scholarly journals Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 582 ◽  
Author(s):  
Hui Yang ◽  
Yikun Wei ◽  
Zuchao Zhu ◽  
Huashu Dou ◽  
Yuehong Qian
Keyword(s):  
Heat Transfer ◽  
Structure Function ◽  
Dissipation Rate ◽  
Large Scale ◽  
Thermal Dissipation ◽  
Small Scale ◽  
Linear Scaling ◽  
Two Dimensional ◽  
Large Scale Circulation ◽  
Rayleigh Benard

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 607 ◽  
pp. 119-139 ◽  
Author(s):  
DENIS FUNFSCHILLING ◽  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Small Scale ◽  
Large Scale Circulation ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

scholarly journals Numerical simulation of helical-vortex effects in Rayleigh-Bénard convection

2006 ◽  
Vol 13 (2) ◽  
pp. 205-222 ◽  
Author(s):  
G. V. Levina ◽  
I. A. Burylov
Keyword(s):  
Large Scale ◽  
Internal Heat ◽  
Main Idea ◽  
Numerical Approach ◽  
Small Scale ◽  
Forcing Function ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract. A numerical approach is substantiated for searching for the large-scale alpha-like instability in thermoconvective turbulence. The main idea of the search strategy is the application of a forcing function which can have a physical interpretation. The forcing simulates the influence of small-scale helical turbulence generated in a rotating fluid with internal heat sources and is applied to naturally induced fully developed convective flows. The strategy is tested using the Rayleigh-Bénard convection in an extended horizontal layer of incompressible fluid heated from below. The most important finding is an enlargement of the typical horizontal scale of the forming helical convective structures accompanied by a cells merging, an essential increase in the kinetic energy of flows and intensification of heat transfer. The results of modeling allow explaining how the helical feedback can work providing the non-zero mean helicity generation and the mutual intensification of horizontal and vertical circulation, and demonstrate how the energy of the additional helical source can be effectively converted into the energy of intensive large-scale vortex flow.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

scholarly journals Marine Rapid Environmental Assessment in the Gulf of Taranto: a multiscale approach

2016 ◽  
Vol 16 (12) ◽  
pp. 2623-2639 ◽  
Author(s):  
Nadia Pinardi ◽  
Vladyslav Lyubartsev ◽  
Nicola Cardellicchio ◽  
Claudio Caporale ◽  
Stefania Ciliberti ◽  
...  
Keyword(s):  
Surface Waters ◽  
Large Scale ◽  
Eastern Mediterranean ◽  
Small Scale ◽  
Multiscale Approach ◽  
Mesoscale Variability ◽  
Large Scale Circulation ◽  
Eddy Field ◽  
Multiscale Sampling ◽  
Circulation Structure

Abstract. A multiscale sampling experiment was carried out in the Gulf of Taranto (eastern Mediterranean) providing the first synoptic evidence of the large-scale circulation structure and associated mesoscale variability. The mapping of the mesoscale and large-scale geostrophic circulation showed the presence of an anticyclonic large-scale gyre occupying the central open ocean area of the Gulf of Taranto. On the periphery of the gyre upwelling is evident where surface waters are colder and saltier than at the center of the gyre. Over a 1-week period, the rim current of the gyre undergoes large changes which are interpreted as baroclinic–barotropic instabilities, generating small-scale cyclonic eddies in the periphery of the anticyclone. The eddies are generally small, one of which can be classified as a submesoscale eddy due to its size. This eddy field modulates the upwelling regime in the gyre periphery.

scholarly journals An Experimental Study on the Aerodynamics and the Heat Transfer of a Suction Side Film Cooled Large Scale Turbine Cascade

1999 ◽  
Author(s):  
Wolfgang Ganzert ◽  
Leonhard Fottner
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Film Cooling ◽  
Total Pressure ◽  
Large Scale ◽  
Suction Side ◽  
Surface Heat ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Surface Heat Transfer

As a part of a more complex research program systematic isothermal investigations on the aerodynamics and heat transfer of a large scale turbine cascade with suction side film cooling were carried out. The film cooling through a row of holes at forty percent chord length on the suction side was supplied by a large plenum chamber. Two injection geometries were hitherto tested and evaluated: cylindrical holes with thirty respectively fifty degrees axial inclination angle and no lateral inclination. Typical engine conditions for the Mach and Reynolds number as well as the inlet turbulence level were maintained. The aerodynamic studies are based on steady state pressure measurements. The static profile pressure distribution together with oil-and-dye flow visualisation gives information on the surface flow conditions and boundary layer development especially in the near hole region. The measured data also comprise local and integral total pressure loss coefficients obtained by pressure probe traversing at mid span downstream of the cascade. The heat transfer examination set-up is based on the steady state liquid crystal technique using a compound of a thermochromic sheet combined with an electrical surface heating layer attached on an adiabatic blade corpus. Two dimensional pseudo colour plots are used for the documentation of the local surface heat transfer coefficient distribution and hot spot estimation. Laterally averaged and statistically analysed data of the surface heat transfer is applied in overall heat transfer examinations. All this data is used for a joint aerodynamic flow and surface heat transfer optimisation of a blowing configuration in suction side film cooled turbine cascade. The most important conclusions can be summarised as follows: Aiming at an optimised design of cylindrical film cooling configurations the axial inclination of the holes should be kept low thus diminishing the suction peak value at the cooling position in the profile pressure distribution and decreasing the mainstream deceleration area upstream of the jets. This also leads to reduced total pressure losses. Through the high influence of the blowing on the aerodynamics the flow in the near hole mixing region is highly three-dimensional. This shows significant effects in the two-dimensional surface distribution and the laterally averaged heat transfer coefficient. Oil-and-dye pictures confirm the observations qualitatively.

Pool Boiling Heat Transfer From Plain and Microporous, Square Pin Finned Surfaces in Saturated FC-72

1999 ◽  
Author(s):  
K. N. Rainey ◽  
S. M. You
Keyword(s):  
Heat Transfer ◽  
Boiling Heat Transfer ◽  
Large Scale ◽  
Pool Boiling ◽  
Nucleate Boiling ◽  
Small Scale ◽  
Surface Microstructure ◽  
Transfer Coefficients ◽  
Microporous Coating ◽  
Nucleate Boiling Heat Transfer

Abstract The present research is an experimental study of “double enhancement” behavior in pool boiling from heater surfaces simulating microelectronic devices immersed in saturated FC-72 at atmospheric pressure. The term “double enhancement” refers to the combination of two different enhancement techniques: a large-scale area enhancement (square pin fin array) and a small-scale surface enhancement (microporous coating). Fin lengths were varied from 0 (flat surface) to 8 mm. Effects of this double enhancement technique on critical heat flux (CHF) and nucleate boiling heat transfer in the horizontal orientation (fins are vertical) are investigated. Results showed significant increases in nucleate boiling heat transfer coefficients with the application of the microporous coating to the heater surfaces. CHF was found to be relatively insensitive to surface microstructure for the finned surfaces except in the case of the surface with 8 mm long fins. The nucleate boiling and CHF behavior has been found to be the result of multiple, counteracting mechanisms: surface area enhancement, fin efficiency, surface microstructure (active nucleation site density), vapor bubble departure resistance, and re-wetting liquid flow resistance.

scholarly journals Combined measurement of velocity and temperature in liquid metal convection

2019 ◽  
Vol 876 ◽  
pp. 1108-1128 ◽  
Author(s):  
Till Zürner ◽  
Felix Schindler ◽  
Tobias Vogt ◽  
Sven Eckert ◽  
Jörg Schumacher
Keyword(s):  
Reynolds Number ◽  
Liquid Metal ◽  
Large Scale ◽  
Scale Up ◽  
Convection Cell ◽  
Small Scale ◽  
Convection Flow ◽  
Large Scale Circulation ◽  
Large Scale Flow ◽  
The Impact

Combined measurements of velocity components and temperature in a turbulent Rayleigh–Bénard convection flow at a low Prandtl number of $Pr=0.029$ and Rayleigh numbers of $10^{6}\leqslant Ra\leqslant 6\times 10^{7}$ are conducted in a series of experiments with durations of more than a thousand free-fall time units. Multiple crossing ultrasound beam lines and an array of thermocouples at mid-height allow for a detailed analysis and characterization of the complex three-dimensional dynamics of the single large-scale circulation roll in a cylindrical convection cell of unit aspect ratio which is filled with the liquid metal alloy GaInSn. We measure the internal temporal correlations of the complex large-scale flow and distinguish between short-term oscillations associated with a sloshing motion in the mid-plane as well as varying orientation angles of the velocity close to the top/bottom plates and the slow azimuthal drift of the mean orientation of the roll as a whole that proceeds on a time scale up to a hundred times slower. The coherent large-scale circulation drives a vigorous turbulence in the whole cell that is quantified by direct Reynolds number measurements at different locations in the cell. The velocity increment statistics in the bulk of the cell displays characteristic properties of intermittent small-scale fluid turbulence. We also show that the impact of the symmetry-breaking large-scale flow persists to small-scale velocity fluctuations thus preventing the establishment of fully isotropic turbulence in the cell centre. Reynolds number amplitudes depend sensitively on beam-line position in the cell such that different definitions have to be compared. The global momentum and heat transfer scalings with Rayleigh number are found to agree with those of direct numerical simulations and other laboratory experiments.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

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