Cylinder Reynolds Number Research Articles

Circular cylinder vortex-synchronization control with a synthetic jet positioned at the rear stagnation point

The flow over a circular cylinder controlled by a two-dimensional synthetic jet positioned at the mean rear stagnation point has been experimentally investigated in a water channel at the cylinder Reynolds numberRe= 950. This is an innovative arrangement and the particle-image-velocimetry measurement indicates that it can lead to a novel and interesting phenomenon. The synthetic-jet vortex pairs induced near the exit convect downstream and interact with the vorticity shear layers behind both sides of the cylinder, resulting in the formation of new induced wake vortices. The present vortex synchronization occurs when the excitation frequency of the synthetic jet is between 1.67 and 5.00 times the natural shedding frequency at the dimensionless stroke length 99.5. However, it is suggested that the strength of the synthetic-jet vortex pair plays a more essential role in the occurrence of vortex synchronization than the excitation frequency. In addition, the wake-vortex shedding is converted into a symmetric mode from its original antisymmetric mode. The symmetric shedding mode weakens the interaction between the upper and lower wake vortices, resulting in a decrease in the turbulent kinetic energy produced by them. It also has a significant influence on the global flow field, including the velocity fluctuations, Reynolds stresses and flow topology. However, their distributions are still dominated by the large-scale coherent structures.

Turbulent Flow through Idealized Emergent Vegetation

This paper presents results of several large-eddy simulations (LES) of turbulent flow in an open channel through staggered arrays of rigid, emergent cylinders, which can be regarded as idealized vegetation. In this study, two cylinder Reynolds numbers, RD=1,340 and RD=500, and three vegetation densities are considered. The LES of the lowest density and at RD=1,340 corresponds to a recently completed laboratory experiment, the data of which is used to validate the simulations. Fairly good agreement between calculated and measured first- and second-order statistics along measurement profiles is found, confirming the accuracy of the simulations. The high resolution of the simulations enables an explicit calculation of drag forces, decomposed into pressure and friction drag, that are exerted on the cylinders. The effect of the cylinder Reynolds number and the cylinder density on the drag and hence on the flow resistance is quantified and in agreement with previous experimental studies. Turbulence structures are visualized through instantaneous pressure fluctuations, isosurfaces of the Q-criterion and contours of vertical vorticity in horizontal planes. Analysis of velocity time signals and distributions of drag and lift forces over time reveals that flow and turbulence are more influenced by the vegetation density than by the cylinder Reynolds number.

Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows

Spatial and temporal frequency dynamics were experimentally tracked via flow visualization for Newtonian fluids as a function of the inner cylinder Reynolds number (Rei) in the flow between concentric, independently rotating cylinders with a radius ratio of 0.912 and an aspect ratio of 60.7. Eight transitions from laminar to turbulent flow were characterized in detail for a stationary outer cylinder, producing highly resolved space–time and frequency–time plots for wavy, modulated and weakly turbulent states. A previously unreported early-modulated wavy vortex flow was found in our high aspect ratio geometry both with and without the presence of a dislocation. The envelope of stability for this flow state was shown to cross into the co-rotating regime, and is present up to Reo ~ 60, where Reo is the outer cylinder Reynolds number. This early modulation is independent of acceleration in the range 0.18 < dRei/dτ < 2.9, where τ is the time nondimensionalized with a viscous time scale. While many of the flow states have been previously observed in geometries with somewhat different radius ratios, we provide new characterization of transitional structures for Reo = 0 in the range 0 < Re* < 21.4, where Re* = Rei/Rec and Rec is the value of Rei at the primary instability. Special attention has been given to ramp rate. For quasi-static ramps, axisymmetric states are stable over the ranges of Re* = [(0–1.17), > 15.4], states characterized by a single distinct temporal frequency for Re* = [(1.17–1.41), (3.56–5.20), (7.85–15.4)], states with multiple temporal frequencies for Re* = [(1.41–3.56), (5.20–7.85)], and a transition from laminar to weakly turbulent vortices occurs at Re* = 5.49. All flow states are characterized by symmetry/symmetry-breaking features as well as azimuthal and axial wavenumbers.

ON THE FORCES AND STROUHAL NUMBERS IN THE LOW REYNOLDS NUMBER WAKES OF TWO CYLINDERS IN TANDEM

The flow around two circular cylinders of equal diameter in tandem arrangement was investigated numerically using the finite volume method in the present study. The code was validated by comparison with previous works at the Reynolds number of 200. A systematic investigation of the relationships of Strouhal number and the aerodynamic forces with cylinder separation and Reynolds number was done. Results demonstrate not only the important combined effects cylinder separation and Reynolds number on the wake aerodynamics, but also on the relative strengths of the forces acting on the two cylinders (both mean and fluctuations)

On the effect of Reynolds number for flow around a row of square cylinders

Flow across a row of identical square cylinders placed side-by-side has been found to show interesting flow patterns which have complex characteristics depending upon the spacing (s/d) between the cylinders and the Reynolds number (Re). The combined effects of cylinder spacing and Reynolds number on the flow across a row of cylinders are numerically studied for 30≤Re≤140 and 1.0≤s/d≤4.0, where s is the surface-to-surface distance between two cylinders and d is the size of cylinder. It is found that the critical Reynolds number for the onset of vortex shedding increases with increase in gap ratio. The Reynolds number is found to have a strong effect on the flow especially at s/d=3.0,4.0. Secondary frequency in the signal for lift and drag coefficients significantly contributes to the forces experienced by the cylinders. It is observed that at s/d=3.0,4.0 the secondary frequency disappears at larger Reynolds number and the primary frequency dominates the flow. This means that the interaction of the wakes behind the cylinders at these gap ratios weakens with an increase in the Reynolds number. It is proposed that wake interaction is strongly influenced by the jets in the gap region, the nature of which alters with spacing and Reynolds number. This is confirmed by computing the average wake size as a function of Reynolds number. Based on this, two critical gap ratios, 2.0 and 4.0 for the range of Reynolds number under consideration are proposed. These gap ratios separate synchronous, quasiperiodic-I and quasiperiodic-II flow regimes depending on the Reynolds number. The mechanism of wake interaction has been studied to bring out these critical gap ratios.

Aerodynamic Forces and Moment on a Sphere or Cylinder Attached to a Wall in a Blasius Boundary Layer

The results presented in this paper quantify the moment on a sphere and the lift, drag and moment on a cylinder when each is attached to a plate over which flows a Blasius boundary layer. For the cylinder the freestream velocity is prescribed to be perpendicular to the cylinder axis. Computational methods were utilized to develop coefficient of lift and drag relationships as functions of particle Reynolds number with respect to diameter. Results for a plate Reynolds number of 32400 were computed over a particle Reynolds number range 0.06 to 49 for the cylinder and 0.1 to 250 for the sphere. The effect of plate Reynolds number on the results was also investigated. As cylinder Reynolds number approaches zero, the lift coefficient approaches a constant value while the drag coefficient asymptotes to infinity. For both geometries the force and moment coefficients monotonically decrease as particle Reynolds number increases. The moment coefficient for the sphere varies only weakly with plate Reynolds number, while for the cylinder the force and moment coefficients increase somewhat as plate Reynolds number increases above 32400. Empirical curves fits to the data are presented.

Effect of Superimposed Pulsating Flow on Liquid-Solid Mass Transfer in Fixed Beds

The liquid-solid mass transfer behaviour of a fixed bed of cylinders has been studied using the dissolution of copper in acidified dichromate solution under pulsating flow conditions. The bed diameter was 100 mm. The depth of the working section was 95 mm and the length and diameter of the cylinders were 19.1 mm. Variables studied were steady flow superficial liquid velocity, and oscillation amplitude and frequency. Data have been correlated as the Sherwood number in terms of Schmidt number and the cylinder Reynolds numbers for steady and oscillatory flow. The form of the correlation permits comparison with literature data for the limiting cases where either of these Reynolds numbers is zero.

Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders

This paper investigates the drag exerted by randomly distributed, rigid, emergent circular cylinders of uniform diameter d. Laboratory measurements are presented for solid volume fraction ϕ=0.091, 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep≡Upd∕ν=25 to 685, where Up=temporally and cross-sectionally averaged pore velocity and ν=kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, CD, decreased with increasing Rep and increased with increasing ϕ under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length ⟨fD¯⟩H to the product of the viscosity, μ, and Up exhibits a linear Rep dependence of the form ⟨fD¯⟩H∕(μUp)=α0+α1Rep, consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, α1 increases monotonically with ϕ. In contrast, α0 is constant within uncertainty for 0.15⩽ϕ⩽0.35, which suggests that viscous drag per unit cylinder length is independent of ϕ in this range.

Interactions of tandem square cylinders at low Reynolds numbers

Two identical square cylinders were installed in tandem in a vertical water tank. The effects of the Reynolds number, spacing ratio and rotation angle of the downstream cylinder on flow characteristic modes, drag coefficients and vortex shedding properties were studied. The particle image velocimetry (PIV) scheme was applied to examine and classify the flow field into three characteristic modes: vortex sheet of the single mode, reattached mode and binary mode. Via topological analysis, the velocity vector field, streamline pattern, and the properties of these flow modes are presented and discussed. In the viscosity-dominant flow field, the Strouhal number decreases as the Reynolds number increases. However, in the inertia-dominant flow field, the Strouhal number increases with the Reynolds numbers and approaches a constant for high Reynolds numbers. The maximum drag coefficient in the vortex sheet of reattached mode is approximately 76% lower than that in the single square cylinder case.

A numerical study of momentum and forced convection heat transfer around two tandem circular cylinders at low Reynolds numbers. Part I: Momentum transfer

This work presents a computational study of the steady, axisymmetric, viscous flow around two circular cylinders in tandem. The vorticity–stream function formulation of the Navier–Stokes equations was chosen. Numerical solutions have been obtained in bipolar cylindrical coordinates. A compact, high-order, finite difference method was used to discretize the model equations. Iterative algorithms were tested to solve the discrete equations. Different cylinders spacing and sizes were considered for the upstream cylinder Reynolds number up to 30. Vorticity and pressure distributions on the cylinders surfaces and drag coefficients are presented and compared with those calculated for an isolated cylinder.

A numerical study of momentum and forced convection heat transfer around two tandem circular cylinders at low Reynolds numbers. Part II: Forced convection heat transfer

This work presents a computational study of the forced convection heat transfer around two circular cylinders in tandem. Axisymmetric, steady, laminar flow around the cylinders was assumed. The temperature inside the cylinders is considered spatially uniform but not constant in time. Numerical solutions have been obtained in bipolar cylindrical coordinates. The finite difference method was used to discretize the equations of the mathematical model. The influence of the model parameters on the heat transfer rate was analysed for the upstream cylinder Reynolds number, Re, varying from 1 to 30 and fluid phase Prandtl number equal to 0.1, 1, 10 and 100.

Turbulence structure in a Taylor–Couette apparatus

Turbulence measurements were made in a Taylor–Couette apparatus as a basis for future flame propagation studies. Results of the present study extend that of earlier work by more complete characterization of the featureless turbulence regime generated by the Taylor–Couette apparatus. Laser Doppler Velocimetry was used to measure Reynolds stresses, integral and micro time scales and power spectra over a wide range of turbulence intensities typically encountered by turbulent pre-mixed hydrocarbon–air flames. Measurements of radial velocity intensities are consistent with earlier axial and circumferential velocity measurements that indicated a linear relationship between turbulence intensity and the Reynolds number based on the average cylinder rotation speed and wall separation distance. Measured integral and micro time scales and approximated integral length scales were all found to decrease with the Reynolds number, possibly associated with a confinement of the largest scales (of the order of the cylinder wall separation distance). Regions of transverse isotropy were discovered in axial–radial cross correlations for average cylinder Reynolds numbers less than 6000 and are predicted to exist also for circumferential cross correlations at higher average Reynolds numbers, greater than 6000. Power spectra for the independent directions of velocity fluctuation exhibited −5/3 slopes, suggesting that the flow also has some additional isotropic characteristics and demonstrating the role of the Taylor–Couette apparatus as a novel means for generating turbulence for flame propagation studies.

Stability and instability of Taylor–Couette flows of a Bingham fluid

We consider in detail the Taylor-Couette problem for a Bingham fluid, presenting a range of analytical and computational results. First, for co-rotating cylinders it is known that the critical inner cylinder Reynolds number Re 1,c , does not increase monotonically with the Bingham number B, over a range of small to moderate B. It is the only situation that we know of where a yield stress fluid flow is less stable that the corresponding Newtonian fluid flow. This effect was discovered independently by Landry (2003, MSc thesis) and Peng & Zhu (J. Fluid Mech. vol. 512, 2004, p. 21), but the mechanism has not been explained. Here we show that the decrease in critical Reynolds number is due to an increase (at small B) in the rate of strain of the basic flow, which amplifies the transfer of energy from the basic flow to the perturbation, via the inertial terms in the energy equation. At larger B, the yielded region contracts and the inertial energy transfer is bounded by the yield stress dissipation. We next consider the effects of large B. For fixed radius and Reynolds number ratios, we show that for sufficiently large B all basic flows have an unyielded fluid layer attached to the outer wall. For these flows we show that there is a similarity mapping that maps both the basic solution and the linear stability problem onto the stability problem for an outer cylinder of radius equal to the yield surface radius. The Reynolds and Bingham numbers of the transformed problems are smaller than that of the original problem, as is the wavenumber k. As B → ∞, the yield surface approaches the inner cylinder, defining a narrow gap limiting problem that differs from the classical narrow gap limit. Via the transformed problem we derive an energy estimate for stability: Re 1,c k c ∼ B 1.5 as B → ∞, which compares well with our computed results for a stationary outer cylinder: Re 1,c ∼B 1.25 and k c ∼ B 0.375 . We also show how Re 1,c ∼ B 1.25 can be deduced from a simple order of magnitude analysis, for a stationary outer cylinder. Finally, we consider the second (classical) narrow gap limit in which the radius ratio η, approaches unity, for fixed B and Reynolds number ratio. We show that Re 1,c ≥ (k 2 [1 + O(B)] + n 2 )/(1-η) 1/2 in this limit.

Flow structure in the downstream of square and circular cylinders

In this experimental work, a technique of digital particle image velocimetry (DPIV) is employed to characterize instantaneous vorticity and time-averaged velocity, vorticity, root mean square (rms) velocities, Reynolds stress correlations and phase-averaged contours in the downstream of circular, sharp-edged square and 45 ∘ orientated square cylinders in a uniform flow. Strouhal numbers for 550≤ Re≤3400 are calculated from wake flow patterns. Shear layers surrounding the recirculation bubble region behind the cylinder are discussed in terms of flow physics and vortex formation lengths of large-scale Kármán vortices. Enhancement levels of Reynolds stress correlations associated with cross-stream velocity are clarified. Finally, flow structures depending on the cylinder geometry and Reynolds number are interpreted with quantitative representations.

Gravity currents in aquatic canopies

A lock exchange experiment is used to investigate the propagation of gravity currents through a random array of rigid, emergent cylinders which represents a canopy of aquatic plants. As canopy drag increases, the propagating front varies from the classic profile of an unobstructed gravity current to a triangular profile. Unlike the unobstructed lock exchange, the gravity current in the canopy decelerates with time as the front lengthens. Two drag‐dominated regimes associated with linear and nonlinear drag laws are identified. The theoretical expression for toe velocity is supported by observed values. Empirical criteria are developed to predict the current regime from the cylinder Reynolds number and the array density.

Intermittency in spiral Poiseuille flow

The results of an experimental study on intermittent spiral vortices observed in a counter-rotating Taylor-Couette system with an additional axial through flow, i.e. Spiral-Poiseuille flow, are presented. Convectively unstable upstream propagating spiral vortices appear in the laminar basic flow from an oscillatory instability and in general become absolutely unstable at higher inner cylinder Reynolds number. It is found that at Reynolds numbers above the absolute stability border the spiral vortices become unstable and a complex flow state showing intermittent bursts appears. The intermittent flow state is characterised by an irregular alternation between clearly distinguishable ‘laminar’ phases corresponding to up-and downstream propagating spiral vortices as well as propagating Taylor vortices. For a sufficiently high rate of axial through flow it is found that intermittency can occur directly from the convectively unstable regime of the upstream propagating spiral vortices.

Unsteady conjugate heat/mass transfer from a circular cylinder in laminar crossflow at low Reynolds numbers

Unsteady conjugate heat/mass transfer between a circular cylinder and a surrounding fluid flow has been analysed. Numerical investigations were carried out for the cylinder Reynolds numbers equal to 2 and 20 and different values of the Prandtl/Schmidt numbers. The heat/mass balance equations were solved numerically in cylindrical coordinates by the ADI finite difference method. The computations yield information regarding the influence of the parameters that characterize the coupling features of the conjugate heat/mass transfer, i.e. the physical properties ratios, on Nusselt/Sherwood numbers and cylinder dimensionless average temperature/concentration. The thermal/mass wake phenomenon were also studied.

Non-isothermal flow of a polymeric liquid passing an asymmetrically confined cylinder

Non-isothermal polymeric flow past an asymmetrically confined cylinder has been analyzed using a finite-element based numerical technique. The fluid model in this numerical simulation is a differential-type non-isothermal Bird–Carreau model describing the non-Newtonian behavior of the melt. The generated thermal field is entirely due to viscous heating. Drag, lift force and heat transfer on the cylinder and other flow characteristics are predicted. The influences of cylinder lateral position and Reynolds number are also investigated.

Scalar transport in random cylinder arrays at moderate Reynolds number

This paper theoretically describes and experimentally verifies two mechanisms leading to longitudinal dispersion of a passive tracer in a random array of circular cylinders. We focus on moderate Reynolds numbers of order 10–1000, specifically the range characterized by unsteady cylinder wakes. In this regime, two mechanisms contribute to dispersion, each associated with a distinct region of the cylinder wakes: (i) the unsteady recirculation zone close to each cylinder, and (ii) the velocity defect behind each cylinder, which extends downstream of the cylinder over a distance of the order of the cylinder spacing. The first mechanism, termed vortex-trapping dispersion, is due to the entrainment of tracer into the unsteady recirculation zone, where it is momentarily trapped and then released. A theoretical expression for this dispersive mechanism is derived in terms of the residence time and size of the recirculation zone. The second mechanism is due to advection through the random velocity field created by the random distribution of the wake velocity defect. We derive an expression for the defect behind an average cylinder, and show that it decays owing to array drag over a length scale called the attenuation length, which is of the order of the cylinder spacing. The superposition of the wake defect behind each cylinder creates the random velocity field. Theoretical predictions for dispersion agree very well with observations of tracer transport in a laboratory cylinder array, correctly capturing the dependence on array density and Reynolds number. The laboratory studies also document a transition in small-scale mixing at cylinder Reynolds number . Below this limit, individual filaments of tracer remain distinct, producing significant fluctuations in the local concentration field. At higher Reynolds number, cylinder wakes contribute sufficient turbulence to erase the filament signature and smooth the tracer distribution.

Fouling effect of water scale on heat transfer around a tube in staggered tube banks

An experimental study has been performed to investigate the forced convection heat transfer around a tube in six scale-deposited circular cylinders of staggered arrangement in a cross-flow of air. The local, mean Nusselt numbers and fouling resistance were estimated. The effects of the scale thickness, the cylinder spacing and Reynolds number were studied to clarify the heat transfer characteristics and compared with those of in-line tube bank. The results are compared with that of clean cylinder. Subsequently, the mean fouling resistance over the entire circumference was estimated from those results as a function of scale thickness, the cylinder spacing and Reynolds number. It is found that the heat transfer of staggered tube banks greatly varies with the fouling of water scale, especially its height. Further, the mean fouling resistance strongly depend upon the cylinder spacing and Reynolds number. Copyright © 2003 John Wiley & Sons, Ltd.