Showing papers on "Rayleigh number published in 2002"
TL;DR: The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse are presented and compared with various recent experimental findings.
Abstract: The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001)] are presented and compared with various recent experimental findings. This dependence Re(Ra,Pr) is more complicated than a simple global power law. For Pr=5.5 and 108
295 citations
TL;DR: In this article, a modified Rayleigh number Ra* is introduced, which does not depend on viscosity or thermal diffusivity, and asymptotic scaling laws for the dependence of various properties on Ra* in the limit of negligible viscosities (E → 0) are estimated from the numerical results.
Abstract: Thermal convection in a rotating spherical shell with free-slip boundaries can excite a dominant mean zonal flow in the form of differentially rotating cylinders concentric to the principal rotation axis. This process is studied numerically for Prandtl numbers of order 1, Ekman numbers in the range E = 3 x 10 -4 -10 -5 , and Rayleigh numbers up to 100× critical. Small-scale convection transfers kinetic energy into the mean zonal flow via Reynolds stresses. For low Ekman number and high Rayleigh number, the force balance is predominantly among the Coriolis, inertial and buoyancy forces, and viscosity plays a minor role. A modified Rayleigh number Ra* is introduced, which does not depend on viscosity or thermal diffusivity, and asymptotic scaling laws for the dependence of various properties on Ra* in the limit of negligible viscosity (E → 0) are estimated from the numerical results. The ratio of kinetic energy in the zonal flow to that in the non-zonal (convective) flow increases strongly with Ra* at low supercritical Rayleigh number, but drops at high values of Ra*. This is probably caused by the gradual loss of geostrophy of the convective columns and a corresponding decorrelation of Reynolds stresses. Applying the scaling laws to convection in the molecular hydrogen envelopes of the large gas planets predicts the observed magnitude of the zonal winds at their surfaces.
253 citations
TL;DR: In this paper, a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity was used to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical.
230 citations
TL;DR: In this article, a series of high-resolution, three-dimensional numerical experiments were conducted to investigate the nature of turbulent compressible convective motions extending from a convection zone into a stable layer below.
Abstract: We present the results of a series of high-resolution, three-dimensional numerical experiments that investigate the nature of turbulent compressible convective motions extending from a convection zone into a stable layer below In such convection, converging flows in the near-surface cellular convecting network create strong downflowing plumes that can traverse the multiple scale heights of the convection zone Such structures can continue their downward motions beyond the convecting region, piercing the stable layer, where they are decelerated by buoyancy braking If these motions mix entropy to an adiabatic state below the convection zone, the process is known as penetration; otherwise it is termed overshooting We find that in threedimensional turbulent compressible convection at the parameters studied, motions generally overshoot a significant fraction of the local pressure scale height but do not establish an adiabatic penetrative region, even at
226 citations
TL;DR: In this article, the authors used a two-field model for the separate modeling of the solid and fluid phase temperature fields in a fluid-saturated porous medium, and considered how the onset criterion for convection in a horizontal layer is affected by the adoption of such a model.
191 citations
TL;DR: In this paper, the early stages of the instability growth in a vertical Hele-Shaw cell were investigated by means of experimental measurements, as well as two-and three-dimensional numerical simulations.
Abstract: Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.
161 citations
TL;DR: In this article, a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated.
Abstract: Natural convection in a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated. The applied sinusoidal temperature is symmetric with respect to the midplane of the enclosure. Numerical calculations are produced for Rayleigh numbers in the range 10 2 to 10 8 , and results are presented in the form of streamlines, isotherm contours, and distributions of local Nusselt number. The circulation patterns are shown to increase in intensity, and their centers to move toward the upper wall corners with increasing Rayleigh number. As a result, the thermal boundary layer is confined near the upper wall regions. The values of the maximum and the minimum local Nusselt number at the upper wall are shown to increase with increasing Rayleigh number. Finally, an increase in the enclosure aspect ratio produces an analogous increase of the fluid circulation intensity.
154 citations
TL;DR: In this paper, it was shown that if the viscosity, ν, and thermal diffusivity, κ, are lowered to zero, with σ ≡ ν/κ fixed, then the energy dissipation per unit mass, σ, also vanishes in this limit.
Abstract: Consider the problem of horizontal convection: a Boussinesq fluid, forced by applying a non-uniform temperature at its top surface, with all other boundaries insulating. We prove that if the viscosity, ν, and thermal diffusivity, κ, are lowered to zero, with σ
≡
ν/κ fixed, then the energy dissipation per unit mass, κ, also vanishes in this limit. Numerical solutions of the two-dimensional case show that despite this anti-turbulence theorem, horizontal convection exhibits a transition to eddying flow, provided that the Rayleigh number is sufficiently high, or the Prandtl number σ sufficiently small. We speculate that horizontal convection is an example of a flow with a large number of active modes which is nonetheless not ‘truly turbulent’ because e→0 in the inviscid limit.
147 citations
TL;DR: In this paper, the vorticity-stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation, which is shown that the outer square boundary can be approximated by a super elliptic function.
Abstract: SUMMARY In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the di;erential quadrature (DQ)method. The vorticity-stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 10 4 to 10 6 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are
146 citations
01 Nov 2002
TL;DR: In this paper, the Nusselt number was measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, and the results showed that the variation in the mean flow was approximately a 1/3 power of the Rayleigh number.
Abstract: New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was . Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.
143 citations
TL;DR: In this article, a numerical visualization of mass and heat transport for convective heat transfer by streamlines and heatlines is comprehensively studied and the consistency of the formulations is especially addressed when dealing with conjugate convection/conduction problem.
TL;DR: A series of single-phase natural circulation tests in a model reactor with rolling motion was performed in order to investigate effects of the rolling motion on its thermal-hydraulic behavior.
TL;DR: The results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001 are summarized in this paper.
Abstract: This paper summarizes the results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001. The primary objectives for the special session were to: (1) determine the most accurate estimate of the critical Rayleigh number above which the flow is unsteady, (2) identify the correct, i.e. best time-dependent benchmark solution for the 8:1 differentially heated cavity at particular values of the Rayleigh and Prandtl numbers, and (3) identify those methods that can reliably provide these results
TL;DR: Nusselt number measurements from high Prandtl number turbulent thermal convection experiments are reported and are found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.
Abstract: We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from 2x10(7) to 3x10(10), all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about 20% over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.
TL;DR: In this article, a general criterion for local thermal equilibrium is presented in terms of parameters of engineering importance which include the Darcy number, the Prandtl number, and the Reynolds number.
TL;DR: In this paper, a theoretical study of mixed convection flow of a micropolar fluid in a parallel plate vertical channel with an asymmetric wall temperature distribution has been presented, and solutions of the governing equations are obtained both analytically and numerically.
TL;DR: In this paper, a scaling analysis for small bottom slopes reveals that a number of flow regimes are possible depending on the Rayleigh number and the relative value of certain non-dimensional parameters describing the flow.
Abstract: The authors have previously reported a model experiment on the unsteady natural convection in a triangular domain induced by the absorption of solar radiation. This issue is reconsidered here both analytically and numerically. The present study consists of two parts: a scaling analysis and a numerical simulation. The scaling analysis for small bottom slopes reveals that a number of flow regimes are possible depending on the Rayleigh number and the relative value of certain non-dimensional parameters describing the flow. In a typical situation, the flow can be classified broadly into a conductive, a transitional or a convective regime determined merely by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. The numerical simulation has verified the scaling results.
TL;DR: In this paper, a two-dimensional solution for unsteady natural convection in an enclosure with a square body was obtained using an accurate and efficient Chevyshev spectral collocation method.
Abstract: A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 103 to 106. When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is hi...
TL;DR: In this paper, the authors used the finite difference method to predict the characteristics of hydromagnetic double-diffusive convective flow of a binary gas mixture in a rectangular enclosure with the upper and lower walls being insulated.
TL;DR: In this paper, the authors considered Laminar steady state natural convection in inclined shallow cavities and found that flow and heat transfer are governed by Rayleigh number, aspect ratio and inclination.
TL;DR: In this paper, velocity and temperature fields in horizontal planes crossing a cylindrical Rayleigh-Benard convection cell in steady rotation about its vertical axis were measured and three basic flow regimes were characterized.
Abstract: We present experimental measurements of velocity and temperature fields in horizontal planes crossing a cylindrical Rayleigh–Benard convection cell in steady rotation about its vertical axis. The range of dimensionless rotation rates Ω is from zero to 5×104 for a Rayleigh number R = 3.2×108. The corresponding range of convective Rossby numbers is ∞ > Ro > 0.06. The patterns of velocity and temperature and the flow statistics characterize three basic flow regimes. For Ro [Gt ] 1, the flow is dominated by vortex sheets (plumes) typical of turbulent convection without rotation. The flow patterns for Ro ∼ 1 are cyclone-dominated, with anticyclonic vortices rare. As the Rossby number continues to decrease, the number of anticyclonic vortex structures begins to grow but the vorticity PDF in the vicinity of the top boundary layer still shows skewness favouring cyclonic vorticity. Velocity-averaging near the top of the cell suggests the existence of a global circulation pattern for Ro [Gt ] 1.
TL;DR: In this article, a bounding principle for the heat transport in Rayleigh-Benard convection with fixed heat flux through the boundaries was formulated, and the relation among the parameter Rˆ, the Nusselt number and the conventional Rayleigh number defined in terms of the temperature drop across the layer, yielding the bound Nu [les ] c3/2Ra1/2.
Abstract: We formulate a bounding principle for the heat transport in Rayleigh–Benard convection with fixed heat flux through the boundaries. The heat transport, as measured by a conventional Nusselt number, is inversely proportional to the temperature drop across the layer and is bounded above according to Nu [les ] cRˆ1/3, where c < 0.42 is an absolute constant and Rˆ = αγβh4/(νκ) is the ‘effective’ Rayleigh number, the non-dimensional forcing scale set by the imposed heat flux κβ. The relation among the parameter Rˆ, the Nusselt number, and the conventional Rayleigh number defined in terms of the temperature drop across the layer, is NuRa = Rˆ, yielding the bound Nu [les ] c3/2Ra1/2.
TL;DR: In this paper, the transient state of natural convection in a vertical cylindrical enclosure is studied numerically for water at high Rayleigh numbers, extending into values characteristic of the turbulent flow regime.
TL;DR: In this article, the conservation of mass, momentum, and energy in Laminar and turbulent natural convection in enclosures with partial partitions was studied by a numerical method, and the results were reduced in terms of the normalized Nusselt number as a function of the Rayleigh number.
TL;DR: In this paper, the first and second law characteristics of fluid flow and heat transfer inside a channel having two parallel plates with finite gap between them were investigated analytically, and the spatial distribution of entropy generation number, irreversibility ratio and Bejan number were presented graphically.
TL;DR: In this article, the effects of heat generation and the porosity of the medium on the streamlines and isotherms are presented, as well as on the rate of heat transfer from the walls of the enclosure.
TL;DR: In this article, an analytical and experimental study of magnetohydrodynamic Rayleigh-Benard convection in a large aspect ratio, 20 × 20 × 10 × 1, rectangular box is presented.
Abstract: This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Benard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.
TL;DR: In this article, the authors investigated how boundary effects modify the well-known criterion for the onset of convection of a Boussinesq fluid in a porous medium where Darcy's law applies.
TL;DR: The experiment demonstrates how the thermal plumes in a closed cell organize themselves both in space and time and generate coherent oscillations in a turbulent environment.
Abstract: A systematic study of temperature oscillations in turbulent thermal convection was carried out in two aspect-ratio-one convection cells filled with water. Temperature correlation functions and local velocity fluctuations were measured over varying Rayleigh numbers and spatial positions across the entire cell. These measurements fully characterize the spatial structure of the temperature oscillation and reveal the mixing and emission dynamics of the thermal plumes near the conducting surface. A sharp transition from a random chaotic state to a correlated turbulent state of finite coherence time is found when the Rayleigh number becomes larger than a critical value Ra(c) approximately equal 5 x 10(7). Above Ra(c) the measured temperature correlation functions show a well-defined oscillation with a finite coherence time. The oscillation period is found to be twice as large as the cell crossing time. The experiment demonstrates how the thermal plumes in a closed cell organize themselves both in space and time and generate coherent oscillations in a turbulent environment.
TL;DR: In this article, the effect of a temperature dependent viscosity on natural convection flow of viscous incompressible fluid from a vertical wavy surface has been investigated using an implicit finite difference method.
Abstract: In the present paper, the effect of a temperature dependent viscosity on natural convection flow of viscous incompressible fluid from a vertical wavy surface has been investigated using an implicit finite difference method Here we have focused our attention on the evaluation of the local skin-friction and the local Nusselt number The governing parameters are the Prandtl number, Pr, ranging from 1 to 100, the amplitude of the waviness of the surface, α, ranging from 00 to 04 and the viscosity variation parameter, e, ranging from 00 to 6