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thermal convection in a Spherical Shell with Melting/Freezing at either or both of Its Boundaries

Journal of Earth Science 2013年第5期24卷 669-682页

作者： Renaud Deguen Institut de Mécanique des Fluides de Toulouse Université de Toulouse (INPT UPS) and CNRS

In a number of geophysical or planetological settings, including Earth＇s inner core, a sili- cate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean--a situa- tion possibly encountered in a number of Jupiter and Saturn＇s icy satellites--a convecting crystalline layer is in contact with a layer of its melt. Allowing for melting/freezing at one or both of the boundaries of the solid layer is likely to affect the pattern of convection in the layer. We study here the onset of thermal convection in a viscous spherical shell with dynamically induced melting/freezing at either or both of its boundaries. It is shown that the behavior of each interface---permeable or impermeable-- depends on the value of a dimensionless number P （one for each boundary）, which is the ratio of a melting/freezing timescale over a viscous relaxation timescale. A small value of P corresponds to perme- able boundary conditions, while a large value of P corresponds to impermeable boundary conditions. Linear stability analysis predicts a significant effect of semi-permeable boundaries when the number P characterizing either of the boundary is small enough： allowing for melting/freezing at either of the boundary allows the emergence of larger scale convective modes. The effect is particularly drastic when the outer boundary is permeable, since the degree 1 mode remains the most unstable even in the case of thin spherical shells. In the case of a spherical shell with permeable inner and outer boundaries, the most unstable mode consists in a global translation of the solid shell, with no deformation. In the limit of a full sphere with permeable outer boundary, this corresponds to the ＂convective translation＂ mode recently proposed for Earth＇s inner core. As another example of possible application, we discuss the case of thermal convection in Enceladus＇ ice shell assuming the presence of a global subsurface ocean, and found that melting/freezing could have an importa

关键词： planetary mantle thermal convection phase change linear stability analysis.

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Numerical simulation of thermal convection of viscoelastic fluids in an open-top porous medium with constant heat flux

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Journal of Hydrodynamics 2015年第1期27卷 52-61页

作者：牛骏石在虹谭文长 Petroleum Exploration and Production Research Institute of SINOPEC State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering College of Engineering Peking University

This paper makes a numerical study of the buoyancy-driven convection of a viscoelastic fluid saturated in an open-top porous square box under the constant heat flux boundary condition. The effects of the relaxation and retardation times on the onset of the oscillatory convection, the convection heat transfer rate and the flow pattern transition are investigated. It is shown that a large relaxation time can destabilize the fluid flow leading to an early onset of the thermal convection and a high heat transfer rate, while a large retardation time tends to stabilize the flow and suppress the convection onset and the heat transfer. After the convection sets in, the flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time, resulting in more complicated flow patterns in the porous medium. Furthermore, with the increase of the ratio of the relaxation time to the retardation time, the fluid may be blocked from flowing through the open-top boundary, which may be caused by the viscoelastic effect. Finally, the comparison of our results with those under isothermal heating boundary conditions reveals that the heat transfer rate correspo- nding to a constant heat flux boundary is always higher.

关键词： thermal convection viscoelastic fluids porous medium constant heat flux

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Heat transfer and plume statistics in turbulent thermal convection with sparse fractal roughness

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Journal of Hydrodynamics 2021年第5期33卷 1065-1077页

作者： Guang-chun Xu Qi Wang Zhen-hua Wan De-jun Sun Department of Modern Mechanics University of Science and Technology of ChinaHefei 230027China

Rough-surface Rayleigh-Benard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratioГ=*** types of fractal roughness elements,which are marked as nl,n2 and n3,are constructed based on the Koch curve and sparsely mounted on both the plates,where n denotes the level of the *** considered Rayleigh numbers Ra range from 10^(7)to 10^(11)with Prandtl number Pr=*** regimes are identified for cases nl,*** Regime I,the scaling exponentsβin the effective Nusselt number Nu vs Ra scaling Nu~Ra^(β)reach up to about ***,when Ra is larger than a critical value Ra_(c),the flow enters RegimeⅡ,with p saturating back to a value close to the smooth-wall case(0.3).Rac is found to increase with increasing n,and for case n3,only Regime I is identified in the studied Ra *** extension of Regime I in case n3 is due to the fact that at high Ra,the smallest roughness elements can play a role to disrupt the thermal boundary *** thermal dissipation rate is studied and it is found that the increasedβin Regime I is related with enhanced thermal dissipation rate in the *** interesting finding is that no clear convection roll structures can be identified for the rough cases,which is different from the smooth case where well-organized convection rolls can be *** difference is further quantified by the detailed analysis of the plume statistics,and it is found that the horizontal profiles of plume density and velocity are relatively flattened due to the absence of clear convection rolls.

关键词： thermal convection Rayleigh-Benard convection rough surface Introduction

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The viscoelastic effects on thermal convection of an Oldroyd-B fluid in open-top porous media

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Journal of Hydrodynamics 2013年第4期25卷 639-642页

The effects of two viscoelastic parameters on the thermal convection of a viscoelastic Oldroyd-B fluid in an open-top porous square box with constant heat flux are investigated. The results show that the increase of relaxation time is able to destabilize the fluid flow leading to a higher heat transfer rate, while the increase of retardation time tends to stabilize the flow and suppress the heat transfer. The flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time, re- suiting in more complicated flow patterns in the porous medium.

关键词： viscoelastic effect thermal convection Oldroyd-B fluids porous medium

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Current trends and future directions in turbulent thermal convection

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Theoretical & Applied Mechanics Letters 2013年第5期3卷 1-12页

作者： Ke-Qing Xia Department of Physics The Chinese University of Hong Kong

The system of turbulent thermal convection is introduced. Progresses in recent decades in the four major areas of research in turbulent convection are briefly reviewed. Some of the recent trends of the field are then discussed, which also serve to point out that the future directions in this important field of fluid mechanics lie in the extension to the non-standard or non-classical Rayleigh-Bénard configuration.

关键词： turbulence thermal convection turbulent heat transport thermal plumes large-scaleflow small-scale turbulence

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thermal convection Mechanics

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Natural Science 2020年第9期12卷 640-643页

作者： Kern E. Kenyon 4632 North Lane Del Mar USA

Assuming thermal convection takes place continuously inside the North Pacific High, an application of physics to the rising sea-warmed air plumes increases understanding of the relatively high air pressure at the sea surface and at the bases of the plumes. Since the ocean is warmer than the air under the NPH, heat is transferred upward decreasing the air density, which should then accelerate upward when no other forces are around to stop it. By Newton’s 3rd law the upward accelerating air will cause an equal but opposite (downward) reaction resulting in high pressure in the air under the rising column. That is the central proposal offered, which is consistent with available observations. New data that confirm the upward acceleration of the heated air are especially needed. Perhaps dye or neutrally buoyant particles could be released from a ship or buoy to make the upward air motion visible.

关键词： High Pressure thermal convection North Pacific

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thermal convection in the North Pacific High Pressure Cell

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Natural Science 2020年第7期12卷 516-519页

作者： Kern E. Kenyon 4632 North Lane Del Mar USA

If it is accepted that thermal convection consistently takes place inside the North Pacific High, as proposed here, then the existence of the NPH, as well as its seasonal variation, will be explained simultaneously, building on an earlier attempt. More observations than available at present would help prove that thermal convection happens and pin down its characteristics, since it is not visible. Also the physics of how thermal convection produces relatively high pressure at sea level needs work.

关键词： North Pacific High thermal convection

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Temporal evolution and scaling of mixing in turbulent thermal convection for inhomogeneous boundary conditions

Temporal evolution and scaling of mixing in turbulent therma...

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第九届全国流体力学学术会议

作者：魏义坤窦华书浙江理工大学机械与自动控制学院流体工程系

Numerical study of two-dimensional(2D)in turbulent thermal convection for inhomogeneous boundary condition is investigated using the lattice Boltzmann method(LBM).This study mainly appraises the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence *** is noted that the flow is dominated by large-scale structures in the turbulence *** plumes emerge at both ends of the every heat source,and increasingly smaller plumes *** is further observed that temporal evolution of the Kolmogorov scale,the kinetic-energy dissipation rates and thermal dissipation rates agree well with the theoretical predictions,which are similar to previous studies for homogeneous boundary *** is also noted that the 2th-order structure functions of velocity and temperature fluctuations and mixed velocity-temperature structure function display a range of linear scaling.

关键词： thermal convection Turbulence Inhomogeneous Boundary Conditions Lattice Boltzmann Method

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Characteristics and suppression of beam distortion in a high repetition rate nanosecond stimulated Brillouin scattering phase conjugation mirror

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High Power Laser Science and Engineering 2024年第2期12卷 69-78页

作者： Yifu Chen Bowen Tan Duo Jin Bin Chen Zhenxu Bai Kun Wang Yulei Wang Zhiwei Lü School of Astronautics Harbin Institute of TechnologyHarbinChina Center for Advanced Laser Technology Hebei University of TechnologyTianjinChina Hebei Key Laboratory of Advanced Laser Technology and Equipment TianjinChina School of Energy and Environmental Engineering Hebei University of TechnologyTianjinChina

The stimulated Brillouin scattering phase conjugation mirror (SBS-PCM) based on liquid media is widely used in high-power laser systems due to its robust thermal load capacity, high energy conversion efficiency and improved beam quality. Nevertheless, with an increase in the pump repetition rate, thermally-induced blooming and optical breakdown can emerge, leading to distortions in the Stokes beam. In this study, we delved into the thermal effects in liquid SBS-PCMs employing hydrodynamic analysis, establishing a relationship between beam profile distortion and the thermal convection field. We calculated the temperature and convection velocity distribution based on the pump light parameters and recorded the corresponding beam profiles. The intensities of the beam profiles were modulated in alignment with the convection directions, reaching a velocity peak of 2.85 mm/s at a pump pulse repetition rate of 250 Hz. The residual sum of squares (RSS) was employed to quantify the extent of beam profile distortion relative to a Gaussian distribution. The RSS escalated to 7.8, in contrast to 0.7 of the pump light at a pump pulse repetition rate of 500 Hz. By suppressing thermal convection using a high-viscosity medium, we effectively mitigated beam distortion. The RSS was reduced to 0.7 at a pump pulse repetition rate of 500 Hz, coinciding with a twentyfold increase in viscosity, thereby enhancing the beam quality. By integrating hydrodynamic analysis, we elucidated and mitigated distortion with targeted solutions. Our research offers an interdisciplinary perspective on studying thermal effects and contributes to the application of SBS-PCMs in high-repetition-rate laser systems by unveiling the mechanism of photothermal effects.

关键词： beam profile high power high repetition rate stimulated Brillouin scattering phase conjugation mirror thermal convection

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Three-Dimensional convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

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Fluid Dynamics & Materials Processing 2024年第9期20卷 1957-1970页

作者： Ivan Shubenkov Tatyana Lyubimova Evgeny Sadilov Computational Fluid Dynamics Laboratory Institute of Continuous Media Mechanics UB RASPerm614068Russia Theoretical Physics Department Perm State UniversityPerm614990Russia

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a *** layer is subjected to a gravitational field and a strictly vertical temperature ***,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)*** boundary conditions considered in the present work allow a conductive state and are representative of typical geological *** an earlier work,we carried out a linear stability analysis of the conductive *** was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal ***,a non-zero velocity component exists in *** the present work,threedimensional non-linear convection regimes are *** original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear *** number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity *** carried out at low supercriticalities show that a direct bifurcation takes *** increasing supercriticality,no transitions to other convective regimes are *** situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

关键词： thermal convection inclined layer porous media vertical temperature gradient

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