Direct Numerical Simulations of Planar and Cylindrical Density Currents

2005 ◽  
Vol 73 (6) ◽  
pp. 923-930 ◽  
Author(s):  
Mariano I. Cantero ◽  
S. Balachandar ◽  
Marcelo H. García ◽  
James P. Ferry
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
The Body ◽  
Density Current ◽  
Density Currents ◽  
Mean Flow ◽  
Viscous Effects ◽  
Spreading Velocity ◽  
Slip Boundary

The collapse of a heavy fluid column in a lighter environment is studied by direct numerical simulation of the Navier-Stokes equations using the Boussinesq approximation for small density difference. Such phenomenon occurs in many engineering and environmental problems resulting in a density current spreading over a no-slip boundary. In this work, density currents corresponding to two Grashof (Gr) numbers are investigated (105 and 1.5×106) for two very different geometrical configurations, namely, planar and cylindrical, with the goal of identifying differences and similarities in the flow structure and dynamics. The numerical model is capable of reproducing most of the two- and three-dimensional flow structures previously observed in the laboratory and in the field. Soon after the release of the heavier fluid into the quiescent environment, a density current forms exhibiting a well-defined head with a hanging nose followed by a shallower body and tail. In the case of large Gr, the flow evolves in a three-dimensional fashion featuring a pattern of lobes and clefts in the intruding front and substantial three-dimensionality in the trailing body. For the case of the lower Gr, the flow is completely two dimensional. The dynamics of the current is visualized and explained in terms of the mean flow for different phases of spreading. The initial phase, known as slumping phase, is characterized by a nearly constant spreading velocity and strong vortex shedding from the front of the current. Our numerical results show that this spreading velocity is influenced by Gr as well as the geometrical configuration. The slumping phase is followed by a decelerating phase in which the vortices move into the body of the current, pair, stretch and decay as viscous effects become important. The simulated dynamics of the flow during this phase is in very good agreement with previously reported experiments.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

scholarly journals Effects of morphology in controlling propagation of density currents in a reservoir using uncalibrated three-dimensional hydrodynamic modeling

2020 ◽  
Author(s):  
Behnam Zamani ◽  
Manfred Koch ◽  
Ben R. Hodges
Keyword(s):  
Hydrodynamic Model ◽  
Large Scale ◽  
Three Dimensional ◽  
Density Current ◽  
Density Currents ◽  
Large Reservoir ◽  
Bottom Water Temperature ◽  
The Difference ◽  
Basin Morphology ◽  
Southwest Iran

In this study, effects of basin morphology are shown to affect density current hydrodynamics of a large reservoir using a three-dimensional (3D) hydrodynamic model that is validated (but not calibrated) with in situ observational data. The AEM3D hydrodynamic model was applied for 5-month simulations during winter and spring flooding for the Maroon reservoir in southwest Iran, where available observations indicated that large-scale density currents had previously occurred. The model results were validated with near-bottom water temperature measurements that were previously collected at five locations in the reservoir. The Maroon reservoir consists of upper and lower basins that are connected by a deep and narrow canyon. Analyses of simulations show that the canyon strongly affects density current propagation and the resulting differing limnological characteristics of the two basins. The evolution of the Wedderburn Number, Lake Number, and Schmidt stability number are shown to be different in the two basins, and the difference is attributable to the morphological separation by the canyon. Investigation of the background potential energy (BPE) changes along the length of the canyon indicated that a density front passes through the upper section of the canyon but is smoothed into simple filling of the lower basin. The separable dynamics of the basins has implications for the complexity of models needed for representing both water quality and sedimentation.

Studies on natural convection-induced flow and thermal behaviour inside electronic equipment cabinet model

2003 ◽  
Vol 217 (3) ◽  
pp. 323-328 ◽  
Author(s):  
M Ishizuka ◽  
Y Kitamura
Keyword(s):  
Natural Convection ◽  
Thermal Behaviour ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Electronic Equipment ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Surface Boundary Layer ◽  
Induced Flow

In the present work, an important basic flow phenomenon, natural convection-induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the energy equation are solved based on the finite difference method. A generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behaviour inside an electronic equipment cabinet model, which is very difficult, if not impossible, to gather by experiment.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

Three-Dimensional Structures in Experimental Density Currents

2007 ◽  
Author(s):  
B. Firoozabadi ◽  
H. Afshin ◽  
E. Safaaee
Keyword(s):  
Salt Solution ◽  
Chemical Elements ◽  
Three Dimensional ◽  
Lateral Spreading ◽  
Current Data ◽  
Density Current ◽  
Density Currents ◽  
Ambient Water ◽  
Data Set ◽  
Bed Slope

Density currents are continuous currents which move down-slope due to the fact that their density is greater than that of ambient water. The density difference is caused by temperature differences, chemical elements, dissolved materials, or suspended sediment. Many researchers have studied the density current structures, their complexities and uncertainties. However, there is not a detailed 3-D turbulent density current data set perfectly. In this work, the structure of 3-dimensional salt solution density currents is investigated. A laboratory channel was used to study the flow resulting from the release of salt solution into freshwater over an inclined bed. The experiments were conducted with different bottom slopes, inlet concentrations and flow rates. In these tests, the instantaneous velocities are measured by an ADV apparatus (Acoustic Doppler Velocimeter). Results show that by increasing the bed-slope and inlet concentrations, the height of the current decreases. As the density current moves downward the channel or by increasing the discharge, the height of the density current increases. Finally, the effects of different variables such as the bed slope, concentration and flow rate of entering fluid on the velocity profile in different distances from the entrance is studied. The entrainment coefficient, lateral spreading and drag coefficient of the bed and shear layer between salt solution and ambient water is discussed.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

scholarly journals Three-dimensional instabilities in compressible flow over open cavities

2008 ◽  
Vol 599 ◽  
pp. 309-339 ◽  
Author(s):  
GUILLAUME A. BRÈS ◽  
TIM COLONIUS
Keyword(s):  
Compressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Vortical Flow ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Mean Flow ◽  
Aspect Ratios ◽  
Open Cavities

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

On the Weis-Fogh mechanism of lift generation

1973 ◽  
Vol 60 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Body ◽  
Navier Stokes ◽  
Encarsia Formosa ◽  
Concentrated Force ◽  
Stagnation Points ◽  
Wing Tips

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.

Experimental Investigation of Turbulence Specifications of 3-D Density Currents

2007 ◽  
Author(s):  
B. Firoozabadi ◽  
H. Afshin ◽  
A. Baghaer Poor
Keyword(s):  
Experimental Investigation ◽  
Turbulence Intensity ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Turbulence Energy ◽  
Density Current ◽  
Turbulence Characteristic ◽  
Acoustic Doppler Velocimeter ◽  
Density Currents ◽  
Flow Rates

The present study investigates the turbulence characteristic of density current experimentally. The 3D Acoustic-Doppler Velocimeter (ADV) was used to measure the instantaneous velocity and characteristics of the turbulent flow. The courses of experiment were conducted in a three-dimensional channel for different discharge flows, concentrations, and bed slopes. Results are expressed at various distances from the inlet, for all flow rates, slopes and concentrations as the distribution of turbulence energy, Reynolds stress and the turbulent intensity. It was concluded that the maximum turbulence intensity happens in both the interface and near the wall. Also it was observed that turbulence intensity reaches its minimum where maximum velocity occurs.

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