Buoyancy Regime Research Articles

Interactional flow physics of freely falling sphere on stagnant water

Abstract The process of water impact and subsequent water entry of rigid objects is essential in engineering applications, including marine, offshore, and aerospace technologies. However, most studies have focused on the impact analysis of the object itself, with limited attention given to its interaction with water and the resulting flow dynamics. This work aims to address this gap by examining the effect of buoyancy on the hydrodynamics of a sphere in freefall, particularly its interaction with stagnant water. The investigation uses computational methodologies validated against experimental results to quantify flow and turbulence parameters, including pressure distribution, flow velocity, and other turbulence parameters for different buoyancy regimes. The study also explores the temporal evolution of the free surface profile to gain insight into the deformation and displacement of water resulting from the impact. The analysis reveals that buoyant spheres generate localized turbulent kinetic energy near the surface, while non-buoyant spheres induce higher, more dispersed turbulence. Pressure peaks at the bottom of the sphere, influenced by fall height but independent of density, while buoyancy affects the pressure distribution over time. Furthermore, buoyancy significantly influences the temporal evolution of pressure distribution and the formation of cavities compared to non-buoyant spheres, which exhibit more concentrated velocity streamlines. These results significantly affect designing and optimizing structures interacting with fluid environments, such as underwater vehicles and offshore platforms. Understanding the interplay between buoyancy and flow characteristics can enhance predictions of hydrodynamic behaviour, improving performance and safety in engineering applications.

Scaling high Rayleigh number natural convection boundary layer statistics: A vertical water tunnel experiment

A high Rayleigh number natural convection boundary layer adjacent to the vertical heated wall was investigated at a large-scale facility. The global Rayleigh number (Rax) measured by the temperature difference between the wall and ambient water and the distance from the bottom of the heated wall reached 1013. Experimental results confirm that the global Nusselt number Nux is scaled by power 1/3 of Rax, which is similar to the well-known asymptote of the previously achieved Rax. The velocity field obtained using particle image velocimetry (PIV) indicated that the buoyancy-dominant outer-layer scaling suggested by Wells and Worster [A geophysical-scale model of vertical natural convection boundary layers, J. Fluid Mech. 609, 111–137 (2008)] was not only applicable to scale the lower-order velocity statistics but was also valid as a reasonable measure of the spatial correlation, probability distribution, and quadrant contribution features in the outer layer. The dynamical behavior of fluid motion captured by PIV supported a robust momentum transfer to positive wall-normal direction, which was sustained by the Q1 and Q3 quadrants. In addition, merging the existing literature and current data suggested that near-wall function can be applied at a moderate Rax; the universality of this wall-function model was confirmed around z×∼0.7 (where z× represents the near-wall scaled wall-normal distance, Kiš and Herwig [The near wall physics and wall functions for turbulent natural convection, Int. J. Heat Mass Transfer 55, 2625–2635 (2012)]). At a larger buoyancy regime, it was expected to follow a canonical boundary layer flow.

A working model for estimating CO2-induced uplift of cap rocks under different flow regimes in CO2 sequestration

In this work we study the deflections of an impermeable caprock in the various flow regimes of the plume evolution in the CO2 sequestration problem. The pressure distributions causing the deflections are determined by three different ways: via CFD simulations, known analytical solutions and a novel model based on mass conservation (plug flow model). We find that the different approaches for calculating the deflections are in very good agreement exhibiting minor deviations near the well; the overall deviations also grow slowly with time. We also find that the magnitude of deflections is inversely proportional to the gravity number, that is, large deflections correspond to the low buoyancy regime. These findings suggest that the deflections are mainly driven by the injected volume of CO2, a fact which is naturally built in the proposed model, dictating a piecewise logarithmic pressure profile which greatly facilitates analytical treatment of the deflection field calculations. This methodology can be used for predicting deflections with relative ease that are useful for caprock uplift and integrity considerations.

Energetics of buoyancy-generated turbulent flows with active scalar: pure buoyant plume

A framework for the budget of Reynolds stress, temperature and density variations, turbulent mass flux and turbulent heat flux is presented for buoyancy-generated turbulent flows with a focus on turbulent plumes. The dynamical interactions between the turbulence generated from the velocity and thermodynamic fluctuations in thermal and heated gas plumes is studied. A large-eddy simulation tool has been used to simulate heavier and lighter than air plumes released from a circular heated source for high Reynolds number (Re). The budget equations are developed using a Favre-averaging approach. Both heated air plumes and heated gas plumes, namely, heated ${\rm SO}_2$ and heated ${\rm CH}_4$ plumes, are included in the study. The study focuses on addressing key questions – does the turbulence kinetic energy (TKE) spectrum follow the classical inertial $-5/3$ spectrum or is there a $-3$ buoyancy regime with a different scaling law? Fundamental pathways for generation of turbulence through velocity fluctuations, and temperature and density fluctuations are discussed. Analysis of the TKE and scalar variance budget equations has demonstrated that multiple mechanisms dominate the transport of Reynolds stresses, and in particular that correlations between the density and the velocity dominates the turbulence production mechanisms. Entrainment is connected to the turbulent transport and pressure-dilation processes.

Pressure build-up analysis in the flow regimes of the CO2 sequestration problem

In this work we analyse theoretically and numerically the pressure build-up on the cap rock of a saline aquifer during CO2 injection in all flow regimes. Flow regimes are specific regions of the parameter space representing the mathematical spread of the plume. The parameter space is defined in terms of the CO2-to-brine relative mobility λ and the buoyancy parameter Γ. In addition to the known asymptotic self-similar solutions for low buoyancy regimes, we introduce two novel ones for the high buoyancy regimes via power series solutions. Explicit results for the peak pressure value on the cap, which arises in the vicinity of the well, are derived and discussed for all flow regimes. The analytical results derived are then applied for cap integrity considerations in six test cases of CO2 geological storage from the PCOR partnership, most of which correspond to high buoyancy conditions. The validity of the self-similar solutions which are late time asymptotics, is verified with CFD numerical simulations with a commercial software. The comparison between the self-similar solutions and CFD for the pressure estimations are in excellent agreement and the self-similar solutions are valid for typical injection durations even for early times.

Flow Regime Analysis of the Pressure Build-Up during CO2 Injection in Saturated Porous Rock Formations

In this work, we are concerned with the theoretical and numerical analysis of the pressure build-up on the cap of an aquifer during CO2 injection in saturated porous rock formations in all flow regimes of the problem. The latter are specific regions of the parameter space of the plume flow, defined by the CO2-to-brine relative mobility and the buoyancy parameter (injection pressure to buoyancy pressure scale ratio). In addition to the known asymptotic self-similar solutions for low buoyancy, we introduce two novel ones for the high buoyancy regimes via power series solutions of asymptotic self-similarity equations. The explicit results for the peak value of pressure on the cap, which arises in the vicinity of the well, are derived and discussed for all flow regimes. The analytical results derived in this work are applied for the purpose of cap integrity considerations in six test cases of CO2 geological storage from the PCOR partnership, most of which correspond to high buoyancy conditions. The validity of the self-similar solutions (late time asymptotics) is verified with CFD numerical simulations performed with the software Ansys-Fluent. The result is that the self-similar solutions and the associated pressure estimations are valid in typical injection durations of interest, even for early times.

Inertial gravity current produced by the drainage of a cylindrical reservoir from an outer or inner edge

We consider the time-dependent flow of a fluid of density $\unicode[STIX]{x1D70C}_{1}$ in a vertical cylindrical container embedded in a fluid of density $\unicode[STIX]{x1D70C}_{2}~({<}\unicode[STIX]{x1D70C}_{1})$ whose side boundary is suddenly removed and the fluid drains freely from the edge. We show that in the inertial–buoyancy regime (large initial Reynolds number) the flow is modelled by the shallow-water equations and bears similarities to a gravity current released from a lock (the dam-break problem) driven by the reduced gravity $g^{\prime }=(1-\unicode[STIX]{x1D70C}_{2}/\unicode[STIX]{x1D70C}_{1})g$. This formulation is amenable to an efficient finite-difference solution. Moreover, we demonstrate that similarity solutions exist, and show that the flow created by the dam break approaches the predicted self-similar behaviour when the volume ratio ${\mathcal{V}}(t)/{\mathcal{V}}(0)\approx 1/2$ where $t$ is time elapsed from the dam break. We considered two cases of drainage: (i) outward from the outer boundary in a full-radius reservoir; and (ii) inward from the inner radius in an annular-shaped reservoir. For the first case the similarity solution is expressed analytically, while the second case is more complicated and requires a numerical solution. In both cases ${\mathcal{V}}(t)/{\mathcal{V}}(0)$ decays like $t^{-2}$, but the details are different. The similarity solutions admit an adjustable virtual-origin constant, which we determine by matching with the finite-difference solution. The analysis is valid for both Boussinesq and non-Boussinesq systems, and a wide range of geometric parameters (inner and outer radii, and height). The importance of the neglected viscous terms increases with time, and eventually the inertial–buoyancy model becomes invalid. An estimate for this occurrence is also provided. The predictions of the model are compared to results of direct numerical simulations; there is good agreement for the position of the interface and for the averaged radial velocity, and excellent agreement for ${\mathcal{V}}(t)/{\mathcal{V}}(0)$. A box model is used for estimating the effect of a partial (over a sector) dam break. This study is an extension of the work for a rectangular reservoir of Momen et al. (J. Fluid Mech., vol. 827, 2017, pp. 640–663). We demonstrate that there are some similarities, but also significant differences, between the rectangular and the cylindrical reservoirs concerning the velocity, shape of the interface and rate of drainage, which are of interest in applications. The overall conclusion is that this simple model captures very well the flow field under consideration.

Axisymmetric three-dimensional gravity currents generated by lock exchange

Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial–buoyancy equilibrium regime and a viscous–buoyancy equilibrium regime. The viscous–buoyancy phase is in good agreement with the model of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), while the inertial phase is consistent with the experiments of Britter (Atmos. Environ., vol. 13, 1979, pp. 1241–1247), conducted for purely axially symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert & Simpson (J. Fluid Mech., vol. 99 (04), 1980, pp. 785–799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. As expected, the slumping phase is governed by the Froude number at the lock’s gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial–buoyancy regime in the presence of hydrodynamic shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant-volume and planar gravity currents, despite their own environmental relevance.

Optimization of magnetically driven directional solidification of silicon using artificial neural networks and Gaussian process models

In directional solidification of silicon, the solid-liquid interface shape plays a crucial role for the quality of crystals. The interface shape can be influenced by forced convection using travelling magnetic fields. Up to now, there is no general and explicit methodology to identify the relation and the optimum combination of magnetic and growth parameters e.g., frequency, phase shift, current magnitude and interface deflection in a buoyancy regime. In the present study, 2D CFD modeling was used to generate data for the design and training of artificial neural networks and for Gaussian process modeling. The aim was to quickly assess the complex nonlinear dependences among the parameters and to optimize them for the interface flattening. The first encouraging results are presented and the pros and cons of artificial neural networks and Gaussian process modeling discussed.

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 1012 not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 1010. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.

Experimental study on growth and spread of dispersed particle-laden plume in a linearly stratified environment

We present results of laboratory experiments conducted to study the evolution, growth, and spreading rate of a dispersed particle-laden plume produced by a constant inflow into a density varying environment. Particles having mean size, \(d_p=100\ \upmu \)m, density \(\rho _p=2500 \ {\text{ kg/m}}^3\), volume fraction, \(\phi _v =\) 0–0.7 % , were injected along with the lighter buoyant fluid into a linearly stratified medium. It was observed that a particle-laden plume intruding at the neutral density layer is characterized by four spreading regimes: (i) radial momentum flux balanced by the inertia force; (ii) inertia buoyancy regime; (iii) fluid-particle inertia regime, and (iv) viscous buoyancy regime. Regimes (i), (ii), and (iv) are similar to that of a single-phase plume, for which \(\phi _v = 0\,\%\). The maximum height, \(Z_m\), for \(\phi _v > 0\,\%\) was observed to be consistently lower than the single-phase case. An empirical parameterization was developed for the maximum height for particle-laden case, and was found to be in very good agreement with the experimental data. In the inertia buoyancy regime, the radial spread of the plume, \(R_f\), for \(\phi _v > 0\,\%\), advanced in time as \(R_f \propto t^{0.68 \pm 0.02}\) which is slower compared to the single-phase plume that propagates at \(R_f \propto t^{0.74 \pm 0.02}\). Due to the presence of particles, ‘particle fall out’ effect occurs, which along with the formation of a secondary umbrella region inhibits the spreading rate and results in slower propagation of the particle-laden plume. The effect of particles on spreading height of plume, \(Z_s\), and thickness of the plume, \(h_p\), were also studied, and these results were compared with the single-phase case. Overall from these experiments, it was found that the evolution, growth, and spread of dispersed particle-laden plume is very different from that of the single-phase plume, and presence of low concentration of particles (\( \phi _v < 1\,\%\)) could have significant effects on the plume dynamics.

Body armour and lateral‐plate reduction in freshwater three‐spined sticklebackGasterosteus aculeatus: adaptations to a different buoyancy regime?

Several factors related to buoyancy were compared between one marine and two freshwater populations of three-spined stickleback Gasterosteus aculeatus. Fish from all three populations had buoyancy near to neutral to the ambient water. This showed that neither marine nor freshwater G. aculeatus used swimming and hydrodynamic lift to prevent sinking. Comparing the swimbladder volumes showed that freshwater completely plated G. aculeatus had a significantly larger swimbladder volume than both completely plated marine and low-plated freshwater G. aculeatus. Furthermore, body tissue density was lower in low-plated G. aculeatus than in the completely plated marine and freshwater fish. The results show that G. aculeatus either reduce tissue density or increase swimbladder volume to adapt to lower water density. Mass measurements of lateral plates and pelvis showed that loss of body armour in low-plated G. aculeatus could explain the tissue density difference between low-plated and completely plated G. aculeatus. This suggests that the common occurrence of plate and armour reduction in freshwater G. aculeatus populations can be an adaptation to a lower water density.

Canceling Buoyancy of Gaseous Fuel Flames in a Gravitational Environment Using an Ion‐Driven Wind

Electric fields applied to combustion plasmas can be used to manipulate the thermofluid flow field to reduce buoyant forces and, hence, convection in locations near and within the flame. The resulting flow field is similar to that which is obtained in microgravity. Previous work has shown that buoyancy is modified in a non-premixed methane-air capillary flame when it burns in a capillary-to-plane configuration and an electric field is applied, and that regions of neutral or microbuoyancy exist, as indicated by the examined temperature and oxidizer profiles. The aim of this article is to examine in more detail this microbuoyancy condition and the coupling between the ion wind and resulting thermofluid flow field. To this end, the voltage-current characteristics (VCC) of CH4, C2H2, C2H4, C2H6, and C3H8 are measured and compared. Soot generated in the C2H(X) and propane flames lead to a hysteresis in the VCC curve whereby increased sooting leads to lower ion currents at constant flow rates and applied potentials. Buoyancy regimes for these flames in this configuration are determined. Methane can achieve the highest flow rate without sooting at the microbuoyant condition, and does not exhibit hysteresis in the VCC for the flow rates examined here. Furthermore, in this geometry, the microbuoyant condition for methane is found to coincide with ion current saturation when the capillary-to-plane distance is varied. These results allow for several simplifications to be made when modeling the flame at these conditions: the imposition of a spherical flame boundary with known ion current, and negligible recombination in the domain.

Axisymmetric Submerged Intrusion in Stratified Fluid

This paper presents the results of laboratory experiments conducted to study the spreading rates of axisymmetric intrusive gravity currents produced by a constant inflow into a stratified body of water. The experiments were conducted over a wide range of initial parameters. A balance of the forces that drive and retard the flow indicate that the intrusion is characterized by four spreading regimes: (1) the radial jet; (2) the radial momentum flux balanced by the inertia force; (3) the pressure (buoyancy) force balanced by the inertia force; and (4) the pressure force balanced by the interfacial drag (viscous force). The experimental results seem to confirm the derived spreading relations. The paper makes three significant contributions. It resolves theoretically and experimentally the existing conflict regarding the proper radial growth of the intrusion in the inertia-buoyancy regime. In addition, it relates the observed transition from the inertia-buoyancy regime to viscous buoyancy regime. It does so using scaling arguments to find the length and time scales for this transition. The paper also gives extensive experimental evidence for the spreading relationships in the inertia-buoyancy and viscous-buoyancy regimes, and it facilitates the determination of the corresponding experimental coefficients.

Physical and numerical analysis of the front of a gravity current on a horizontal bottom

In this paper, numerical and experimental approaches are applied to analyse the dynamics of the front of a gravity current. This study focused on two parameters: internal density and velocity fields. The salt concentration was determined by a potentiometric process. The internal velocities were determined using an optical device and an image-processing system. The structure of the head of the gravity current was analysed. Its density was measured and two stages of evolution were observed. This analysis allows us to coufirm the existence of two important stages. Forxf&amp;lt;xs, where the dynamics depend on the initial condition, the flow consists of a head and body and the front density is constant. Forxf&amp;gt;xs, we show that the density of the front decreases and evolves towards the Hallworth and others (1993) law. From a comparison between the experiments and the numerical model, we show that the numerical model, which is based on Navier–Stokes equations and on thek−Lturbulence model (whereLis the height of the gravity current), can predict well flow in the slump regime and in the inertia–buoyancy regime with smoothed results in the transition from the head to the body of the gravity current.

Physical and numerical analysis of the front of a gravity current on a horizontal bottom

In this paper, numerical and experimental approaches are applied to analyse the dynamics of the front of a gravity current. This study focused on two parameters: internal density and velocity fields. The salt concentration was determined by a potentiometric process. The internal velocities were determined using an optical device and an image-processing system. The structure of the head of the gravity current was analysed. Its density was measured and two stages of evolution were observed. This analysis allows us to coufirm the existence of two important stages. For xf &lt; xs, where the dynamics depend on the initial condition, the flow consists of a head and body and the front density is constant. For xf &gt; xs, we show that the density of the front decreases and evolves towards the Hallworth and others (1993) law. From a comparison between the experiments and the numerical model, we show that the numerical model, which is based on Navier–Stokes equations and on the k−L turbulence model (where L is the height of the gravity current), can predict well flow in the slump regime and in the inertia–buoyancy regime with smoothed results in the transition from the head to the body of the gravity current.

Neutral buoyancy and the structure of mid‐ocean ridge magma reservoirs

The mechanical structure of the regions for shallow storage and lateral intrusion of mid‐ocean ridge basalt (MORB) is explored in part by examining the density range appropriate for picritic‐to‐tholeiitic liquids and liquid + crystal mixtures, and its relationship to the nonlinear density‐depth structure of the ridge. Magma density spans the range 2.6 to at least 2.82 Mg m−3 and incorporates the effects of fractional crystallization on the density evolution, the incorporation of olivine phenocrysts and the contributions of water in melt phase density reductions. The melt and melt + crystal density band crosses the in situ rock density curve over the ≈1 to ≈3 km depth interval beneath the volcanic surface. Within that averaged interval, picritic‐to‐tholeiitic melt and melt + crystal mixtures are in approximate mechanical equilibrium with their surroundings, and the interval is referred to as the MORB horizon of neutral buoyancy (HNB). The detailed locations of the transition regions between the negative and neutral buoyancy and between the neutral and positive buoyancy regimes are dependent on melt phase composition as well as the presence of suspended mineral phases and their identity. In the East Pacific Rise, the HNB has a 1:1 correspondence with the inferred location of the sheeted dike complex and the seismically detected minimum compressional wave velocity region. In ophiolite complexes the region corresponds to the sheeted dike complex and the uppermost isotropic gabbros. Above the HNB is the region of negative buoyancy (seafloor to an averaged ≈1 km depth) within which, negative buoyancy forces may induce the descent of nonvesiculated melt. This region corresponds to the pillow basalt ± sediment sequence. The region of positive buoyancy extends from ≈3 km to the depth of melt generation, and picritic melt ascends in dikes and veins of finite height ≈500 m to ≈11 km and relatively narrow width ≈20 mm to ≈100 cm. The finite strengths of high‐temperature fluid‐weakened rocks mandate finite height melt parcels along the ascent pathway. The magmatic source region is therefore never hydraulically connected with the surface nor with the near‐surface reservoir. Thus relatively locally integrated buoyancy has a natural role in the ascent of melt from the source region to the region of neutral buoyancy. During the final stages of magma ascent, hydrothermal fluid circulation enshrouds the HNB in a three‐dimensional envelope, as suggested by the depth extent of alteration mineralogy in ophiolite complexes. While hydrothermal cooling may play an important role in arresting the ascent of magma in very low spreading‐rate environments, gravitational equilibrium represents the effectively dominant theme in intermediate and high spreading‐rate regions such as the East Pacific Rise. Elastic crack penetration of rheological transition zones near the HNB identify modes of crack‐tip morphologic changes as a function of Young's modulus ratios (E2/E1) above and beneath the transition and affect the style of intrusion, while melt buoyancy determines the ultimate equilibrium resting place. Elastic crack stability considerations relate the vertical magma pressure gradients for tholeiitic (∇PT) and picritic (∇Pp) magmas to the vertically varying gradient in the horizontal stress component (∇σH) and suggest further subdivision into two horizons of neutral buoyancy: one for tholeiitic magma (HNBT), and one for the picritic liquid + olivine mixtures (HNBP). These intervals are very approximate but are estimated as ≈600 m to ≈1400 m and ≈1400 to ≈3000 m depth, respectively, beneath the East Pacific Rise axis. As oceanic lithosphere is created at the rise axis and spreads laterally, the horizons of negative buoyancy and neutral buoyancy ride with it and may continue to modulate the subsurface magma dynamics that influence off‐axis volcanism.

Numerical simulation of surface tension- and combined buoyancy-driven convection in a liquid layer heated by a hot wire

The characteristics of convection in liquid layers heated below the free surface are numerically studied. The mechanisms for convection are buoyancy and variation of surface tension with respect to temperature. Specific computations are performed to stress the influence of heat transfer at the interface and of interfacial viscosities. The transition between Marangoni and buoyancy regimes, when heating by an infinite hot wire located below the free surface, is investigated.