Buoyancy-driven Flow Research Articles

Contactless Ultrasonic Treatment in Direct Chill Casting

Uniformity of composition and grain refinement are desirable traits in the direct chill (DC) casting of non-ferrous alloy ingots. Ultrasonic treatment is a proven method for achieving grain refinement, with uniformity of composition achieved by additional melt stirring. The immersed sonotrode technique has been employed for this purpose to treat alloys both within the launder prior to DC casting and directly in the sump. In both cases, mixing is weak, relying on buoyancy-driven flow or in the latter case on acoustic streaming. In this work, we consider an alternative electromagnetic technique used directly in the caster, inducing ultrasonic vibrations coupled to strong melt stirring. This ‘contactless sonotrode’ technique relies on a kilohertz-frequency induction coil lowered towards the melt, with the frequency tuned to reach acoustic resonance within the melt pool. The technique developed with a combination of numerical models and physical experiments has been successfully used in batch to refine the microstructure and to degas aluminum in a crucible. In this work, we extend the numerical model, coupling electromagnetics, fluid flow, gas cavitation, heat transfer, and solidification to examine the feasibility of use in the DC process. Simulations show that a consistent resonant mode is obtainable within a vigorously mixed melt pool, with high-pressure regions at the Blake threshold required for cavitation localized to the liquidus temperature. It is assumed that extreme conditions in the mushy zone due to cavitation would promote dendrite fragmentation and coupled with strong stirring, would lead to fine equiaxed grains.

Numerical investigation of heat transfer from heat sources placed in a horizontal rectangular channel

In this study, three dimensional mixed convection heat transfer from discrete heat sources placed in a horizontal rectangular channel has been investigated numerically. 8x4 flush-mounted discrete heat sources were mounted on the lower and upper surfaces of the channel. Air is used as working fluid (Pr0.7). The heaters at the bottom and at the top wall were kept at a constant heat flux. Side walls, upper and lower walls are insulated and considered adiabatic. Nusselt number distributions and the effect of the Grashof number (5.8x106≤ Gr* ≤ 2.3x107) and Reynolds number (150 ≤ Re ≤ 971) on the buoyancy-driven secondary flow have been investigated. Distributions of velocity vectors and temperature contours have been determined by the numerical method, and the results have been presented in detail. Governing equations were solved by the control volume method using suitable boundary conditions. The numerical parametric study was made for aspect ratio of AR=8, at various Reynolds and Grashof numbers.

Comparative Assessment of Liquid Sodium and Gallium as Emergency Coolants in Nuclear Energy Applications

Abstract The influence of the thermophysical variable properties on the buoyancy-driven flows of liquid sodium and gallium established in a cylindrical cavity is numerically investigated, for the entire range of Rayleigh number corresponding to practical applications. Axisymmetric turbulent simulations (initially steady) are obtained, considering appropriate boundary and reference conditions for simulating the emergency cooling of a nuclear reactor. The results obtained for different heating intensities are analyzed and compared. In the case of sodium, the expected decay in the heat transfer coefficients is less relevant than that previously obtained for airflows. In turn, strong differences in the gallium thermal behavior are encountered. In fact, a trend opposite to that of sodium is detected for wide ranges of Rayleigh number and heating parameter. Additional transient simulations are carried out to complete a comparative assessment of the performance of both liquid sodium and gallium as cooling agents.

Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top

The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (ω) are varied from 103 to 106, 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, ω and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by ω and Pr.

Introducing compressibility with SIMPLE algorithm

A comparative assessment between SIMPLE and its variant SIMPLE-C is conducted based on two-dimensional (2-D) incompressible flows, using a cell-centered finite-volume Δ-formulation on a collocated grid. The SIMPLE-C (SIMPLE Compressibility) scheme additionally combines the concept of artificial compressibility (AC) with the pressure Poisson equation, provoking the diagonal dominance of influence coefficients. An improved nonlinear momentum interpolation scheme is employed at the cell face in discretizing the continuity equation to suppress pressure oscillations. The pseudo-time step Δti remains the same in both schemes to conserve an analogous scaling with momentum and scalar nodal influence coefficients. Numerical experiments in reference to buoyancy-driven cavity flow dictate that both contrivances execute a residual smoothing enhancement, facilitating an avoidance of the velocity/pressure under-relaxation (UR). However, compared with the SIMPLE approach, included benefits of the SIMPLE-C method are the use of larger Courant numbers, enhanced robustness and convergence. Excellent consistency is obtained between results available in the literature and numerical solutions obtained by both SIMPLE and SIMPLE-C solvers. The segregated SIMPLE algorithm is finally reformulated in conjunction with a new slope/flux limiter function to predict fluid flow at all speeds. Numerical results show that the compressible variant of SIMPLE replicates correct shock speed, well-resolved shock front, contact discontinuity and rarefaction waves when compared with analytical solutions. Compressible laminar flows are computed to further support the accuracy and robustness of proposed algorithm.

Isolated buoyant convection in a two-layered porous medium with an inclined permeability jump

Abstract

Improved scaling analysis of the transient buoyancy-driven flow induced by a linear temperature gradient

The transient convective boundary layer flow induced by a linear temperature gradient and its subsequent intrusion flow are investigated in an open cavity with scaling analysis in this study. Scale laws quantifying the buoyancy-driven convective flow are obtained. Compared to previous similar studies, the present scaling analysis is predominantly improved by adopting a two-dimensional decomposition of the specified thermal gradient rather than following the traditional one-dimensional approach, in which way thermal restrains are greatly eliminated. Consequently, the obtained scales are much more generalised and convenient to use. They can also be extended to some problems where the previous scale laws are not handily applicable. It is demonstrated that both unsteady and steady convective boundary layers are two dimensional, which is fundamentally different from the well-known one dimensional growth in homogenous heating problems. An unsteady intrusion flow is considered in this study. Two flow Scenarios are identified for the intrusion and several possible flow regimes are found in each Scenario. A total of 120 transient cases are calculated by numerical simulations and the numerical data are compared against the scaling results. A reasonable agreement is obtained supporting the employed two-dimensional decomposition method and validating the derived scales.

Carbon Dioxide Storage in Deltaic Saline Aquifers: Invasion Percolation and Compositional Simulation

Summary Storage of large amounts of carbon dioxide (CO2) within deep underground aquifers has great potential for long-term mitigation of climate change. The U.S. Gulf Coast is an attractive target for CO2 storage because of the favorable formation properties for injection and containment of CO2. Deltaic formations are one of the primary targeted depositional environments in the Gulf Coast. In this paper, we investigate CO2 storage in deltaic saline aquifers through a combination of geological modeling and flow simulation. The approach presented in this paper based on a combination of invasion percolation and compositional reservoir simulation focuses on buoyancy-dominant flow of CO2 in the long term and its pressure-driven flow in the short term. The results provide insights into how to screen and identify prospective locations for CO2 storage and determine the underlying geological features controlling CO2 migration for a basin-scale study. The geological model in our study is developed based on a laboratory-scale three-dimensional (3D) flume experiment replicating the formation of a delta structure and populated with geologic properties according to Miocene Gulf of Mexico natural analogues. We used invasion percolation simulations to understand the buoyancy-driven flow and the relationship between architecture, stratigraphy, and fluid migration pathways. The results were used to develop an upscaled model for compositional simulation with the key features of the original geological model and to determine injection schemes that maximize the injection capacity and minimize the amount of mobile CO2 in the formation. To achieve this, we used compositional reservoir simulations to study the pressure-driven flow and phase behavior. The results of invasion percolation simulations were used to identify the key stratigraphic units affecting CO2 migration. The realistic geometries and high resolution of the model facilitate the transfer of results from synthetic to subsurface data. The results allow for the analysis of deltaic depositional environments, important stratigraphic surfaces, and their impact on CO2 storage. The reservoir simulation model and phase behavior were validated against available field and laboratory data. The results of reservoir simulations were used to investigate the effects of main mechanisms, such as gas trapping and solubilization, on storage capacity. We compared our simulation results based on invasion percolation (buoyancy driven) and reservoir simulation (pressure driven). The comparison is helpful to understand the strengths and weaknesses of each approach and determine best practices to evaluate CO2 migration within similar formations. The unique and extremely well-characterized deltaic model allows for unprecedented representation of the depositional aquifer architecture. This research combines geologic modeling, flow simulation, and application for CO2 storage. The integrated conclusions will constrain predictions of actual subsurface flow performance and CO2 storage capacity in deltaic systems while identifying potential risks and primary stratigraphic migration pathways. This research provides insights on prediction of CO2 storage performance and characterization of prospective saline aquifers.

Gravity currents over fixed beds of monodisperse spheres

Abstract

How does three-dimensional canopy geometry affect the front propagation of a gravity current?

Large-eddy simulations are performed to investigate how three-dimensional canopy geometry affects the front propagation of an incoming gravity current under a given initial forcing. A regular array of rigid square cylinders are used to represent the distributed canopy elements. It is shown that the conventional geometrical parameter of submerged canopies in constant-density flows (ah, where a is the frontal area per canopy volume and h is the canopy height) is misleading when applied to buoyancy-driven flows due to the additional complexity arising from the internal density gradients. Instead, the present study suggests a new geometrical framework consisting of a canopy density (ϕ) and a canopy-to-current height ratio (h̃), which can jointly provide an unambiguous description of the state of the current–canopy interaction. Two propagation regimes of the gravity current are identified, either along the channel bed (through-flow) or above the canopy’s top boundary (over-flow). Our analysis reveals that ϕ and h̃ counteract each other’s effect on the transition of flow regimes. Large ϕ implies a strong suppression of horizontal advection within the canopy and thus promotes the through-to-over flow transition; in contrast, large h̃ tends to promote the over-to-through flow transition due to the lack of sufficient potential energy to overcome the height jump. The end product is a complex variation pattern of a propagation regime and front velocity in the two-dimensional ϕ–h̃ parameter space.

Numerical simulations of buoyancy-driven flows using adaptive mesh refinement: structure and dynamics of a large-scale helium plume

The physical characteristics and evolution of a large-scale helium plume are examined through a series of numerical simulations with increasing physical resolution using adaptive mesh refinement (AMR). The five simulations each model a 1-m-diameter circular helium plume exiting into a $$(4~\hbox {m})^3$$ domain and differ solely with respect to the smallest scales resolved using the AMR, spanning resolutions from 15.6 mm down to 0.976 mm. As the physical resolution becomes finer, the helium–air shear layer and subsequent Kelvin–Helmholtz instability are better resolved, leading to a shift in the observed plume structure and dynamics. In particular, a critical resolution is found between 3.91 and 1.95 mm, below which the mean statistics and frequency content of the plume are altered by the development of a Rayleigh–Taylor (RT) instability near the centerline in close proximity to the plume base. Comparisons are made with prior experimental and computational results, revealing that the presence of the RT instability leads to reduced centerline axial velocities and higher puffing frequencies than when the instability is absent. An analysis of velocity and scalar gradient quantities, and the dynamics of the vorticity in particular, show that gravitational torque associated with the RT instability is responsible for substantial vorticity production in the flow. The grid-converged simulations performed here indicate that very high spatial resolutions are required to accurately capture the near-field structure and dynamics of large-scale plumes, particularly with respect to the development of fundamental flow instabilities.

Microorganisms time-mixed convection nanofluid flow by the stagnation domain of an impulsively rotating sphere due to Newtonian heating

The present article delineates a numerical analysis of buoyancy-driven nanofluid flow of gyrotactic time-mixed bioconvection heat transfer in stagnation domain of an impulsively revolving sphere due to convective boundary condition. Zero mass flux boundary condition has been merged to gain physically realistic computations. Nanofluid has been expressed in terms of the impacts of Brownian movement and thermophoresis. The given system of partial differential equations depicting the flow are mutated into a dimensionless formulas. The solution methodology involved for the constituted equations is followed by implementing an implicit finite difference approach. The acquired computations are given in terms of surface shear stress, rate of heat transfer, the density rate number of the motile microorganisms, velocity, temperature, concentration and density of motile microorganisms fluctuations. Due to gained outcomes the rotation λ and time ξ parameters have a strong impact on the flow, heat and density of motile microorganisms transfer rates, λ and time lead to strengthen all of F″(ξ,0),-θ′(ξ,0) and -N′(ξ,0). Parameters, like rotation and mixed convection exert a vigor aspect on nanofluid velocity, temperature and microorganisms density and their fluctuations rate. The surface shear stress F″(ξ,0) is mightily influenced by magnetic field parameter M. Besides, comparison amid the earlier published data and the present numerical computations are evaluated for the limiting cases, which are noticed to be in an excellent agreement.

On the morphology and amplitude of 2D and 3D thermal anomalies induced by buoyancy-driven flow within and around fault zones

Abstract. In the first kilometers of the subsurface, temperature anomalies due to heat conduction processes rarely exceed 20–30 ∘C. When fault zones are sufficiently permeable, fluid flow may lead to much larger thermal anomalies, as evidenced by the emergence of thermal springs or by fault-related geothermal reservoirs. Hydrothermal convection triggered by buoyancy effects creates thermal anomalies whose morphology and amplitude are not well known, especially when depth- and time-dependent permeability is considered. Exploitation of shallow thermal anomalies for heat and power production partly depends on the volume and temperature of the hydrothermal reservoir. This study presents a non-exhaustive numerical investigation of fluid flow models within and around simplified fault zones, wherein realistic fluid and rock properties are accounted for, as are appropriate boundary conditions. 2D simplified models point out relevant physical mechanisms for geological problems, such as “thermal inheritance” or pulsating plumes. When permeability is increased, the classic “finger-like” upwellings evolve towards a “bulb-like” geometry, resulting in a large volume of hot fluid at shallow depth. In simplified 3D models wherein the fault zone dip angle and fault zone thickness are varied, the anomalously hot reservoir exhibits a kilometer-sized “hot air balloon” morphology or, when permeability is depth-dependent, a “funnel-shaped” geometry. For thick faults, the number of thermal anomalies increases but not the amplitude. The largest amplitude (up to 80–90 ∘C) is obtained for vertical fault zones. At the top of a vertical, 100 m wide fault zone, temperature anomalies greater than 30 ∘C may extend laterally over more than 1 km from the fault boundary. These preliminary results should motivate further geothermal investigations of more elaborated models wherein topography and fault intersections would be accounted for.

A simple direct heating thermal immersed boundary-lattice Boltzmann method for its application in incompressible flow

A simple direct heating thermal immersed boundary-lattice Boltzmann method for buoyancy-driven incompressible flow with complex geometry boundaries is developed to simulate natural convection with curved boundary. In the newly developed method, both Dirichlet and Neumann boundary conditions in macroscopic equation are deduced into a novel mesoscopic discrete heat source. The mesoscopic discrete heat source consists of simplified explicit discrete heat source scheme which reduces the computational complexities and is introduced into lattice Boltzmann equation for temperature field, which extends the idea of the previous direct forcing IB-LBM. Both isothermal boundary condition (i.e. Dirichlet boundary condition) and constant heat flux boundary condition (i.e. Neumann boundary condition) are considered in our simulations. The efficiency and accuracy of the present method are demonstrated by simulating both two dimensional and three dimensional thermal flow with curved boundaries. Numerical results indicate that the efficiency and accuracy of the present method are well consistent with experimental and the other numerical results. The present method has also been successfully applied to three dimensional simulations of natural convection in a thin annulus with adiabatic wall at both vertical sides.

The transport and thermodynamic characteristics of thermally oscillating phenomena in a buoyancy-driven supercritical fuel flow

To ameliorate the thermal management of a regenerative cooling system in an advanced engine, the turbulence characteristics and entropy generation in a buoyancy-driven supercritical hydrocarbon fuel flow are numerically explored in detail. Several common buoyancy criteria (Gr/Re2, Gr/Re2.7 and Grq/Grth) are established and a three-dimensional numerical model is solved with an advanced LES model. The turbulence characteristics demonstrate that the complex and anisotropic transport properties dramatically redistribute the flow structure and thermal field and the buoyancy-induced production, Pb=−gρuj'‾, is strongly related to the heat transfer regime. The thermal characteristics, ρ(uihs‾−ui‾hs‾), indicate that the laminar flow weakens the wall-normal turbulent heat flux, and the buoyancy-driven flow is responsible for the change of stream-wise turbulent heat flux. Based on the second law of thermodynamics, the two typical irreversible entropy generations are discussed, and interestingly, the existing oscillations enlarge the diffusion of local heat entropy and promote the wider heat transfer. The results provide a methodological guidance for thermal management of engines cooling systems.

Buoyancy-driven ventilation of an enclosure containing a convective area heat source

Buoyancy-driven ventilation of an enclosure containing a convective area heat source with low surface emissivity is studied in this paper. Based on the dynamics of turbulent plumes generated from an area heat source, the mathematical models for dimensionless thermal stratification height are deduced and integrated into a unified formula in this study. And a mathematical model governing the transition zone between these two zones is derived and developed. In order to test the validity of the theoretical model, a series of simulated models were conducted to compare theoretical results with simulated results. It was found that the transition zone will disappear directly when virtual origin distance zv/Ds≥−1.14, which results in that the thermal stratification height can only be obtained in the zones close to the area source and far away from the area source. And the thermal stratification height varies widely when the A∗/H2 values are from 0 to 0.1. In addition, thermal stratification height is negatively correlated with the dimensionless source diameter ξs. This study can be used as a basis for follow-up study of buoyancy-driven flows by area heat source in naturally ventilated building.

Characterization of thermal-dependent conductivity in Cattaneo–Christov (CC)-based buoyancy-driven incompressible flow

The idea of thermal-dependent conductivity in transportation of heat has essential significance in ample industrial utilizations. The aspect of heat transportation in furnaces, fibrous, boilers, porous burners, foam insulations, etc. are instances of conduction aspect where temperature differ, and for this reason, alteration in conductivity is extremely higher. Some convected heat transportation processes encompass the thermal-dependent conductivity concept that can be scrutinized in chilling of electronic mechanism structural design along with heat exchangers. Taking into consideration the above-mentioned practicality of thermal-dependent conductivity, we analyzed buoyancy-driven stagnant-point flow subjected to heat sink and heat source. Cattaneo–Christov model which modify the traditional energy expression (i.e., energy expression obtained due to Fourier expression) is considered for modeling. The mathematical systems are simplified via application of boundary-layer theory. These systems are transfigured into dimensionless ODEs by utilizing similarity approach. The modeled dimensionless systems are evaluated employing homotopy procedure. Besides, novel characteristics of non-dimensional factors are inspected via pictorial outcomes.

Computational Study of the Effect of Homogeneous and Heterogeneous Bubbly Flows on Bulk Gas-Liquid Heat Transfer.

A numerical investigation is performed on buoyancy-driven homogeneous and heterogeneous bubbly flows to compare the bulk gas-liquid heat transfer effectiveness for Prandtl (Pr) numbers 0.2-20 and void fractions 0.3-0.5. For this purpose, transient two-fluid model simulations of bubbles rising in a stagnant pool of liquid are conducted in a rectangular box by applying periodic boundary conditions to all the sides. The temperature difference ( ) between gas and liquid phase is averaged over the rectangular box and monitored with respect to time, the heat transfer rate is studied based on the time at which the tends to zero. The results of numerical study show that at low Pr numbers, faster decay of is observed for homogeneous flow of bubbles indicating higher heat transfer rate in comparison with the heterogeneous flow of bubbles for the same void fraction. On the contrary, for high Pr numbers, higher heat transfer rate is observed in heterogeneous flow compared to the homogeneous. The comparison of heat transfer behavior between different void fractions for heterogeneous flow show that, for low Pr numbers higher heat transfer rate is achieved for void fraction 0.4 in comparison with void fraction 0.5. And for high Pr numbers, higher heat transfer is observed for void fraction 0.5 in comparison with void fraction 0.4.

Mesoscopic modeling of equiaxed and columnar solidification microstructures under forced flow and buoyancy-driven flow in hypergravity: Envelope versus phase-field model

Quantitative modeling of solidification microstructures growing under the influence of convection is a challenging multiscale problem. It is of particular interest in processes where strong flow is present, such as centrifugal casting of Ti–Al alloys, where hypergravity strongly reinforces the buoyancy-driven flow. We present the coupling of the mesoscopic envelope model for dendritic solidification with fluid flow. We use the model to investigate columnar and equiaxed dendritic growth of the β-solidifying Ti–45 at.%Al under the influence of flow. The calculations are compared to phase-field results in 2D. For equiaxed growth the case of forced flow is treated. For columnar growth, the influence of buoyancy-driven flow on the growing structure and on the primary dendrite arm spacing is characterized for gravity levels ranging from 0 to ± 15 g. The computational cost of the mesoscopic simulations is around two orders of magnitude lower than that of phase field. We show that the mesoscopic model can accurately reproduce the microstructure characteristics, such as grain shape and primary arm spacing (PDAS), as long as the dendrite tip remains parabolic. When flow effects in columnar growth are strong enough to change the tip shape and induce tip splitting events, the mesoscopic envelope model does not reproduce the resulting branched microstructures. It does however predict the corresponding PDAS reduction at the correct gravity level.

Magneto-fluid dynamic and second law analysis in a hot porous cavity filled by nanofluid and nano-encapsulated phase change material suspension with different layout of cooling channels

Heat transfer, free convective flow and entropy generation of water, Al2O3-water, and nano encapsulated phase change material (NEPCM) diluted in water as NEPCM-water suspension in a hot enclosure is studied. The enclosure is a square porous cavity which heated from below, and the remained walls are thermally insulated. The cavity is cooled by four cooling channels with three different configurations (CONF 1–3). By considering internally heat generation, the impacts of the magnetic field (Ha = 0 and 100), Darcy number (Da=0.001 and 100) and laminar Rayleigh number (Ra=104, 105, and 106) at an equal concentration of nanoparticle and NEPCM (ϕ=2%) are evaluated by finite volume method (FVM) using ANSYS Fluent. The dimensionless form of the governing equations and entropy generation are used to tune the primitive parameters of the CFD code. The validation test and grid verification check are performed to guarantee the accuracy of the results. The results show that the average Nusselt number decreases from CONF1 to CONF3. The buoyancy effect amplified in higher Rayleigh number and porous medium while the magnetic field controls the buoyancy-driven flow. In addition, at low Rayleigh number, the cavity that contains the NEPCM-water suspension is desirable due to its heat transfer capability and low irreversibility.