinetics, has to be modeled. Employing the information of the three sub-models mass balances for the reactants at each finite control volume inside the CFB combustion chamber can be formulated. The model was validated against data from measurements in the large-scale combustor of Chalmers University of Technology in Go¨teborg/Sweden. Concentration gradients concerning the char phase are only moderate. However, the spatial distribution of the oxygen shows strong non-uniformities, especially under conditions of staged combustion. In further predictive calculations, the influence of the fuel supply arrangement on the emissions of industrial sized CFB boilers was studied. Furthermore, the influence of the fuel composition on the feeding technique has been examined. High volatile fuels tend to form plumes of unburned hydrocarbons near the fuel feed point, and might therefore need more feed points per square meter cross-section area. Since the average gas residence time in the primary cyclone of a CFB plant is about 30–40% of the total gas residence time, a considerable burn-off of not completely oxidized gas species may occur here. An effectively used cyclone may remedy to a certain extent the negative impacts of incomplete mixing in the combustion chamber.

scholarly journals Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

2016 ◽  
Vol 791 ◽  
Author(s):  
Xiaozhou He ◽  
Eberhard Bodenschatz ◽  
Guenter Ahlers
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Cylindrical Sample ◽  
Ultimate State ◽  
Large Scale Circulation ◽  
Classical State ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present measurements of the orientation ${\it\theta}_{0}$ and temperature amplitude ${\it\delta}$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh–Bénard convection (RBC) with aspect ratio ${\it\Gamma}\equiv D/L=1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr\simeq 0.8$. The results for ${\it\theta}_{0}$ revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth’s Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity $D_{{\it\theta}}$ and a corresponding Reynolds number $Re_{{\it\theta}}$ for Rayleigh numbers over the range $2\times 10^{12}\lesssim Ra\lesssim 1.5\times 10^{14}$. In the classical state ($Ra\lesssim 2\times 10^{13}$) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351–386) for $Ra\lesssim 10^{11}$ and $Pr=4.38$, which gave $Re_{{\it\theta}}\propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_{{\it\theta}}\propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_{V}$ (He et al., New J. Phys., vol. 17, 2015, 063028). At larger $Ra$ the data for $Re_{{\it\theta}}(Ra)$ revealed a transition to a new state, known as the ‘ultimate’ state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_{V}(Ra)$ at $Ra_{1}^{\ast }\simeq 2\times 10^{13}$ and $Ra_{2}^{\ast }\simeq 8\times 10^{13}$. In the ultimate state we found $Re_{{\it\theta}}\propto Ra^{0.40\pm 0.03}$. Recently, Skrbek & Urban (J. Fluid Mech., vol. 785, 2015, pp. 270–282) claimed that non-Oberbeck–Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as ‘ultimate’.

scholarly journals The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection

2009 ◽  
Vol 638 ◽  
pp. 383-400 ◽  
Author(s):  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Large Scale ◽  
Lateral Displacement ◽  
Torsional Oscillation ◽  
Restoring Force ◽  
Large Scale Circulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Sloshing Mode ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In agreement with a recent experimental discovery by Xi et al. (Phys. Rev. Lett., vol. 102, 2009, paper no. 044503), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling & Ahlers (Phys. Rev. Lett., vol. 92, 2004, paper no. 1945022004). We show that both modes can be described by an extension of a model developed previously Brown & Ahlers (Phys. Fluids, vol. 20, 2008, pp. 105105-1–105105-15; Phys. Fluids, vol. 20, 2008, pp. 075101-1–075101-16). The extension consists of permitting a lateral displacement of the LSC circulation plane away from the vertical centreline of the sample as well as a variation of the displacement with height (such displacements had been excluded in the original model). Pressure gradients produced by the sidewall of the container on average centre the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model yields the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude and probability distributions of the displacements.

Thermal convection in inclined cylindrical containers

2016 ◽  
Vol 790 ◽  
Author(s):  
Olga Shishkina ◽  
Susanne Horn
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Large Scale ◽  
Direct Numerical Simulations ◽  
Large Scale Circulation ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Small Inclination

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle ${\it\beta}$, $0\leqslant {\it\beta}\leqslant {\rm\pi}/2$, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number $\mathit{Nu}$ and Reynolds number $\mathit{Re}$. The considered Rayleigh numbers $\mathit{Ra}$ range from $10^{6}$ to $10^{8}$, the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the $\mathit{Nu}\,({\it\beta})/\mathit{Nu}(0)$ dependence is not universal and is strongly influenced by a combination of $\mathit{Ra}$ and $\mathit{Pr}$. Thus, with a small inclination ${\it\beta}$ of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small $\mathit{Pr}$, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to ${\it\beta}={\rm\pi}/2$, $\mathit{Nu}$ and $\mathit{Re}$ decrease with increasing ${\it\beta}$ in all considered cases. Generally, the $\mathit{Nu}({\it\beta})/\mathit{Nu}(0)$ dependence is a complicated, non-monotonic function of ${\it\beta}$.

Boil-Off Gas Formation inside Large Scale Liquefied Natural Gas (LNG) Tank Based on Specific Parameters

2012 ◽  
Vol 229-231 ◽  
pp. 690-694 ◽  
Author(s):  
Mohamad Shukri Zakaria ◽  
Kahar Osman ◽  
Md. Nor Musa
Keyword(s):  
Natural Gas ◽  
Large Scale ◽  
Seawater Temperature ◽  
Three Dimensional ◽  
Ambient Air ◽  
Calculation Model ◽  
Liquefied Natural Gas ◽  
Three Dimensional Model ◽  
Ambient Seawater ◽  
Lng Tank

Liquefied Natural Gas (LNG) fleets are coasting with various condition and behavior. These variable leads to different type of LNG fleets build every year with unavoidable generated Boil-off Gas (BOG). Estimation of BOG generated inside LNG tank play significant role in determines the ship specification and management method of BOG including venting, propulsion or requalification. Hence, in the present study, the right choices of boundary condition and parameter have been implementing in order to have good estimation amount of BOG evaporates for specific LNG tank. Three dimensional model of cargo with capacity 160000 m3 LNG carrier are simulate using ANSYS Fluent with specific ambient air temperature of 5oC and ambient seawater temperature of 0oC have been chosen as a calculation case, gain the total heat transfer rate and Boil-off Rate (BOR). The result shows that the calculation model and simulation are feasible with typical LNG fleet specification and International Marine Organization (IMO) standard.

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