Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime

2014 ◽  
Vol 759 ◽  
pp. 751-781 ◽  
Author(s):  
Eric K. W. Poon ◽  
Andrew S. H. Ooi ◽  
Matteo Giacobello ◽  
Gianluca Iaccarino ◽  
Daniel Chung
Keyword(s):  
Shear Layer ◽  
Flow Regime ◽  
Rotation Rate ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Surface Velocity ◽  
Stream Velocity ◽  
Shear Layer Instability ◽  
Sphere Surface ◽  
Rotating Sphere

AbstractThe flow past a transversely rotating sphere at Reynolds numbers of $\mathit{Re}=500{-}1000$ is directly simulated using an unstructured finite volume collocated code. The effect of rotation rate on the flow is studied by increasing the dimensionless rotation rate, ${\it\Omega}^{\ast }$, from 0 to 1.20, where ${\it\Omega}^{\ast }$ is the maximum sphere surface velocity normalised by the free stream velocity. This study investigates the marked unsteadiness of the flow structures at $\mathit{Re}=500{-}1000$. Comparison with previous numerical data (Giacobello et al., J. Fluid Mech., vol. 621, 2009, pp. 103–130; Kim, J. Mech. Sci. Technol., vol. 23, 2009, pp. 578–589) reveals a new flow regime, namely a ‘shear layer–stable foci’ regime, besides the widely reported ‘vortex shedding’ and ‘shear layer instability’ regimes. The ‘shear layer–stable foci’ regime is observed at $\mathit{Re}=500$ and ${\it\Omega}^{\ast }=1.00$; $\mathit{Re}=640{-}1000$ and ${\it\Omega}^{\ast }\geqslant 0.80$. In this flow regime, the shear layer on the advancing side of the sphere (where the sphere surface velocity vector opposes the free stream velocity) shortens significantly while fluid from the retreating side (opposite to the advancing side) is drawn towards the mid-plane normal to the peripheral velocity. This results in the formation of a stable focus near the onset of the shear layer instability. This stable focus becomes more pronounced with increasing $\mathit{Re}$ and ${\it\Omega}^{\ast }$. It increases the oscillation magnitude and decreases the oscillation frequency of the hydrodynamic forces.

Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow

2018 ◽  
Vol 857 ◽  
pp. 878-906 ◽  
Author(s):  
T. Nagata ◽  
T. Nonomura ◽  
S. Takahashi ◽  
Y. Mizuno ◽  
K. Fukuda
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Rotation Rate ◽  
Free Stream ◽  
Rotating Sphere ◽  
Free Stream Mach Number ◽  
Low Reynolds

In this study, direct numerical simulation of the flow around a rotating sphere at high Mach and low Reynolds numbers is conducted to investigate the effects of rotation rate and Mach number upon aerodynamic force coefficients and wake structures. The simulation is carried out by solving the three-dimensional compressible Navier–Stokes equations. A free-stream Reynolds number (based on the free-stream velocity, density and viscosity coefficient and the diameter of the sphere) is set to be between 100 and 300, the free-stream Mach number is set to be between 0.2 and 2.0, and the dimensionless rotation rate defined by the ratio of the free-stream and surface velocities above the equator is set between 0.0 and 1.0. Thus, we have clarified the following points: (1) as free-stream Mach number increased, the increment of the lift coefficient due to rotation was reduced; (2) under subsonic conditions, the drag coefficient increased with increase of the rotation rate, whereas under supersonic conditions, the increment of the drag coefficient was reduced with increasing Mach number; and (3) the mode of the wake structure becomes low-Reynolds-number-like as the Mach number is increased.

An experimental study of round jets in cross-flow

1996 ◽  
Vol 306 ◽  
pp. 111-144 ◽  
Author(s):  
R. M. Kelso ◽  
T. T. Lim ◽  
A. E. Perry
Keyword(s):  
Flow Visualization ◽  
Shear Layer ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Stream Velocity ◽  
Hot Wire ◽  
Vortex System ◽  
Freestream Velocity ◽  
Round Jets ◽  
Topological Features

The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.

Shear Layer Driven Acoustic Modes in a Cylindrical Cavity

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
David B. Stephens ◽  
Francisco R. Verdugo ◽  
Gareth J. Bennett
Keyword(s):  
Shear Layer ◽  
Cylindrical Cavity ◽  
Stream Flow ◽  
Acoustic Pressure ◽  
Free Stream ◽  
Mode Switching ◽  
Stream Velocity ◽  
Azimuthal Mode ◽  
Mode Oscillation ◽  
Cavity Opening

This paper describes the interior acoustic pressure of a cylindrical cavity driven by a shear layer. Existing cavity flow literature is generally focused on rectangular cavities, where the resonance is either longitudinal or the result of excited depth modes inside the cavity. The design of the present circular cavity is such that azimuthal duct modes can be excited in various combinations with depth modes depending on free stream velocity. An acoustic simulation of the system was used to identify the modes as a function of frequency when the system is driven by an acoustic point source. With appropriate manipulation of the free stream flow, abrupt mode switching and mode oscillation were both observed, and a condition with a dominant azimuthal mode was found. The strength of the lock-on was documented for the various resonance conditions, and the effects of the cavity opening size and location were studied.

CFD Study of the Pressure Distribution on the Back of a 3-D Bluff Body (CUBE) of Air Flow in Different Reynolds Numbers

2009 ◽  
Author(s):  
Mohammad Javad Izadi ◽  
Pegah Asghari ◽  
Malihe Kamkar Delakeh
Keyword(s):  
Reynolds Number ◽  
Bluff Body ◽  
Free Stream ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
The Body ◽  
Stream Velocity ◽  
Bluff Bodies ◽  
Unsteady Forces ◽  
Flow Round

The study of flow around bluff bodies is important, and has many applications in industry. Up to now, a few numerical studies have been done in this field. In this research a turbulent unsteady flow round a cube is simulated numerically. The LES method is used to simulate the turbulent flow around the cube since this method is more accurate to model time-depended flows than other numerical methods. When the air as an ideal fluid flows over the cube, flow separate from the back of the body and unsteady vortices appears, causing a large wake behind the cube. The Near-Wake (wake close to the body) plays an important role in determining the steady and unsteady forces on the body. In this study, to see the effect of the free stream velocity on the surface pressure behind the body, the Reynolds number is varied from one to four million and the pressure on the back of the cube is calculated numerically. From the results of this study, it can be seen that as the velocity or the Reynolds number increased, the pressure on the surface behind the cube decreased, but the rate of this decrease, increased as the free stream flow velocity increased. For high free stream velocities the base pressure did not change as much and therefore the base drag coefficient stayed constant (around 1.0).

An experimental investigation of the flow around a circular cylinder: influence of aspect ratio

1994 ◽  
Vol 258 ◽  
pp. 287-316 ◽  
Author(s):  
C. Norberg
Keyword(s):  
Aspect Ratio ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Infinite Cylinder ◽  
Stream Velocity ◽  
Subcritical Regime ◽  
End Plate ◽  
Aspect Ratios ◽  
The Mean ◽  
Stable Flow

The investigation is concentrated on two important quantities – the Strouhal number and the mean base suction coefficient, both measured at the mid-span position. Reynolds numbers from about 50 to 4 × 104 were investigated. Different aspect ratios, at low blockage ratios, were achieved by varying the distance between circular end plates (end plate diameter ratios between 10 and 30). It was not possible, by using these end plates in uniform flow and at very large aspect ratios, to produce parallel shedding all over the laminar shedding regime. However, parallel shedding at around mid-span was observed throughout this regime in cases when there was a slight but symmetrical increase in the free-stream velocity towards both ends of the cylinder. At higher Re, the results at different aspect ratios were compared with those of a ‘quasi-infinite cylinder’ and the required aspect ratio to reach conditions independent of this parameter, within the experimental uncertainties, are given. For instance, aspect ratios as large as L/D = 60–70 were needed in the range Re ≈ 4 × 103–104. With the smallest relative end plate diameter and for aspect ratios smaller than 7, a bi-stable flow switching between regular vortex shedding and ‘irregular flow’ was found at intermediate Reynolds number ranges in the subcritical regime (Re ≈ 2 × 103).

Force and Stability Measurements on Models of Submerged Pipelines

1971 ◽  
Vol 93 (4) ◽  
pp. 1290-1298 ◽  
Author(s):  
J. F. Wilson ◽  
H. M. Caldwell
Keyword(s):  
Free Stream ◽  
Ground Plane ◽  
Orientation Angle ◽  
Reynolds Numbers ◽  
Ocean Floor ◽  
Stream Velocity ◽  
Piping System ◽  
Lift And Drag ◽  
Vertical Spacing ◽  
Fixed End

The effect of currents on pipes anchored just above the ocean floor is the subject of this study. Lift, drag, and stability of two parallel pipes, parallel to a flat plane (the sea floor) were measured for simulated ocean currents up to two knots at several subcritical, free stream Reynolds numbers. First, a wind tunnel was utilized to find the lift and drag coefficients on two parallel, rigid, cylindrical models. The effects of horizontal spacing, vertical spacing from the ground plane, and orientation angle of the horizontal free stream velocity were observed. These results were compared to date available for the single and double cylinder cases where the ground plane was absent. Second, a water tow tank was utilized to observe conditions for vortex-shedding induced vibrations for fixed end, flexible, parallel cylinders. The natural frequencies and buoyancies of these models simulated pipelines of reasonable span clamped to evenly spaced anchor blocks. A numerical example illustrates the use of these data in the design of a dynamically stable piping system close to the ocean floor.

Numerical investigation of laminar–turbulent transition in laminar separation bubbles: the effect of free-stream turbulence

2018 ◽  
Vol 858 ◽  
pp. 714-759 ◽  
Author(s):  
Shirzad Hosseinverdi ◽  
Hermann F. Fasel
Keyword(s):  
Shear Layer ◽  
Free Stream ◽  
Low Frequency ◽  
Transition Process ◽  
Shear Layer Instability ◽  
Laminar Separation ◽  
Free Stream Turbulence ◽  
Turbulent Transition ◽  
Separated Shear Layer ◽  
Separation Bubbles

The role of free-stream turbulence (FST) in the hydrodynamic instability mechanisms and transition to turbulence in laminar separation bubbles (LSBs) was investigated using direct numerical simulations (DNS). Towards this end, a set of highly resolved DNS have been carried out, where isotropic FST fluctuations with intensities from 0.1 % to 3 % are introduced to investigate the relevant physical mechanisms governing the interaction of separation and transition in LSBs. For disturbance-free simulations, i.e. without FST, laminar–turbulent transition involves a Kelvin–Helmholtz (KH) instability of the separated shear layer. For LSBs subjected to FST, vortical FST fluctuations penetrate the approaching attached laminar boundary layer upstream of the separation location and induce slowly growing low-frequency disturbances, so-called Klebanoff (K) modes, which cause a spanwise modulation with a distinct spanwise wavelength. Simultaneously, the FST enhances the initial levels of instability waves with frequencies in the frequency range of the KH instability, but at much smaller amplitude levels compared to the K-modes. Results from the calculations based on the linearized Navier–Stokes equations and comparison with DNS results reveal that the K-mode exhibits exponential growth in the separated shear layer until it reaches a peak amplitude. At the same time, two-dimensional (2D) disturbance waves are also exponentially amplified, in fact at larger growth rate compared to the K-mode, due to the primary (convective) shear-layer instability mechanism until they saturate downstream of the peak amplitude associated with the K-mode. Therefore, based on detailed spectral analysis and modal decompositions for the separation bubbles investigated, the transition process is the result of two different mechanisms: (i) strong amplification of high-frequency (order of the shedding frequency), essentially 2D or weakly oblique fluctuating disturbances and (ii) low-frequency, three-dimensional K-modes caused by FST. Depending on the intensity of the FST, one of these mechanisms would dominate the transition process, or both mechanisms act together and contribute simultaneously. The net effect of these two events is an acceleration of transition for an increased level of FST intensity, which in turn leads to a reduction of the extent of the separation bubble in streamwise and wall-normal directions. The ‘roll-up’ into spanwise large-scale vortical structures resulting from the shear-layer instability, and the eventual breakdown of these structures, strongly contribute to the reattachment process. The spanwise coherence of these ‘rollers’ deteriorates due to the presence of large-amplitude K-modes, thus effectively weakening their strength for high levels of FST intensities ($Tu>1\,\%$).

Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity

1991 ◽  
Vol 233 ◽  
pp. 613-631 ◽  
Author(s):  
Renwei Mei ◽  
Christopher J. Lawrence ◽  
Ronald J. Adrian
Keyword(s):  
Reynolds Number ◽  
Free Stream ◽  
Low Frequency ◽  
Reynolds Numbers ◽  
Free Stream Velocity ◽  
Creeping Flow ◽  
Stream Velocity ◽  
Velocity Difference ◽  
Long Time ◽  
The Time Domain

Unsteady flow over a stationary sphere with small fluctuations in the free-stream velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady Stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the force has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & Mckee (1984) wherein for a particle introduced to a turbulent flow the initial velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effects of Reynolds number on the unsteady drag due to the fluctuating free-stream velocity are presented. The implications for particle motion in turbulence are discussed.

Mechanism of drag reduction by a surface trip wire on a sphere

2011 ◽  
Vol 672 ◽  
pp. 411-427 ◽  
Author(s):  
KWANGMIN SON ◽  
JIN CHOI ◽  
WOO-PYUNG JEON ◽  
HAECHEON CHOI
Keyword(s):  
Boundary Layer ◽  
Drag Reduction ◽  
Separation Bubble ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Stream Velocity ◽  
Sphere Diameter ◽  
Sphere Surface ◽  
Streamwise Location

The effect of a surface trip wire on the flow around a sphere is experimentally investigated at subcritical Reynolds numbers of Re = 0.5 × 105 – 2.8 × 105 based on the free-stream velocity U∞ and sphere diameter d. By varying the streamwise location (20° – 70° from the stagnation point) and diameter (0.33 × 10−2 < k/d < 1.33 × 10−2) of a trip wire, we measure the drag, surface pressure distribution and boundary layer velocity profiles above the sphere surface, and conduct flow visualization. Depending on the size and streamwise location of the trip wire, three different flow characteristics are observed above the sphere surface. For low Reynolds numbers, the disturbance induced by the trip wire decays downstream and main separation occurs at a streamwise location similar to that of a smooth sphere. As the Reynolds number is increased, laminar separation is delayed farther downstream by the disturbance from the trip wire and the transition to turbulence occurs along the separated shear layer, resulting in the flow reattachment to the sphere surface and thus forming a secondary separation bubble on the sphere surface. Then, the main separation is delayed due to high momentum near the surface and the drag is significantly reduced. When the trip wire produces even larger disturbances through the separation and reattachment right at the trip-wire location for higher Reynolds numbers, the boundary layer flow becomes turbulent soon after the trip-wire location and the main separation is delayed, resulting in drag reduction.

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