Session EH: Convection and Buoyancy Driven Flows III

Direct Actuation of Small-Scale Motions for Enhanced Heat Transfer in a Straight Channel

Heat transfer enhancement by small-scale flow interactions that are induced within the core flow of a heated, high-aspect ratio straight channel are investigated experimentally. Direct actuation of small scale motions is provided by streamwise-embedded piezoelectrically-driven cantilevered reeds that span the entire channel height. Deliberate interactions between the reeds and a given core flow lead to the formation of time-periodic vorticity concentrations over a range of vibration frequencies that are advected with the core flow and induce small-scale motions near the channel's surfaces. Heat transfer measurements are obtained using novel, microfabricated heaters with integrated temperature sensors that are deposited on a silicon substrate. It is shown that the actuation disrupts the thermal boundary layers and result in a significant enhancement of the local and global heat transfer along the channel compared to the baseline (unactuated) flow. The interactions between the reed-induced motions and the channel internal surfaces and mixing within the core flow are investigated in detail using high resolution particle image velocimetry (PIV) with emphasis on local and global heat transfer across the channel boundaries.   

Influence of temperature-dependent fluid properties on heat transfer in turbulent channel flow

Forced-convection heat transfer in turbulent liquid flows is parametrized by a correlation between the Nusselt number, $Nu$, the flow Reynolds number, $Re$, and the Prandtl number, $Pr$. Most of existing expressions for such $Nu=f(Re,Pr)$ correlation were developed under the assumption of negligible dependence of the thermo-physical properties of the liquid on temperature. This may be a bottleneck when system optimization is required. In this work we use pseudo-spectral direct numerical simulation to investigate the influence of temperature-dependent fluid properties on the overall turbulent heat transfer. In particular, we focus on turbulent channel flow of water, and we let viscosity vary with temperature at fixed $Pr$. Compared to the case of constant thermo-physical properties, it is observed that, already at low $Re$, temperature-dependent variations alter velocity profiles, and modify both the Nusselt number and the friction factor significantly (up to about 10 \%).   

Viscous Lock-Exchange in Rectangular Cells: Calculation and Experiments

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a $2D$ Stokes flow between two parallel horizontal boundaries separated by a vertical height, $H$, and, recently, for a cylindrical tube. In this presentation, we calculate it, analytically, for a rectangular channel (horizontal thickness $b$, vertical height $H$) of any aspect ratio ($H/b$) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios ($1/10-10$). We also discuss the $2D$ Stokes-Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used. An extension to the case where the density contrast between the two fluids is generated by a chemical reaction is also discussed.   

Natural Convection in a Slot Subject to a Spatially Distributed Heating

Natural convection in a fluid contained in an infinite horizontal slot subject to a spatially distributed heating has been investigated for a wide range of Prandtl numbers Pr. Detailed results are presented for the case of the lower wall subject to heating being a sinusoidal function of one of the coordinate, with its spatial distribution described by the heating wave number $\alpha$ and its intensity expressed in terms of the Rayleigh number Ra. The primary response of the system, which represents a forced response, consists of convection in the form of rolls whose structure is determined by the particular values of Ra and $\alpha$. Linear stability of convective motion has been considered and conditions leading to the emergence of roll instability have been identified. Two mechanisms of instability motion at the onset have been identified. In the case of moderate $\alpha$ the pattern of instability is generally locked-in with the pattern of heating according to the relation $\delta _{cr}=\alpha$/2. In the case of large $\alpha$, the critical disturbance wave number approaches value $\delta _{cr}$ = 1.56 and the fluid response is similar to that found in the case of a uniformly heated wall. The first mechanism dominates if the spatial modulation of the flow is sufficiently strong while the second one dominates in the case of weak spatial modulation.   

Three-dimensional extraction and analysis of thermal plumes in turbulent Rayleigh-B\'enard convection

We report a new method for extracting the thermal plumes (TPs) in turbulent Rayleigh-B\'enard convection (RBC) which allows us to analyze the properties of the TPs and the background fluid. The investigation is based on direct numerical simulations of RBC in a cube ($8\times10^6 \le Ra \le 5\times10^9$) filled with fluid of Prandtl number $Pr = 4.38$. The basis of our extraction method is the idea that plumes convectively transport heat through the fluid, so that a heat flux threshold can be employed to extract the TPs. It is shown that this method yields reliable results over a wide range of $Ra$ and at any vertical wall distance $z$. Characteristic quantities of the flow are investigated on the boundaries of the TPs and the mean properties of the TPs and the background fluid are investigated as a function of the vertical coordinate. The $Ra$-scaling of a characteristic length scale of the TPs is examined and compared to taht of the thermal boundary layer thickness.   

Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Benard convection

The shapes of the velocity and temperature profiles near the horizontal conducting plates' center regions in turbulent Rayleigh-Benard convection are studied numerically and experimentally over the Rayleigh number range spanning from 10$^8$ to 3x10$^{11}$ and the Prandtl number range 0.7$\sim $5.4. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses. The study further shows that the Prandtl-Blasius boundary layer in turbulent thermal convection not only holds in a time-averaged sense, but is also valid in an instantaneous sense most of the time.   

Numerical Simulations of Rapidly Rotating Convection with Boundary Topography

The Earth's magnetic field is generated by vigorous convective motions in the molten iron outer core. Observations over the last 400 years show that while many of the morphological features of the geomagnetic field change over time, others appear to have remained fixed relative to the Earth's solid mantle. In addition, investigations of the Earth's rotation rate, or length of day (LOD), show that the mantle and core are strongly coupled. One possible mechanism to explain the geomagnetic field and LOD observations is the interaction of convective motions with topographic features at the core-mantle boundary (CMB). To examine the effects of CMB topography on the dynamics of the Earth's core, we present results from a suite of quasigeostrophic, thermal convection simulations with boundary topography. The primary effects of the topography are an increase in heat flow and zonal flow magnitude. We find that the topography leads to the formation of closed streamlines in the lee of the topography, bearing resemblance to the structures observed in the geomagnetic field. Furthermore, the effects of the topography become more pronounced as the Ekman number is reduced, suggesting CMB topography may be important in controlling the convective dynamics in the core.   

Plumes and Fountains in a Cross-Wind

Sour gas flares attempt to burn off hydrogen sulfide (H2S), a poisonous gas that can kill at concentrations higher than 100PPM. Because in some areas of the Rocky Mountain foothills the concentration of the gas before burning can be has high as 20\%, flaring must be extremely efficient to prevent disaster. Recent studies have shown that cross-winds can reduce the efficiency to 30\% meaning the concentration of unburned gas at the source can be as high as 60000PPM. Engineers rely on atmospheric dispersion to reduce the concentration to tolerable levels before the plume extends to the ground. To predict the dispersion of the gas close to the source, the US Environmental Protection Agency uses a numerical model, AERMOD, that heuristically adapts plume theory to account for the effects of winds and atmospheric inversions. They do not account for the fact that H2S is heavier than air at room temperature and so would tend to pool in valleys after cooling. We have performed laboratory experiments to examine the dynamics of positively and negatively buoyant plumes in uniform and stratified environments with a uniform background flow. The results are then compared with the predictions of the AERMOD model.   

Experimental study of natural convection inside a differentially heated enclosure with internal heat generation

This study is motivated by the use of natural convection correlations in the early stages of thermal design. While correlations are widely available for benchmark geometries, in practice compartments may have many heated surfaces and several heat generating objects. An experimental investigation is undertaken to examine the influence of cavity differential heating on the natural convection flow from an isothermal circular horizontal cylinder. The square compartment, of length (L), contains the centrally positioned cylinder of diameter 0.1L. The vertical walls are differentially heated, while the remainders are assumed adiabatic. Steady-state temperature measurements were taken in 15 different locations inside the cavity. The air flow fields and velocities were measured using a 2D PIV system. Results are presented in the form of Nusselt number correlations, velocity vector maps and boundary layer profiles for different values of the Rayleigh number and temperature difference ratio (T*). A circular airflow was observed inside the compartment. The plume rising from the cylinder interferes with this stream with varying results depending on Ra and T*. The flow structures become increasingly dominated by the presence of the cylinder with increasing Ra and T* despite the Grashof number for the cylinder being several orders of magnitude lower than that for the cavity.   

Buoyancy-Induced Columnar Vortices for Power Generation

Large-scale inherent instability of a thermally stratified, solar-heated air layer is exploited for power generation by deliberately enhancing the formation of intense columnar vortices such that each vortex drives a vertical-axis turbine. In nature, buoyancy-driven vortices (``dust devils'') occur spontaneously, with core diameters of 1-50 m at the surface, heights up to one kilometer, with induced air flow of considerable angular and linear momentum. Meter-scale laboratory experiments have demonstrated the nucleation and sustainment of strong buoyancy-driven vortices over a plane heated surface driven by a controllable power source. The present investigation focuses on the characterization of the columnar vortex and passive control of its core structure and strength for harvesting mechanical energy. It is shown that vortices having cores with nearly-uniform vorticity distributions can be ``anchored'' to small ground protrusions, and their circulation and angular momentum can be controlled by geometrical modifications of these surface protrusion and simple flow vanes.