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1
Salimi, Hamidreza, Karl-Heinz Wolf, and Johannes Bruining. "Negative-Saturation Approach for Compositional Flow Simulations of Mixed CO2/Water Injection Into Geothermal Reservoirs Including Phase Appearance and Disappearance." SPE Journal 17, no. 02 (2012): 502–22. http://dx.doi.org/10.2118/142924-pa.
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Summary Cold mixed CO2/water injection into hot-water reservoirs can be used for simultaneous geothermal-energy (heat) production and subsurface CO2 storage. This paper studies this process in a 2D geothermal homogeneous reservoir, a layered reservoir, and a heterogeneous reservoir represented by a stochastic-random field. We give a set of simulations for a variety of CO2/water-injection ratios. In this process, often regions of two-phase flow are connected to regions of single-phase flow. Different systems of equations apply for single-phase and two-phase regions. We develop a solution approach, called the nonisothermal-negative-saturation (NegSat) solution approach, to solve efficiently nonisothermal compositional flow problems (e.g., CO2/water injection into geothermal reservoirs) that involve phase appearance, phase disappearance, and phase transitions. The advantage of this solution approach is that it circumvents using different equations for single-phase and two-phase regions and the ensuing unstable switching procedure. In the NegSat approach, a single-phase multicomponent fluid is replaced by an equivalent fictitious two-phase fluid with specific properties. The equivalent properties are such that the extended saturation of a fictitious gas is negative in the single-phase aqueous region. We discuss the salient features of the simulations in detail. When two phases are present at the injection side, heterogeneity and layering lead to more CO2 storage compared with the homogeneous case because of capillary trapping. In addition, layering avoids movement of the CO2 to the upper part of the reservoir and thus reduces the risk of leakage. Our results also show that heterogeneity and layering change the character of the solution in terms of useful-energy production and CO2 storage. The simulations can be used to construct a plot of the recovered useful energy vs. maximally stored CO2. Increasing the amount of CO2 in the injection mixture leads to bifurcation points at which the character of the solution in terms of energy production and CO2 storage changes. For overall injected-CO2 mole fractions less than 0.04, the result with gravity is the same as the result without gravity. For larger overall injected-CO2 mole fractions, however, the plot without gravity differs from the plot with gravity because of early breakthrough of a supercritical-CO2 tongue near the caprock. The plot of the useful energy (exergy) vs. the CO2-storage capacity in the presence of gravity shows a Z-shape. The top horizontal part represents a branch of high exergy recovery and a relatively lower storage capacity, whereas the bottom part represents a branch of lower exergy recovery and a higher storage capacity.
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SETA, TAKESHI, KOJI KONO, and SHIYI CHEN. "LATTICE BOLTZMANN METHOD FOR TWO-PHASE FLOWS." International Journal of Modern Physics B 17, no. 01n02 (2003): 169–72. http://dx.doi.org/10.1142/s021797920301728x.
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A lattice Boltzmann method (LBM) for two-phase nonideal fluid flows is proposed based on a particle velocity-dependent forcing scheme. The resulting macroscopic dynamics via the Chapman-Enskog expansion recover the full set of thermohydrodynamic equations for nonideal fluids. Numerical verification of fundamental properties of thermal fluids, including thermal conductivity and surface tension, agrees well with theoretical predictions. Direct numerical simulations of two-phase phenomena, including phase-transition, bubble deformation and droplet falling and bubble rising under gravity are carried out, demonstrating the applicability of the model.
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Chen, Shi Zhong, Yu Hou Wu, Hong Sun, and Hong Tan Liu. "An Improved Two-Phase Flow and Transport Model for the PEM Fuel Cell." Advanced Materials Research 105-106 (April 2010): 691–94. http://dx.doi.org/10.4028/www.scientific.net/amr.105-106.691.
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A two-phase flow, multi-component model has been optimized for a PEM (Proton Exchange Membrane) Fuel Cell. The modeling domain consists of the membrane, two catalyst layers, two diffusion layers, and two channels. Both liquid and gas phases are considered in the entire cathode and anode, including the channel, the diffusion layer and the catalyst layer. The Gravity effect on liquid water was considered in channels. Typical two-phase flow distributions in the cathode gas channel, gas diffuser and catalyst layer are presented. Source term and porosity term were optimized. Based on the simulation results, it is found that two-phase flow characteristics in the cathode depend on the current density, operating temperature, and cathode and anode humidification temperatures. Water mass fraction for the fuel cell with anode upward is higher than that the case with cathode-upward. Liquid water with the case of cathode-upward blocks pores in the gas diffuser layer leading to increasing the concentration polarization. Gravity of liquid water exerts the effect on the water mass fraction in the cathode.
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Zheng, Zhong, and Jerome A. Neufeld. "Self-similar dynamics of two-phase flows injected into a confined porous layer." Journal of Fluid Mechanics 877 (September 2, 2019): 882–921. http://dx.doi.org/10.1017/jfm.2019.585.
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We study the dynamics of two-phase flows injected into a confined porous layer. A model is derived to describe the evolution of the fluid–fluid interface, where the effective saturation of the injected fluid is zero. The flow is driven by pressure gradients due to injection, the buoyancy due to density contrasts and the interfacial tension between the injected and ambient fluids. The saturation field is then computed after the interface evolution is obtained. The results demonstrate that the flow behaviour evolves from early-time unconfined to late-time confined behaviours. In particular, at early times, the influence of capillary forces drives fluid flow and produces a new self-similar spreading behaviour in the unconfined limit that is distinct from the gravity current solution. At late times, we obtain two new similarity solutions, a modified shock solution and a compound wave solution, in addition to the rarefaction and shock solutions in the sharp-interface limit. A schematic regime diagram is also provided, which summarises all possible similarity solutions and the time transitions between them for the partially saturating flows resulting from fluid injection into a confined porous layer. Three dimensionless control parameters are identified and their influence on the fluid flow is also discussed, including the viscosity ratio, the pore-size distribution and the relative contributions of capillary and buoyancy forces. To underline the relevance of our results, we also briefly describe the implications of the two-phase flow model to the geological storage of $\text{CO}_{2}$, using representative geological parameters from the Sleipner and In Salah sites.
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Xie, Fangfang, Xiaoning Zheng, Michael S. Triantafyllou, Yiannis Constantinides, Yao Zheng, and George Em Karniadakis. "Direct numerical simulations of two-phase flow in an inclined pipe." Journal of Fluid Mechanics 825 (July 20, 2017): 189–207. http://dx.doi.org/10.1017/jfm.2017.417.
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We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.
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Zidane, Ali, and Abbas Firoozabadi. "Fracture-Cross-Flow Equilibrium in Compositional Two-Phase Reservoir Simulation." SPE Journal 22, no. 03 (2017): 950–70. http://dx.doi.org/10.2118/184402-pa.
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Summary Compositional two-phase flow in fractured media has wide applications, including carbon dioxide (CO2) injection in the subsurface for improved oil recovery and for CO2 sequestration. In a recent work, we used the fracture-crossflow-equilibrium (FCFE) approach in single-phase compressible flow to simulate fractured reservoirs. In this work, we apply the same concept in compositional two-phase flow and show that we can compute all details of two-phase flow in fractured media with a central-processing-unit (CPU) time comparable with that of homogeneous media. Such a high computational efficiency is dependent on the concept of FCFE, and the implicit solution of the transport equations in the fractures to avoid the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. The implicit solution of two-phase compositional flow in fractures has some challenges that do not appear in single-phase flow. The complexities arise from the upstreaming of the derivatives of the molar concentration of component i in phase α(cα,i) with respect to the total molar concentration (ci) when several fractures intersect at one interface. In addition, because of gravity, countercurrent flow may develop, which adds complexity when using the FCFE concept. We overcome these complexities by providing an upstreaming technique at the fracture/fracture interface and the matrix/fracture interface. We calculate various derivatives at constant volume V and temperature T by performing flash calculations in the fracture elements and the matrix domain to capture the discontinuity at the matrix/fracture interface. We demonstrate in various examples the efficiency and accuracy of the proposed algorithm in problems of various degrees of complexity in eight-component mixtures. In one example with 4,300 elements (1,100 fracture elements), the CPU time to 1 pore volume injection (PVI) is approximately 3 hours. Without the fractures, the CPU time is 2 hours and 28 minutes. In another example with 7,200 elements (1,200 fracture elements), the CPU time is 4 hours and 8 minutes; without fractures in homogeneous media, the CPU time is 2 hours and 53 minutes.
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van Odyck, Daniel E. A., Sean Lovett, Franck Monmont, and Nikolaos Nikiforakis. "An efficient shock capturing scheme for multicomponent multiphase thermal flow in porous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (2012): 3413–40. http://dx.doi.org/10.1098/rspa.2012.0152.
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This paper is concerned with multicomponent, two-phase, thermal fluid flow in porous media. The fluid model consists of component conservation equations, Darcy's law for volumetric flow rates and an enthalpy conservation equation. The model is closed with an equation of state and phase equilibrium conditions that determine the distribution of the chemical components into phases. The sequential formulation described in a previous article is used to build a second-order shock capturing scheme for the conservation equations using a primitive-variable-based linear reconstruction. The fluxes at the cell faces are calculated using an approximate Riemann solver. The method is validated and evaluated by means of one- and two-dimensional problems, including a gravity inversion test.
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Ujita, Hiroshi, Satoru Nagata, Minoru Akiyama, Masanori Naitoh, and Hirotada Ohashi. "Development of LGA & LBE 2D Parallel Programs." International Journal of Modern Physics C 09, no. 08 (1998): 1203–20. http://dx.doi.org/10.1142/s0129183198001096.
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A lattice-gas Automata two-dimensional program was developed for analysis of single and two-phase flow behaviors, to support the development of integrated software modules for Nuclear Power Plant mechanistic simulations. The program has single-color, which includes FHP I, II, and III models, two-color (Immiscible lattice gas), and two-velocity methods including a gravity effect model. Parameter surveys have been performed for Karman vortex street, two-phase separation for understanding flow regimes, and natural circulation flow for demonstrating passive reactor safety due to the chimney structure vessel. In addition, lattice-Boltzmann Equation two-dimensional programs were also developed. For analyzing single-phase flow behavior, a lattice-Boltzmann-BGK program was developed, which has multi-block treatments. A Finite Differential lattice-Boltzmann Equation program of parallelized version was introduced to analyze boiling two-phase flow behaviors. Parameter surveys have been performed for backward facing flow, Karman vortex street, bent piping flow with/without obstacles for piping system applications, flow in the porous media for demonstrating porous debris coolability, Couette flow, and spinodal decomposition to understand basic phase separation mechanisms. Parallelization was completed by using a domain decomposition method for all of the programs. An increase in calculation speed of at least 25 times, by parallel processing on 32 processors, demonstrated high parallelization efficiency. Application fields for microscopic model simulation to hypothetical severe conditions in large plants were also discussed.
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Shi, Bohui, Jiaqi Wang, Yifan Yu, Lin Ding, Yang Liu, and Haihao Wu. "Investigation on the Transition Criterion of Smooth Stratified Flow to Other Flow Patterns for Gas-Hydrate Slurry Flow." International Journal of Chemical Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/9846507.
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A stability criterion for gas-hydrate slurry stratified flow was developed. The model was based on one-dimensional gas-liquid two-fluid model and perturbation method, considering unstable factors including shear stress, gravity, and surface tension. In addition, mass transfer between gas and liquid phase caused by hydrate formation was taken into account by implementing an inward and outward natural gas hydrates growth shell model for water-in-oil emulsion. A series of gas-hydrate slurry flow experiments were carried out in a high-pressure (>10 MPa) horizontal flow loop. The transition criterion of smooth stratified flow to other flow patterns for gas-hydrate slurry flow was established and validated and combined with experimental data at different water cuts. Meanwhile, parameters of this stability criterion were defined. This stability criterion was proved to be efficient for predicting the transition from smooth to nonsmooth stratified flow for gas-hydrate slurry.
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Lamine, Sadok, and Michael G. Edwards. "Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids." Computer Methods in Applied Mechanics and Engineering 292 (August 2015): 171–94. http://dx.doi.org/10.1016/j.cma.2014.12.022.
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Timoshin, Sergei N., and Pallu Thapa. "On-wall and interior separation in a two-fluid boundary layer." Journal of Engineering Mathematics 119, no. 1 (2019): 1–21. http://dx.doi.org/10.1007/s10665-019-10016-8.
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Abstract A two-fluid boundary layer is considered in the context of a high Reynolds number Poiseuille–Couette channel flow encountering an elongated shallow obstacle. The flow is laminar, steady and two-dimensional, with the boundary layer shown to have the pressure unknown in advance and a specified displacement (a condensed boundary layer). The focus is on the detail of the flow reversal triggered by the obstacle. The interface between the two fluids passes through the boundary layer which, in conjunction with the effects of gravity and distinct densities in the two fluids, leads to several possible topologies of the reversed flow, including a conventional on-wall separation, interior flow reversal above the interface, and several combinations of the two. The effect of upstream influence due to a transverse pressure variation under gravity is mentioned briefly.
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Capecelatro, Jesse, Olivier Desjardins, and Rodney O. Fox. "On fluid–particle dynamics in fully developed cluster-induced turbulence." Journal of Fluid Mechanics 780 (September 7, 2015): 578–635. http://dx.doi.org/10.1017/jfm.2015.459.
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At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.
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Shokrpour Roudbari, M., G. Şimşek, E. H. van Brummelen, and K. G. van der Zee. "Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method." Mathematical Models and Methods in Applied Sciences 28, no. 04 (2018): 733–70. http://dx.doi.org/10.1142/s0218202518500197.
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While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.
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Han, Ji-Young, and Jong-Jin Baik. "Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part I: Uniform Basic-State Flow." Journal of the Atmospheric Sciences 66, no. 4 (2009): 947–65. http://dx.doi.org/10.1175/2008jas2915.1.
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Abstract Convectively forced mesoscale flows in three dimensions are theoretically investigated by examining the transient response of a stably stratified atmosphere to convective heating. Solutions for the equations governing small-amplitude perturbations in a uniform basic-state wind with specified convective heating are analytically obtained using the Green function method. In the surface pulse heating case, it is explicitly shown that the vertical displacement at the center of the 3D steady heating decreases as fast as t−1 for large t. Hence, unlike in two dimensions, the steady state is approached in three dimensions. In the finite-depth steady heating case, the perturbation vertical velocity field in the stationary mode shows a main updraft region extending over the heating layer and V-shaped upward and downward motions above and below the heating layer. Including the third dimension results in a stronger updraft at an early stage, a weaker compensating downward motion, and a weaker stationary gravity wave field in a quasi-steady state than in the case of two dimensions. An examination of flow response fields for various vertical structures of convective heating indicates that stationary gravity waves above the main updraft region become strong in intensity as the height of the maximum convective heating increases. In response to the transient heating, a main updraft region extending over the heating layer no longer appears at a dissipation stage of deep convection. Instead, alternating regions of upward and downward motion with an upstream phase tilt appear.
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BONNECAZE, ROGER T., and JOHN R. LISTER. "Particle-driven gravity currents down planar slopes." Journal of Fluid Mechanics 390 (July 10, 1999): 75–91. http://dx.doi.org/10.1017/s0022112099004917.
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Particle-driven gravity currents, as exemplified by either turbidity currents in the ocean or ignimbrite flows in the atmosphere, are buoyancy-driven flows due to a suspension of dense particles in an ambient fluid. We present a theoretical study on the dynamics of and deposition from a turbulent current flowing down a uniform planar slope from a constant-flux point source of particle-laden fluid. The flow is modelled using the shallow-water equations, including the effects of bottom friction and entrainment of ambient fluid, coupled to an equation for the transport and settling of the particles. Two flow regimes are identified. Near the source and for mild slopes, the flow is dominated by a balance between buoyancy and bottom friction. Further downstream and for steeper slopes, entrainment also affects the behaviour of the current. Similarity solutions are also developed for the simple cases of homogeneous gravity currents with no settling of particles in the friction-dominated and entrainment-dominated regimes. Estimates of the width and length of the deposit from a monodisperse particle-driven gravity current with settling are derived from scaling analysis for each regime, and the contours of the depositional patterns are determined from numerical solution of the governing equations.
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FOSTER, M. R., P. W. DUCK, and R. E. HEWITT. "The unsteady Kármán problem for a dilute particle suspension." Journal of Fluid Mechanics 474 (January 10, 2003): 379–409. http://dx.doi.org/10.1017/s0022112002002690.
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We consider the unsteady three-dimensional Kármán flow induced by the impulsive rotation of an infinite rotating plane immersed in an incompressible viscous fluid with a dilute suspension of small solid monodisperse spherical particles. The flow is described in terms of a ‘dusty gas’ model, which treats the discrete phase (particles) and the continuous phase (fluid) as two continua occupying the same space and interacting through a Stokes drag mechanism. The model is extended to allow for a local gravitational acceleration in a direction parallel to the axis of rotation, and is valid for cases in which gravity acts either in the same direction as or in the opposite direction to the Ekman axial flow induced by the rotation of the plane.Analysis based on the theory of characteristics shows that the role of gravity is crucial to the treatment of the discrete-phase equations, particularly in regard to the appropriate boundary conditions to be applied at the solid surface. Other notable features include the presence of an essential singularity in the solution when gravity is absent; indeed this phenomenon may help to explain some of the difficulties encountered in previous studies of this type. If the gravitational force is directed away from the rotating surface, a number of other interesting features arise, including the development of discontinuities in the particle distribution profiles, with corresponding particle-free regions contained between the interface and the rotating boundary. These ‘shock’ features can be associated with a critical axial location in the boundary layer at which a balance is achieved between Ekman suction induced by the rotating boundary and the influence of gravitational effects acting to move particles away from the boundary.
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Smith, Ronald B., Qingfang Jiang, and James D. Doyle. "A Theory of Gravity Wave Absorption by a Boundary Layer." Journal of the Atmospheric Sciences 63, no. 2 (2006): 774–81. http://dx.doi.org/10.1175/jas3631.1.
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Abstract A one-layer model of the atmospheric boundary layer (BL) is proposed to explain the nature of lee-wave attenuation and gravity wave absorption seen in numerical simulations. Two complex coefficients are defined: the compliance coefficient and the wave reflection coefficient. A real-valued ratio of reflected to incident wave energy is also useful. The key result is that, due to horizontal friction, the wind response in the BL is shifted upstream compared to the phase of disturbances in the free atmosphere. The associated flow divergence modulates the thickness of the BL so that it partially absorbs incident gravity waves. A simple expression is derived relating the reflection coefficient to the attenuation and wavelength shift of trapped lee waves. Results agree qualitatively with the numerical simulations, including the effects of increased surface roughness and heat flux.
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Hogg, Andrew J., Mohamad M. Nasr-Azadani, Marius Ungarish, and Eckart Meiburg. "Sustained gravity currents in a channel." Journal of Fluid Mechanics 798 (June 10, 2016): 853–88. http://dx.doi.org/10.1017/jfm.2016.343.
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Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.
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Kim, Changsung Sean, Cetin Kiris, Dochan Kwak, and Tim David. "Numerical Simulation of Local Blood Flow in the Carotid and Cerebral Arteries Under Altered Gravity." Journal of Biomechanical Engineering 128, no. 2 (2005): 194–202. http://dx.doi.org/10.1115/1.2165691.
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A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction∕dilatation and consequent changes in flow conditions.
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Fogliatto, Ezequiel Oscar, Alejandro Clausse, and Federico Eduardo Teruel. "Simulation of phase separation in a Van der Waals fluid under gravitational force with Lattice Boltzmann method." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 9 (2019): 3095–109. http://dx.doi.org/10.1108/hff-11-2018-0682.
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PurposeThis paper aims to assess the accuracy of Lattice Boltzmann method (LBM) for numerical simulation of the stratification of a Van der Waals (VdW) fluid subjected to a gravity field and non-uniform temperature distribution. A sensitivity analysis of the influence of the pseudopotential parameters and the grid resolution is presented. The effect of gravity force on interface densities, density profiles and liquid volume fraction is studied.Design/methodology/approachThe D2Q9 multiple-relaxation-time pseudopotential LBM for two-phase flow is proposed to simulate the phase separation. The analytical solution for density profiles in a one-dimensional problem is derived and used as a benchmark case to validate the numerical results.FindingsThe numerical results reproduce the analytical density profiles with great accuracy over a wide range of simulation conditions, including variations of the gravity and temperature fields. Particularly, the numerical simulations are able to represent the effect of gravity on the existence and position of the liquid–vapor boundary of an ideal pure substance in thermodynamic equilibrium. The sensitivity of the results to variations of the calibration parameters of the VdW pseudopotential was assessed.Research limitations/implicationsThe numerical simulations were performed assuming a VdW fluid in a 2-D cavity with one periodic direction for which analytical solutions for benchmarking purposes are possible to obtain.Originality/valueThe following fundamental question is addressed: Is the pseudopotential LBM capable of simulating accurately the liquid–vapor equilibrium under gravity forces and temperature gradients? Moreover, regarding that the pseudopotential model requires the calibration of several internal parameters to achieve thermodynamic consistency, the sensitivity of the results to variations of these parameters is assessed.
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Wang, Peng, Jie Zhang, and Ning Huang. "An Idealized 3D Model of Interfacial Instability of Aeolian Bedform." Applied Sciences 11, no. 19 (2021): 8956. http://dx.doi.org/10.3390/app11198956.
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An idealized morphodynamic model is constructed for formation of the aeolian sand ripples from small bottom perturbations of a two-dimensional sand bed. The main goal of the analysis is to evaluate the influence of the gravity flow (including “impact-induced gravity flow” in the reptation flux and “topography-induced gravity flow” in the creep flux) on the formation of the aeolian sand ripples and to clarify the relative contribution of various factors to the bed instability. A 3D linear stability analysis reveals that gravity flow appreciably affects the dynamics behaviors of aeolian sand ripples, which decreases the growth rate of sand ripples, tends to stabilize the sand bed, and leads to longer wavelength. We found that the competition between the destabilizing effect of reptation flow and the stabilizing effects of gravity flow leads to pattern selection. The along-crest diffusion of topography driven by impact and gravity is beneficial to the transverse stability of sand ripples, producing sand ripples with straighter and more continuous crests. For moderate values of D, the most unstable mode has zero value of the transverse wavenumber (ky = 0), thus corresponding to aeolian ripples with crests perpendicular to the wind. Moreover, when the impact angle is 9–16°, it has little effect on the characteristics of sand ripples for the initial stage of ripple development. For every increase of the impact angle by 1°, the initial wavelength only increases by about 1.5%. In conclusion, the influence of the gravity flow on the dynamics of sand ripples formation stage cannot be neglected.
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POZRIKIDIS, C. "Gravity-driven creeping flow of two adjacent layers through a channel and down a plane wall." Journal of Fluid Mechanics 371 (September 25, 1998): 345–76. http://dx.doi.org/10.1017/s0022112098002213.
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We study the stability of the interface between (a) two adjacent viscous layers flowing due to gravity through an inclined or vertical channel that is confined between two parallel plane walls, and (b) two superimposed liquid films flowing down an inclined or vertical plane wall, in the limit of Stokes flow. In the case of channel flow, linear stability analysis predicts that, when the fluids are stably stratified, the flow is neutrally stable when the surface tension vanishes and the channel is vertical, and stable otherwise. This behaviour contrasts with that of the gravity-driven flow of two superimposed films flowing down an inclined plane, where an instability has been identified when the viscosity of the fluid next to the plane is less than that of the top fluid, even in the absence of fluid inertia. We investigate the nonlinear stages of the motion subject to finite-amplitude two-dimensional perturbations by numerical simulations based on boundary-integral methods. In both cases of channel and film flow, the mathematical formulation results in integral equations for the unknown interface and free-surface velocity. The properties of the integral equation for multi-film flow are investigated with reference to the feasibility of computing a solution by the method of successive substitutions, and a deflation strategy that allows an iterative procedure is developed. In the case of channel flow, the numerical simulations show that disturbances of sufficiently large amplitude may cause permanent deformation in which the interface folds or develops elongated fingers. The ratio of the viscosities and densities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns. Comparing the numerical results with the predictions of a model based on the lubrication approximation shows that the simplified approach can only describe a limited range of motions. In the case of film flow down an inclined plane, we develop a method for extracting the properties of the normal modes, including the ratio of the amplitudes of the free-surface and interfacial waves and their relative phase lag, from the results of a numerical simulation for small deformations. The numerical procedure employs an adaptation of Prony's method for fitting a signal described by a time series to a sum of complex exponentials; in the present case, the signal is identified with the cosine or sine Fourier coefficients of the interface and free-surface waves. Numerical simulations of the nonlinear motion confirm that the deformability of the free surface is necessary for the growth of small-amplitude perturbations, and show that the morphology of the interfacial patterns developing subject to finite-amplitude perturbations is qualitatively similar to that for channel flow.
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YOON, BUM-SANG, and YURIY A. SEMENOV. "Separated inviscid sheet flows." Journal of Fluid Mechanics 678 (May 3, 2011): 511–34. http://dx.doi.org/10.1017/jfm.2011.123.
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A steady sheet flow of an inviscid incompressible fluid along a curvilinear surface ending with a rounded trailing edge is considered in the presence of gravity. The effect of surface tension is ignored. The formulation of the problem is applicable to the study of free-surface flows over obstacles in channels, weirs and spillways, and pouring flows. An advanced hodograph method is employed for solving the problem, which is reduced to a system of two integro-differential equations in the velocity modulus on the free surface and in the slope of the bottom surface. These equations are derived from the dynamic and kinematic boundary conditions. The Brillouin–Villat criterion is applied to determine the location of the point of flow separation from the rounded trailing edge. Results showing the effect of gravity on the flow detachment and the geometry of the free boundaries are presented over a wide range of Froude numbers including both subcritical and supercritical flows. For supercritical flows two families of solutions for an arbitrary bottom shape are reproduced. It is shown that the additional condition requiring the free surface to be flat at a finite distance from the end of the channel selects a unique solution for a given bottom height and geometry for supercritical flows. This solution is continuous in going from the subcritical to the supercritical flow regime.
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Hernandez-Duenas, Gerardo, Ulises Velasco-García, and Jorge X. Velasco-Hernández. "A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 5 (2019): 1433–57. http://dx.doi.org/10.1051/m2an/2019003.
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Directional drilling in oil and gas extraction can encounter difficulties such as accumulation of solids in deviated pipes. Motivated by such phenomenon, we consider a model for isentropic two-phase flows through deviated pipes. The system of partial differential equations is aimed at simulating the dynamics between a particle bed and a gas phase. The pipe can be either horizontal or vertically deviated where the effects of gravity are incorporated. Furthermore, the acceleration or deceleration due to friction between phases is investigated and spectral properties of the hyperbolic system of balance laws are described. The existence and characterization of steady states under appropriate conditions is analyzed. A new type of steady states arises when a balance between gas and solid phases results in a non-uniform solid particle bed and vanishing solid velocity. This state corresponds to an accumulation of sedimented solids. A central-upwind scheme that preserves the positivity of the gas and solid densities and volume fractions is presented. Including an application of the model to an analysis of accumulation of solids, a variety of numerical tests is presented to show the merits of the scheme.
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Jamili, A., G. P. P. Willhite, and D. W. W. Green. "Modeling Gas-Phase Mass Transfer Between Fracture and Matrix in Naturally Fractured Reservoirs." SPE Journal 16, no. 04 (2011): 795–811. http://dx.doi.org/10.2118/132622-pa.
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Summary Gas injection in naturally fractured reservoirs maintains the reservoir pressure and increases oil recovery primarily by gravity drainage and to a lesser extent by mass transfer between the flowing gas in the fracture and the porous matrix. Although gravity drainage has been studied extensively, there has been limited research on mass-transfer mechanisms between the gas flowing in the fracture and fluids in the porous matrix. This paper presents a mathematical model that describes the mass transfer between a gas flowing in a fracture and a matrix block. The model accounts for diffusion and convection mechanisms in both gas and liquid phases in the porous matrix. The injected gas diffuses into the porous matrix through gas and liquid phases, causing the vaporization of oil in the porous matrix, which is transported by convection and diffusion to the gas flowing in the fracture. Compositions of equilibrium phases are computed using the Peng-Robinson EOS. The mathematical model was validated by comparing calculations to two sets of experimental data reported in the literature (Morel et. al. 1990; Le Romancer et. al. 1994), one involving nitrogen (N2) flow in the fracture and the second with carbon dioxide (CO2) flow. The matrix was a chalk. The resident fluid in the porous matrix was a mixture of methane and pentane. In the N2-diffusion experiment, liquid and vapor phases were initially present, while in the CO2 experiment, the matrix was saturated with liquid-hydrocarbon and water phases. Calculated results were compared with the experimental data, including recovery of each component, saturation profiles, and pressure gradient between matrix and fracture. Agreement was generally good. The simulation revealed the presence of countercurrent flow inside the block. Diffusion was the main mass-transfer mechanism between matrix and fracture during N2 injection. In the CO2 experiment, diffusion and convection were both important.
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di Marzo, M., and M. J. Casarella. "Film Condensation Over a Horizontal Cylinder for Combined Gravity and Forced Flow." Journal of Heat Transfer 107, no. 3 (1985): 687–95. http://dx.doi.org/10.1115/1.3247478.
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The problem of laminar film condensation of a saturated vapor flowing over a cold horizontal cylinder is investigated. A rigorous formulation of the governing equations for the vapor boundary layer and the condensed liquid film, including both the gravity-driven body forces and the imposed pressure gradient caused by the vapor flow, is presented. A generalized transformation of the governing equations allows a wide range of Froude numbers to be investigated. A unique value of the Froude number is defined which allows a distinction between the gravity-dominated flow (Fr→0) and the forced flow (Fr→∞) and basically defines the overlap region for the two solution domains. Numerical solutions are obtained in the merging flow regions controlled by both driving forces. The effects of density/viscosity ratio at the liquid-vapor interface, Prandtl number, Jakob number, and Froude number on the heat transfer characteristics are presented.
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CRNKOVIĆ, Č., M. DOUGLAS, and G. MOORE. "LOOP EQUATIONS AND THE TOPOLOGICAL PHASE OF MULTI-CUT MATRIX MODELS." International Journal of Modern Physics A 07, no. 31 (1992): 7693–711. http://dx.doi.org/10.1142/s0217751x92003483.
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We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of 2×2 matrices. We derive from it loop equations which can be expressed as Virasoro constraints on the partition function. We discover a “pure topological” phase of the theory in which all correlation functions are determined by recursion relations. We also examine macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to dense polymers.
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Chang, Tong-Bou, Bai-Heng Shiue, Yi-Bin Ciou, and Wai-Io Lo. "Analytical Investigation into Effects of Capillary Force on Condensate Film Flowing over Horizontal Semicircular Tube in Porous Medium." Mathematical Problems in Engineering 2021 (March 17, 2021): 1–10. http://dx.doi.org/10.1155/2021/6693512.
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A theoretical investigation is performed into the problem of laminar filmwise condensation flow over a horizontal semicircular tube embedded in a porous medium and subject to capillary forces. The effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method. For analytical convenience, several dimensionless parameters are introduced, including the Jakob number Ja, Rayleigh number Ra, and capillary force parameter Boc. The resulting dimensionless governing equation is solved using the numerical shooting method to determine the effect of capillary forces on the condensate thickness. A capillary suction velocity can be obtained mathematically in the calculation process and indicates whether the gravity force is greater than the capillary force. It is shown that if the capillary force is greater than the condensate gravity force, the liquid condensate will be sucked into the two-phase zone. Under this condition, the condensate film thickness reduces and the heat transfer performance is correspondingly improved. Without considering the capillary force effects, the mean Nusselt number is also obtained in the present study as N u ¯ | V 2 ∗ = 0 = 2 R a D a / J a 1 / 2 ∫ 0 π 1 + cos θ 1 / 2 d θ .
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Stober, Gunter, Svenja Sommer, Carsten Schult, Ralph Latteck, and Jorge L. Chau. "Observation of Kelvin–Helmholtz instabilities and gravity waves in the summer mesopause above Andenes in Northern Norway." Atmospheric Chemistry and Physics 18, no. 9 (2018): 6721–32. http://dx.doi.org/10.5194/acp-18-6721-2018.
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Abstract. We present observations obtained with the Middle Atmosphere Alomar Radar System (MAARSY) to investigate short-period wave-like features using polar mesospheric summer echoes (PMSEs) as a tracer for the neutral dynamics. We conducted a multibeam experiment including 67 different beam directions during a 9-day campaign in June 2013. We identified two Kelvin–Helmholtz instability (KHI) events from the signal morphology of PMSE. The MAARSY observations are complemented by collocated meteor radar wind data to determine the mesoscale gravity wave activity and the vertical structure of the wind field above the PMSE. The KHIs occurred in a strong shear flow with Richardson numbers Ri < 0.25. In addition, we observed 15 wave-like events in our MAARSY multibeam observations applying a sophisticated decomposition of the radial velocity measurements using volume velocity processing. We retrieved the horizontal wavelength, intrinsic frequency, propagation direction, and phase speed from the horizontally resolved wind variability for 15 events. These events showed horizontal wavelengths between 20 and 40 km, vertical wavelengths between 5 and 10 km, and rather high intrinsic phase speeds between 45 and 85 m s−1 with intrinsic periods of 5–10 min.
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Burlot, A., B. J. Gréa, F. S. Godeferd, C. Cambon, and J. Griffond. "Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence." Journal of Fluid Mechanics 765 (January 15, 2015): 17–44. http://dx.doi.org/10.1017/jfm.2014.726.
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AbstractWe study unconfined homogeneous turbulence with a destabilizing background density gradient in the Boussinesq approximation. Starting from initial isotropic turbulence, the buoyancy force induces a transient phase toward a self-similar regime accompanied by a rapid growth of kinetic energy and Reynolds number, along with the development of anisotropic structures in the flow in the direction of gravity. We model this with a two-point statistical approach using an axisymmetric eddy-damped quasi-normal Markovian (EDQNM) closure that includes buoyancy production. The model is able to match direct numerical simulations (DNS) in a parametric study showing the effect of initial Froude number and mixing intensity on the development of the flow. We further improve the model by including the stratification timescale in the characteristic relaxation time for triple correlations in the closure. It permits the computation of the long-term evolution of unstably stratified turbulence at high Reynolds number. This agrees with recent theoretical predictions concerning the self-similar dynamics and brings new insight into the spectral energy distribution and anisotropy of the flow.
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Eckermann, Stephen D., Dave Broutman, Jun Ma, et al. "Dynamics of Orographic Gravity Waves Observed in the Mesosphere over the Auckland Islands during the Deep Propagating Gravity Wave Experiment (DEEPWAVE)." Journal of the Atmospheric Sciences 73, no. 10 (2016): 3855–76. http://dx.doi.org/10.1175/jas-d-16-0059.1.
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Abstract On 14 July 2014 during the Deep Propagating Gravity Wave Experiment (DEEPWAVE), aircraft remote sensing instruments detected large-amplitude gravity wave oscillations within mesospheric airglow and sodium layers at altitudes z ~ 78–83 km downstream of the Auckland Islands, located ~1000 km south of Christchurch, New Zealand. A high-altitude reanalysis and a three-dimensional Fourier gravity wave model are used to investigate the dynamics of this event. At 0700 UTC when the first observations were made, surface flow across the islands’ terrain generated linear three-dimensional wave fields that propagated rapidly to z ~ 78 km, where intense breaking occurred in a narrow layer beneath a zero-wind region at z ~ 83 km. In the following hours, the altitude of weak winds descended under the influence of a large-amplitude migrating semidiurnal tide, leading to intense breaking of these wave fields in subsequent observations starting at 1000 UTC. The linear Fourier model constrained by upstream reanalysis reproduces the salient aspects of observed wave fields, including horizontal wavelengths, phase orientations, temperature and vertical displacement amplitudes, heights and locations of incipient wave breaking, and momentum fluxes. Wave breaking has huge effects on local circulations, with inferred layer-averaged westward flow accelerations of ~350 m s−1 h−1 and dynamical heating rates of ~8 K h−1, supporting recent speculation of important impacts of orographic gravity waves from subantarctic islands on the mean circulation and climate of the middle atmosphere during austral winter.
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PANFILOV, M., and M. BUÈS. "Asymptotic model of the mobile interface between two liquids in a thin porous stratum." Journal of Fluid Mechanics 473 (December 10, 2002): 59–81. http://dx.doi.org/10.1017/s0022112002002355.
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We propose a new generalized model to describe deformations of the mobile interface separating two immiscible liquids in a porous medium. The densities and the viscosities of the fluids can have any value. The horizontal size of the interface is much greater than the vertical size of the domain. Unlike the classical theory, the new model describes gravitational non-equilibrium processes, including the Rayleigh–Taylor instability which appears in the form of a negative apparent diffusion parameter. Several flow regimes are established depending on the ratio between gravity and the elastic fluid/medium forces, and between the vertical and horizontal flow rates. The model is used to analyse the evolution of the interface during the free spreading of one liquid over another. This is characterized by the presence of interface degeneration points. The explicit solution to the problem of oil and water flow towards a well is presented as an application to oil reservoirs.
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McAlister, G., R. Ettema, and J. S. Marshall. "Wind-Driven Rivulet Breakoff and Droplet Flows in Microgravity and Terrestrial-Gravity Conditions." Journal of Fluids Engineering 127, no. 2 (2004): 257–66. http://dx.doi.org/10.1115/1.1881696.
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A study is reported of the wind-driven breakoff of rivulets and subsequent droplet flows on a horizontal plate subject to different normal gravitational states, ranging from zero- to terrestrial-gravity conditions (1 g), and including some data for partial gravity conditions (between 0.1 g and 0.38 g). The study entailed experiments conducted in the authors’ laboratory at the University of Iowa and onboard the NASA KC-135, parabolic-flight aircraft. The wind-driven rivulets exhibited a breakoff phenomenon over a broad range of flow rates, in which a “head” at the tip of the rivulet broke off periodically to form a droplet that advected down the plate. The rivulet breakoff phenomena was sensitive to the normal gravitational force acting on the plate. For instance, the frequency of rivulet breakoff was nearly an order-of-magnitude greater for the 0 g condition than for the same flow in the 1 g condition. The droplet shape and behavior were observed to be quite different between the two cases. It was furthermore found in all cases examined that wind-driven rivulet and droplet flows are markedly different from gravitationally driven flows. These differences arise primarily from the role of form drag on the droplets and on the raised ridge of the rivulet and pool flows near the moving contact line.
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Lister, John R., and Ross C. Kerr. "The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface." Journal of Fluid Mechanics 203 (June 1989): 215–49. http://dx.doi.org/10.1017/s0022112089001448.
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Viscous gravity currents resulting from the introduction of fluid between an upper layer of fluid of lesser density and a lower layer of greater density are analysed. The nonlinear equations governing the spread and shape of the intrusion are formulated for the cases of intrusion at low Reynolds number between deep ambient layers and of flow over a shallow layer of viscous fluid with a rigid lower boundary. Similarity solutions of these equations are obtained in both two-dimensional and axisymmetric geometries, under the assumption that the volume of intruding fluid increases with time like tα. The theoretical predictions are shown to be in reasonable agreement with experimental observations of the spreading of glucose syrups and of viscous hydrocarbons between fluid layers of differing densities. Scaling arguments are used to derive many new results for the rates of spread of intrusions in a wide variety of further situations. A compendium of spreading relations, including some previously isolated results, is derived within a coherent framework and tabulated.
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Klemp, Joseph B., Richard Rotunno, and William C. Skamarock. "On the dynamics of gravity currents in a channel." Journal of Fluid Mechanics 269 (June 25, 1994): 169–98. http://dx.doi.org/10.1017/s0022112094001527.
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We attempt to clarify the factors that regulate the propagation and structure of gravity currents through evaluation of idealized theoretical models along with two-dimensional numerical model simulations. In particular, we seek to reconcile research based on hydraulic theory for gravity currents evolving from a known initial state with analyses of gravity currents that are assumed to be at steady state, and to compare these approaches with both numerical simulations and laboratory experiments. The time-dependent shallow-water solution for a gravity current propagating in a channel of finite depth reveals that the flow must remain subcritical behind the leading edge of the current (in a framework relative to the head). This constraint requires that hf/d ≤ 0.347, where hf is the height of the front and d is the channel depth. Thus, in the lock-exchange problem, inviscid solutions corresponding to hf/d = 0.5 are unphysical, and the actual currents have depth ratios of less than one half near their leading edge and require dissipation or are not steady. We evaluate the relevance of Benjamin's (1968) well-known formula for the propagation of steady gravity currents and clarify discrepancies with other theoretical and observed results. From two-dimensional simulations with a frictionless lower surface, we find that Benjamin's idealized flow-force balance provides a good description of the gravity-current propagation. Including surface friction reduces the propagation speed because it produces dissipation within the cold pool. Although shallow-water theory over-estimates the propagation speed of the leading edge of cold fluid in the ‘dam-break’ problem, this discrepancy appears to arise from the lack of mixing across the current interface rather than from deficiencies in Benjamin's front condition. If an opposing flow restricts the propagation of a gravity current away from its source, we show that the propagation of the current relative to the free stream may be faster than predicted by Benjamin's formula. However, in these situations the front propagation remains dependent upon the specific source conditions and cannot be generalized.
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Hur, H., T. Y. Huang, Z. Zhao, P. Karunanayaka, and T. F. Tuan. "A theoretical model analysis of the sudden narrow temperature-layer formation observed in the ALOHA-93 Campaign." Canadian Journal of Physics 80, no. 12 (2002): 1543–58. http://dx.doi.org/10.1139/p02-056.
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The behavior of temperature and wind profiles observed on 21 October 1993 in the ALOHA-93 Campaign is theoretically and numerically analyzed. A sudden temperature rise took place in a very narrow vertical region (34 km) at about 87 km. Simultaneously observed radar wind profiles and mesospheric airglow wave structures that show a horizontal phase speed of 35 m/s and a period of about half an hour strongly suggest that a critical level may occur in the proximity of that altitude and that the energy dissipation due to the interaction of the gravity wave with the critical level causes the temperature rise. The numerical model used is a solution to the gravity wave mean-flow interaction in the critical layer, including a simple cooling mechanism and a wave-energy dissipation simulated by the "optical model" technique. The solutions for the temperature variations so obtained show good agreement with the observed temperature profiles at different times, providing a quantitative explanation for the temperature inversion layer as a phenomenon of gravity wave critical layer interaction. PACS Nos.: 91.10V, 94.10D
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van den Bremer, T. S., C. Whittaker, R. Calvert, A. Raby, and P. H. Taylor. "Experimental study of particle trajectories below deep-water surface gravity wave groups." Journal of Fluid Mechanics 879 (September 20, 2019): 168–86. http://dx.doi.org/10.1017/jfm.2019.584.
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Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.
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Liu, Z. X., Y. T. Luo, W. B. Luo, B. X. Li, and X. W. Wu. "Selective leaching of Mo from an off-grade gravity lead concentrate in Na2CO3 solution." Journal of Mining and Metallurgy, Section B: Metallurgy 55, no. 2 (2019): 253–59. http://dx.doi.org/10.2298/jmmb181128027l.
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The selective leaching of Mo from an off-grade gravity lead concentrate was investigated in Na2CO3 solution using air as an oxidant. The leaching behaviors of Mo and Pb were predicted by the thermodynamic phase diagrams of Pb-Mo-C-H2O system. The oxidation mechanisms of those sulfides in the off-grade gravity lead concentrate were confirmed by the methods of X-ray diffraction (XRD) and scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDS). The influence of operating factors on the leaching behaviors of Mo and Pb, including Na2CO3 concentration, liquid-to-solid ratio, temperature, and leaching time, were studied. Under these optimum leaching conditions (Na2CO3 2 M, leaching time 8 h, temperature 75?C, air-flow rate 2.0 m3/h and L/S ratio of 10/1 mL/g), the extraction of Mo and Pb was up to 97.70 and 0.73 %, respectively.
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Bölöni, Gergely, Bruno Ribstein, Jewgenija Muraschko, Christine Sgoff, Junhong Wei, and Ulrich Achatz. "The Interaction between Atmospheric Gravity Waves and Large-Scale Flows: An Efficient Description beyond the Nonacceleration Paradigm." Journal of the Atmospheric Sciences 73, no. 12 (2016): 4833–52. http://dx.doi.org/10.1175/jas-d-16-0069.1.
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Abstract With the aim of contributing to the improvement of subgrid-scale gravity wave (GW) parameterizations in numerical weather prediction and climate models, the comparative relevance in GW drag of direct GW–mean flow interactions and turbulent wave breakdown are investigated. Of equal interest is how well Wentzel–Kramer–Brillouin (WKB) theory can capture direct wave–mean flow interactions that are excluded by applying the steady-state approximation. WKB is implemented in a very efficient Lagrangian ray-tracing approach that considers wave-action density in phase space, thereby avoiding numerical instabilities due to caustics. It is supplemented by a simple wave-breaking scheme based on a static-instability saturation criterion. Idealized test cases of horizontally homogeneous GW packets are considered where wave-resolving large-eddy simulations (LESs) provide the reference. In all of these cases, the WKB simulations including direct GW–mean flow interactions already reproduce the LES data to a good accuracy without a wave-breaking scheme. The latter scheme provides a next-order correction that is useful for fully capturing the total energy balance between wave and mean flow. Moreover, a steady-state WKB implementation as used in present GW parameterizations where turbulence provides by the noninteraction paradigm, the only possibility to affect the mean flow, is much less able to yield reliable results. The GW energy is damped too strongly and induces an oversimplified mean flow. This argues for WKB approaches to GW parameterization that take wave transience into account.
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Hornung, H. G. "A model problem for a supersonic gas jet from a moon." Journal of Fluid Mechanics 795 (April 22, 2016): 950–71. http://dx.doi.org/10.1017/jfm.2016.184.
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Some celestial bodies such as planets, moons and comets (here referred to as moons for simplicity) emit jets of material at speeds that in some instances are large enough to escape gravity. Previous investigations have shown this problem to be highly complex, e.g. involving multi-phase flows, phase changes, radiation and gas rarefaction effects. In order to learn from exploring a manageable parameter space, and to provide a limiting case, the present study considers a much simpler model situation in which the material of the jet is an inviscid, non-heat-conducting, perfect gas that issues radially at the surface of the moon with sonic velocity. Theoretical considerations show that the escape velocity of a gas is much smaller than that of a solid body. An analytical solution is obtained for the maximum height reached by a jet in steady flow. A computational parameter study of unsteady, inviscid, axisymmetric flow, including the effect of an atmosphere, provides a rich picture of the features and behaviour of the model jet. The deficit of the computed maximum steady-state penetration height below the isentropic theoretical value may be explained by the effect of the atmosphere and of dissipation in shock waves that occur in the computed flows. Many of the features of the gas jet are qualitatively mirrored in an experiment using a water flow analogy in which the gravitational field is simulated by a surface of suitable shape.
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Faug, Thierry, Mohamed Naaim, and Florence Naaim-Bouvet. "Experimental and numerical study of granular flow and fence interaction." Annals of Glaciology 38 (2004): 135–38. http://dx.doi.org/10.3189/172756404781814870.
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AbstractDense snow avalanches are regarded as dry granular flows. This paper presents experimental and numerical modelling of deposition processes occurring when a gravity-driven granular flow meets a fence. A specific experimental device was set up, and a numerical model based on shallow-water theory and including a deposition model was used. Both tools were used to quantify how the retained volume upstream of the fence is influenced by the channel inclination and the obstacle height. We identified two regimes depending on the slope angle. In the slope-angle range where a steady flow is possible, the retained volume has two contributions: deposition along the channel due to the roughness of the bed and deposition due to the fence. The retained volume results only from the fence effects for higher slopes. The effects of slope on the retained volume also showed these two regimes. For low slopes, the retained volume decreases strongly with increasing slope. For higher slopes, the retained volume decreases weakly with increasing slope. Comparison between the experiments and computed data showed good agreement concerning the effect of fence height on the retained volume.
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Antoine, G. O., E. de Langre, and S. Michelin. "Optimal energy harvesting from vortex-induced vibrations of cables." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2195 (2016): 20160583. http://dx.doi.org/10.1098/rspa.2016.0583.
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Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable’s geometry. The optimal strategy is found to consist systematically in a concentration of the harvesting devices at one of the cable’s ends, relying on deformation waves along the cable to carry the energy towards this harvesting site. Furthermore, we show that the performance of systems based on VIV of flexible cables is significantly more robust to flow velocity variations, in comparison with a rigid cylinder device. This results from two passive control mechanisms inherent to the cable geometry: (i) the adaptability to the flow velocity of the fundamental frequencies of cables through the flow-induced tension and (ii) the selection of successive vibration modes by the flow velocity for cables with gravity-induced tension.
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Yao, Zhiyuan, and Zhaoming Gan. "Hot gas flows on a parsec scale in the low-luminosity active galactic nucleus NGC 3115." Monthly Notices of the Royal Astronomical Society 492, no. 1 (2019): 444–55. http://dx.doi.org/10.1093/mnras/stz3474.
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ABSTRACT NGC 3115 is known as the low-luminosity active galactic nucleus that hosts the nearest (z ∼ 0.002) billion-solar-mass supermassive black hole (∼1.5 × 109 M⊙). Its Bondi radius rB (∼3.6 arcsec) can be readily resolved with Chandra, which provides an excellent opportunity to investigate the accretion flow on to a supermassive black hole. In this paper, we perform two-dimensional hydrodynamical numerical simulations, tailored for NGC 3115, on the mass flow across the Bondi radius. Our best fittings for the density and temperature agree well with the observations of the hot interstellar medium in the centre of NGC 3115. We find that the flow properties are determined solely by the local galaxy properties in the galaxy centre: (1) stellar winds (including supernova ejecta) supply the mass and energy sources for the accreting gas; (2) similar to in the one-dimensional calculations, a stagnation radius rst ∼ 0.1 rB is also found in the two-dimensional simulations, which divides the mass flow into an inflow–outflow structure; (3) the radiatively inefficient accretion flow theory applies well inside the stagnation radius, where the gravity is dominated by the supermassive black hole and the gas is supported by rotation; (4) beyond the stagnation radius, the stellar gravity dominates the spherical-like fluid dynamics and causes the transition from a steep density profile outside to a flat density profile inside the Bondi radius.
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Wei, Cao, Shiqing Cheng, Gang Chen, et al. "Parameters evaluation of fault-karst carbonate reservoirs with vertical beads-on-string structure based on bottom-hole pressure: Case studies in Shunbei Oilfield, Tarim Basin of Northwestern China." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 76 (2021): 59. http://dx.doi.org/10.2516/ogst/2021037.
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Tarim Basin newly discovered the fault-karst carbonate reservoirs, which are formed by the large-scale tectonic fault activities and multiple-stage karstification. Four kinds of mediums coexist in the reservoirs, including the large cave, vug, tectonic fracture and matrix. The tectonic fractures interconnect with large caves in series to form the vertical beads-on-string structure, which is the most common connection pattern in reservoirs. To provide a well test method for evaluating this type of structure, this work firstly presents a multi-fracture-region multi-cave-region series connection physical model by simplifying vertical beads-on-string structure. We consider four kinds of mediums in the proposed physical model, including large caves, small vugs, high-angle tectonic fracture and rock matrix. The fracture regions mainly contain fracture, vug and matrix mediums. The cave regions contain cave medium. The corresponding mathematical model is also developed, in which the flow in fracture regions obeys the Darcy’s law, while the flow in cave regions is assumed to obey free flow. Furthermore, the gravity is taken into account because the flow is along the vertical direction. Then the typical flow regimes are analyzed and sensitivity analysis is conducted on crucial parameters. Results indicate that (a) the typical feature of vertical beads-on-string structure on type curves is that the cave storage regimes and linear flow regimes alternately appear; (b) the type curves will exhibit the cave storage regimes with unit-slope pressure derivative for the existence of large caves, which is different from the inter-porosity flow regimes for the existence of the vugs (slope ≠ 1); (c) the gravity effect could lead to unit-slope pressure and pressure derivative curves, which can be regarded as closed boundary in a peculiar sense; (d) gravity effect is difficult to be observed from well test curves with about 2-weeks test duration in real application. Finally, two cases from Shunbei Oilfield are interpreted to illustrate the practicability and feasibility of proposed method.
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Poulos, Gregory S., James E. Bossert, Thomas B. McKee, and Roger A. Pielke. "The Interaction of Katabatic Flow and Mountain Waves. Part II: Case Study Analysis and Conceptual Model." Journal of the Atmospheric Sciences 64, no. 6 (2007): 1857–79. http://dx.doi.org/10.1175/jas3926.1.
Full textAbstract:
Via numerical analysis of detailed simulations of an early September 1993 case night, the authors develop a conceptual model of the interaction of katabatic flow in the nocturnal boundary layer with mountain waves (MKI). A companion paper (Part I) describes the synoptic and mesoscale observations of the case night from the Atmospheric Studies in Complex Terrain (ASCOT) experiment and idealized numerical simulations that manifest components of the conceptual model of MKI presented herein. The reader is also referred to Part I for detailed scientific background and motivation. The interaction of these phenomena is complicated and nonlinear since the amplitude, wavelength, and vertical structure of the mountain-wave system developed by flow over the barrier owes some portion of its morphology to the evolving atmospheric stability in which the drainage flows develop. Simultaneously, katabatic flows are impacted by the topographically induced gravity wave evolution, which may include significantly changing wavelength, amplitude, flow magnitude, and wave breaking behavior. In addition to effects caused by turbulence (including scouring), perturbations to the leeside gravity wave structure at altitudes physically distant from the surface-based katabatic flow layer can be reflected in the katabatic flow by transmission through the atmospheric column. The simulations show that the evolution of atmospheric structure aloft can create local variability in the surface pressure gradient force governing katabatic flow. Variability is found to occur on two scales, on the meso-β due to evolution of the mountain-wave system on the order of one hour, and on the microscale due to rapid wave evolution (short wavelength) and wave breaking–induced fluctuations. It is proposed that the MKI mechanism explains a portion of the variability in observational records of katabatic flow.
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Frønsdal, Christian. "Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750017. http://dx.doi.org/10.1142/s0219887817500177.
Full textAbstract:
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein–Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier–Stokes–Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the [Formula: see text]-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
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Zgheib, N., A. Ooi, and S. Balachandar. "Front dynamics and entrainment of finite circular gravity currents on an unbounded uniform slope." Journal of Fluid Mechanics 801 (July 21, 2016): 322–52. http://dx.doi.org/10.1017/jfm.2016.325.
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We report on the dynamics of circular finite-release Boussinesq gravity currents on a uniform slope. The study comprises a series of highly resolved direct numerical simulations for a range of slope angles between $5^{\circ }$ and $20^{\circ }$. The simulations were fixed at Reynolds number $Re=5000$ for all slopes considered. The temporal evolution of the front is compared to available experimental data. One of the interesting aspects of this study is the detection of a converging flow towards the centre of the gravity current. This converging flow is a result of the finite volume of the release coupled with the presence of a sloping boundary, which results in a second acceleration phase in the front velocity of the current. The details of the dynamics of this second acceleration and the redistribution of material in the current leading to its development will be discussed. These finite-release currents are invariably dominated by the head where most of the mixing and ambient entrainment occurs. We propose a simple method for defining the head of the current from which we extract various properties including the front Froude number and entrainment coefficient. The Froude number is seen to increase with steeper slopes, whereas the entrainment coefficient is observed to be weakly dependent on the bottom slope.
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White, Brian L., and Karl R. Helfrich. "Rapid gravitational adjustment of horizontal shear flows." Journal of Fluid Mechanics 721 (March 13, 2013): 86–117. http://dx.doi.org/10.1017/jfm.2013.41.
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AbstractThe evolution of a horizontal shear layer in the presence of a horizontal density gradient is explored by three-dimensional numerical simulations. These flows exhibit characteristics of both free shear flows and gravity currents, but have complex dynamics due to strong interactions between the turbulent features of each. Vertical vortices produced by horizontal shear are tilted and stretched by the gravitational adjustment, rapidly enhancing vorticity. Shear intensification at frontal convergences produces high-wavenumber vertical vorticity and the slumping of the density interface produces horizontal Kelvin–Helmholtz vortices typical of a gravity current. The interaction between these instabilities promotes a rapid transition to three-dimensional turbulence. The flow development depends on the relative time scales of shear instability and gravitational adjustment, described by a parameter $\gamma $ (where the limits $\gamma \rightarrow \infty $ and $\gamma \rightarrow 0$ represent a pure gravity current and a pure mixing layer, respectively). The growth rate of three-dimensional instability and the mixing increase for smaller $\gamma $. When $\gamma $ is sufficiently small, there are two distinct regimes: an early period of during which the interface grows rapidly, followed by horizontal diffusive growth. Numerical results are consistent with field observations of tidal separation flows in the Haro Strait (Farmer, Pawlowicz & Jiang, Dyn. Atmos. Oceans., vol. 36, 2002, pp. 43–58), including the magnitude of downwelling vertical currents, horizontal scales of surface vortex features and mixing rate.
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HÄRTEL, CARLOS, ECKART MEIBURG, and FRIEDER NECKER. "Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries." Journal of Fluid Mechanics 418 (September 10, 2000): 189–212. http://dx.doi.org/10.1017/s0022112000001221.
Full textAbstract:
Direct numerical simulations are performed of gravity-current fronts in the lock-exchange configuration. The case of small density differences is considered, where the Boussinesq approximations can be adopted. The key objective of the investigation is a detailed analysis of the flow structure at the foremost part of the front, where no previous high-resolution data were available. For the simulations, high-order numerical methods are used, based on spectral and spectral-element discretizations and compact finite differences. A three-dimensional simulation is conducted of a front spreading along a no-slip boundary at a Reynolds number of about 750. The simulation exhibits all features typically observed in experimental flows near the gravity-current head, including the lobe-and-cleft structure at the leading edge. The results reveal that the flow topology at the head differs from what has been assumed previously, in that the foremost point is not a stagnation point in a translating system. Rather, the stagnation point is located below and slightly behind the foremost point in the vicinity of the wall. The relevance of this finding for the mechanism behind the lobe-and-cleft instability is discussed. In order to explore the high-Reynolds-number regime, and to assess potential Reynolds-number effects, two-dimensional simulations are conducted for Reynolds numbers up to about 30 000, for both no-slip and slip (i.e. shear-stress free) boundaries. It is shown that although quantitative Reynolds-number effects persist over the whole range examined, no qualitative changes in the flow structure at the head can be observed. A comparison of the two-dimensional results with laboratory data and the three-dimensional simulation provides evidence that a two-dimensional model is able to capture essential features of the flow at the head. The simulations also show that for the free-slip case the shape of the head agrees closely with the classical inviscid theory of Benjamin.
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Osundare, Olusegun Samson, Gioia Falcone, Liyun Lao, and Alexander Elliott. "Liquid-Liquid Flow Pattern Prediction Using Relevant Dimensionless Parameter Groups." Energies 13, no. 17 (2020): 4355. http://dx.doi.org/10.3390/en13174355.
Full textAbstract:
Accurate predictions of flow patterns in liquid-liquid flow are critical to the successful design and operation of industrial and geo-energy systems where two liquids are jointly transported. Unfortunately, there is no unified flow pattern map, because all published maps are based on limited ranges of dimensional parameters. Dimensional analysis was performed on oil-water horizontal flows, to obtain some relevant dimensionless parameter groups (DPG) for constructing flow pattern maps (FPM). The following combinations of DPG were used: (i) the ratio of mixture Reynolds number to Eötvös number versus water fraction, (ii) the ratio of Weber number to Eötvös number versus water fraction, (iii) the mixture Froude number versus water fraction, (iv) the water Froude number versus oil Froude number, (v) the ratio of gravity force to viscous force versus water fraction. From twelve published experimental studies, 2696 data points were gathered and analysed covering a variety of flow patterns including stratified, stratified mixed, dispersed oil in water, dispersed water in oil, annular and slug flows. Based on the performed analysis, it was found that flow patterns could occupy more than one isolated region on the DPG-based flow pattern map. None of the combinations of DPG can mark out all the considered flow patterns, however, some combinations of DPG are particularly suitable for marking out the regions associated with some flow patterns.