Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification

2010 ◽  
Vol 646 ◽  
pp. 415-439 ◽  
Author(s):  
HARISH N DIXIT ◽  
RAMA GOVINDARAJAN
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Density Stratification ◽  
Low Reynolds Numbers ◽  
Density Interface ◽  
Lower Reynolds Number ◽  
Number Flow ◽  
Good Agreement

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh–Taylor (CRT) instability and a spiral Kelvin–Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

scholarly journals Investigation of Riblet Geometry and Start Locations of Herringbone Riblets on Pressure Losses in a Linear Cascade at Low Reynolds Numbers

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Qiang Liu ◽  
Shan Zhong ◽  
Lin Li
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Effective Control ◽  
Slight Reduction ◽  
Turning Angle ◽  
Low Reynolds Numbers ◽  
Pressure Losses ◽  
Lower Reynolds Number ◽  
Displacement Thickness ◽  
Low Reynolds

Abstract In this paper, the effects of an array of herringbone riblets with different riblet geometry (height and spacing) and start locations on the pressure losses in a cascade of diffuser blades are investigated over a range of low Reynolds numbers (0.50 × 105–1.00 × 105). The herringbone riblets with a given geometry are found to produce a profound modification to the wake structure above certain critical Reynolds numbers. It is also found that within the range of parameters tested an increase in riblet height and riblet spacing results in an onset of significant control effect at a lower Reynolds number, which is accompanied by a slight reduction in zone-averaged loss coefficient and flow turning angle. An upstream shift of the start position of the riblet array along the blades enables the riblets to become effective at a lower Reynolds number at the expense of a reduced loss reduction and flow turning angle. A semi-empirical relationship between the ratio of riblet height to local baseline boundary layer displacement thickness and the critical Reynolds number is established using the present experimental data. A preliminary methodology for designing the herringbone riblets to ensure an effective control of 2D flow separations around the mid-span of diffuser blades over a specified range of Reynolds numbers is also proposed.

A Theory of Sharp-Edged Orifices

1937 ◽  
Vol 4 (2) ◽  
pp. A53-A54
Author(s):  
W. E. Howland
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Discharge Coefficient ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Low Reynolds Numbers ◽  
Circular Orifice ◽  
Coefficient Of Discharge ◽  
Theoretical Considerations ◽  
Good Agreement

Abstract The author presents a figure in which the coefficient of discharge Cd, velocity Cv, and contraction Cc determined by several investigators are plotted logarithmically as points against Reynolds’ numbers. Curves for the coefficients drawn by the author, based on theoretical considerations, show good agreement with the experimental data, thus throwing some light upon the basic phenomena of the discharge of sharp-edged orifices. The variation of the coefficient of discharge of a circular orifice as a function of the Reynolds number is explained as a purely viscous phenomenon for low Reynolds numbers, and by means of a momentum analysis for higher speeds. The analysis presented by the author leads to the development of several formulas for the discharge coefficient, which formulas are in fair agreement with experimental results.

The Quadrant Edge Orifice—A Fluid Meter for Low Reynolds Numbers

1960 ◽  
Vol 82 (3) ◽  
pp. 729-733 ◽  
Author(s):  
M. Bogema ◽  
P. L. Monkmeyer
Keyword(s):  
Reynolds Number ◽  
Discharge Coefficient ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Roughness Effects ◽  
Low Reynolds Numbers ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Low Reynolds

Tests have been conducted to determine the usefulness of the quadrant edge orifice as a fluid-metering device for low Reynolds number flow. As a result of numerous laboratory tests to determine the behavior of the discharge coefficient with changing Reynolds number, the following are discussed: The range of constant discharge coefficient, reproducibility of orifice plates, diameter ratio effects, upstream roughness effects, reinstallation effects, and effects of pressure tap location.

Steady inlet flow in stenotic geometries: convective and absolute instabilities

2008 ◽  
Vol 616 ◽  
pp. 111-133 ◽  
Author(s):  
M. D. GRIFFITH ◽  
T. LEWEKE ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Base Flow ◽  
Arterial Stenosis ◽  
Working Fluid ◽  
Straight Tube ◽  
Inlet Flow ◽  
Low Reynolds Numbers ◽  
Lower Reynolds Number

Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing.

Instability of the buoyancy layer on an evenly heated vertical wall

2007 ◽  
Vol 587 ◽  
pp. 453-469 ◽  
Author(s):  
G. D. McBAIN ◽  
S. W. ARMFIELD ◽  
GILLES DESRAYAUD
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Prandtl Number ◽  
Travelling Waves ◽  
Vertical Wall ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Linearized Stability ◽  
The Stability ◽  
Volume Method

The stability of the buoyancy layer on a uniformly heated vertical wall in a stratified fluid is investigated using both semi-analytical and direct numerical methods. As in the related problem in which the excess temperature of the wall is specified, the basic laminar flow is steady and one-dimensional. Here flows varying in time and with height are considered, the behaviour being determined by the fluid's Prandtl number and a Reynolds number proportional to the ratio of two temperature gradients: the horizontal one imposed at the wall and the vertical one existing in the far field. For low Reynolds numbers, the flow is stable with variation only in the wall-normal direction. For Reynolds numbers greater than a critical value, depending on the Prandtl number, the flow is unstableand supports two-dimensional travelling waves. The critical Reynolds number and other properties have been obtained via linearized stability analysis and are shown to accuratelypredict the behaviour of the full nonlinear solution obtained numerically for Prandtl number 7. The stability analysis employs a novel Laguerre collocation scheme while the direct numerical simulations use a second-order finite volume method.

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

A Computational Study on Airfoils at a Low Reynolds Number

2000 ◽  
Author(s):  
Ajit Pal Singh ◽  
S. H. Winoto ◽  
D. A. Shah ◽  
K. G. Lim ◽  
Robert E. K. Goh
Keyword(s):  
Reynolds Number ◽  
Computational Analysis ◽  
Computational Study ◽  
Low Reynolds Number ◽  
Micro Air Vehicles ◽  
Reynolds Numbers ◽  
Aerodynamic Performance ◽  
Low Reynolds Numbers ◽  
Study Results ◽  
Low Reynolds

Abstract Performance characteristics of some low Reynolds number airfoils for the use in micro air vehicles (MAVs) are computationally studied using XFOIL at a Reynolds number of 80,000. XFOIL, which is based on linear-vorticity stream function panel method coupled with a viscous integral formulation, is used for the analysis. In the first part of the study, results obtained from the XFOIL have been compared with available experimental data at low Reynolds numbers. XFOIL is then used to study relative aerodynamic performance of nine different airfoils. The computational analysis has shown that the S1223 airfoil has a relatively better performance than other airfoils considered for the analysis.

An Experimental Investigation of the Effect of Freestream Turbulence on the Wake of a Separated Low-Pressure Turbine Blade at Low Reynolds Numbers

1999 ◽  
Vol 122 (2) ◽  
pp. 431-433 ◽  
Author(s):  
C. G. Murawski ◽  
K. Vafai
Keyword(s):  
Reynolds Number ◽  
Turbine Blade ◽  
Turbulence Intensity ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Freestream Turbulence ◽  
Suction Surface ◽  
Low Reynolds Numbers ◽  
Low Pressure Turbine ◽  
Flow Reynolds Number

An experimental study was conducted in a two-dimensional linear cascade, focusing on the suction surface of a low pressure turbine blade. Flow Reynolds numbers, based on exit velocity and suction length, have been varied from 50,000 to 300,000. The freestream turbulence intensity was varied from 1.1 to 8.1 percent. Separation was observed at all test Reynolds numbers. Increasing the flow Reynolds number, without changing freestream turbulence, resulted in a rearward movement of the onset of separation and shrinkage of the separation zone. Increasing the freestream turbulence intensity, without changing Reynolds number, resulted in shrinkage of the separation region on the suction surface. The influences on the blade’s wake from altering freestream turbulence and Reynolds number are also documented. It is shown that width of the wake and velocity defect rise with a decrease in either turbulence level or chord Reynolds number. [S0098-2202(00)00202-9]

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