Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThermal convection with mixed thermal boundary conditions: Effects of insulating lids at the top
59
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3times10^{9}leq Ra_F leq 1.8times10^{11}$ and cylindrical cells in the range $1.4times10^{10}leq Ra_F leq 1.2times10^{12}$ with the Prandtl number Pr fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading order level, the magnitude of temperature fluctuation in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function (PDF) in the bulk is essentially invariant with respect to both insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_F$, the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical one.
rate research
Read More
A series of direct numerical simulations of Rayleigh-Benard convection, the flow in a fluid layer heated from below and cooled from above, were conducted to investigate the effect of mixed insulating and conducting boundary conditions on convective flows. Rayleigh numbers between $text{Ra}=10^7$ and $text{Ra}=10^9$ were considered, for Prandtl numbers $text{Pr}=1$ and $text{Pr}=10$. The bottom plate was divided into patterns of conducting and insulating stripes. The size ratio between these stripes was fixed to unity and the total number of stripes was varied. Global quantities such as the heat transport and average bulk temperature and local quantities such as the temperature just below the insulating boundary wall were investigated. For the case with the top boundary divided into two halves, one conducting and one insulating, the heat transfer was found to be approximately two thirds of the fully conducting case. Increasing the pattern frequency increased the heat transfer which asymptotically approached the fully conducting case, even if only half of the surface is conducting. Fourier analysis of the temperature field revealed that the imprinted pattern of the plates is diffused in the thermal boundary layers, and cannot be detected in the bulk. With conducting-insulating patterns on both plates, the trends previously described were similar, however, the half-and-half division led to a heat transfer of about a half of the fully conducting case instead of two-thirds. The effect of the ratio of conducting and insulating areas was also analyzed, and it was found that even for systems with a top plate with only $25%$ conducting surface, heat-transport of $60%$ of the fully conducting case can be seen. Changing the 1D stripe pattern to 2D checkerboard tessellations does not result in a significantly different response of the system.
We report an experimental study aiming to clarify the role of boundary conditions (BC) in high Rayleigh number $10^8 < {rm{Ra}} < 3 times 10^{12}$ turbulent thermal convection of cryogenic helium gas. We switch between BC closer to constant heat flux (CF) and constant temperature (CT) applied to the highly conducting bottom plate of the aspect ratio one cylindrical cell 30 cm in size, leading to dramatic changes in the temperature probability density function and in power spectral density of the temperature fluctuations measured at the bottom plate, while the dynamic thermal behaviour of the top plate and bulk convective flow remain unaffected. Within our experimental accuracy, we find no appreciable changes in Reynolds number Re(Ra) scaling, in the dimensionless heat transfer efficiency expressed via Nusselt number Nu(Ra) scaling, nor in the rate of direction reversals of large scale circulation.
Recently, in Zhang et al. (2020), it was found that in rapidly rotating turbulent Rayleigh-Benard convection (RBC) in slender cylindrical containers (with diameter-to-height aspect ratio $Gamma=1/2$) filled with a small-Prandtl-number fluid ($Pr approx0.8$), the Large Scale Circulation (LSC) is suppressed and a Boundary Zonal Flow (BZF) develops near the sidewall, characterized by a bimodal PDF of the temperature, cyclonic fluid motion, and anticyclonic drift of the flow pattern (with respect to the rotating frame). This BZF carries a disproportionate amount ($>60%$) of the total heat transport for $Pr < 1$ but decreases rather abruptly for larger $Pr$ to about $35%$. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent RBC in containers of different $Gamma$ and in a broad range of $Pr$ and $Ra$. Direct numerical simulations for $0.1 leq Pr leq 12.3$, $10^7 leq Ra leq 5times10^{9}$, $10^{5} leq 1/Ek leq 10^{7}$ and $Gamma$ = 1/3, 1/2, 3/4, 1 and 2 show that the BZF width $delta_0$ scales with the Rayleigh number $Ra$ and Ekman number $Ek$ as $delta_0/H sim Gamma^{0} Pr^{{-1/4, 0}} Ra^{1/4} Ek^{2/3}$ (${Pr<1, Pr>1}$) and the drift frequency as $omega/Omega sim Gamma^{0} Pr^{-4/3} Ra Ek^{5/3}$, where $H$ is the cell height and $Omega$ the angular rotation rate. The mode number of the BZF is 1 for $Gamma lesssim 1$ and $2 Gamma$ for $Gamma$ = {1,2} independent of $Ra$ and $Pr$. The BZF is quite reminiscent of wall mode states in rotating convection.
Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-Benard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as $0.588Pr^{-1/2}$ for $Prll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*llPr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocity boundary layer thickness with that evaluated in the direct numerical simulations by Stevens, Verzicco, and Lohse (J. Fluid Mech. 643, 495 (2010)) gives very good agreement. Based on the Prandtl--Blasius type considerations, we derive a lower-bound estimate for the minimum number of the computational mesh nodes, required to conduct accurate numerical simulations of moderately high (boundary layer dominated) turbulent Rayleigh-Benard convection, in the thermal and kinetic boundary layers close to bottom and top plates. It is shown that the number of required nodes within each boundary layer depends on Nu and Pr and grows with the Rayleigh number Ra not slower than $simRa^{0.15}$. This estimate agrees excellently with empirical results, which were based on the convergence of the Nusselt number in numerical simulations.
We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-B{e}nard convection cell. It is found that thermal plumes are not emitted periodically, but randomly and continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
