We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with hot interior and cold exterior. With a constraint of fixed kinetic energy, the optimal flows are all essentially the same in the conformal coordinates. In the physical coordinates, they consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With the constraint of fixed enstrophy (or fixed rate of viscous dissipation), a geometry-dependent metric factor appears in the equations. The conformal coordinates are useful here because they map the problems to a rectangular domain, facilitating numerical solutions. With a small enstrophy budget, the optimal flows are dominated by vortices which have the same size as the flow domain.
A fully non-dimensional correlation for the Nusselt number associated to cooling processes in vertical storage tanks under laminar natural convection is presented. The derived correlation depends on the average temperature and can be used for the improvement of temperature profiles found from global methods. A Finite Volume method is employed using a transient bi-dimensional model in cylindrical coordinates and is experimentally validated. Forty cases of cooling with four aspect ratios, five overall heat transfer coefficients and two different volumes are considered. Thermal losses for the env…
In the present work, the effects of diffuse and collimated radiation on the symmetrical cooling case of natural convection in a two-dimensional cavity heated from the bottom have been investigated, numerically. The cavity is convectively heated from the bottom with heat transfer coefficient of 50 W/m2K and free stream temperature 305 K, while both vertical walls of cavity are isothermal at temperature of 296 K. The top wall is adiabatic and all walls are opaque for radiation heat transfer. For collimated case, a small semitransparent window of non-dimensional width of 0.05 at height of 0.7 has…
We examine the role of small-scale granulation in helping to drive supergranulation and even larger scales of convection. The granulation is modeled as localized cooling events introduced at the upper boundary of a 3-D simulation of compressible convection in a rotating spherical shell segment. With a sufficient number of stochastic cooling events compared to uniform cooling, we find that supergranular scales are realized, along with a differential rotation that becomes increasingly solar-like.
We investigate the convective cooling of a fluid with a quadratic equation of state by performing three-dimensional direct numerical simulations of a flow with a fixed top-boundary temperature, which is lower than the initial fluid temperature. We consider fluid temperatures near the density maximum, where the nonlinearity is expected to be important. When the equation of state is nonlinear, the resultant vertical transport of heat is fundamentally different and significantly lower than the predictions derived for a linear equation of state. Further, three dimensionless groups parameterize the…
The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wave number and time. The method is applied to transient Rayleigh-Benard-Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and pur…
The present paper numerically analyzes a passive cooling system using enclosures with different geometries filled with thermal conductivity-enhanced phase change material (PCM). A numerical code is developed using an unstructured finite-volume method and an enthalpy-porosity technique to solve for natural convection coupled to a solid-liquid phase change. Five geometries containing the same volume of PCM are compared while cooling the same surface. The unsteady evolution of the melting front and the velocity and temperature fields is detailed. Other indicators of cooling efficiency are monitor…
We find steady channel flows that are locally optimal for transferring heat from fixed-temperature walls, under the constraint of a fixed rate of viscous dissipation (enstrophy = $Pe^2$), also the power needed to pump the fluid through the channel. We generate the optima with net flux as a continuation parameter, starting from parabolic (Poiseuille) flow, the unique optimum at maximum net flux. Decreasing the flux, we eventually reach optimal flows that concentrate the enstrophy in boundary layers of thickness $\sim Pe^{-2/5}$ at the channel walls, and have a uniform flow with speed $\sim Pe^{…
We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-Bénard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $λ$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $λ$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^α$ where $Nu$ is …
The phenomenon of convection is found in a wide variety of settings on different scales -- from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing astrophysical events with the convective zones of stars. Given its importance in these diverse areas, the process of convection has been the focus of many research studies over the past two centuries. However, much less research has been conducted on how the presence of an obstruction in the flow can impact convection. In this work, we find that the presence of an obst…
After the sunset, under calm and clear sky conditions, aerosol laden surface air-layer, cools radiatively to the upper atmosphere. Predominant effect of the radiative cooling on the vertical temperature profile extends to several hundred meters from the surface. This results in the development of a stable, nocturnal inversion layer. However, ground surface, owing to its higher thermal inertia, lags in the cooling process. Due to this about a meter thick air layer just above the ground can be (2-6)deg Celsius cooler than the ground. Thus, at the surface an unstable convective layer is present, …
Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Bénard convection. In the low-latitude region $\mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $\mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equato…
The feasibility of using a thermomagnetically pumped ferrofluid to enhance the performance of a natural convection cooling loop is investigated. First, a simplified analytical estimate for the thermomagnetic pumping action is derived, and then design rules for optimal solenoid and ferrofluid are presented. The design rules are used to set up a medium-scale (1 m, 10-1000 W) case study, which is modeled using a previously published and validated model (Aursand et al. [1]). The results show that the thermomagnetic driving force is significant compared to the natural convection driving force, and …
As they keep cooling and contracting, Solar System giant planets radiate more energy than they receive from the Sun. Applying the first and second principles of thermodynamics, one can determine their cooling rate, luminosity, and temperature at a given age. Measurements of Saturn's infrared intrinsic luminosity, however, reveal that this planet is significantly brighter than predicted for its age. This excess luminosity is usually attributed to the immiscibility of helium in the hydrogen-rich envelope, leading to "rains" of helium-rich droplets. Existing evolution calculations, however, sugge…
The present work investigates the internal flow structure of two condensing droplets of aqueous solution during interaction. The velocity of fluid inside the droplets was investigated by confocal micro-PIV technique. Condensation on the droplets was carried out inside a closed chamber by creating a difference in vapor pressure between the droplet interface and a reservoir fluid surrounding the droplet in the room temperature without any cooling. Condensation on the droplet leads to spatial variation of solute concentration inside the droplet causing buoyancy driven Rayleigh convection. Fluid f…
Coupled mixed convective and stratified systems are common in natural flows. To study experimentally the associated dynamics, we use a singular property of water: its non-linear equation of state is characterised by a maximum density close to $4^{\circ}$C. By heating the top of a tank at $35^{\circ}$C and cooling the bottom at $0^{\circ}$C, a two-layer configuration spontaneously appears. The convective motion in the bottom layer consists mostly of a large-scale circulation and rising cold plumes. This turbulent flow generates propagating internal gravity waves in the upper stably-stratified l…
The goal of this report is to present the final project conducted in order to fulfill the requirements of the M.Sc. degree at the Department of Mechanical Engineering, Ben-Gurion University (BGU) of the Negev. The project comprises theoretical research investigating natural convection compressible flow with high temperature differences and with complex geometries. The research motivation comes from long-term research investigating and simulating the steady state and transient multiphase flow regimes existing in the reactor core, that was established by the Soreq Nuclear Center. The main object…
The paper presents the comparative study of the vortex-induced cooling of a heated channel for the four different cross-sections of the rigid cylinder, i.e., circular, square, semi-circular, and triangular, with or without the rigid/flexible splitter plate at the Reynolds number (based on the hydraulic diameter) of 200. The study presents a comprehensive analysis of the flow and thermal performance for all the cases. For flexible plate cases, a partitioned approach is invoked to solve the coupled fluid-structure-convection problem. The simulations show the reduction in the thermal boundary lay…
The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times10^{9}\leq Ra_F \leq 1.8\times10^{11}$ and cylindrical cells in the range $1.4\times10^{10}\leq Ra_F \leq 1.2\times10^{12}$ 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 magnitu…
The absorption of light or radiation drives turbulent convection inside stars, supernovae, frozen lakes and the Earth's mantle. In these contexts, the goal of laboratory and numerical studies is to determine the relation between the internal temperature gradients and the heat flux transported by the turbulent flow. This is the constitutive law of turbulent convection, to be input into large-scale models of such natural flows. However, in contrast with the radiative heating of natural flows, laboratory experiments have focused on convection driven by heating and cooling plates: the heat transpo…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed source, is passively advected and diffused, and exits through the boundary at a fixed temperature. We seek an advecting flow to optimize this exchange. Previous work on energy-constrained cooling with a constant source has conjectured that global optimizers should resemble convection rolls; we prove one-sided bounds on energy-constrained cooling corresponding to,…
This paper treats topology optimization of natural convection problems. A simplified model is suggested to describe the flow of an incompressible fluid in steady state conditions, similar to Darcy's law for fluid flow in porous media. The equations for the fluid flow are coupled to the thermal convection-diffusion equation through the Boussinesq approximation. The coupled non-linear system of equations is discretized with stabilized finite elements and solved in a parallel framework that allows for the optimization of high resolution three-dimensional problems. A density-based topology optimiz…
