Inertial gravity currents produced by fluid drainage from an edge

2017 ◽  
Vol 827 ◽  
pp. 640-663 ◽  
Author(s):  
Mostafa Momen ◽  
Zhong Zheng ◽  
Elie Bou-Zeid ◽  
Howard A. Stone
Keyword(s):  
Differential Equations ◽  
Gravity Current ◽  
Experimental Studies ◽  
Dynamical Behaviour ◽  
Rectangular Domain ◽  
Dimensionless Time ◽  
Horizontal Length ◽  
High Reynolds ◽  
End Wall ◽  
Similar Phase

We present theoretical, numerical and experimental studies of the release of a finite volume of fluid instantaneously from an edge of a rectangular domain for high Reynolds number flows. For the cases we considered, the results indicate that approximately half of the initial volume exits during an early adjustment period. Then, the inertial gravity current reaches a self-similar phase during which approximately 40 % of its volume drains and its height decreases as $\unicode[STIX]{x1D70F}^{-2}$, where $\unicode[STIX]{x1D70F}$ is a dimensionless time that is derived with the typical gravity wave speed and the horizontal length of the domain. Based on scaling arguments, we reduce the shallow-water partial differential equations into two nonlinear ordinary differential equations (representing the continuity and momentum equations), which are solved analytically by imposing a zero velocity boundary condition at the closed end wall and a critical Froude number condition at the open edge. The solutions are in good agreement with the performed experiments and direct numerical simulations for various geometries, densities and viscosities. This study provides new insights into the dynamical behaviour of a fluid draining from an edge in the inertial regime. The solutions may be useful for environmental, geophysical and engineering applications such as open channel flows, ventilations and dam-break problems.

The role of anomalous modes in Taylor─Couette flow

1992 ◽  
Vol 439 (1906) ◽  
pp. 341-357 ◽  
Keyword(s):  
Experimental Studies ◽  
Reynolds Numbers ◽  
Dynamical Behaviour ◽  
Taylor Vortex ◽  
Taylor Vortex Flow ◽  
Wide Range ◽  
Taylor Couette ◽  
High Reynolds ◽  
Stability Limits ◽  
The Mathematical Model

One of the classic examples of a fluid mechanical bifurcation is the appearance of Taylor vortex flow in a viscous fluid contained between concentric rotating cylinders. A natural consequence of the mathematical model due to D. G. Schaeffer, which has been most successful in describing this phenomenon in a finite system, is the presence of ‘anomalous modes’ in the steady solution set. These are cellular flows that exist in contradiction to the commonly held belief that the radial flow close to the ends is necessarily directed towards the inner cylinder because of the presence of an Ekman boundary layer. To date anomalous modes have only been studied in a restricted parameter range, but here we report the results of numerical and experimental studies that cover a wide range of parameter space. It is shown that the lower stability limits for anomalous modes are removed to high Reynolds numbers when the gap between the cylinders is reduced. This perhaps explains why this class of flow remained undiscovered in over fifty years of study of the Taylor─Couette problem until the work of T. B. Benjamin. We also consider the implications of these results for the organization of dynamical behaviour in the Taylor─Couette system.

Effect of Boundary Layer Suction on Aerodynamic Performance of High-Turning Compressor Cascade

2013 ◽  
Author(s):  
Longxin Zhang ◽  
Shaowen Chen ◽  
Hao Xu ◽  
Jun Ding ◽  
Songtao Wang
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Studies ◽  
Aerodynamic Performance ◽  
Parameter Distribution ◽  
Compressor Cascade ◽  
Boundary Layer Suction ◽  
End Wall ◽  
Low Speed Wind Tunnel ◽  
Good Agreement

Compared with suction slots, suction holes are (1) flexible in distribution; (2) alterable in size; (3) easy to fabricate and (4) high in strength. In this paper, the numerical and experimental studies for a high turning compressor cascade with suction air removed by using suction holes in the end-wall at a low Mach numbers are carried out. The main objective of the investigation is to study the influence of different suction distributions on the aerodynamic performance of the compressor cascade and to find a better compound suction scheme. A numerical model was first made and validated by comparing with the experimental results. The computed flow visualization and exit parameter distribution showed a good agreement with experimental data. Second, the model was then used to simulate the influence of different suction distributions on the aerodynamic performance of the compressor cascade. A better compound suction scheme was obtained by summarizing numerical results and tested in a low speed wind tunnel. As a result, the compound suction scheme can be used to significantly improve the performance of the compressor cascade because the corner separation gets further suppressed.

scholarly journals Near-Wake Observations behind Azimuthally Perforated Disks With Varying Hole Layout and Porosity in Smooth Airstreams at High Reynolds Numbers

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Raf Theunissen ◽  
Robert Worboys
Keyword(s):  
Drag Coefficient ◽  
Experimental Studies ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Mean Flow ◽  
Flow Topology ◽  
Near Wake ◽  
Two Component ◽  
High Reynolds ◽  
Component Particle

Porous disks are commonly encountered in experimental studies dealing with flow through objects such as wind turbines, parachutes, and fluidic devices to regulate pressure and/or downstream turbulence. Perforations are typically staggered and only porosity is altered to attain the required disk drag coefficient, despite a documented influence of topology. Few works have reported, however, to which extent the spatial distribution of the circular perforations affect the mean flow pertaining freestanding disks, and for this reason, this work presents a first, more systematic study focused on the effect of azimuthally varying hole topology and porosity on disk drag and near-wake characteristics. An experimental study performed in airflows of negligible freestream turbulence at Reynolds numbers in the order of 105 is reported and related to the existing literature to ensure reliability. Complementary to drag measurements, near-wake surveys have been performed on a variety of perforation layouts using two-component laser Doppler velocimetry and two-component particle image velocimetry. It is shown that minor changes in perforations can cause drastic changes in near-wake flow topology and no perforation layout can be consistently associated with highest drag. Explicit empirical expressions for drag coefficient linked with the simplified topologies considered have been derived.

Vortex Simulation of Propagating Stall in a Linear Cascade of Airfoils

1986 ◽  
Vol 108 (3) ◽  
pp. 304-312 ◽  
Author(s):  
C. G. Speziale ◽  
F. Sisto ◽  
S. Jonnavithula
Keyword(s):  
Experimental Studies ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Vortex Sheets ◽  
Discrete Vortex ◽  
Linear Cascade ◽  
Attached Flow ◽  
Tracing Algorithm ◽  
High Reynolds ◽  
Stagger Angle

A numerical simulation of propagating stall in a linear cascade of airfoils at high Reynolds numbers is conducted using a vortex method which was first developed by Spalart [7] for this problem. In this approach, the vorticity is discretized into a large collection of vortex blobs whose motion is tracked in time by the use of a well-known vortex tracing algorithm based on the Euler equation. The near-wall effects of viscosity are accounted for by the creation of discrete vortex sheets at the boundaries of the airfoils consistent with the no-slip condition. These boundary vortices are then released into the flow field downstream of the separation points which are obtained from a boundary-layer routine. Calculations are presented for a variety of flow geometries. It is demonstrated that (for a given cascade of airfoils, disturbance wavelength, and stagger angle) several different flow regimes are obtained: Attached flow at lower angles of attack and a chaotic deep stall configuration at larger angles of attack with a narrow intermediate range of such angles where propagating stall occurs. The physical characteristics of this propagating stall are parameterized and a quantitative study of the effects of camber and imposed wavelength is conducted. Comparisons are made with previous theoretical and experimental studies.

Energy balances for axisymmetric gravity currents in homogeneous and linearly stratified ambients

2008 ◽  
Vol 616 ◽  
pp. 303-326 ◽  
Author(s):  
MARIUS UNGARISH ◽  
HERBERT E. HUPPERT
Keyword(s):  
High Reynolds Number ◽  
Gravity Current ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Fluid System ◽  
Dense Fluid ◽  
High Reynolds ◽  
Energy Balances ◽  
Two Fluid

We analyse the exchange of energy for an axisymmetric gravity current, released instantaneously from a lock, propagating over a horizontal boundary at high Reynolds number. The study is relevant to flow in either a wedge or a full circular geometry. Attention is focused on effects due to a linear stratification in the ambient. The investigation uses both a one-layer shallow-water model and Navier–Stokes finite-difference simulations. There is fair agreement between these two approaches for the energy changes of the dense fluid (the current). The stratification enhances the accumulation of potential energy in the ambient and reduces the energy decay (dissipation) of the two-fluid system. The total energy of the axisymmetric current decays considerably faster with distance of propagation than for the two-dimensional counterpart.

scholarly journals Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells

2011 ◽  
Vol 138 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Chae Young Cha ◽  
Enrique Santos ◽  
Akira Amano ◽  
Takao Shimayoshi ◽  
Akinori Noma
Keyword(s):  
Differential Equations ◽  
Cell Model ◽  
Equilibrium Points ◽  
Experimental Studies ◽  
Companion Paper ◽  
Membrane Excitability ◽  
Β Cells ◽  
Pancreatic Β Cells ◽  
Single Action ◽  
Functional Components

In our companion paper, the physiological functions of pancreatic β cells were analyzed with a new β-cell model by time-based integration of a set of differential equations that describe individual reaction steps or functional components based on experimental studies. In this study, we calculate steady-state solutions of these differential equations to obtain the limit cycles (LCs) as well as the equilibrium points (EPs) to make all of the time derivatives equal to zero. The sequential transitions from quiescence to burst–interburst oscillations and then to continuous firing with an increasing glucose concentration were defined objectively by the EPs or LCs for the whole set of equations. We also demonstrated that membrane excitability changed between the extremes of a single action potential mode and a stable firing mode during one cycle of bursting rhythm. Membrane excitability was determined by the EPs or LCs of the membrane subsystem, with the slow variables fixed at each time point. Details of the mode changes were expressed as functions of slowly changing variables, such as intracellular [ATP], [Ca2+], and [Na+]. In conclusion, using our model, we could suggest quantitatively the mutual interactions among multiple membrane and cytosolic factors occurring in pancreatic β cells.

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