Lock-exchange gravity currents propagating in a channel containing an array of obstacles

2015 ◽  
Vol 765 ◽  
pp. 544-575 ◽  
Author(s):  
Ayse Yuksel Ozan ◽  
George Constantinescu ◽  
Andrew J. Hogg
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Drag Coefficient ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Release Time ◽  
Exchange Flow ◽  
Layer Model ◽  
Shallow Layer

AbstractLarge eddy simulation (LES) is used to investigate the evolution of Boussinesq gravity currents propagating through a channel of height $H$ containing a staggered array of identical cylinders of square cross-section and edge length $D$. The cylinders are positioned with their axes horizontal and perpendicular to the (streamwise) direction along which the lock-exchange flow develops. The effects of the volume fraction of solids, ${\it\phi}$, the Reynolds number and geometrical parameters describing the array of obstacles on the structure of the lock-exchange flow, total drag force acting on the gravity current, front velocity and global energy budget are analysed. Simulation results show that the currents rapidly transition to a state in which the extra resistance provided by the cylinders strongly retards the motion and dominates the dissipative processes. A shallow layer model is also formulated and similarity solutions for the motion are found in the regime where the driving buoyancy forces are balanced by the drag arising from the interaction with the cylinders. The numerical simulations and this shallow layer model show that low-Reynolds-number currents transition to a drag-dominated regime in which the resistance is linearly proportional to the flow speed and, consequently, the front velocity, $U_{f}$, is proportional to $t^{-1/2}$, where $t$ is the time measured starting at the gate release time. By contrast, high-Reynolds-number currents, for which the cylinder Reynolds number is sufficiently high that the drag coefficient for most of the cylinders can be considered constant, transition first to a quadratic drag-dominated regime in which the front speed determined from the simulations is given by $U_{f}\sim t^{-0.25}$, before undergoing a subsequent transition to the aforementioned linear drag regime in which $U_{f}\sim t^{-1/2}$. Meanwhile, away from the front, the depth-averaged gravity current velocity is proportional to $t^{-1/3}$, a result that is in agreement with the shallow water model. It is suggested that the difference between these two is due to mixing processes, which are shown to be significant in the numerical simulations, especially close to the front of the motion. Direct estimation of the drag coefficient $C_{D}$ from the numerical simulations shows that the combined drag parameter for the porous medium, ${\it\Gamma}_{D}=C_{D}{\it\phi}(H/D)/(1-{\it\phi})$, is the key dimensionless grouping of variables that determines the speed of propagation of the current within arrays with different $C_{D},{\it\phi}$ and $D/H$.

Front dynamics and entrainment of finite circular gravity currents on an unbounded uniform slope

2016 ◽  
Vol 801 ◽  
pp. 322-352 ◽  
Author(s):  
N. Zgheib ◽  
A. Ooi ◽  
S. Balachandar
Keyword(s):  
Froude Number ◽  
Temporal Evolution ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Acceleration Phase ◽  
Simple Method ◽  
Entrainment Coefficient ◽  
Converging Flow ◽  
Front Dynamics

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.

The front speed of intrusions into a continuously stratified medium

2007 ◽  
Vol 594 ◽  
pp. 369-377 ◽  
Author(s):  
DIOGO BOLSTER ◽  
ALICE HANG ◽  
P. F. LINDEN
Keyword(s):  
Numerical Simulations ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Stratified Medium ◽  
Fluid Density ◽  
Neutral Buoyancy ◽  
Front Speed ◽  
Predicted Values ◽  
Good Agreement

This paper examines intrusive Boussinesq gravity currents, propagating into a continuously stratified fluid. We develop a model, based on energy arguments, to predict the front speed of such an intrusive gravity current from a lock release. We find that the depth at which the intrusion occurs, which corresponds to the level of neutral buoyancy (i.e. the depth where the intrusion density equals the stratified fluid density), affects the front speed. The maximum speeds occur when the intrusion travels along the top and bottom boundaries and the minimum speed occurs at mid-depth. Experiments and numerical simulations were conducted to compare to the theoretically predicted values, and good agreement was found.

Gravity currents propagating into shear

2015 ◽  
Vol 778 ◽  
pp. 552-585 ◽  
Author(s):  
M. M. Nasr-Azadani ◽  
E. Meiburg
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Steady State ◽  
High Reynolds Number ◽  
Gravity Current ◽  
Gravity Currents ◽  
Maximum Energy ◽  
Channel Height ◽  
High Reynolds ◽  
The Given

An analytical vorticity-based model is introduced for steady-state inviscid Boussinesq gravity currents in sheared ambients. The model enforces the conservation of mass and horizontal and vertical momentum, and it does not require any empirical closure assumptions. As a function of the given gravity current height, upstream ambient shear and upstream ambient layer thicknesses, the model predicts the current velocity as well as the downstream ambient layer thicknesses and velocities. In particular, it predicts the existence of gravity currents with a thickness greater than half the channel height, which is confirmed by direct numerical simulation (DNS) results and by an analysis of the energy loss in the flow. For high-Reynolds-number gravity currents exhibiting Kelvin–Helmholtz instabilities along the current/ambient interface, the DNS simulations suggest that for a given shear magnitude, the current height adjusts itself such as to allow for maximum energy dissipation.

scholarly journals Particle-driven gravity currents

1993 ◽  
Vol 250 ◽  
pp. 339-369 ◽  
Author(s):  
Roger T. Bonnecaze ◽  
Herbert E. Huppert ◽  
John R. Lister
Keyword(s):  
Particle Concentration ◽  
Local Density ◽  
Gravity Current ◽  
Pressure Head ◽  
Viscous Sublayer ◽  
Gravity Currents ◽  
Momentum Balance ◽  
Exchange Flow ◽  
Mean Flow ◽  
Ambient Fluid

Gravity currents created by the release of a fixed volume of a suspension into a lighter ambient fluid are studied theoretically and experimentally. The greater density of the current and the buoyancy force driving its motion arise primarily from dense particles suspended in the interstitial fluid of the current. The dynamics of the current are assumed to be dominated by a balance between inertial and buoyancy forces; viscous forces are assumed negligible. The currents considered are two-dimensional and flow over a rigid horizontal surface. The flow is modelled by either the single- or the two-layer shallow-water equations, the two-layer equations being necessary to include the effects of the overlying fluid, which are important when the depth of the current is comparable to the depth of the overlying fluid. Because the local density of the gravity current depends on the concentration of particles, the buoyancy contribution to the momentum balance depends on the variation of the particle concentration. A transport equation for the particle concentration is derived by assuming that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through the viscous sublayer at the bottom of the current. The boundary condition at the moving front of the current relates the velocity and the pressure head at that point. The resulting equations are solved numerically, which reveals that two types of shock can occur in the current. In the late stages of all particle-driven gravity currents, an internal bore develops that separates a particle-free jet-like flow in the rear from a dense gravity-current flow near the front. The second type of bore occurs if the initial height of the current is comparable to the depth of the ambient fluid. This bore develops during the early lock-exchange flow between the two fluids and strongly changes the structure of the current and its transport of particles from those of a current in very deep surroundings. To test the theory, several experiments were performed to measure the length of particle-driven gravity currents as a function of time and their deposition patterns for a variety of particle sizes and initial masses of sediment. The comparison between the theoretical predictions, which have no adjustable parameters, and the experimental results are very good.

Gravity currents impinging on bottom-mounted square cylinders: flow fields and associated forces

2009 ◽  
Vol 631 ◽  
pp. 65-102 ◽  
Author(s):  
E. GONZALEZ-JUEZ ◽  
E. MEIBURG ◽  
G. CONSTANTINESCU
Keyword(s):  
Drag Coefficient ◽  
Flow Structure ◽  
Gravity Current ◽  
Three Dimensional ◽  
Gravity Currents ◽  
Constant Density ◽  
Two Dimensional ◽  
Drag And Lift ◽  
The Impact ◽  
Three Dimensional Simulations

The unsteady drag and lift generated by the interaction of a gravity current with a bottom-mounted square cylinder are investigated by means of high-resolution Navier–Stokes simulations. Two-dimensional simulations for Reynolds numbers (Re) O(1000) and three-dimensional simulations for Re = O(10000) demonstrate that the drag coefficient increases exponentially towards a maximum as the current meets the cylinder, then undergoes strong fluctuations and eventually approaches a quasi-steady value. The simulation results show that the maximum drag coefficient can reach a value of 3, with the quasi-steady value being O(1), which should aid in selecting a design drag coefficient for submarine structures under the potential impact of gravity currents. The transient drag and lift fluctuations after impact are associated with the Kelvin–Helmholtz vortices in the mixing layer between the gravity current and the ambient fluid. As these vortices pass over the cylinder, they cause the convection of separated flow regions along the bottom wall towards the cylinder. In two-dimensional simulations at Re = O(10000), these flow structures are seen to be unrealistically coherent and to persist throughout the interaction, thus resulting in a noticeable overprediction of the drag and lift fluctuations. On the other hand, the impact of the current on the cylinder is seen to be very well captured by two-dimensional simulations at all Re values. Three-dimensional simulations lead to excellent agreement with available experimental data throughout the flow/structure interaction. They show that the spanwise variation of the drag is determined by the gravity current's lobe-and-cleft structure at impact and by an unsteady cellular flow structure similar to that found in constant-density flows at later times. A comparison between gravity-current flows and corresponding constant-density flows shows the hydrostatic drag component to be important for gravity currents.

scholarly journals Gravity current propagation up a valley

2014 ◽  
Vol 762 ◽  
pp. 417-434 ◽  
Author(s):  
Catherine S. Jones ◽  
Claudia Cenedese ◽  
Eric P. Chassignet ◽  
P. F. Linden ◽  
Bruce R. Sutherland
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Rectangular Channel ◽  
Gravity Current ◽  
Gravity Currents ◽  
Momentum Transport ◽  
Front Speed

AbstractThe advance of the front of a dense gravity current propagating in a rectangular channel and V-shaped valley both horizontally and up a shallow slope is examined through theory, full-depth lock–release laboratory experiments and hydrostatic numerical simulations. Consistent with theory, experiments and simulations show that the front speed is relatively faster in the valley than in the channel. The front speed measured shortly after release from the lock is 5–22 % smaller than theory, with greater discrepancy found in upsloping V-shaped valleys. By contrast, the simulated speed is approximately 6 % larger than theory, showing no dependence on slope for rise angles up to ${\it\theta}=8^{\circ }$. Unlike gravity currents in a channel, the current head is observed in experiments to be more turbulent when propagating in a V-shaped valley. The turbulence is presumably enhanced due to the lateral flows down the sloping sides of the valley. As a consequence, lateral momentum transport contributes to the observed lower initial speeds. A Wentzel–Kramers–Brillouin like theory predicting the deceleration of the current as it runs upslope agrees remarkably well with simulations and with most experiments, within errors.

On the origin of the drag force on dimpled spheres

2019 ◽  
Vol 879 ◽  
pp. 147-167 ◽  
Author(s):  
Nikolaos Beratlis ◽  
Elias Balaras ◽  
Kyle Squires
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Drag Coefficient ◽  
Drag Force ◽  
Direct Numerical Simulations ◽  
Critical Regime ◽  
Drag Coefficients ◽  
Wall Flow ◽  
Smooth Sphere ◽  
Near Wall

It is well established that dimples accelerate the drag crisis on a sphere. The result of the early drag crisis is a reduction of the drag coefficient by more than a factor of two when compared to a smooth sphere at the same Reynolds number. However, when the drag coefficients for smooth and dimpled spheres in the post-critical regime are compared, the latter is higher by a factor of two to three. To understand the origin of this behaviour, we conducted direct numerical simulations of the flow around a dimpled sphere, which is similar to commercially available golf balls, in the post-critical regime. By comparing the results to those for a smooth sphere, it is found that dimples, although effective in accelerating the drag crisis, impose a local drag penalty, which contributes significantly to the overall drag force. This finding challenges the broadly accepted view that dimples only indirectly affect the drag force on a sphere by energizing the near-wall flow and delaying global separation.

scholarly journals On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

2000 ◽  
Vol 408 ◽  
pp. 149-177 ◽  
Author(s):  
PAUL F. CHOBOTER ◽  
GORDON E. SWATERS
Keyword(s):  
Numerical Simulations ◽  
Linear Stability ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Laboratory Data ◽  
Gravity Current ◽  
Gravity Currents ◽  
Finite Amplitude ◽  
Rotating System ◽  
A Current

The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections of that layer are not small with respect to its scale height. The upper-layer dynamics are quasi-geostrophic, with the Eulerian velocity field principally driven by baroclinic stretching and a background topographic vorticity gradient.Necessary conditions for instability, a semicircle-like theorem for unstable modes, bounds on the growth rate and phase velocity, and a sufficient condition for the existence of a high-wavenumber cutoff are presented. The linear stability equations are solved exactly for the case where the gravity current initially corresponds to an annulus flow with parabolic height profile with two incroppings, i.e. a coupled front. The dispersion relation for such a current is solved numerically, and the characteristics of the unstable modes are described. A distinguishing feature of the spatial structure of the perturbations is that the perturbations to the downslope incropping are preferentially amplified compared to the upslope incropping. Predictions of the model are compared with recent laboratory data, and good agreement is seen in the parameter regime for which the model is valid. Direct numerical simulations of the full model are employed to investigate the nonlinear regime. In the initial stage, the numerical simulations agree closely with the linear stability characteristics. As the instability develops into the finite-amplitude regime, the perturbations to the downslope incropping continue to preferentially amplify and eventually evolve into downslope propagating plumes. These finally reach the deepest part of the topography, at which point no more potential energy can be released.

On the propagation of gravity currents over and through a submerged array of circular cylinders

2017 ◽  
Vol 831 ◽  
pp. 394-417 ◽  
Author(s):  
Jian Zhou ◽  
Claudia Cenedese ◽  
Tim Williams ◽  
Megan Ball ◽  
Subhas K. Venayagamoorthy ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Circular Cylinders ◽  
Dimensional Parameter ◽  
Flow Interruption ◽  
Line Array ◽  
Through Flow ◽  
Array Density

The propagation of full-depth lock-exchange bottom gravity currents past a submerged array of circular cylinders is investigated using laboratory experiments and large eddy simulations. Firstly, to investigate the front velocity of gravity currents across the whole range of array density $\unicode[STIX]{x1D719}$ (i.e. the volume fraction of solids), the array is densified from a flat bed ($\unicode[STIX]{x1D719}=0$) towards a solid slab ($\unicode[STIX]{x1D719}=1$) under a particular submergence ratio $H/h$, where $H$ is the flow depth and $h$ is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing $\unicode[STIX]{x1D719}$. Next, a new geometrical framework consisting of a streamwise array density $\unicode[STIX]{x1D707}_{x}=d/s_{x}$ and a spanwise array density $\unicode[STIX]{x1D707}_{y}=d/s_{y}$ is proposed to account for organized but non-equidistant arrays ($\unicode[STIX]{x1D707}_{x}\neq \unicode[STIX]{x1D707}_{y}$), where $s_{x}$ and $s_{y}$ are the streamwise and spanwise cylinder spacings, respectively, and $d$ is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current–array interaction compared with the array density given by $\unicode[STIX]{x1D719}=(\unicode[STIX]{x03C0}/4)\unicode[STIX]{x1D707}_{x}\unicode[STIX]{x1D707}_{y}$. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes ($\unicode[STIX]{x1D707}_{x}$: small for in-line array and arbitrary for staggered array; $\unicode[STIX]{x1D707}_{y}$: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion ($\unicode[STIX]{x1D707}_{x}$: small; $\unicode[STIX]{x1D707}_{y}$: large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: small). The most remarkable difference between in-line and staggered arrays is the non-existence of skimming-flow in the latter due to the flow interruption by the offset rows. Our analysis reveals that as $\unicode[STIX]{x1D719}$ increases, the change of flow regime from through-flow towards over- or skimming-flow is responsible for increasing the gravity current front velocity.

scholarly journals A Numerical and Experimental Study of the Aerodynamics and Stability of a Horizontal Parachute

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mazyar Dawoodian ◽  
Abdolrahman Dadvand ◽  
Amir Hassanzadeh
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Numerical Simulations ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Flow Conditions ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
The Stability ◽  
Good Agreement

The flow past a parachute with and without a vent hole at the top is studied both experimentally and numerically. The effects of Reynolds number and vent ratio on the flow behaviour as well as on the drag coefficient are examined. The experiments were carried out under free-flow conditions. In the numerical simulations, the flow was considered as unsteady and turbulent and was modelled using the standard - turbulence model. The experimental results reveal good agreement with the numerical ones. In both the experiments and numerical simulations, the Reynolds number was varied from 85539 to 357250 and the vent ratio was increased from zero to 20%. The results show that the drag coefficient decreases by increasing the Reynolds number for all the cases tested. In addition, it was found that at low and high Reynolds numbers, the parachutes, respectively, with 4% vent ratio and without vent are deemed more efficient. One important result of the present work is related to the effect of vent ratio on the stability of the parachute.

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