Turbulent fountains in one- and two-layer crossflows

2011 ◽  
Vol 689 ◽  
pp. 254-278 ◽  
Author(s):  
Joseph K. Ansong ◽  
Alexandra Anderson-Frey ◽  
Bruce R. Sutherland
Keyword(s):  
Relative Density ◽  
Laboratory Experiments ◽  
Gravity Current ◽  
Density Difference ◽  
Ambient Fluid ◽  
Initial Momentum ◽  
The One

AbstractThe Lagrangian theory developed for fountains in a stationary fluid is extended to predict the path and breadth of a fountain in a one- and two-layer fluid with a moderate crossflow. The predictions compare well with the results of laboratory experiments of fountains in a one-layer fluid. The empirical spreading parameter determined from the one-layer experiments is used in the theory for fountains in a two-layer crossflow. Though qualitatively correct, the theory underpredicts the height and radius of the fountains. Similar to the behaviour of fountains in two-layer stationary ambients, the fountain in a two-layer crossflow is observed to exhibit three regimes of flow: it may penetrate the interface, eventually returning to the level of the source where it spreads as a propagating gravity current; upon descent, it may be trapped at the interface where it spreads as a propagating intrusion; it may do both, partially descending to the source and partially being trapped at the interface. These regimes are classified theoretically and empirically. The theoretical classification compared the buoyancy excess of the descending flow to the density difference between the two layers. The regimes are also classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid.

Fountains impinging on a density interface

2008 ◽  
Vol 595 ◽  
pp. 115-139 ◽  
Author(s):  
JOSEPH K. ANSONG ◽  
PATRICK J. KYBA ◽  
BRUCE R. SUTHERLAND
Keyword(s):  
Experimental Study ◽  
Relative Density ◽  
Constant Velocity ◽  
Gravity Current ◽  
Return Flow ◽  
Experimental Measurements ◽  
Ambient Fluid ◽  
Initial Momentum ◽  
Front Position ◽  
Homogeneous Environment

We present an experimental study of an axisymmetric turbulent fountain in a two-layer stratified environment. Interacting with the interface, the fountain is observed to exhibit three regimes of flow. It may penetrate the interface, but nonetheless return to the source where it spreads as a radially propagating gravity current; the return flow may be trapped at the interface where it spreads as a radially propagating intrusion or it may do both. These regimes have been classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid. The maximum vertical distance travelled by the fountain in a two-layer fluid has been theoretically determined by extending the theory developed for fountains in a homogeneous environment. The theory compares favourably with experimental measurements. We have also developed a theory to analyse the initial speeds of the resulting radial currents. The spreading currents exhibited two different flow regimes: a constant-velocity regime and an inertia-buoyancy regime in which the front position, R, scales with time, t, as R ∼ t3/4. These regimes were classified using a critical Froude number which characterized the competing effects of momentum and buoyancy in the currents.

scholarly journals Effect of Sand Relative Density inside the Geotextile Pillow on the Bearing Capacity of Pad Foundation

2015 ◽  
Vol 773-774 ◽  
pp. 1428-1432 ◽  
Author(s):  
Mia Wimala ◽  
Herianto Wibowo
Keyword(s):  
Bearing Capacity ◽  
Relative Density ◽  
Factor Of Safety ◽  
Laboratory Experiments ◽  
Ultimate Bearing Capacity ◽  
Performance Criteria ◽  
Sand Surface ◽  
Foundation Model ◽  
The One ◽  
Underlying Soil

A foundation is used to support a building or structure and transmits loads directly to the underlying soil or rock. It must provide an adequate factor of safety against failure of the supporting strata, as well as failure of any excessive settlement which can interfere the function of the structure. Ultimate bearing capacity of a specific foundation is one parameter commonly used to describe the performance criteria of both the soil and the structure above. It can be improved by the inclusion of reinforcements in the ground such as geotextiles. In practice, geotextiles are normally placed directly on the soil in the form of sheet and then covered with aggregates. This research was conducted specifically to investigate the effect of different sand relative densities inside the geotextile pillow, an alternative of geotextile installations in practices, on the bearing capacity of pad foundation by laboratory experiments. A-10 cm x 10 cm pad foundation model was developed in a 1 m3 box filled with sand to actualize this experiment. Geotextile sheet was formed into a pillow, filled with sand with different relative densities and placed at a predetermined depth from the sand surface. As a result, the bearing capacity of the pad foundation model was proved to increase by 50% using a sheet of geotextile compared to the one without any geotextile. Moreover, to the same condition, the use of a geotextile pillow with different sand relative densities inside the pillow, i.e. 30%, 50% and 70% remarkably improved the bearing capacity of the pad foundation model from 150% to 525%. Among the experiment results using a geotextile pillow, the 66.67% addition of sand relative density increased the bearing capacity of a pad foundation model by 100% and 150% with 133.33% of sand relative density. It showed that the increase of the sand relative density inside the geotextile pillow was directly proportional to the increase of the bearing capacity of the pad foundation model.

Simulation of a lock-release gravity current based on a non-hydrostatic model

2019 ◽  
Vol 19 (6) ◽  
pp. 1802-1808
Author(s):  
Xueqing Zhang ◽  
Jinzhen Yu ◽  
Yilei Feng
Keyword(s):  
Laboratory Experiments ◽  
Gravity Current ◽  
Wave Model ◽  
Ambient Fluid ◽  
Forward Movement ◽  
Circular Flow ◽  
Front Position ◽  
Hydrostatic Model ◽  
The Difference ◽  
Better Than

Abstract Gravity currents are important in many fields, including the estuarine sciences, meteorology and hydraulic engineering. The NHWAVE (non-hydrostatic wave) model was applied to simulate the detailed interface structure between a lock-release gravity current and the ambient fluid. The simulated structures, including the front height, front position and velocity of the current, are consistent with the results of laboratory experiments. However, the internal structure of the current is different from that revealed by previous research. The Kelvin–Helmholtz phenomenon in the interface and the interface vortices were successfully captured by the NHWAVE model. The difference in velocity between the front and rear vortices leads to entrainment, further causing changes in the shapes and amount of vortices. Flow field results obtained by the NHWAVE model reveal the existence of a significant circular flow, as well as some small eddies within it. The significant circular flow supports the forward movement of the current, whereas the small eddies reflect interface vortices. In contrast, hydrostatic simulation with the same model settings fails to capture the vortices. This research shows that the NHWAVE model performs better than a hydrostatic model when simulating the Kelvin–Helmholtz instability phenomenon and vortex entrainment in a lock-release gravity current.

Mixing in Symmetric Holmboe Waves

2007 ◽  
Vol 37 (6) ◽  
pp. 1566-1583 ◽  
Author(s):  
W. D. Smyth ◽  
J. R. Carpenter ◽  
G. A. Lawrence
Keyword(s):  
Shear Layer ◽  
Effective Viscosity ◽  
Laboratory Experiments ◽  
Density Difference ◽  
Transition To Turbulence ◽  
Mixing Efficiency ◽  
Effective Diffusivities ◽  
Key Parameter

Abstract Direct simulations are used to study turbulence and mixing in Holmboe waves. Previous results showing that mixing in Holmboe waves is comparable to that found in the better-known Kelvin–Helmholtz (KH) billows are extended to cover a range of stratification levels. Mixing efficiency is discussed in detail, as are effective diffusivities of buoyancy and momentum. Entrainment rates are compared with results from laboratory experiments. The results suggest that the ratio of the thicknesses of the shear layer and the stratified layer is a key parameter controlling mixing. With that ratio held constant, KH billows mix more rapidly than do Holmboe waves. Among Holmboe waves, mixing increases with increasing density difference, despite the fact that the transition to turbulence is delayed or prevented entirely by the stratification. Results are summarized in parameterizations of the effective viscosity and diffusivity of Holmboe waves.

On symmetric intrusions in a linearly stratified ambient: a revisit of Benjamin's steady-state propagation results

2021 ◽  
Vol 929 ◽  
Author(s):  
M. Ungarish
Keyword(s):  
Steady State ◽  
Control Volume ◽  
Gravity Current ◽  
Head Loss ◽  
Stability Criteria ◽  
Ambient Fluid ◽  
Height Ratio ◽  
Stagnation Line ◽  
Volume Analysis ◽  
State Propagation

Previous studies have extended Benjamin's theory for an inertial steady-state gravity current of density $\rho _{c}$ in a homogeneous ambient fluid of density $\rho _{o} < \rho _{c}$ to the counterpart propagation in a linearly stratified (Boussinesq) ambient (density decreases from $\rho _b$ to $\rho _{o}$ ). The extension is typified by the parameter $S = (\rho _{b}-\rho _{o})/(\rho _{c}-\rho _{o}) \in (0,1]$ , uses Long's solution for the flow over a topography to model the flow of the ambient over the gravity current, and reduces well to the classical theory for small and moderate values of $S$ . However, for $S=1$ , i.e. $\rho _b = \rho _c$ , which corresponds to a symmetric intrusion, various idiosyncrasies appear. Here attention is focused on this case. The control-volume analysis (balance of volume, mass, momentum and vorticity) produces a fairly compact analytical formulation, pending a closure for the head loss, and subject to stability criteria (no inverse stratification downstream). However, we show that plausible closures that work well for the non-stratified current (like zero head loss on the stagnation line, or zero vorticity diffusion) do not produce satisfactory results for the intrusion (except for some small ranges of the height ratio of current to channel, $a = h/H$ ). The reasons and insights are discussed. Accurate data needed for comparison with the theoretical model are scarce, and a message of this paper is that dedicated experiments and simulations are needed for the clarification and improvement of the theory.

A Laboratory Study of the Velocity Structure in an Intrusive Gravity Current

2000 ◽  
Author(s):  
Ryan J. Lowe
Keyword(s):  
Particle Tracking ◽  
Laboratory Experiments ◽  
Velocity Structure ◽  
Gravity Current ◽  
Current Theory ◽  
Head Region ◽  
Front Speed ◽  
Energy Conserving ◽  
The Stability ◽  
Lock Gate

Abstract Laboratory experiments were performed in which an intrusive gravity current was observed using shadowgraph and particle tracking methods. The intrusion was generated in a two-layer fluid with a sharp interface by mixing the fluid behind a vertical lock-gate and then suddenly withdrawing the gate from the tank. The purpose of the experiments is to determine the structure of the velocity field inside the intrusion as well as the stability characteristics of the interface. Soon after the removal of the lock-gate the speed of the front of the intrusive gravity current reached a constant speed. The observed structure of the flow inside the intrusion shows a “head region” where the flow is nearly uniform, followed by a region of intense mixing and high velocities and finally followed by another region of fairly uniform velocity with a speed slightly faster than the front speed. The results show that the maximum centerline velocity is about 50% greater than the front speed and corresponds to the position in the intrusion where the strongest Kelvin- Helmholtz billows form. Closer to the front, the relative flow within the head is weak, which explains why Benjamin’s (1968) energy-conserving gravity current theory accurately predicts the behavior of dissipative gravity currents.

Numerical Study of Functionally Graded Materials

2007 ◽  
Vol 29-30 ◽  
pp. 311-314
Author(s):  
K.M. Naryanappa ◽  
M. Krishna ◽  
S.C. Sharma ◽  
H.N. Narasimha Murthy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Relative Density ◽  
Rotational Speed ◽  
Solidification Front ◽  
Density Difference ◽  
Solidification Time ◽  
Pouring Temperature ◽  
Rich Region

One-dimensional comprehensive mathematical model coupling particle movement and thermal conduction in the casting mould system is developed. A formula for pressure in liquid metal during the centrifuge process is derived. The model takes into consideration the propagation of solidification front and movement of particles due to centrifugal acceleration which takes place either in the same or in opposite direction to that of the solidification front depending on the relative density difference between the particles and melts. In the force balance expression, repulsive force term is incorporated for the particles that are at the vicinity of the solid/liquid interface to calculate the particle segregation pattern in the casting region The effects of various process parameters such as, rotational speed of the mold, size of the reinforcing material, relative density difference between the particle and melt, initial pouring temperature of the liquid melt, mold pre-heating temperature, heat transfer coefficient between the casting/mold interface are studied. It is noted that for a given set of operating conditions, the thickness of the particle rich region in the composite decreases with increase in rotational speed, particle size, relative density difference between the particle and melt, initial pouring temperature and initial mold temperature. With decrease in the heat transfer coefficient between the casting/mold interface, the solidification time increases which, in turn, results in more intense segregation of solid particulates. Again, with increase in the initial volume fraction of the solid particulates, both the solidification time as well as the final thickness of the particulate rich region increase.

scholarly journals Optimal perturbation growth in axisymmetric intrusions

2016 ◽  
Vol 811 ◽  
Author(s):  
Bruce R. Sutherland ◽  
C. P. Caulfield
Keyword(s):  
Gravity Current ◽  
Optimal Growth ◽  
Base Flow ◽  
Optimal Perturbation ◽  
Target Time ◽  
Experimental Parameters ◽  
Radial Spokes ◽  
Perturbation Energy ◽  
The One ◽  
Perturbation Growth

The cylindrical lock-release laboratory experiments of Sutherland & Nault (J. Fluid Mech., vol. 586, 2007, pp. 109–118) showed that a radially advancing symmetric intrusive gravity current spreads not as an expanding annulus (as is the case for bottom-propagating gravity currents), but rather predominantly along azimuthally periodic radial ‘spokes’. Here, we investigate whether the spokes are associated with azimuthal perturbations that undergo ‘optimal’ growth. We use a nonlinear axisymmetric numerical simulation initialised with the experimental parameters to compute the time-evolving axisymmetric base state of the collapsing lock fluid. Using fields from this rapidly evolving base state together with the linearised perturbation equations and their adjoint, the ‘direct–adjoint looping’ method is employed to identify, as a function of the azimuthal wavenumber $m$, the vertical–radial structure of the set of initial perturbations that exhibit the largest total perturbation energy gain over a target time $T$. Of this set of perturbations, the one that extracts energy fastest, and so is expected to be observed to emerge first from the base flow, has azimuthal wavenumber comparable to the number of spokes observed in the experiment.

scholarly journals Gas Mixing and Final Mixture Composition Control in Simple Geometry Micro-mixers via DSMC Analysis

Micromachines ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 178 ◽  
Author(s):  
Stavros Meskos ◽  
Stefan Stefanov ◽  
Dimitris Valougeorgis
Keyword(s):  
Relative Density ◽  
Molecular Mass ◽  
Hard Sphere ◽  
Density Difference ◽  
Mixture Composition ◽  
Minor Effect ◽  
Mixing Length ◽  
Mass Ratio ◽  
Gas Mixing ◽  
A Minor

The mixing process of two pressure driven steady-state rarefied gas streams flowing between two parallel plates was investigated via DSMC (Direct Simulation Monte Carlo) for different combinations of gases. The distance from the inlet, where the associated relative density difference of each species is minimized and the associated mixture homogeneity is optimized, is the so-called mixing length. In general, gas mixing progressed very rapidly. The type of gas surface interaction was clearly the most important parameter affecting gas mixing. As the reflection became more specular, the mixing length significantly increased. The mixing lengths of the HS (hard sphere) and VHS (variable hard sphere) collision models were higher than those of the VSS (variable soft sphere) model, while the corresponding relative density differences were negligible. In addition, the molecular mass ratio of the two components had a minor effect on the mixing length and a more important effect on the relative density difference. The mixture became less homogenous as the molecular mass ratio reduced. Finally, varying the channel length and/or the wall temperature had a minor effect. Furthermore, it was proposed to control the output mixture composition by adding in the mixing zone, the so-called splitter, separating the downstream flow into two outlet mainstreams. Based on intensive simulation data with the splitter, simple approximate expressions were derived, capable of providing, once the desired outlet mixture composition was specified, the correct position of the splitter, without performing time consuming simulations. The mixing analysis performed and the proposed approach for controlling gas mixing may support corresponding experimental work, as well as the design of gas micro-mixers.

scholarly journals On the dynamics of starting plumes

2017 ◽  
Vol 833 ◽  
Author(s):  
N. Bhamidipati ◽  
Andrew W. Woods
Keyword(s):  
Laboratory Experiments ◽  
Added Mass ◽  
Rate Of Change ◽  
Small Scale ◽  
Maximum Height ◽  
Ambient Fluid ◽  
A Value ◽  
Proposed Model ◽  
The Difference ◽  
Reasonable Description

We explore the dynamics of starting plumes by analysis of a series of new small-scale laboratory experiments combined with a theoretical model for mass, momentum, and buoyancy conservation. We find that the head of the plume ascends with a speed which is approximately 0.6 times the characteristic speed of the fluid in the following steady plume, in accord with Turner (J. Fluid Mech., vol. 13 (03), 1962, pp. 356–368), and so the fluid released from the source eventually catches the head of the flow. On reaching the top of the plume it recirculates and mixes in the plume head. We estimate that approximately $0.61\pm 0.04$ of the total buoyancy released from the source accumulates in the plume head, with the remainder in the following steady plume. Using measurements of the volume of the head, we estimate that a fraction $0.16\pm 0.08$ of the volume of the head is entrained directly from the ambient, with the remainder of the fluid in the head being supplied by the following steady plume. These results imply that the buoyancy force exerted on the plume head plus the momentum flux supplied by the following plume exceeds the rate of change of momentum of the plume head even including the added mass of the plume head. We propose that the difference is associated with a drag force resulting from the displacement of ambient fluid around the plume head. Using our experimental data, we estimate that the drag coefficient $C_{d}$ has a value $4.2\pm 1.4$, with the range in values associated with the uncertainty in our estimate of entrainment of fluid directly into the plume head. As a test, the proposed model is shown to provide a reasonable description of a starting plume rising through a stratified environment in the region below the maximum height of rise of the associated steady plume, although, above this point, the shape of the plume head changes and the model breaks down.

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