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.

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).

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.

The Magnus Effect: A Summary of Investigations to Date

1961 ◽  
Vol 83 (3) ◽  
pp. 461-470 ◽  
Author(s):  
W. M. Swanson
Keyword(s):  
Reynolds Number ◽  
Free Stream ◽  
Mathematical Problem ◽  
Experimental Results ◽  
Stream Velocity ◽  
Magnus Force ◽  
Drag Forces ◽  
Number Ratio ◽  
Magnus Effect ◽  
Lift And Drag

The Magnus force on a rotating body traveling through a fluid is partly responsible for ballistic missile and rifle shell inaccuracies and dispersion and for the strange deviational behavior of such spherical missiles as golfballs and baseballs. A great deal of effort has been expended in attempts to predict the lift and drag forces as functions of the primary parameters, Reynolds number, ratio of peripheral to free-stream velocity, and geometry. The formulation and solution of the mathematical problem is of sufficient difficulty that experimental results give the only reliable information on the phenomenon. This paper summarizes some of the experimental results to date and the mathematical attacks that have been made on the problem.

Unsteady RANS Simulation of Flow Around a 5:1 Rectangular Cylinder at High Reynolds Numbers

2012 ◽  
Author(s):  
Muk Chen Ong
Keyword(s):  
Free Stream ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Stream Velocity ◽  
High Reynolds Numbers ◽  
Rectangular Cylinder ◽  
Mean Pressure ◽  
Unsteady Rans ◽  
High Reynolds

The unsteady flows around a stationary two dimensional rectangular cylinder with chord-to-thickness ratio B/D = 5.0 at high Reynolds numbers, ReB = 5×105, 1×106, 1.5×106 and 2×106 (based on the free stream velocity and the chord length), are investigated numerically by solving the Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with a standard high Reynolds number k-ε turbulence model. The objective of the present study is to evaluate whether the model is applicable for engineering design within this flow regime. Hydrodynamic results (such as time-averaged drag coefficient, root-mean-square of fluctuating lift coefficient, Strouhal number and mean pressure distribution around the rectangular cylinder) are compared with published experimental data. The mechanism of vortex shedding is also discussed.

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.

Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number

1994 ◽  
Vol 270 ◽  
pp. 133-174 ◽  
Author(s):  
Renwei Mei
Keyword(s):  
Reynolds Number ◽  
Dynamic Equation ◽  
High Frequency ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Velocity ◽  
Particle Dynamic ◽  
History Force ◽  
The Time Domain ◽  
Oscillating Sphere

Unsteady flow due to an oscillating sphere with a velocity U0cosωt’, in which U0 and ω are the amplitude and frequency of the oscillation and t’ is time, is investigated at finite Reynolds number. The methods used are: (i) Fourier mode expansion in the frequency domain; (ii) a time-dependent finite difference technique in the time domain; and (iii) a matched asymptotic expansion for high-frequency oscillation. The flow fields of the steady streaming component, the second and third harmonic components are obtained with the fundamental component. The dependence of the unsteady drag on ω is examined at small and finite Reynolds numbers. For large Stokes number, ε = (ωa2/2v)½ [Gt ] 1, in which a is the radius of the sphere and v is the kinematic viscosity, the numerical result for the unsteady drag agrees well with the high-frequency asymptotic solution; and the Stokes (1851) solution is valid for finite Re at ε [Gt ] 1. For small Strouhal number, St = ωa/U0 [Lt ] 1, the imaginary component of the unsteady drag (Scaled by 6πU0pfva, in which Pf is the fluid density) behaves as Dml ∼ (h0Stlog St–h1St), m = 1,3,5… This is in direct contrast to an earlier result obtained for an unsteady flow over a stationary sphere with a small-amplitude oscillation in the free-stream velocity (hereinafter referred to as the SA case) in which D1∼ –h1St (Mei, Lawrence & Adrian 1991). Computations for flow over a sphere with a free-stream velocity U0(1–α1+α1cosωt’) at Re = U02a/v = 0.2 and St [Lt ] 1 show that h0 for the first mode varies from 0 (at α1 = 0) to around 0.5 (at α1 = 1) and that the SA case is a degenerated case in which the logarithmic dependence of the drag in St is suppressed by the strong mean uniform flow.The numerical results for the unsteady drag are used to examine an approximate particle dynamic equation proposed for spherical particles with finite Reynolds number. The equation includes a quasi-steady drag, an added-mass force, and a modified history force. The approximate expression for the history force in the time domain compares very well with the numerical results of the SA case for all frequencies; it compares favourably for the PO case for moderate and high frequencies; it underestimates slightly the history force for the PO case at low frequency. For a solid sphere settling in a stagnant liquid with zero initial velocity, the velocity history is computed using the proposed particle dynamic equation. The results compare very well with experimental data of Moorman (1955) over a large range of Reynolds numbers. The present particle dynamic equation at finite Re performs consistently better than that proposed by Odar & Hamilton (1964) both qualitatively and quantitatively for three different types of spatially uniform unsteady flows.

Laminar flow past a sphere rotating in the streamwise direction

2002 ◽  
Vol 461 ◽  
pp. 365-386 ◽  
Author(s):  
DONGJOO KIM ◽  
HAECHEON CHOI
Keyword(s):  
Laminar Flow ◽  
Rotational Speed ◽  
Lift Force ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Velocity ◽  
Streamwise Direction ◽  
Vortical Structures ◽  
Flow Past ◽  
Flow Past A Sphere

Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.

Droplet pair interactions in a shock-wave flow field

1989 ◽  
Vol 202 ◽  
pp. 467-497 ◽  
Author(s):  
S. Temkin ◽  
G. Z. Ecker
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Free Stream ◽  
Droplet Diameter ◽  
Weak Shock ◽  
Reynolds Numbers ◽  
Stream Velocity ◽  
Wave Flow ◽  
Paraboloid Of Revolution ◽  
Maximum Decrease

Binary interactions between water droplets of nearly equal size in the flow field behind a weak shock wave were studied experimentally. The droplets had diameters of about 270 mm, and the Reynolds numbers, based on this diameter and on the relative velocity between the droplets and the free stream, ranged from about 130 to about 600. In this paper we report only data for Re < 150, corresponding to non-deforming droplets. The droplets in a given pair were aligned so that each pair fell on a plane parallel to the direction of the incoming flow. In this manner, the second droplet in the pair was ‘behind’ the first, at horizontal distances ranging from 1.5 to 11 diameters, and at vertical distances from the dividing streamline ranging from −3 to 6 diameters. We have quantified the interaction in terms of drag force changes on the droplets, and show that the first, or upstream, droplet is not affected by the second, but that the second experiences significant reductions for vertical distances of about one droplet diameter or less. At the smallest horizontal distances, the maximum decrease observed was about 50%, relative to its isolated value. We also show that the drag changes clearly demarcate a wake behind the first droplet. Further, on the basis of these changes, we define a region of influence attached to the first droplet, where the free-stream velocity is significantly reduced. For the droplets used in this study, this region is a slender paraboloid of revolution, having a length of about 15 diameters and a radius of about one diameter.

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