Bottom Plate Temperature Research Articles

Research on the significance of coupling effects of multiple process parameters in 3D printing based on orthogonal experimental method

Abstract For the semi-cylindrical model, orthogonal experiments and range analysis methods are used to explore the effects of four process parameters, namely layer thickness, printing speed, nozzle temperature, and bottom plate temperature, on the cross-sectional profile error and height error of FDM type 3D printing. This paper summarizes the optimal process plan for various errors and the significance of their impact, providing a certain reference for the coupling mechanism and significance research of process parameters.

Enhancing heat transfer in thermosyphons: The role of self-rewetting nanofluids, and filling ratios for improved performance

This study investigates the complex dynamics of heat transfer and phase change within a flat-shaped thermosyphon, examining various parameters and working fluids. The research explores the effects of different working fluids, filling ratios, and heat inputs on the system's thermal performance. This study employs an axisymmetric model, to enhance the accuracy of the solution compared to a 2D model while maintaining a low computational cost. To validate our numerical model, we conducted comprehensive comparisons with experimental data, including the axisymmetric model, and capturing the nanofluid effects. Remarkably, our simulations consistently align with the experimental findings, demonstrating a high degree of accuracy and reliability in our model.The findings show that self-rewetting nanofluids exhibit superior heat transfer capabilities and a reduced risk of dry-out compared to traditional working fluids. Notably, self-rewetting fluids and self-rewetting nanofluids exhibit a unique behavior, reversed surface tension trends with rising temperatures, which effectively prevents dry-out by attracting liquid to hot regions. Additionally, the enhanced thermal conductivity of nanofluids during boiling enhances their performance furthermore. Also, the research studies the impact of filling ratios on temperature profiles and heat transfer rates, emphasizing the importance of higher filling ratios in lowering bottom plate temperatures. These insights offer valuable guidance for optimizing thermosyphons in applications like electronic cooling.

Evaluation of high-speed aircraft thermal management system based on spray cooling technology: Energy analysis, global cooling, and multi-objective optimization

With the increase in aircraft speed, the aerodynamic heating on the aircraft wall has become one of the key factors restricting flight safety. Although passive thermal protection can solve the thermal protection problem of the aircraft body, there will always be some heat transferred into the cabin. And the temperature of the cabin interior environment and cabin wall increases, which reduces safety. The spray cooling system with R134a as a coolant can reduce the cabin wall temperature to 275 K, and the temperature drop rate can reach 1.05 K/s, so that the cabin cooling needs can be realized. The refrigeration system is used to connect the spray system with the fuel loop to form the closed-air spray cooling heat management system of the aircraft. The refrigeration system and the tandem radiator are optimized according to the genetic algorithm. After repeated iterations with different design parameters, the exergy efficiency and COP of the refrigeration system can reach 80 % and 2.36, and the pressure loss and the bottom plate temperature of the microchannel heat exchanger are 0.98 Mpa and 313 K, respectively. According to the analysis of the efficiency of the heat management system, the ejector efficiency, the energy efficiency ratio (EER) of the total system, and the required primary fluid flow rate, the required primary flow rate is at least 0.0027 kg/s to drive the thermal management system, EER of high-speed aircraft thermal management system can reach 15.62 %, exergy efficiency of the refrigeration system and the ejector efficiency can reach 44 % and 1 4% respectively.

Heat Transfer Enhancement of Microchannel with Jets and Ribs

In this paper, we propose a new microchannel heat sink with ribs and jets, which can not only increase the heat transfer performance but also improve the fluid flow in the microchannel. The effects of different shapes of ribs and inlet aspect ratios on the performance evaluation criteria at various Reynolds numbers are discussed. At an inlet Reynolds number of 3000, the maximum temperature of the modified microchannel heat sink is 8.78% lower than that of the smooth microchannel, and the performance evaluation criteria is increased by 0.94. Under the same conditions, the bottom plate temperature difference of the hydrofoil rib microchannel jets is 3.4% lower than that of the cylindrical rib microchannel jets; and the triangular-shaped ribs increase the heat transfer and cause greater pressure loss penalty due to the formation of a larger swirl zone in the back area. The jet inlet parameters can effectively improve the heat transfer coefficient of the microchannel. In terms of the heat transfer capability and the uniformity of the bottom plate temperature, the hydrofoil rib microchannel with jets has the best heat dissipation effect when the jet inlet parameter is .

A simplified core catcher model for the containment code AC2/COCOSYS

In Generation 3+ NPPs such as EPR or WWER-1200 the ex-vessel core catcher presents a key component of the severe accident mitigation concept. A simplified core catcher model in the containment code COCOSYS (part of AC2 code package) is developed to consider core melt retention and cooling phenomena in core catchers for containment simulations. The model enables the characterization of the corium in the core catcher including processes in the corium conditioning phase (melting of sacrificial material in the core catcher, oxidation of metallic components, possible layer flip) and the long-term cooling phase (evolution of long-term corium pool bulk temperature and changes in physical state). The core catcher model is based on the existing molten corium / concrete interaction (MCCI) model in COCOSYS with additions for melt retention within water-cooled structures and input data can be adapted to simulate various core catcher design features of e. g. NPPs with EPR or WWER.The current state of the model, including basic assumptions, calculation methods, simplifications, and two application examples are outlined. The recalculation of the water-cooled basemat test OECD WCB-1 shows that the experimental data regarding e. g. the ablation of the sacrificial concrete on top of the water-cooled basemat, corium pool temperature and heat fluxes at water-cooled interfaces can be adequately reproduced by the COCOSYS simulation, when using empirical data for the heat transfer, including the MCCI phase. These empirical heat transfer data agree well with findings obtained from recent analytical work on MCCI tests. However, the model does not predict high local bottom plate temperatures as observed in the WCB-1 test due to a restriction of the model to quasi-steady state processes. The second calculation example demonstrates the current modelling features when applied to an axisymmetric geometry of a reactor-scale core catcher. With view to reactor-scale, the model is ready for a further verification, like e.g. comparison with other analytical core catcher approaches.

VISUALIZATION RESEARCH OF DROPLET FREEZING ON AN INCLINED TITANIUM SURFACE

Freezing of droplets on inclined cold surfaces was investigated through their visualization. A DSA100 Droplet Surface Analyzer was employed to study the effects of surface tilt angle and temperature on the phase transition time of droplets of various sizes. The post-freezing contact diameter and contact angle between the droplets and the titanium surface were measured and analyzed. From these experimental studies and the related analysis it appears that the freezing time of droplets on cold surfaces at different tilt angles (15°, 30°, 45°, 60°, 75°, and 90°) is the longest when the bottom plate is tilted at 45°. As the tilted surface temperature is reduced, the droplet shape as it froze hardly changes with increasing tilt angle, and at the same time the freezing time of the droplets at each inclination angle is further reduced with decreasing bottom plate temperature. The experiments show that the deformation of a freezing 20-μL droplet on an inclined cold surface is more pronounced than that of a 1-μL droplet. The phase transition time of a large-volume droplet also decreases as the cold plate inclination increases. Thermodynamic equations are also employed to explain the longest droplet phase transition time which occurs at an inclination of 45°.

Molecular hints of two-step transition to convective flow via streamline percolation.

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However, its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.

Dehydrogenation of perhydro-dibenzyltoluene for hydrogen production in a microchannel reactor

A preliminary study regarding the dehydrogenation of perhydro-dibenzyltoluene as a liquid organic hydrogen carrier with switching from a stirred tank reactor to a continuous flow microchannel reactor is presented. The hydrogen production percentage in the case of a continuous flow microchannel reactor was found greater when compared to that of a stirred tank reactor. The hydrogen production was increased from 64.1% to 82.2% with the increase in bottom plate temperature from 260 to 320 °C for 0.01 mL/min flow rate. A maximum of 88% of hydrogen was generated for a 40 hours of operation, at a bottom wall temperature of 290 °C. The kinetic model for the microchannel reactor dehydrogenation was presented with a pre-exponential factor of 3.272 s−1 and activation energy of 13.79 kJ/mol. The results revealed that a continuous microchannel reactor can be an appropriate technology for the dehydrogenation of perhydro-dibenzyltoluene.

Universal properties of penetrative turbulent Rayleigh-Bénard convection

Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. We chose the most relevant example, namely thermally driven flow of water with a temperature around $T_m\approx 4^\circ\rm{C}$, where it has its density maximum. We pick the Rayleigh-B\'enard geometry with the bottom plate temperature $T_b > 4^\circ\rm{C}$ and the top plate temperature $T_t \le 4^\circ\rm{C}$. Next to the overall thermal driving strength set by the temperature difference $\Delta = T_b - T_t$ (the Rayleigh number $Ra$ in dimensionless form), the crucial new control parameter as compared to standard Rayleigh-B\'enard convection is the density inversion parameter $\theta_m \equiv (T_m - T_t ) / \Delta$. The crucial response parameters are the relative mean mid-height temperature $\theta_c$ and the overall heat transfer (i.e., the Nusselt number $Nu$). We theoretically derive the universal (i.e., $Ra$-independent) dependence $\theta_c (\theta_m) =(1+\theta_m^2)/2$, which holds for $\theta_m$ below a $Ra$-dependent critical value, beyond which $\theta_c (\theta_m)$ sharply decreases and drops down to $\theta_c=1/2$ at $\theta_m=\theta_{m,c}$. Our direct numerical simulations with $Ra$ up to $10^{10}$ are consistent with these results. The critical density inversion parameter $\theta_{m,c}$ can be precisely predicted by a linear stability analysis. The heat flux $Nu(\theta_m)$ monotonically decreases with increasing $\theta_m$ and we can theoretically derive a universal relation for the relative heat flux $Nu(\theta_m)/Nu(0)$. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large $\theta_m$.

Thermal and Flow Behavior of a Droplet Fluid Wetted by Parallel Hydrophobic Walls

Thermal analysis of a locally heated droplet located in two parallel plates with hydrophobic surfaces is considered. The spacing between the parallel plates is altered to modify the three-phase contact line of the droplet on both hydrophobic surfaces. The thermal state of the walls is altered via changing temperature difference between the parallel plates while initiating the droplet heat transfer. In this case, the bottom plate temperature is increased, while the top plate temperature is kept constant. The thermal field developed inside the droplet is obtained numerically incorporating the conditions used in the experiments. The influence of the droplet volume on the Nusselt and the Bond numbers is examined for the cases of droplets formed (i) on a hydrophobic plate and (ii) in between two parallel plates with hydrophobic wetting state. It is found that the droplet wetted by the parallelly located hydrophobic plates alters the circulation cell structure formed inside the droplet. Temperature field extends further inside the droplet as the wetted diameter is extended on the hydrophobic surfaces. The Nusselt number attains larger values for the two-plate case than the free droplet on a single plate case. The Bond number remains less than unity for the free and two-plate wetted droplets.

The Effect of Porosity on The Temperature Spectrum Area and Heat Transfer in Chamber with Porous Media Under the Saturated Vapour Flow

This study aims to determine the porosity effect on the temperature spectrum area and heat transfer in chamber containing porous media. Porous media is modelled in a chamber and fluidized tangentially. The porosity value of porous media is varied by 10%, 20%, 30%, 38%, and 40%. Fluid flowed and at the same time used as a heat source is saturated vapour with a temperature of 323 K with an entry speed into the chamber of 2.5 m/s. The ambient temperature outside the chamber is kept constant at 298 K, while the chamber bottom plate temperature, which is also the heat-sink is kept constant at 283 K. The porous media material is aluminium. This research was carried out using ANSYS Workbench 14.5, which solve the equation for mass, momentum, and energy conservation. The results of the study show that porosity affects the temperature spectrum area in the vapour channel and inside the porous media layer. The smaller porous media porosity, further expanding the high-temperature spectrum in the vapour channel, but constricting the low-temperature spectrum in both the vapour channel and porous media layer. Together with convection heat, porosity plays an important role in forming three patterns of temperature distribution along the vapour channel. In the heat transfer in the porous media layer, even though the conduction effect is stronger than convection, but the effect of temperature difference between porous media surfaces is greater than the effect of porosity.

Study on Characteristics of Heat Transfer and Flow Resistance in Random Porous Foam Metal

Porous foam metal has great application prospects in the field of compact heat exchangers. The characteristics of heat transfer and resistance for foam metal with random structure and different porosities (30%, 50%, 70% and 90%) were studied by finite element method in this study. The generated foam structures can be considered as homogeneous model and has better heat exchange capacity at higher inlet flow rate, and the boundary layer can develop well along the flow direction. The open–cell foammetal structure has a uniform heat transfer perpendicular to the flow direction. The bottom plate temperature of the low–porosity structure is more uniform at low flow rates. The intermediate porosities (50% and 70%) at high flow rates has a higher uniformity. As the porosity decreases, the internal pressure increases significantly and the pressure loss also becomes significantly larger. The corresponding optimal porosity is 57%, 66% and 76% at inlet flow rates of 0.001 m/s, 0.01 m/s and 0.1 m/s, respectively.

Large-scale flow and Reynolds numbers in the presence of boiling in locally heated turbulent convection

We report on an experimental study of the large-scale flow (LSF) and Reynolds numbers in turbulent convection in a cylindrical sample with height equal to its diameter and heated locally around the center of its bottom plate (locally heated convection). The sample size and shape are the same as those of Narezo Guzman et al. [D. Narezo Guzman, J. Fluid Mech. 787, 331 (2015)JFLSA70022-112010.1017/jfm.2015.701; D. Narezo Guzman, J. Fluid Mech. 795, 60 (2016)JFLSA70022-112010.1017/jfm.2016.178]. Measurements are made at a nearly constant Rayleigh number as a function of the mean temperature, both in the presence of controlled boiling (two-phase flow) and for the superheated fluid (one-phase flow). Superheat values Tb-Ton up to about 11 K (Tb is the bottom-plate temperature and Ton is the lowest Tb at which boiling is observed) are used. The LSF is less organized than it is in (uniformly heated) Rayleigh-Benard convection (RBC), where it takes the form of a single convection roll. Large-scale-flow-induced sinusoidal azimuthal temperature variations (like those found for RBC) could be detected only in the lower portion of the sample, indicating a less organized flow in the upper portions. Reynolds numbers are determined using the elliptic model (EM) of He and Zhang [G.-W. He and J.-B. Zhang, Phys. Rev. E 73, 055303(R) (2006)PLEEE81539-375510.1103/PhysRevE.73.055303]. We found that for our system the EM is applicable over a wide range of space and time displacements, as long as these displacements are within the inertial range of the temporal and spatial spectrum. At three locations in the sample the results show that the vertical mean-flow velocity component is reduced while the fluctuation velocity is enhanced by the bubbles of the two-phase flow. Enhancements of velocity fluctuations up to about 60% are found at the largest superheat values. Local temperature measurements within the sample reveal temperature oscillations that also used to determine a Reynolds number. These results are generally consistent with the mean-flow EM results and show a two-phase-flow enhancement of up to about 30%.

Vapour-bubble nucleation and dynamics in turbulent Rayleigh–Bénard convection

Vapour bubbles nucleating at micro-cavities etched into the silicon bottom plate of a cylindrical Rayleigh–Bénard sample (diameter $D=8.8$ cm, aspect ratio ${\it\Gamma}\equiv D/L\simeq 1.00$ where $L$ is the sample height) were visualized from the top and from the side. A triangular array of cylindrical micro-cavities (with a diameter of $30~{\rm\mu}\text{m}$ and a depth of $100~{\rm\mu}\text{m}$) covered a circular centred area (diameter of 2.5 cm) of the bottom plate. Heat was applied to the sample only over this central area while cooling was over the entire top-plate area. Bubble sizes and frequencies of departure from the bottom plate are reported for a range of bottom-plate superheats $T_{b}-T_{on}$ ($T_{b}$ is the bottom-plate temperature, $T_{on}$ is the onset temperature of bubble nucleation) from 3 to 12 K for three different cavity separations. The difference $T_{b}-T_{t}\simeq 16$ K between $T_{b}$ and the top plate temperature $T_{t}$ was kept fixed while the mean temperature $T_{m}=(T_{b}+T_{t})/2$ was varied, leading to a small range of the Rayleigh number $Ra$ from $1.4\times 10^{10}$ to $2.0\times 10^{10}$. The time between bubble departures from a given cavity decreased exponentially with increasing superheat and was independent of cavity separation. The contribution of the bubble latent heat to the total enhancement of heat transferred due to bubble nucleation was found to increase with superheat, reaching up to 25 %. The bubbly flow was examined in greater detail for a superheat of 10 K and $Ra\simeq 1.9\times 10^{10}$. The condensation and/or dissolution rates of departed bubbles revealed two regimes: the initial rate was influenced by steep thermal gradients across the thermal boundary layer near the plate and was two orders of magnitude larger than the final condensation and/or dissolution rate that prevailed once the rising bubbles were in the colder bulk flow of nearly uniform temperature. The dynamics of thermal plumes was studied qualitatively in the presence and absence of nucleating bubbles. It was found that bubbles enhanced the plume velocity by a factor of four or so and drove a large-scale circulation (LSC). Nonetheless, even in the presence of bubbles the plumes and LSC had a characteristic velocity which was smaller by a factor of five or so than the bubble-rise velocity in the bulk. In the absence of bubbles there was strongly turbulent convection but no LSC, and plumes on average rose vertically.

Experimental validation of thermal design of top shield for a pool type SFR

An Integrated Top Shield Test Facility towards validation of thermal design of top shield for a pool type SFR has been conceived, constructed & commissioned. Detailed experiments were performed in this experimental facility having full-scale features. Steady state temperature distribution within the facility is measured for various heater plate temperatures in addition to simulating different operating states of the reactor. Following are the important observations (i) jet cooling system is effective in regulating the roof slab bottom plate temperature and thermal gradient across roof slab simulating normal operation of reactor, (ii) wire mesh insulation provided in roof slab-main vessel annulus is effective in obtaining gradual thermal gradient along main vessel top portion and inhibiting the setting up of cellular convection within annulus and (iii) cellular convection with four distinct convective cells sets in the annular gap between roof slab and small rotatable plug measuring ∼ϕ4m in diameter & gap width varying from 16mm to 30mm. Repeatability of results is also ensured during all the above tests.The results presented in this paper is expected to provide reference data for validation of thermal hydraulic models in addition to serving as design validation of jet cooling system for pool type SFR.

Heat-flux enhancement by vapour-bubble nucleation in Rayleigh–Bénard turbulence

We report on the enhancement of turbulent convective heat transport due to vapour-bubble nucleation at the bottom plate of a cylindrical Rayleigh–Bénard sample (aspect ratio 1.00, diameter 8.8 cm) filled with liquid. Microcavities acted as nucleation sites, allowing for well-controlled bubble nucleation. Only the central part of the bottom plate with a triangular array of microcavities (etched over an area with diameter of 2.5 cm) was heated. We studied the influence of the cavity density and of the superheat $T_{b}-T_{on}$ ($T_{b}$ is the bottom-plate temperature and $T_{on}$ is the value of $T_{b}$ below which no nucleation occurred). The effective thermal conductivity, as expressed by the Nusselt number $\mathit{Nu}$, was measured as a function of the superheat by varying $T_{b}$ and keeping a fixed difference $T_{b}-T_{t}\simeq 16$ K ($T_{t}$ is the top-plate temperature). Initially $T_{b}$ was much larger than $T_{on}$ (large superheat), and the cavities vigorously nucleated vapour bubbles, resulting in two-phase flow. Reducing $T_{b}$ in steps until it was below $T_{on}$ resulted in cavity deactivation, i.e. in one-phase flow. Once all cavities were inactive, $T_{b}$ was increased again, but they did not reactivate. This led to one-phase flow for positive superheat. The heat transport of both one- and two-phase flow under nominally the same thermal forcing and degree of superheat was measured. The Nusselt number of the two-phase flow was enhanced relative to the one-phase system by an amount that increased with increasing $T_{b}$. Varying the cavity density (69, 32, 3.2, 1.2 and $0.3~\text{mm}^{-2}$) had only a small effect on the global $\mathit{Nu}$ enhancement; it was found that $\mathit{Nu}$ per active site decreased as the cavity density increased. The heat-flux enhancement of an isolated nucleating site was found to be limited by the rate at which the cavity could generate bubbles. Local bulk temperatures of one- and two-phase flows were measured at two positions along the vertical centreline. Bubbles increased the liquid temperature (compared to one-phase flow) as they rose. The increase was correlated with the heat-flux enhancement. The temperature fluctuations, as well as local thermal gradients, were reduced (relative to one-phase flow) by the vapour bubbles. Blocking the large-scale circulation around the nucleating area, as well as increasing the effective buoyancy of the two-phase flow by thermally isolating the liquid column above the heated area, increased the heat-flux enhancement.

Heat transfer in cryogenic helium gas by turbulent Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1

We present experimental results on the heat transfer efficiency of cryogenic turbulent Rayleigh–Bénard convection (RBC) in a cylindrical cell 0.3 m in both diameter and height which has improvements with respect to various corrections connected with finite thermal conductivity of sidewalls and plates. The heat transfer efficiency described by the Nusselt number is investigated for the range of Rayleigh number , with the Prandtl number varying such that , using cryogenic He gas with well-known and in situ tunable properties as a working fluid. For our data (both corrected and uncorrected) agree with suitably corrected data from similar cryogenic experiments and are consistent with . Up to , our data could be treated as Oberbeck-Boussinesq data. For , the heat transfer efficiency becomes affected by non-Oberbeck–Boussinesq (NOB) effects, causing asymmetry of the top and bottom boundary layers. For , the Nusselt number closely follows if and are evaluated on the basis of the working fluid properties at the directly measured bulk temperature, , and suitable corrections are taken into account. In contrast, if the mean temperature is determined as an arithmetic mean of the bottom and top plate temperatures, displays spurious crossover to higher γ that might be misinterpreted as a transition to the ultimate Kraichnan regime. The second step of our analysis, reported here for the first time, is to ignore the NOB effects affecting the top half of the RBC cell. We replace it by the inverted nearly OB bottom half in order to eliminate the boundary layer asymmetry. This leads to the effective temperature difference , where denotes the bottom plate temperature, and to effective and values. The effective heat transfer efficiency obtained, showing no tendency of crossover to the ultimate regime up to in , is reported and discussed.

Theoretical and experimental investigation of the performance of back-pass solar air heaters

This paper presents a study dealing with the experimental and theoretical analysis of a flat plate solar air heater. The air collectors were tested experimentally for the tilt angle of 35$^{\circ}$ and 2 m $s^{-1}$ air velocity, and ambient temperature, inlet temperature, outlet temperature, absorber plate temperature, bottom plate temperature, solar radiation, air velocity, and airflow velocity from the duct were measured. The outlet air temperature and energy and exergy efficiencies of the collector were calculated theoretically. The results showed that the collector has the maximum mean outlet temperature for the airflow velocity of 1 m $s^{-1}$, duct height of 0.001 m, triple glass cover, and length of 3 m; the maximum mean energy efficiency for the airflow velocity of 4 m $s^{-1}$, duct height of 0.04 m, triple glass cover, and length of 1 m; and the maximum mean exergy efficiency for the airflow velocity of 1 m $s^{-1}$, duct height of 0.005 m, triple glass cover, and length of 3 m. This study demonstrated the superiority of exergy analysis over energy analysis before the decision regarding design parameters.

Nematic–isotropic phase transition in turbulent thermal convection

AbstractWe report on turbulent Rayleigh–Bénard convection of a nematic liquid crystal while it undergoes a transition from the nematic to the isotropic phase in a cylindrical convection cell with a height equal to twice the diameter (aspect ratio $\Gamma = 0. 50$). The difference between the top and bottom plate temperature $ \mathrm{\Delta} T= {T}_{b} - {T}_{t} $ was held constant, while the average temperature ${T}_{m} = ({T}_{b} + {T}_{t} )/ 2$ was varied. There was a significant increase of the transported heat when the phase transition temperature ${T}_{NI} $ was between ${T}_{b} $ and ${T}_{t} $. Measurements of the temperatures along the sidewall of the sample as a function of ${T}_{m} $ showed several ranges with qualitatively different behaviour of quantities such as the time-averaged sidewall temperature, temperature gradient, or temperature fluctuations. We interpret these different ranges in terms of properties of the thermal boundary layers close to the top and bottom plates whose stability and nature depends on the location within the sample of ${T}_{NI} $.

Flow organization in two-dimensional non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water

Non-Oberbeck–Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh–Bénard turbulence are numerically analysed. The working fluid is water. We focus on the temperature profiles, the centre temperature, the Nusselt number and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh numberRa(withRaup to 108) for fixed temperature difference Δ between top and bottom plates and as functions of Δ (‘non-Oberbeck–Boussinesqness’) for fixedRawith Δ up to 60K. All results are consistent with the available experimental NOB data for the centre temperatureTcand the Nusselt number ratioNuNOB/NuOB(the label OB meaning that the Oberbeck–Boussinesq conditions are valid). For the temperature profiles we find – due to plume emission from the boundary layers – increasing deviations from the extended Prandtl–Blasius boundary layer theory presented in Ahlerset al. (J. Fluid Mech., vol. 569, 2006, p. 409) with increasingRa, while the centre temperature itself is surprisingly well predicted by that theory. For given non-Oberbeck–Boussinesqness Δ, both the centre temperatureTcand the Nusselt number ratioNuNOB/NuOBonly weakly depend onRain theRarange considered here.BeyondRa≈ 106the flow consists of a large diagonal centre convection roll and two smaller rolls in the upper and lower corners, respectively (‘corner flows’). Also in the NOB case the centre convection roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 faster (for Δ = 40K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced centre roll lead to an enhancement of the volume averaged energy based Reynolds number$Re^E \,{=}\, \langle\frac{1}{2} \bu^2 \rangle^{1/2} L/\nu$of about 4% to 5% for Δ = 60K. Moreover, we find$Re^E_{\it NOB}/Re^E_{\it OB} \,{\approx}\, (\beta (T_c)/\beta (T_m))^{1/2}$, with β the thermal expansion coefficient andTmthe arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of β in the numerics, the NOB modifications ofReEis less than 1% even at Δ = 60K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water.