Buoyancy-driven Flow Research Articles

On the dynamics of buoyant jets in a linearly stratified ambient

We report mean flow and turbulence characteristics of a buoyant jet evolving in a linearly stratified ambient with stratification strength N=0.4 s−1. The velocity and density fields are captured experimentally using simultaneous particle image velocimetry and planar laser-induced fluorescence technique. We report our findings by strategically choosing four axial locations such that it covers different flow regimes; namely, momentum-dominated region, buoyancy-dominated region, neutral buoyant layer, and plume cap region. The results at these axial locations are presented as a function of the radial co-ordinate to provide a whole field picture of the flow dynamics. From the mean axial velocity and density fields, it is seen that the velocity and the scalar (density) widths are of the same magnitude in the momentum-dominated region but show significant difference in the buoyancy-dominated region and beyond. It is also seen that the axial velocity for the buoyant jet is consistently higher than pure jet at different axial locations due to buoyancy-aided momentum. With the help of turbulent kinetic energy (TKE) budget analysis, it is seen that the shear production (P) and TKE dissipation (ϵ) for a buoyant jet are higher compared to the case of pure jet at different axial locations, cementing the role of buoyancy and stratification on the flow dynamics. Further, it is observed that the buoyancy flux (B) aids and destroys TKE intermittently in the radial direction, and it is at least O(102) smaller than P, ϵ, and the mean flow buoyancy flux (F). Finally, the relative strength of the turbulent transport of momentum to that of scalar in the radial direction is quantified using the turbulent Prandtl number, Prt. It is seen that Prt ≈1 upto the neutral buoyant layer and ≈ 0.6 in the plume cap region. The current set of results obtained from experiments are first of its kind and elucidates various aspects of the flow which hitherto remained unknown and will also prove to be useful in testing numerical simulations for buoyancy-driven flows.

Thermal management and optimization of the reactor geometry for adsorbed natural gas storage systems subjected to free convection and radiative environment

The present investigation explores the effects of the reactor geometry (i.e., the aspect ratio of cylindrical and annular reactors with and without fins, fin spacing, the aspect ratio of fins for finned reactors, and outer to inner diameter ratio for annular unfinned reactors) on the heat and mass transfer characteristics of the adsorbed natural gas storage system employing passive cooling techniques. The authors try to capture how the geometric modification changes the surrounding buoyancy-driven flow physics and improves the proposed novel reactor's storage performance. The study also considers surface radiation, which significantly improves the heat transfer rate, especially for the reactor with lower internal thermal resistance. An attempt is made to reduce the internal thermal resistance of the adsorbent bed by adding 10% graphite by mass and suitably modeling the bed's thermal conductivity and thermal capacity. The result shows that, in terms of adsorbed amount and heat transfer rate, the reactors with an aspect ratio (AR) of 7.8 outperform the other aspect ratios. The simultaneous effects of reactor aspect ratio and fins spacing on the heat transfer and adsorption rates are expounded, and the optimum fin spacing as a function of reactor aspect ratio and diameter ratio (i.e., fin diameter to reactor diameter) is obtained. The best annular reactor outperforms the cylindrical reactor with and without fin in terms of volumetric and gravimetric storage capacity. The annular finned reactor achieves a maximum 33% improvement in storage capacity compared to the adiabatic case and isothermal efficiency of 90%.

Buoyancy-driven bubbly flows: scaling of velocities in bubble columns operated in the heterogeneous regime

The hydrodynamics of bubble columns in the heterogeneous regime is revisited. Focusing on air–water systems at large aspect ratio, we show from dimensional analysis that buoyancy equilibrates inertia, and that velocities scale as $(gD\varepsilon )^{1/2}$ , where $D$ is the bubble column diameter, $\varepsilon$ the void fraction and $g$ the gravitational acceleration. From new experiments in a $0.4$ m diameter column with ${{O}}(10^3)$ particle Reynolds number bubbles and from a detailed analysis of published data, we confirm the self-organization prevailing in the heterogeneous regime, and that the liquid flow rate is only set by the column diameter $D$ . Besides, direct liquid and gas velocity measurements demonstrate that the relative velocity increases above the terminal velocity $U_T$ in the heterogeneous regime, and that it tends to ${\sim }2.4 U_T$ at very large gas superficial velocities $V_{sg}$ . The proposed velocity scaling is shown to hold for liquid and gas mean velocities and for their standard deviations. Furthermore, it is found to be valid over a wide range of conditions, corresponding to Froude numbers $Fr=V_{sg}/(gD)^{1/2}$ from 0.02 to 0.5. Then, the relevance of this scaling for coalescing media is discussed. Moreover, following the successful prediction of the void fraction with a Zuber & Findlay approach at the beginning of the heterogeneous regime, we show how the void fraction is correlated with $Fr$ . Further investigations are finally suggested to connect the increase in relative velocity with meso-scale structures known to exist in the heterogeneous regime.

Neighborhood scale traffic pollutant dispersion subject to different wind-buoyancy ratios: A LES case study in Singapore

This study explores the buoyancy effect on traffic pollutant dispersion at neighborhood scale, in which a wide range of wind-buoyancy ratios is examined. Pollutant dispersion is solved using a Large Eddy Simulation (LES) turbulence model, where realistic urban morphology and historical traffic pollutant emission data are adopted. For no incoming wind condition, thermal plumes develop and entrain horizontal flow near ground level. This neighborhood scale buoyancy-driven flow leads to air pollutant dispersion, which is as strong as wind-driven dispersion in the target area. As a result, urban air pollutant accumulation is limited due to buoyancy, regardless of ambient wind conditions. A light incoming wind can flush upward thermal plumes downstream when the Richardson number (Ri) reaches 25.5. The interplay of the approaching wind and upward plumes from urban surfaces leads to an oscillatory flow, which intensifies local turbulence and enhances the pollutant removal rate. At the pedestrian level, the neighborhood scale average NO2 concentration due to the traffic emission ranges from 4.1μg/m3 to 4.8μg/m3. The minimum value is found for a weak incoming wind condition, (coupling with buoyancy, Ri = 25.5) and the maximum value is observed for the no incoming wind condition (Ri = ∞). The modelling result analysis clarifies how buoyancy-related dispersion, emission location, surrounding urban density, and incoming wind affect local pollutant concentrations. The research outputs highlight the importance of these coupling effects in the air pollutant dispersion evaluation in real urban areas.

Buoyancy-driven mixed convection flow of FENE-P fluids over a flat plate

The primary purpose of this study is to investigate the buoyancy mixed convection flow of non-Newtonian fluid over a flat plate. The addition of a small amount of polymers into a Newtonian solvent raises the viscosity and generates elastic properties in the resulting solution. To study the behavior of these viscoelastic fluids, finite extensible nonlinear elastic constitutive equations along with Peterlin’s closure (FENE-P model) are used. Along with mass, momentum and energy equations, viscoelastic constitutive equations are also used to examine the rheology of the resulting polymer solution. Similarity transformations are introduced to convert the governing equations into nondimensional forms. The nondimensional equations are solved using the fourth-order boundary value solver in MATLAB. The distribution of the velocity and temperature fields is displayed graphically under the impact of various involved parameters like Eckert number (Ec), Richardson number (Ri), Prandtl number (Pr). The addition of polymers increases the friction among the different fluid layers, leading to viscous dissipation in the fluid. The presented model’s validation is done with the Newtonian fluid to verify the results. The Nusselt number is also computed and analyzed to study the heat transfer rate. The effects of viscoelastic parameters like Weissenberg number (W[Formula: see text]), polymer viscosity ratio ([Formula: see text]) and polymer extensibility parameter ([Formula: see text]) on heat transfer rate are also shown graphically. Buoyancy parameter (Richardson number, [Formula: see text]) represents the dominance of natural convection relative to that of forced convection. The temperature of the resulting fluid falls with the increase in the value of Ri. The Nusselt number tends to decrease with increasing Richardson number when viscous dissipation effects are active.

Heat transport analysis in buoyancy-driven flow of Maxwell fluid induced by a vertically stretching sheet inspired by Cattaneo Christov theory

We used non-Fourier's approach to model the heat transfer equations in magneto-hydrodynamic Maxwell nanofluid flow due to vertical stretching sheet under the influence of buoyancy force. The impact of uniform transverse magnetic field is also considered. This problem is analyzed with two heating processes: constant wall temperature (CWT) and prescribed surface temperature (PST). The heat and mass transport features are explored by implementing the modified Fourier's and Fick's laws.The governing equations are transformed into ordinary differential equations (ODEs) through appropriate similarity transformations. The resulting equations are solved numerically using the bvp4c program in MATLAB. The impact of physical parameter on the velocity, thermal, and solutal distributions is discussed in detail and presented graphically for aiding the flow. In this study, the velocity boosts unsteadiness parameter and thermal buoyancy parameter. Both velocity and temperature behave in opposite ways when affected by a magnetic field. Moreover, the building strength of the thermal relaxation time parameter does not escalate the thermal transport.

Second law analysis of a 3D magnetic buoyancy-driven flow of hybrid nanofluid inside a wavy cubical cavity partially filled with porous layer and non-Newtonian layer

The current paper presents numerical results of the 3D buoyancy-driven flow of a hybrid nanofluid in a cubical cavity in the presence of a magnetic field. The computational domain comprises two layers: a non-Newtonian fluid layer and a hybrid nanofluid layer. The temperature disparity within the domain results from heating the wavy bottom wall and cooling both sidewalls while the top wall is insulated. A magnetic field is applied on the positive z-axis. To encounter the non-Newtonian layer influence, the power-law model is considered. The solution of the governing equations is obtained by the Galerkin FEM method. The effects of geometrical parameters of the problem are discussed and illustrated. The results indicate that by simultaneously using non-Newtonian Fe3O4/MWCNT hybrid nanofluid and porous media, the heat exchange in the 3-D cavity is positively affected by the growth in Rayleigh number, Darcy number as well as the height of the porous layer. Furthermore, it is negatively affected by the rise of the magnetic field, corrugation number, and a minor degree when the flow index n was increased due to the pseudo-plastic fluid's high viscosity and shear force.

Modeling and analytical analysis of dual diffusive Williamson nanoliquid considering generalized heat-mass concepts

The primary objective of this investigation is to explore the Cattaneo–Christov flux models impact on Williamson nanofluid over a stretching surface. Buongiorno’s model featuring diffusions (Brownian and thermophoretic) is opted for nonlinear analysis. Buoyancy-driven nonlinear convection flow in stagnation region is modeled. Surface is permeable and transpiration effects are considered. Energy expression captures heat source/sink aspects. The nondimensional differential systems are tackled analytically via homotopy analysis method (HAM). The profiles of dimensionless temperature, concentration and skin friction are examined graphically for the attributes of multiple physical parameters. It is revealed that the heat transfer elevates with the increment of thermophoresis, heat source and Brownian motion parameters while it dwindles with the improvement of thermal relaxation parameter. The mass transfer strengthens with the enlargement of thermophoresis parameter while diminishing with the enhancement of solutal relaxation and Brownian motion parameters. The skin friction is elevated for higher values of material variable against nonlinear mixed convection parameter.

Convective-radiative magnetized dissipative nanofluid (CNTs-water) transport in porous media, using Darcy–Brinkman–Forchheimer model

The main objective of this investigation is to deliberate the novel analysis of buoyancy-driven nanofluid flow across a vertical stretching surface embedded in a porous medium with the consideration of an inclined magnetic field and heating effects caused by viscosity, thermal radiations, and heat source factor. A material made of glass ball is applied as the porous medium. Water is regarded as a base fluid, while carbon nanotubes are termed as the nanoparticles. The governing equations are formulated by employing fundamental laws. With the application of appropriate non-similar transformations, the emerging flow system is translated into dimensionless differential form. The obtained coupled, non-similar system of nonlinear partial differential equations (PDEs) is tackled by employing local non-similarity technique up to second level of iterations in conjunction with the Lobatto III technique in MATLAB. According to the findings, increasing the Hartmann number diminishes fluid velocity while augmentation in radiation parameter and nanoparticle volume fraction raises the temperature profile. Moreover, nanofluids contain MWCNTs as such nanoparticles exhibit larger estimations of Nusselt number than SWCNTs-water nanofluid. Authors introduced appropriate transformations for considered problem and argued the local non-similarity approach for simulating the dimensionless structure. To the best of authors' observations, no such study is yet published in literature.

Heat transfer analysis of a pulse-heated microwire in CO2 at supercritical pressures

This paper analyzes the characteristics of convective heat transfer of a pulse-heated platinum microwire cooling in CO2 under supercritical pressures based on experimental data. The microwire undergoes a rapid temperature rise of around 664 K within 0.35 ms. An inverse problem is formulated and numerically solved to extract heat transfer data from experimental measurements. In addition, a predictive model for the convective heat transfer coefficient is developed to fully close the equation set. Results are interpreted based on the bulk pressure from 7.38 to 9 MPa and bulk temperature from 295 to 325 K. The convective heat flux of CO2 generally decreases with time, and in the medium-term, the reduction is slightly decelerated owing to buoyancy-driven flows. This demonstrates that high-pressure and low-temperature bulk states generally exert larger convective heat flux to cool the microwire. During the early 10 ms, the time-averaged convective heat flux is of the order of 1 MW/m2, resulting in rapid cooling. This value shows a weak critical enhancement upon crossing the Widom line. During the remaining time, the time-averaged convective heat flux drops to the order of 0.1 MW/m2. Such a drop in heat flux is more obvious in low-bulk-density cases, leading to a relatively long time for sufficient W cooling.

Modeling the dispersion and mixing of light gases in enclosed spaces using the Method of Moments

Leakage of light flammable gases in buildings or enclosed spaces may cause significant environmental and safety hazards. This study proposes a transient reduced-order model for the dispersion and mixing of light gases in closed rooms using the Method of Moments (MoM). The MoM model solves the moments of the species pdf transport equation in the vertical direction of the room. The evaluated moments are used to generate the horizontal distribution of the species at any time and height in the room. This provides a better representation of the species distribution in the room compared to a well-known analytical model called the ‘filling-box model’ and computationally faster model compared to CFD alternatives. The MoM model is demonstrated for a buoyant methane release in a closed room. The results are benchmarked by using Fire Dynamics Simulator (FDS), which is a computational fluid dynamics (CFD) model used for buoyancy-driven flows, including fire. The MoM model represents good performance compared to FDS in significantly faster time (4 min on a single core vs. 4 days and 7 h on 33 cores in parallel). The model can be used to investigate toxicity, fire, or explosion hazard scenarios, which helps developing prevention systems and mitigation strategies.

An analytical study of the unsteady nonlinear convection flow of nanofluids in an infinitely rectangular channel

An analytical study of the unsteady, nonlinear buoyancy-driven convection flow of nanofluids in a horizontal infinitely long channel under the influence of an external magnetic field is carried out. Analytical solutions for velocity components, temperature, and pressure gradients are determined by considering a particular form of the stream function and the temperature field and an appropriate separation of variables. The analytical solutions are expressed by two functions that satisfy diffusion-type partial differential equations, solved by employing the Laplace and Fourier transforms. The obtained solutions are new in the literature. These solutions are suitable for studying various flows of nanofluids in channels or verifying some numerical schemes applied to solve similar problems. The movement of a water-based nanofluid with aluminum oxide nanoparticles and heat transfer is investigated using the obtained analytical solutions. The influence of the volume fraction of nanoparticles on temperature, velocity, and pressure is analyzed with numerical simulations and graphical illustrations. It is found that the heat transfer process can be improved by changing the volume fraction of nanoparticles. Also, the pressure gradients can be modified by the presence of nanoparticles.

Instabilities of the natural convection around a cone in thermally stratified medium.

In this paper, we provide a mathematical description of the onset of instability for buoyancy-driven flow around a cone. The self-similar solutions of the basic flow are derived, where the ambient fluid and the cone have independent temperature gradients. The linear instability properties are investigated by utilizing the Chebyshev collocation method. It is demonstrated that the neutral curves have a two-lobed structure and that changing the Grashof number has only quantitative influence on stability. The critical streamwise location increases when the half-apex angle is increased, and the unstable range of the wave number diminishes. According to the examination of eigenfunction profiles and the progression of the two spatial branches in the (α_{i},α_{r}) planes, the primary instabilities on the surface of cone are identified as type-I mode and type-II mode. The energy analysis is investigated for a typical situation to gain a physical insight, where it is demonstrated that besides the viscous dissipation, the streamline curvature and buoyancy-driven effects are dominant for the type-I mode while inviscid effect plays an essential role in type II. These encouraging results are expected to be conducive to understanding buoyancy-driven systems.

Vortex flow affected by disk rotation in an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out to explore the effects of disk rotation on the vortex flows induced in a round jet of air impinging onto a heated horizontal disk confined in a vertical cylindrical chamber. The experiment is conducted for the jet-disk separation distance at 20.0 mm and 40.0 mm. The jet flow rate is varied from 0 to 5.4 slpm (standard liter per minute) for the jet Reynolds number Rej ranging from 0 to 730. The disk rotation speed varies from 0 to 35.0 rpm for the rotational Reynolds number ranging from 0 to 2725. The temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0°C for the Rayleigh number ranging from 0 to 150,325. The data from the present study for the ratio of jet disk-disk separation distance to the jet diameter (denoted as HDj) are compared. The results indicate that at the disk rotation rate Ω ≥ 10.0 rpm the secondary inertia-driven roll is completely wiped out for HDj = 4. For HDj = 2 at a higher disk rotation rate of Ω ≥ 20.0 rpm, the buoyancy-driven roll can be substantially squeezed by the disk rotation to become smaller and weaker. Meanwhile, the primary inertia-driven roll is stretched out to become slender and weaker. But for HDj = 4, due to a stronger buoyancy-driven vortex flow at a higher jet-disk separation distance, a higher Ω is needed to stabilize the buoyancy-driven roll.

Numerical modeling of mixed convection near a vertical heat source in saturated granular soils

Accurate design of energy geostructures such as energy piles requires an exact prediction of soil thermal responses close to the embedded heat sources in the ground. In saturated soil, both heat conduction and heat convection facilitate heat transfer in the soil medium. Conventional analyses of heat transfer in saturated porous medium classified heat convection into two categories: (i) natural convection that could happen in the hydrostatic condition and (ii) forced convection that occurs due to the groundwater flow in the soil medium. This paper demonstrates that, in the presence of groundwater flow, the natural convection in the form of buoyancy-driven flow plays a prominent role in temperature distribution through saturated soil as well as the forced convection. A finite element analysis is performed to study the effects of groundwater velocity and soil permeability on the behavior of a fluid-saturated porous medium (soil). The results confirm that neglecting the natural convection can lead to inaccurate results. Furthermore, a novel expression is defined to estimate the importance of natural convection in heat transfer mechanisms in the soil medium.

Convective and absolute instabilities in inclined buoyancy layers

The linear instability of the buoyancy-driven flow adjacent to an inclined heated wall immersed in a thermally stratified medium is studied theoretically and numerically. For the temporally unstable system, spatiotemporal stability analysis is carried out to delineate the parameter space (Grashof number, Prandtl number, and tile angle) for convective/absolute instability. We provide an example of an absolute instability of the buoyancy layer on an inclined buoyancy layer. It is shown that the tile angle and Prandtl number have a dramatic influence on the spatial-temporal properties of the flow. For fixed Pr = 6.7, increasing tile angle decreases the domain of absolute instability, and when tile angle is greater than 20°, the absolute instability disappears. The flow will change from convectively unstable to absolutely unstable with the increase of Pr. Results from the direct numerical simulation are in agreement with the predictions of the linear temporal and spatial-temporal instabilities. These encouraging results should be helpful for understanding such a buoyancy-driven flow system.

Finite-amplitude instability of the buoyancy boundary layer in a thermally stratified medium

The finite-amplitude instability of the buoyancy-driven boundary layer is considered on a vertical plate immersed in a thermally stratified ambient medium, where the wall and surrounding fluid have different temperature gradients. Although the linear stability in this configuration has been investigated, the finite-amplitude solution arising from the critical instability has been studied only for specific parameter values. We extend this by using the amplitude expansion method. The primary bifurcations to the two-dimensional least unstable mode for different temperature gradient ratios ( $0 \leqslant \lambda \leqslant 10$ ) and Prandtl numbers ( $10^{-1} \leqslant Pr \leqslant 10^{4}$ ) are investigated. Only supercritical bifurcations are found to occur when $0 \leqslant \lambda < 2$ and $Pr \leqslant 2800$ , while subcritical bifurcations are also found for larger values of temperature gradient ratio and Prandtl number. Analysis of the contribution of the nonlinear terms in the Landau coefficient reveals that the interaction of the modification of the mean flow and second harmonic for velocity with the fundamental mode for temperature plays an important role in subcritical bifurcation. Based on the Landau equation, the threshold amplitude of the nonlinear equilibrium solution is discussed as well. These encouraging results should be helpful for understanding such a buoyancy-driven flow system.

The Combined Impact of Thermal Radiation and Thermophoresis on Buoyancy-Driven Flow Near an Inclined Porous Plate

Abstract This report presents a similarity solution for the buoyancy-driven flow of viscous incompressible fluid past an inclined porous plate influenced by nonlinear thermal radiation and thermophoresis. The boundary layer equations are reduced to some set of ODEs through similarity variables. Furthermore, the ODEs are converted to IVP through the shooting technique. The numerical solution is obtained through the Runge–Kutta algorithm in Maple software. The impact of the emergence parameters present in the mathematical model is explained through graphs and tables. Results obtained showed that with combined effects of suction/injection and nonlinear thermal radiation, the heat transfer rate is directly proportional to the angle of inclination but inversely proportional to plate shear stress and mass transfer rate. Furthermore, it was observed that the heat transfer rate declines with higher buoyancy force but enhances the plate shear stress. Also, the mass transfer rate could be enhanced with a higher thermophoresis effect. Suction propagates the velocity and temperature profiles whereas it decreases the rate of particle concentration, while the contrast is true for injection. In addition, nonlinear thermal radiation complements the fluid temperature, particle concentration, and fluid transport.

Discrete Phase Analysis of Self Heating Particles Over an Immersion Liquid Cooled High Power Blue Light-Emitting Diode With Suspended Phosphor Particles

Abstract In recent years, the interaction of unrestricted particles with dispersed multiphase flows has been linked to a number of important engineering applications. Among these applications, the novel idea of immersion-cooled phosphor particles, which has the potential of significantly increasing the thermal limits of phosphor converted white light-emitting diode (LEDs) (Pc-WLEDs), has yet to be thoroughly investigated. With this objective, this research utilizes the discrete phase modeling (DPM) technique for the characterization of phosphor location and movements within a buoyancy-driven flow, which is the determining factor in the optical behavior of the newly proposed Pc-WLED configuration. Two-phase flow analysis is conducted to characterize particle movement. Heat transfer, flow, and energy paths of self-heating phosphor particles are extracted, and the influence of particle sizes is analyzed in detail. The results show that with immersion liquid cooling, the highest phosphor particle temperature is recorded to be under 420 K, while larger size particles introduce higher heat transfer rates to the Pc-WLED package for the same number of particles. Moreover, depending on the particle size and position, individual phosphor particles can follow a different trajectory that can affect the probability of obtaining white light emission.

Impact of Thermal Source-Sink Arrangements on Buoyant Convection in a Nanofluid-Filled Annular Enclosure

AbstractThis investigation is devoted to analyze the buoyancy-driven flow behavior and associated thermal dissipation rate in a nanofluid-filled annular region with five different single source-sink and three different dual source-sink arrangements along the vertical surfaces. The remaining region on the vertical boundaries and horizontal surfaces are kept adiabatic. Numerical simulations have been performed by employing the finite difference method. To analyze the impacts of different nanofluids, nanoparticle volume fraction, Rayleigh number, size, and arrangement of sources and sinks, the results are graphically represented through streamline and isotherm contours, thermal profiles, average Nusselt number, and cup-mixing temperature. The results showed that identifying an optimum location and length of source-sink with a proper selection of other control parameters can lead to enhanced thermal transport and thermal mixing in the enclosure. In particular, middle-middle thermally active location and placing source-sink separately on the vertical walls lead to the production of maximum heat transport compared to other single and dual source-sink arrangements, respectively. Also, among the two nanofluids considered in the current investigation, larger enhancement in thermal transport has been achieved for Cu-water nanofluid. The calculated enhancement ratio of the heat dissipation rate enhances with an increment in nanoparticle concentration.