Particle-driven Gravity Currents Research Articles

Polydisperse particle-driven gravity currents propagating into a stratified ambient in containers of general cross sections

Polydisperse particle-driven gravity currents propagating into a stratified ambient in containers of general cross sections

Inadequacy of fluvial energetics for describing gravity current autosuspension

Gravity currents, such as sediment-laden turbidity currents, are ubiquitous natural flows that are driven by a density difference. Turbidity currents have provided vital motivation to advance understanding of this class of flows because their enigmatic long run-out and driving mechanisms are not properly understood. Extant models assume that material transport by gravity currents is dynamically similar to fluvial flows. Here, empirical research from different types of particle-driven gravity currents is integrated with our experimental data, to show that material transport is fundamentally different from fluvial systems. Contrary to current theory, buoyancy production is shown to have a non-linear dependence on available flow power, indicating an underestimation of the total kinetic energy lost from the mean flow. A revised energy budget directly implies that the mixing efficiency of gravity currents is enhanced.

Direct numerical simulations of intrusive density- and particle-driven gravity currents

In the present study, mesopycnal flows are investigated using direct numerical simulations. In particular, intrusive density- and particle-driven gravity currents in the lock exchange setup are simulated with the high-order finite-difference framework Xcompact3d. To account for the settling velocity of particles, a customized Fick's law for the particle-solution species is used with an additional term incorporating a constant settling velocity proportional to the concentration of particles. A general energy budget equation is presented, for which the energy can migrate across the domain's boundaries. The relevant main features of intrusive gravity currents, such as front velocity, energy exchanges, sedimentation rate, deposit profile, and deposit map are discussed with the comparison between two- and three-dimensional simulations. In particular, the influence of the Grashof number, the interface thickness, the energy exchanges, the sedimentation process, and how the presence of more than one particle fraction may change the flow dynamics are investigated. The results are in good agreement with previous experiments and theoretical work, in particular for the prediction of the front velocity. For the particle-driven case, the suspended mass evolution along with the sedimentation rate suggests the occurrence of three different stages. In the first stage after the lock release, the particle mixture tends to suspend itself due to gravitational forces. Once most of the particle-mixture mass is suspended, the current intrudes while increasing its velocity, reaching its kinetic energy peak. In the last stage, the particles are deposited at a nearly constant sedimentation rate. As a result, the front velocity constantly decelerates.

Propagation, deposition, and suspension characteristics of constant-volume particle-driven gravity currents

In this laboratory study, propagation behaviour, particle deposition patterns, and suspension characteristics of non-cohesive particle-driven gravity currents formed under constant-volume release conditions were investigated. The experimental gravity currents were created in a two-dimensional lock exchange type tank using two different particles (silicon carbide and glass beads) with four different median diameters. Video imaging and image processing techniques were utilized to monitor the current propagation, laser diffraction size analysis and dry weighing techniques were utilized to examine the size and mass characteristics of the deposits and suspensions, and acoustic Doppler velocimetry was utilized for flow velocity measurements for turbulence analysis. Our observations showed that the experimental gravity currents experienced two different propagation phases based upon the particle settling regimes. The first propagation phase was named as the propagation with the turbulence-dominated settling (TDS) and the later propagation phase was named as the propagation with gravity-dominated settling (GDS). It is found that a critical turbulent Reynolds number value (estimated to be O(1)) delineates the settling regimes, hence determines the transition between the propagation phases. With increasing particle settling velocity, the observed propagation phases in our experimental currents showed increasing deviations from the slumping, inertia-buoyancy, and viscous–buoyancy propagation phases that have been reported for homogeneous constant-volume gravity currents with no or negligible settling in the literature. Propagation observations showed that the initial median particle diameters of the currents have negligible effect on the current propagation characteristics during the TDS phase, but become important during the GDS phase. The currents with smaller initial median particle diameters propagated faster and a longer distance in the GDS phase than their counterparts with larger median particle diameters. The deposited particle characteristics indicated that particles of different sizes settle at similar speeds during the TDS phase due to turbulent mixing and the settling speed becomes dependent on the particle size during the GDS phase. As a result, size sorting of the deposited particles became more pronounced during the GDS phase. At the earlier stages of propagation, the vertical profiles of suspended particle concentrations in the current head showed some extent of vertical uniformity due to turbulent mixing around the half height of the current head. On the other hand, at the later stages of propagation, suspended particle concentration profiles exhibited an exponential profile. Deposited and suspended particle characteristics showed that horizontal particle sorting, that is size grading of particles in the flow direction, was more pronounced than the vertical particle sorting, that is size grading of particles at different elevations within the current head.

CFD Modelling of Particle-Driven Gravity Currents in Reservoirs

Reservoir sedimentation results in ongoing loss of storage capacity all around the world. Thus, effective sediment management in reservoirs is becoming an increasingly important task requiring detailed process understanding. Computational fluid dynamics modelling can provide an efficient means to study relevant processes. An existing in-house hydrodynamic code has been extended to model particle-driven gravity currents. This has been realised through a buoyancy term which was added as a source term to the momentum equation. The model was successfully verified and validated using literature data of lock exchange experiments. In addition, the capability of the model to optimize venting of turbidity currents as an efficient sediment management strategy for reservoirs was tested. The results show that the concentration field during venting agrees well with observations from laboratory experiments documented in literature. The relevance of particle-driven gravity currents for the flow field in reservoirs is shown by comparing results of simulations with and without buoyant forces included into the model. The accuracy of the model in the area of the bottom outlet can possibly be improved through the implementation of a non-upwind scheme for the advection of velocity.

Experiments on the sedimentation front in steady particle-driven gravity currents

We present an experimental investigation of steady particle-driven gravity currents with Reynolds numbers in the range 500–1600, and with the ratio of the initial current speed to the fall speed of the particles, S = u 0 /u fall , in the range 5 < S < 160. We identify three regimes: (i) For S < 10, the particles settle close to the source at a velocity corresponding to their fall speed, consistent with the observation of sedimenting fronts in classical settling column experiments. (ii) In the range 10 < S < 40, a steady gravity current develops within the tank. The experiments show that the depth of the gravity current gradually decreases away from the source and dye added to the source liquid appears above the gravity current along its entire length, suggesting that there is a sedimentation front, so that the volume and momentum fluxes of the current gradually decrease with distance from the source. We find that as S increases, the descent speed of the sedimentation front decreases relative to the fall speed of the particles, and the run-out length of the gravity current increases. We note that the density of the interstitial fluid corresponds to the density of the ambient fluid, so that any reduction in buoyancy of the gravity current is attributed to the sedimentation of particles on the floor of the tank and we do not observe lofting of the interstitial fluid. (iii) For 40 < S < 160, the gravity currents reach the end of our experimental tank and we no longer observe a sedimentation front. For these experiments, it appears that the entrainment at the top of the current begins to match the sedimentation and so the current depth does not change significantly over the scale of the tank, but a larger scale experimental system would be needed to explore the full run-out behaviour for these larger values of S. For the intermediate case, 10 < S < 40, we develop a model for the conservation of volume, momentum and buoyancy fluxes in the current, accounting for the sedimentation front and the release of fluid at the top surface of the gravity current, and we compare this with our new experimental data.

A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport

A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.

Asymptotic similarity solutions for particle-driven gravity currents in non-rectangular cross-section channels of power-law form

Abstract We consider a high-Reynolds particle-driven gravity current (GC) propagating in channel above a horizontal boundary. The bottom and the top of the channel are at z = 0 , H and its cross-section is given by − f ( z ) ≤ y ≤ f ( z ) for 0 ≤ z ≤ H , where f ( z ) is a power-law function f ( z ) = z α . We focus attention on the similarity stage of propagation of the current using a shallow-water (SW) model. While it is possible to derive the analytical similarity solutions for the homogeneous GC (for which the density of the current remains constant during the propagation), such similarity-solutions do not exist for the particle-driven GCs. We extend the similarity solutions of homogeneous GC to particle-driven currents by developing an asymptotic expansions and derive approximations of such solutions for channels of typical rectangular, triangular and parabolic forms. Comparison with the numerical solution of the SW equations shows that the leading-order asymptotic results are a good approximation in the domain of expected validity. However, out of bounds of this domain the numerical solutions systematically depart from the first-order asymptotic solutions, suggesting the need to include higher-order terms in the asymptotic series.

Polydisperse particle-driven gravity currents in non-rectangular cross section channels

We consider a high-Reynolds-number gravity current generated by polydisperse suspension of n types of particles distributed in a fluid of density ρi. Each class of particles in suspension has a different settling velocity. The current propagates along a channel of non-rectangular cross section into an ambient fluid of constant density ρa. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general form −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion. We solve the problem by a finite-difference numerical code to present typical height h, velocity u, and mass fractions of particle (concentrations) (ϕ( j), j = 1, …, n) profiles. The runout length of suspensions in channels of power-law cross sections is analytically predicted using a simplified depth-averaged “box” model. We demonstrate that any degree of polydispersivity adds to the runout length of the currents, relative to that of equivalent monodisperse currents with an average settling velocity. The theoretical predictions are supported by the available experimental data. The present approach is a significant generalization of the particle-driven gravity current problem: on the one hand, now the monodisperse current in non-rectangular channels is a particular case of n = 1. On the other hand, the classical formulation of polydisperse currents for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model.

LES mesh resolution requirements for particledriven gravity currents

In this study we investigate the influence of grid resolution on a near-wall resolved LES model of a lock-exchange particle-driven gravity current. The simulations are performed using the finite volume Boussinesq code SnS with a Smagorinsky turbulence model for a buoyant Reynolds number of 60,000 on 4 grid sizes. According to previous studies, two-point correlations are most appropriate to estimate LES resolution. With the largest scales of the flow being resolved by more than 20 cells, well-resolved LES is obtained for grid resolutions of 1925×62×125 and finer. In addition, in order to apply the turbulence model correctly, we show that the velocity power spectrum densities provide useful information for the maximum cell size. The ratio of the subgrid scale viscosity to the molecular viscosity and the subgrid scale shear-stress to the resolved Reynolds stress show good convergence with grid refinement. The ratios vSGS / &lt;0.3 above the current and τSGS (u'v')ave &lt; 0.05 inside the mixing layer, are chosen as threshold values, based on our evaluation study.

On the propagation of particulate gravity currents in circular and semi-circular channels partially filled with homogeneous or stratified ambient fluid

We present a combined theoretical-experimental investigation of particle-driven gravity currents advancing in circular cross section channels in the high-Reynolds number Boussinesq regime; the ambient fluid is either homogeneous or linearly stratified. The predictions of the theoretical model are compared with experiments performed in lock–release configuration; experiments were performed with conditions of both full-depth and partial-depth locks. Two different particles were used for the turbidity current, and the full range 0≤S≤1 of the stratification parameter was explored (S = 0 corresponds to the homogeneous case and S = 1 when the density of the ambient fluid and of the current are equal at the bottom). In addition, a few saline gravity currents were tested for comparison. The results show good agreement for the full-depth configuration, with the initial depth of the current in the lock being equal to the depth of the ambient fluid. The agreement is less good for the partial-depth cases and is improved by the introduction of a simple adjustment coefficient for the Froude number at the front of the current and accounting for dissipation. The general parameter dependencies and behaviour of the current, although influenced by many factors (e.g., mixing and internal waves), are well predicted by the relatively simple model.

Particle-driven gravity currents in non-rectangular cross section channels

We consider a high-Reynolds-number gravity current generated by suspension of heavier particles in fluid of density ρi, propagating along a channel into an ambient fluid of the density ρa. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion which is produced by release from rest of a fixed volume of mixture from a lock. We solve the problem by the finite-difference numerical code to present typical height h(x, t), velocity u(x, t), and volume fraction of particles (concentration) ϕ(x, t) profiles. The methodology is illustrated for flow in typical geometries: power-law (f(z) = zα and f(z) = (H − z)α, where α is positive constant), trapezoidal, and circle. In general, the speed of propagation of the flows driven by suspensions decreases compared with those driven by a reduced gravity in homogeneous currents. However, the details depend on the geometry of the cross section. The runout length of suspensions in channels of power-law cross sections is analytically predicted using a simplified depth-averaged “box” model. The present approach is a significant generalization of the classical gravity current problem. The classical formulation for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model.

High-fidelity simulations of the lobe-and-cleft structures and the deposition map in particle-driven gravity currents

The evolution of a mono-disperse gravity current in the lock-exchange configuration is investigated by means of direct numerical simulations for various Reynolds numbers and settling velocities for the deposition. We limit our investigations to gravity currents over a flat bed in which density differences are small enough for the Boussinesq approximation to be valid. The concentration of particles is described in an Eulerian fashion by using a transport equation combined with the incompressible Navier-Stokes equations. The most interesting results can be summarized as follows: (i) the settling velocity is affecting the streamwise vortices at the head of the current with a substantial reduction of their size when the settling velocity is increased; (ii) when the Reynolds number is increased the lobe-and-cleft structures are merging more frequently and earlier in time, suggesting a strong Reynolds number dependence for the spatio-temporal evolution of the head of the current; (iii) the temporal imprint of the lobe-and-cleft structures can be recovered from the deposition map, suggesting that the deposition pattern is defined purely and exclusively by the structures at the front of the current.

A local boundary integral method for two-dimensional particle-driven gravity currents simulation

A meshless local boundary integral equation method (LBIEM) is used to analyse gravity currents flow in two-dimensional domains. The method solves the incompressible Navier–Stokes equations with a transport equation for the particle concentration. The characteristic-based split scheme is used to solve the governing equations. The LBIEM basic equations are derived via interpolation using radial basis functions. Two numerical test cases are presented here; both are focused on the typical lock-exchange channel flow. The LBIEM procedure produces stable solutions with results comparable to those of other conventional methods.

Numerical simulation of particle-driven gravity currents

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) \({k-\epsilon}\) scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG \({k-\epsilon}\) and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration Co/Ci by the gravity current varies as a function of the particle diameter ds. We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (ds is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG \({k-\epsilon}\) turbulence closure scheme for field scale investigation of particle-driven gravity currents.

Large-eddy simulation of particle-driven gravity currents using the Relaxation-Term model

We present Large-Eddy Simulations (LES) of two laboratory-scale lock-exchange flows at Grashof numbers of up to 108 and a Schmidt number of unity. The unresolved subgrid scales (SGS) are modeled with the Relaxation-Term (RT) approach. We compare the LES results with those of fully resolved Direct Numerical Simulations (DNS) to rate the quality of the approach. We find that reductions of the grid resolution by factors of about four in each spatial and in the temporal direction are feasible compared to marginally resolved DNS. This corresponds to a reduction of computer time by about two orders of magnitude.

Gravity currents from a line source in an ambient flow

We present a mainly theoretical study of high-Reynolds-number planar gravity currents in a uniformly flowing deep ambient. The gravity currents are generated by a constant line source of fluid, and may also be supplied with a source of horizontal momentum and a source of particles. We model the motion using a shallow-water approximation and represent the effects of the ambient flow by imposing a Froude-number condition in a moving frame. We present analytic and numerical expressions for the threshold ambient flow speed above which no upstream propagation can occur at long times. For homogeneous gravity currents in an ambient flow below threshold, we find similarity solutions in which the up- and downstream fronts spread at a constant rate and the current propagates indefinitely in both directions. For gravity currents consisting of both interstitial fluid of a different density to the ambient and a sedimenting particle load, we find long-time asymptotic solutions for ambient flow strengths below threshold. These consist of a steady particle-rich near-source region, in which settling and advection of particles balance, and an effectively particle-free frontal region. The homogeneous behaviour of the fronts ensures that they also spread at a constant rate and therefore can propagate upstream indefinitely. For gravity currents driven solely by a sedimenting particle load, we find numerically that a single regime exists for ambient flow strengths below threshold. In these solutions, settling balances advection near the source leading to a steady region, which joins on to a complex frontal boundary layer. The upstream front progressively decelerates. Our solutions for homogeneous and particle-driven gravity currents compare well with published experimental results.

Mixing and dissipation in particle-driven gravity currents

Results are presented from a high-resolution computational study of particle-driven gravity currents in a plane channel. The investigation was conducted in order to obtain better insight into the energy budget and the mixing behaviour of such flows. Two- and three-dimensional simulations are discussed, and the effects of different factors influencing the flow are examined in detail. Among these are the aspect ratio of the initial suspension reservoir, the settling speed of the particles, and the initial level of turbulence in the suspension. While most of the study is concerned with the lock-exchange configuration, where the initial height of the suspension layer is equal to the height of the channel, part of the analysis is also done for a deeply submerged case. Here, the suspension layer is only one-tenth of the full channel height. Concerning the energy budget, a careful analysis is undertaken of dissipative losses in the flow. Dissipative losses arising from the macroscopic fluid motion are distinguished from those due to the microscopic flow around each sedimenting particle. It is found that over a large range of settling velocities and suspension reservoir aspect ratios, sedimentation accounts for roughly half of all dissipative losses. The analysis of the mixing behaviour of the flow concentrates on the mixing between interstitial and ambient fluid, which are taken to be of identical density. The former is assumed to carry a passive contaminant, whose dispersion with time is analysed qualitatively and quantitatively by means of Lagrangian markers. The simulations show the mixing between interstitial and ambient fluid to be more intense for larger values of the particle settling velocity. Finally, the question is addressed of whether or not initial turbulence in the suspension may exert a significant effect on the flow evolution. To this end, results from three simulations with widely different levels of initial kinetic energy are compared. While the initial turbulence level strongly affects the mixing within the current, it has only a small influence on the front velocity and the overall sedimentation rate.

An experimental study of particle-driven gravity currents on steep slopes with entrainment of particles

Abstract. Results of laboratory experiments are presented in which a finite suspension of sawdust particles was released instantaneously into a rectangular channel immersed in a water tank. Two kinds of gravity currents were studied: currents with or without entrainment of particles from the bed. Experiments were repeated for two slopes: 30° and 45°. We observed that the velocity of the front was significantly in-creased as particle entrainment occurred. In addition, our experiments showed that the front kept a quasi-constant velocity for both runs. This might suggest that the flow regime corresponded to the "slumping regime" or "adjustment phase" described earlier by Huppert and Simpson (1980).

Fundamentals of Drill Cuttings Pile Formation in the Sea

The fundamental process of contaminated pile formation by depositing drill cuttings into the sea is discussed. A new mathematical model of these processes is developed and tested against small-scale laboratory experiments. The experimental study shows how the piles are formed by the development of a particle-laden plume descending to the sea flow which spreads laterally, over a considerable distance, as a particle-driven gravity current. The model predictions are applied to interpret published field data measurements. These results show that the thickness of drill cuttings piles decreases rapidly with distance from the initial source of cuttings and, that when natural biodegradation occurs, only a smaller fraction of the pile area or mass requires treatment.