The ESDU standard also outlines theoretical guidelines for the formulation of mean pressure coefficients (Cp) across a circular cylinder. Figures 13 and. Mean forces, pressure and flow field velocities for circular cylindrical structures: single cylinder with two-dimensional flow, Data Item ESDU Goliger, A.M. Engineering Sciences Data Unit (ESDU International, London). ESDU data item Gartshore, I.S. () The effects of freestream turbulence on the drag of .

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Published on Sep View Download For current status, contact ESDU. The data are founded on an evaluation of all the relevant information, bothpublished and unpublished, and are invariably supported by original work of ESDU staff engineers or consultants. The whole process is subject to independent review for which crucial support is provided by industrial companies,government research laboratories, universities and others from around the world through the participation of someof their leading experts on ESDU Technical Committees.

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The Panel has benefited from the participation of members from several engineering disciplines. Flint has been appointed to represent the interests of structural engineering as the nominee of the Institutionof Structural Engineers.

Continued on inside back cover ChairmanMr T. Cockrell University of Leicester Prof. Flint Flint and NeillMr D. Whitbread National Maritime Institute. Single Cylinder with Two-dimensional Flow1. ESDU critical Reynolds number, i. Only single cylinders are considered in this Item; mean forceson cylinders in groups will be the subject of a separate Data Item.

In the present context the data applywhen the effect of the flow around the free end or ends can be ignored e. Reference 1 provides additional information in the form of correction factors which can be applied to thesedata to account for end effects and shear flow effects, such as those associated with cantilever structures inthe non-uniform atmospheric wind.

The circular cylinder is one of the most commonly occurring shapes in engineering structures. Typicalexamples are chimney stacks, towers, storage tanks, silos, cables, pipe lines, space vehicles and missiles,and elements of structures such as lattice towers and off-shore structures.

Other examples are pipes andstruts inside ducts but in these cases the confinement effects due to the proximity of the duct walls must betaken into account see ESDU In many situations the overall response mean and fluctuating ofthe structure to the approaching flow, such as the atmospheric wind, is needed for design purposes.

ThisItem provides data for estimating the mean components of loading. The fluctuating components, such asthose arising from buffeting by a turbulent flow or from vortex shedding, must also be considered;ESDU provides methods for estimating the maximum design loading due to buffeting byatmospheric turbulence along the wind direction and Reference 8 deals with the across-flow response dueto vortex shedding. The following data can be obtained from this data Item.

It must be emphasised that with circular cylindrical structures there are a number of parameters that canhave a very significant effect on the flow-induced forces. The effects of the following parameters areparticularly important and can be taken into account when estimating data from this Item.

Read the generalbackground notes referred to in the appropriate Sections of interest. Section 8 contains two workedexamples and Appendix A provides a general description of the features of the flow around acircular cylinder. Drag coefficients of plain cylinders 3Force coefficients of inclined cylinders 4Drag coefficients of stranded cables 5. Reynolds number up to full-scale values 3,Roughness of cylinder surface up to 3, 3.

This means that either the cylinder is sufficiently long that end effects, which induce athree dimensional flow around the tip, are essentially localised to that region or that end effects areminimised by placing the cylinder between end plates.

In this latter situation truly representativetwo-dimensional conditions will only prevail if the length to diameter ratio of the cylinder is greater thanabout 5 or 6; this then allows the three-dimensional cell-like structure of the wake associated with vortexshedding to develop naturally. Correction factors to account for finite-length cylinders in shear orboundary-layer flow, such as the atmospheric wind, are provided in Reference 1.

Other limitations on the use of the data are either implied by the comments in the text and the Figures orby the range of experimental data used to derive the various correlations summarised in the Table inAppendix D.

### Line types: Drag & lift data

Where possible the data have been interpolated and extrapolated to conditions other thanthose for which experimental data are available. The uncertainties of the data presented are, in general, indicated on the appropriate Figures or discussed inthe related text.

The following notes provide a background to the derivation of the data. The flow pattern around a circular cylinder and the resulting drag coefficient are primarily determinedby the position of the separation points at which the upstream boundary layer leaves the cylinder surfaceto form the wake region.

The location of the separation points is primarily determined by the Reynoldsnumber and turbulence characteristics of the approaching flow and by the roughness of the cylinder surface.

The flow pattern development from very low to very high Reynolds numbers, and the general effects ofturbulence and surface roughness, are described in Appendix A for conditions where compressibility effectscan be ignored Mach number less than 0. In practice, the drag coefficient of a two-dimensionalcircular cylinder can be correlated with flow and surface roughness conditions in the formas given by Figures 1a to 1c.

The effective Reynolds number is a modified Reynoldsnumber incorporating the factordependent on the turbulence characteristics of the approaching flow,and dependent on the surface roughness parameter. The derivation of these factors is described in Sections 3. The procedure for evaluating CD0 is described in Section 3. In addition Section 3. It may be defined as the ratio of Re for a smooth cylinder giving a specified valueof CD0 to Re for a rough cylinder in the same free-stream giving the same CD0, both measured in thetransition region following ReD ; in practice it is related to.

This relationship is shown in Figure 2which has esdy derived from an analysis of data for cylinders with uniformly distributed roughness.

However, Figure esduu and Figure 1c. Some approximate values of the quantity for a number of different surfaces are given in Table These values are equivalent sand-grain roughness heights, the derivation of which is discussed inAppendix B. Considerable variation in these values can apply as indicated in Table It is also importantto remember that the deterioration of a surface with time usually increases the surface roughness and, unlessspecial maintenance procedures are employed, this should be taken into account when selecting anappropriate value of.

The physical reasons for this and for therapid variation of CD0 with Re in dsdu transition region are explained in Appendix A. An analysis of datafrom various sources see Appendix D shows that the effect of free-stream turbulence on CD0 becomesincreasingly important for Re greater than about although its effect decreases again for thevalue of Re at which CD0 begins to fall in the transition region and is negligible for. For agiven surface roughness this effect is represented in Equation 3.

This parameterdepends on Re and Recrit, which in turn is determined by andand is given by. Figure 3aprovides values of as a function of the turbulence parameter.

The parameters and represent the intensity and scale of the turbulence in the approaching flow Appendix A explains thephysical significance of these properties and typical values are given in Table If then the factor and steps 4 to 8 can be ignored. Typically, for a low-turbulence wing-tunnel flow, is about 1. In practice, thedata in Figures 1 to 3 show that the addition of moderate eseu roughness and sometimes an increase inturbulence in the approaching flow can be used to promote supercritical flow conditions at Reynoldsnumbers when the flow would otherwise have been subcritical, as illustrated in Sketch 3.

For example,referring to Sketch 3. It cannot be used for groups of cylinders since wake-interferenceeffects nullify the Reynolds number equivalence. It cannot be used when Re is less that about 3 sinceroughness then has no significant effect on the flow regime. It can only esu used sensibly over a relativelysmall range of effective Reynolds numbers.

## ESDU 80025c-1986.pdf

However, the Data Item can be used to provide guidance inascertaining the degree of additional roughness and turbulence that would be required to generate theappropriate supercritical flow conditions in a wind-tunnel test. Examples areleg members of lattice structures and off-shore structures, bridge cables and pipe lines. The ezdu presentedin this Section provide force coefficients giving either the drag force or the force normal to the cylinder axis.

The method of allowing for cylinder inclination depends on whether the flow is subcritical or supercritical. For subcritical flow the simple cross-flow theory given in Section 4. For supercritical flow the evidence is that this simple cross-flow theory underestimates orCN for relatively smooth two-dimensional cylinders and should not be used; Section 4. The critical flow velocity corresponding to Recrit for an inclined cylinder is found to be lower than thatfor the same cylinder normal to the flow.

In practice the critical Reynolds number is approximatelyindependent of if expressed in terms of the streamwise components so that 4. Thereason for this is that while for the laminar boundary layer and the associated pressuredistribution tends to depend only on the cross-flow dsdu, when transition to turbulent flow in theboundary layer has occurred the subsequent development and separation of the boundarylayer are adversely affected by the three dimensional nature of the turbulent wake flow.

This exerts aconsiderable influence on the pressure distribution and increases the flow-induced forces over thosepredicted using simple cross-flow theory. An analysis of the available data15, 44 indicates that in this flow regime the force coefficients may beestimated using, 4.

Appendix C providesequations representing the data in Figure 4. ESDU The data for in Figure 4 for smooth or relatively smooth cylinders can be taken to apply up to say. For very rough cylinders the adverse effect of the roughness elements causing earlierseparation edu the boundary layer from the cylinder is unlikely to be made significantly worse by thethree-dimensional wake effects induced by cylinder inclination.

For this reason it is probable that the simplecross-flow theory described in Section 4. Between and 10 values of between the two extreme recommendations arelikely to apply as indicated in Figure 4 and by the Equations in Appendix C. No data have been 8002 toverify these tentative recommendations and this is clearly an important area needing further research.

In the absence of any other information asimilar procedure may be used for using the appropriate data in Section 4. The correlation follows the trend of a collection of data22, 47which show a scatter of about 0. The experimentaldata indicate that for smooth flow conditions the rapid fall in CD0 with Re occurs at a Reynoldsnumber of between 2 and 3 Insufficient data are available for to indicate how CD0 varies for.

For stranded cables 800255 are inclined to the approaching flow it may be assumed that the simple cross-flowtheory described in Section 4. In this case Recrit based on streamwise components can be takenas the value of Re in Figure 5 at which the rapid fall in CD0 begins. The use of shrouds fitted to the top 25 per cent of circular cylindricalstructures has also been shown to be effective in reducing oscillatory motion due to vortex shedding.

Theperforations in the cylinder act to reduce the tendency to shed strong vortices. Drag coefficient data for a uniformly perforated cylinder are presented in Figure 6 as a function of theopen-area ratio. Similar data for a cylinder enclosed by a perforated shroud are given in Figure 7. Inthis case data are provided giving CD0 for the cylinder-shroud combination and the component of this totalCD0 acting on the shroud. Particular features to note in Figure 6 and 7 are that i the drag coefficient of a perforated cylinder can begreater than that for an equivalent solid cylinder and ii that with shrouded cylinders the drag coefficientof the inner cylinder can be negative.

Since the data on which Figures 6 and 7 are based are limited to specific configurations they have beenextrapolated to other open-area ratios and cylinder-to-shroud diameters using methods outlined inSection 5. An approximate estimate of the drag of a perforated cylinder is given by considering two perforatedplates in series using data presented in Item Nos and Correction factors for the extreme cases where and 1.

This forms the basis for Figure 6.