A Closer Investigation of the Mean Aerodynamic Forces for Two Staggered Circular Cylinders in Cross-Flow

2002 ◽  
Author(s):  
D. Sumner ◽  
M. D. Richards
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Incidence Angle ◽  
Cross Flow ◽  
Local Maximum ◽  
Circular Cylinders ◽  
Aerodynamic Forces ◽  
Gap Flow ◽  
The Mean ◽  
Small Increments

Two circular cylinders of equal diameter in a staggered configuration, with centre-to-centre pitch ratios of P/D = 1.125 – 4.0, were tested in the subcritical Reynolds number regime, at Re = 3.0×104 – 8.0×104. The incidence angle of the cylinder configuration was varied in small increments from α = 0° – 90° and the mean aerodynamic forces were measured on both the upstream and downstream cylinders. Based on the force measurements, the behaviour of the cylinders was broadly grouped into three categories, depending on P/D. For closely spaced staggered configurations, P/D = 1.125 – 1.25, the aerodynamic forces on both the upstream and downstream cylinders varied significantly with α. Several critical incidence angles were identified for each cylinder that corresponded to local maximum, minimum, or discontinuous behaviour in the forces, which were related to shear layer reattachment and the influence of the gap flow. For moderately spaced staggered configurations, P/D = 1.5 – 2.5, shear layer reattachment and the subsequent transition to gap flow at small α were responsible for the inner lift peak, a corresponding minimum drag, and a loss of lift with increasing α, which becomes more abrupt as P/D is increased. For widely spaced staggered configurations, P/D = 3.0 – 4.0, the two cylinders undergo Ka´rma´n vortex shedding for the entire range of α. At small α, the forces on the downstream cylinder are affected by vortex impingement, and the outer lift peak replaces the inner lift peak. This outer lift peak exhibits some sensitivity to the Reynolds number.

Vortex Shedding From Two Circular Cylinders in a Staggered Arrangement

2003 ◽  
Author(s):  
D. Sumner ◽  
M. D. Richards
Keyword(s):  
Strouhal Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Incidence Angle ◽  
Power Spectra ◽  
Circular Cylinders ◽  
Aerodynamic Forces ◽  
Staggered Arrangement ◽  
Pitch Ratio ◽  
Small Increments

Vortex shedding from two circular cylinders of equal diameter in a staggered configuration was studied experimentally in the subcritical Reynolds number regime, for Re = 3.2×104–7.4×104. The dimensionless centre-to-centre pitch ratio of the staggered cylinders was ranged from P/D = 1.125–4.0, and the incidence angle was varied in small increments from α = 0°–90°. The behaviour of the Strouhal number measurements was broadly classified according to whether the cylinders were closely, moderately, or widely spaced, corresponding to P/D < 1.5, 1.5 ≤ P/D ≤ 2.5, and P/D > 2.5, respectively. For closely spaced staggered configurations, the flow around the cylinders is similar to a single bluff body, and only a single Strouhal number is measured. For moderately spaced cylinders, two distinct Strouhal numbers are measured when α > 30°, but there is considerable scatter in the Strouhal data when α < 30°. For widely spaced cylinders, the Strouhal numbers remain close to that of a single circular cylinder, in contrast to the behaviour of the aerodynamic forces. Evidence of the outer lift peak is seen in the power spectra for the downstream cylinder.

Wake Formation for an Oscillating Small-Incidence-Angle Cylinder Pair in Cross-Flow

2011 ◽  
Author(s):  
Mir M. Hayder
Keyword(s):  
Incidence Angle ◽  
Flow Direction ◽  
Incident Angle ◽  
Cross Flow ◽  
Wake Flow ◽  
Circular Cylinders ◽  
Mean Flow ◽  
Small Incidence ◽  
The Mean ◽  
Wake Formation

The wake region of a pair of equal-diameter staggered circular cylinders in cross-flow is investigated experimentally for Reynolds numbers, based on the mean flow velocity, U, and the cylinder diameter, D, within the range 540 ≤ Re ≤ 755. The centre-to-centre pitch ratio and stagger angle of the cylinders at their mean position are P/D = 2.0 and α = 16°, respectively. In an earlier study, wake formation of a small-incident-angle cylinder pair was investigated for forced oscillation (transverse to the flow direction) of the upstream cylinder only. The present study is aimed to reveal the modification of the wake when the oscillation is shifted from the upstream to downstream cylinder or vice versa. Results with cylinder excitation frequencies in the range 0.07 ≤ feD/U ≤ 1.10 are reported. It is observed that for both upstream and downstream cylinder oscillations with frequency feD/U ≤ 0.10 the wake flow patterns remain essentially the same as those of the corresponding static cases. However, for frequency feD/U &gt; 0.10 the wake undergoes considerable modification vis-a`-vis when the cylinders are stationary, and the flow pattern within the wake is strongly dependent on feD/U value. As also observed in the previous study, there are distinct regions of synchronization between the dominant wake periodicities and the cylinder oscillation over the whole range of feD/U. These synchronizations involve sub- and super-harmonics as well as fundamental synchronizations and are the result of the formation of two rows of vortices, one on either side of the combined wake of the cylinder pair. The manner in which the wake responds to the cylinder oscillation depends strongly on whether it is the upstream or downstream cylinder which is oscillating. Flow-visualization images suggests that the synchronizations on the mean-flow side of the downstream cylinder occur from the outer vortices shed by the downstream cylinder, and those on the mean-flow side of the upstream cylinder occur from the vortices formed by the interaction of the two gap shear layers and the outer shear layer separated from the upstream cylinder.

Closely Spaced Circular Cylinders in Cross-Flow and a Universal Wake Number

2004 ◽  
Vol 126 (2) ◽  
pp. 245-249 ◽  
Author(s):  
David Sumner
Keyword(s):  
Vortex Shedding ◽  
Bluff Body ◽  
Incidence Angle ◽  
Cross Flow ◽  
Base Pressure ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Aerodynamic Forces ◽  
Single Vortex ◽  
Total Drag

To investigate the effectiveness of a universal wake number for groups of closely spaced bluff bodes, staggered cylinder configurations with center-to-center pitch ratios of P/D=1.125 and 1.25, and incidence angles from α=0 deg–90 deg, were tested in the subcritical Reynolds number regime. The aerodynamic forces, base pressure, and vortex shedding frequencies were measured for the upstream and downstream cylinders, and were found to be strongly dependent on the incidence angle and small changes in the flow pattern. The Griffin number was found to be an appropriate universal wake number for the closely spaced staggered cylinders, based on the total drag force acting on the two cylinders, and the average base pressure for the two cylinders. The results suggest that the single vortex wake of a pair of closely spaced staggered cylinders is broadly comparable to the wake of a solitary bluff body, and that the universal wake number concept can be extended to groups of closely spaced bluff bodies.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Energy and Exergy Analyses of Tube Banks in Waste Heat Recovery Applications

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2094 ◽  
Author(s):  
Mustafa Erguvan ◽  
David MacPhee
Keyword(s):  
Energy Efficiency ◽  
Reynolds Number ◽  
Heat Recovery ◽  
Waste Heat ◽  
Cross Flow ◽  
Exergy Efficiency ◽  
Circular Cylinders ◽  
Published Data ◽  
Energy And Exergy ◽  
Exergy Analyses

In this study, energy and exergy analyses have been investigated numerically for unsteady cross-flow over heated circular cylinders. Numerous simulations were conducted varying the number of inline tubes, inlet velocity, dimensionless pitch ratios and Reynolds number. Heat leakage into the domain is modeled as a source term. Numerical results compare favorably to published data in terms of Nusselt number and pressure drop. It was found that the energy efficiency varies between 72% and 98% for all cases, and viscous dissipation has a very low effect on the energy efficiency for low Reynolds number cases. The exergy efficiency ranges from 40–64%, and the entropy generation due to heat transfer was found to have a significant effect on exergy efficiency. The results suggest that exergy efficiency can be maximized by choosing specific pitch ratios for various Reynolds numbers. The results could be useful in designing more efficient heat recovery systems, especially for low temperature applications.

Strouhal Number for VIV Excitation of Long Slender Structures

2018 ◽  
Author(s):  
Andrew E. Potts ◽  
Douglas A. Potts ◽  
Hayden Marcollo ◽  
Kanishka Jayasinghe
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Degrees Of Freedom ◽  
Measurement Techniques ◽  
Cross Flow ◽  
Degree Of Freedom ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom ◽  
Shedding Frequency ◽  
Eddy Shedding

The prediction of Vortex-Induced Vibration (VIV) of cylinders under fluid flow conditions depends upon the eddy shedding frequency, conventionally described by the Strouhal Number. The most commonly cited relationship between Strouhal Number and Reynolds Number for circular cylinders was developed by Lienhard [1], whereby the Strouhal Number exhibits a consistent narrow band of about 0.2 (conventional across the sub-critical Re range), with a pronounced hump peaking at about 0.5 within the critical flow regime. The source data underlying this relationship is re-examined, wherein it was found to be predominantly associated with eddy shedding frequency about fixed or stationary cylinders. The pronounced hump appears to be an artefact of the measurement techniques employed by various investigators to detect eddy-shedding frequency in the wake of the cylinder. A variety of contemporary test data for elastically mounted cylinders, with freedom to oscillate under one degree of freedom (i.e. cross flow) and two degrees of freedom (i.e. cross flow and in-line) were evaluated and compared against the conventional Strouhal Number relationship. It is well established for VIV that the eddy shedding frequency will synchronise with the near resonant motions of a dynamically oscillating cylinder, such that the resultant bandwidth of lock-in exhibits a wider range of effective Strouhal Numbers than that reflected in the narrow-banded relationship about a mean of 0.2. However, whilst cylinders oscillating under one degree of freedom exhibit a mean Strouhal Number of 0.2 consistent with fixed/stationary cylinders, cylinders with two degrees of freedom exhibit a much lower mean Strouhal Number of around 0.14–0.15. Data supports the relationship that Strouhal Number does slightly diminish with increasing Reynolds Number. For oscillating cylinders, the bandwidth about the mean Strouhal Number value appears to remain largely consistent. For many practical structures in the marine environment subject to VIV excitation, such as long span, slender risers, mooring lines, pipeline spans, towed array sonar strings, and alike, the long flexible cylinders will respond in two degrees of freedom, where the identified difference in Strouhal Number is a significant aspect to be accounted for in the modelling of its dynamic behaviour.

VIV Response and Drag Measurements of Circular Cylinders Fitted With Permeable Meshes

2015 ◽  
Author(s):  
Murilo M. Cicolin ◽  
Gustavo R. S. Assi
Keyword(s):  
Reynolds Number ◽  
Long Range ◽  
Flow Direction ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Peak Response ◽  
Vortex Induced Vibrations ◽  
Different Types ◽  
Cylindrical Tubes ◽  
Low Mass

Experiments have been carried out on models of rigid circular cylinders fitted with three different types of permeable meshes to investigate their effectiveness in the suppression of vortex-induced vibrations (VIV). Measurements of amplitude of vibration and drag force are presented for models with low mass and damping which are free to respond in the cross-flow direction. Results for two meshes made of ropes and cylindrical tubes are compared with the VIV response of a bare cylinder and that of a known suppressor called the “ventilated trousers” (VT). All three meshes achieved an average 50% reduction of the peak response when compared with that of the bare cylinder. The sparse mesh configuration presented a similar behaviour to the VT, while the dense mesh produced considerable VIV response for an indefinitely long range of reduced velocity. All the three meshes have increased drag when compared with that of the bare cylinder. Reynolds number ranged from 5,000 to 25,000 and reduced velocity was varied between 2 and 15.

The intense vorticity structures near the turbulent/non-turbulent interface in a jet

2011 ◽  
Vol 685 ◽  
pp. 165-190 ◽  
Author(s):  
Carlos B. da Silva ◽  
Ricardo J. N. dos Reis ◽  
José C. F. Pereira
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Isotropic Turbulence ◽  
Tangential Velocity ◽  
Sharp Decrease ◽  
Good Representation ◽  
Micro Scale ◽  
Vortex Model ◽  
Burgers Vortex ◽  
The Mean

AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

Fluid Flow and Heat Transfer Around Two Circular Cylinders in Side-by-Side Arrangement

2004 ◽  
Author(s):  
Minter Cheng
Keyword(s):  
Nusselt Number ◽  
Flow Velocity ◽  
Incompressible Flows ◽  
Temperature Fields ◽  
Circular Cylinders ◽  
Rapid Reduction ◽  
Nusselt Numbers ◽  
Gap Flow ◽  
Pitch Ratio ◽  
The Mean

Incompressible flows passing through two circular cylinders in side-by-side arrangement are investigated numerically. The calculations are carried out with pitch ratios from 1.1 to 2.0 at Reynolds number of 1000. The flow and temperature fields, flow interference, and the local and the mean Nusselt numbers are studied in this research. It is observed that for the pitch ratios in the range of 2.0 and 1.5, the emerging jet between cylinders deflects and one wide and one narrow wakes behind the cylinders are formed. The gap flow velocity increases as the pitch ratio decreases and consequently increases the mean Nusselt number of the cylinders. As the pitch ratio decreases and is less than 1.5, the jet deflection is more severe and the gap flow velocity starts to decrease slowly, which results in reducing the mean Nusselt number of the cylinders. Due to the rapid reduction of the narrow wake size, the mean Nusselt number of the cylinder with narrow wake shows an uprising tendency for the decreasing pitch ratio less than 1.2.

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