Journal o[ Wind Engineering and Industrial Aerodynamics, 33 (1990) 53-62 53 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

CONCEPTUAL OVERVIEW OF LAMINAR AND TURBULENT FLOWS PAST

SMOOTH AND ROUGH C IRCULAR CYL INDERS

M.M. ZDRAVKOVICH

Department of Aeronautical and Mechanical Engineering, Salford University, Salford (Gt. Britain)

Summary

Flow around a circular cylinder is governed by three transitions: in-the-near-wake, along the free shear layers and along the boundary layers. Each transition is characterized by several flow regimes which are sensitive to disturbances. The variation of mean and fluctuating lift and drag coefficients, friction and pressure coefficients are compiled in the range 10< Re< 10 8 for the disturbance-free flow.

The concept of possible inversion of influencing to governing parameters and vice versa is applied to rough cylinders and turbulent flow. The free stream turbulence and surface roughness affect differently the three transitions and may cause an obliteration of some flow regimes in addition to moving the transition state as a whole to lower Reynolds number.

Keywords Circular cylinder, flow regimes, free-stream turbulence, surface roughness

I. CONCEPTUAL INTRODUCTION

A pecu l ia r feature of f low around a l l b lu f f bodies in genera l and around a circular cylinder in particular is that transition from laminar to turbulent flow does not occur simultaneously in all disturbed regions. Instead, a distinct succession of transition states takes place over an enormous range of Reynolds numbers, see Roshko and Fiszdon(1969).

Each transition state is sensitive to extremely small disturbances, like free stream turbulence, surface roughness and many others. The disturbances can initiate each transition at a lower Reynolds number and can modify or inhibit some flow structures. This means that the Reynolds number is expected to be a single ~Lgverning parameter only for the disturbance-free flow.

The second peculiar feature of flow around bluff bodies is that the disturbances expressed through the influencing parameters may become the governing parameters in some transition states. When the disturbances exceed a certain value the flow becomes governed by them and not by the Reynolds number. This important feature of the flow around cylinders has not yet been sufficiently appreciated.

Only two kinds of disturbances will be discussed in this review: free stream turbulence and surface roughness. They are the most common disturbances in practical applications.

The free stream turbulence is described by the intensity T i, scale T s and frequency spectrum Tf of random three-dlmenslonal velocity fluctuations. It will be shown that the influencing parameters T i and T s affect different transition states in a different way.

0167-6105/90/$03.50 1990 Elsevier Science Publishers B.V.

54

The sur face roughness oan be character i zed by at ]eas t two i n t ' luenc ing parameters : the re la t ive s i ze of the roughness , r . and i t s texture . Most of t i le research was car r ied out by the even ly roughened sur t 'nce descr ibed by the r/[I parameter wh i le the uneven sur face roughness a t t rac ted l i t t le a t tent ion w i th the poss ib le except ion of t r ipp ing w i res .

2. TRANSITION STATES

The s ta te of f low d is turbed by the cy l inder may be fu l l y laminar L, a ser ies of t rans i t ions T r or fu l l y tu rbu lent T. Typ ica l t rans i t ion s ta tes of f low around the c i rcu la r cy l inder a re sketched in F ig . 1. The f i r s t t rans i t ion s ta te occurs in the ~ake, F ig . la , where laminar vor t i ces become turbu lent due to th ree-d imens iona l d i s to r t ions fu r ther downstream. The turbu lence spreads upst ream by the inc reas ing Reyno lds number, but the f ree -shear layers sur round ing the nearwake remaln laminar .

The second t rans i t ion s ta te in F ig . lb occurs in the f ree -shear layers . The t rans i t ion reg ion gradua l ly moves upst ream towards the separat ion po in t w i th inc reas ing Reyno lds number.

The th i rd t rans i t ion around separat ion , see F ig . l c was h i s to r i ca l l y d i scovered f i r s t on spheres in 1912 and on cy l inders by Tay lo r (1915) . Th is t rans i t ion produces the la rgest e f fec t on the drag fo rce . There i s an ext remely compl i ca ted in teract ion between the separat ion and t rans i t ion be fore the boundary layers become fu l l y tu rbu lent a long the separat ion l ine .

The four th and las t t rans i t ion s ta te takes p lace in the boundary layers away from the separat ion as dep ic ted in F ig . ld . The upst ream movement of the t rans i t ion reg ion w i th inc reas ing Reyno lds number eventua l ly reaches the s tagnat ion po in t . Beyond the end of the four th t rans i t ion s ta te a l l reg ions of the d i s turbed f low are fo l l y tu rbu lent .

The l i s t of f l ow s ta tes and adopted notat ion i s as fo l lows :

1 L Laminar in a l l reg ions of f low 2 TrW Trans i t ion in wake, laminar e l sewhere 3 TrSL T rans i t ion in f ree shear layers , wake turbu lent 4 TrS T rans i t ion around separat ion , boundary layer laminar 5 TrBL Transition in boundary layers 6 T Turbulent in al l regions of flow

The states TrS and TrBL can be treated as one because separation is the upper l imit of the boundary layer.

3. PROPOSED CLASSIFICATION OF DISTURBANCE-FREE FLOW REGIMES

The accumulated experimental observations have revealed an enormous var ie ty of regular and i r regu lar flow patterns around c i rcu lar cyl inders. The d i s t inc t flow pattern with a l imited var iat ion pers is ts only over a range of Reynolds numbers and wil l be cal led a flow__re igj_me. The flow regimes are expected to be confined within a fixed range of Reynolds numbers only for Nenuine disturbance

-free flows. The uncertainty hidden behind 'genuine' precludes speci f icat ion of any flow regime by the f ixed Reynolds number.

Each state of flow can be subdivided into flow regimes as observed experimentally. The flow regimes are as follows:

L1 - 'creeping' flow (no-separation) 0 < Re < 4 to 5 L2 - steady separated region (closed near-wake) 4 to 5 < Re < 30 to 48 L3 periodic laminar wake 30 to 40 < Re < 150 to 200 TrWI - t rans i t ion of laminar vort ices in wake 150 to 200 < Re < 200 to 25(I. TrW2 - t rans i t ion of vort ices during formation 200 to 250 < Re < 350 to 500 TrSLI - t rans i t ion waves in free shear layers 350 to 500 < Re < lk to 2k TrSL2 - t rans i t ion vort ices in free shear layers Ik to 2k < Re < 20k to 40k TrSL3 - fu l ly turbulent shear layers 20k to 4Ok < Re < lOOk to 200k TrSO - onset of t rans i t ion on separation IOOk to 200k < Re < 320k to 340k

55

TrSI - single separation bubble regime 320k to 340k < Re < 380k to 400k TrS2 - two-bubble regime 380k to 400k < Re < 500k to IM (IM = 106 ) TrS3 - supercr]tica] regime 500k to 1M < Re < 3.5M to 6M. TrBL4 - t ranscr i t i ca l regime, 3.5M to 6 < Re < 6M to 8M TI - postcr i t ioa l regime Re > 8M T2 - ultimate regime Re ~

The variat ion of the flow pattern in these regimes causes continuous or discontinuous changes of the f luctuating and time-averaged(mea~ forces exerted on the cylinder. The mean drag force expressed through the drag coeff icient C D consists of the f r ic t ion drag coeff icient CDf and pressure drag coeff icient CDp. Fig. 2 shows that a l l three drag coeff icients fa l l steeply with r is ing Re in the laminar state, (L1 and L2) owing to a more rapid increase of the dynamic pressure (or 2) than viscous resistance (~V). The formation of Karman vortex street in L3 produces a r ise in CDp and a f luctuating l i f t coeff icient CLI "

The transi t ion in wake TrW changes the trend and both CDp and CLI decrease. The appearance of t ransi t ion waves in TrSL1 elongates the nearwake unti l CDmin is reached and CL 1 becomes negl igible. The transi t ion vortices in free shear layers shorten the vortex formation region in TrSL2 causing an increase in C D and CLI see Gerrard (1966). At the end of TrSL2, CDf becomes negl igible and C D = CDp. The end of the transi t ion in free shear layers TrSL3 is characterised by the invariance of C D, CL 1 and CDI due to the short and invariable vortex formation region.

The third t ransi t ion state affects separation of boundary layers. At f i r s t in TrSO the elongation of the vortex formation region causes a decrease in C D and CLI with l i t t le change in separation point. Then suddenly the separated shear layers are suf f ic ient ly turbulent to reattach and form a separation bubble. The bubble forms at f i r s t only on one side of the cylinder TrSI, see Bearman (1969). The sudden appearance of the bubble and delayed f inal turbulent separation up to 140 causes a discontinuous fa l l in C D and CLI, r ise in Strouhal number and the appearance of a large mean l i f t coeff icient, C L = 1.2.

At higher Reynolds number in TrS2, the second separation bubble is suddenly formed on the other side of the cylinder. This causes another discontinuous fa l l in C D, C L and CL I as depicted in Fig. 2.

TrS3 is marked by the spanwise disruption and fragmentation of separation bubbles leading to an irregular separation l ine. The la t te r seems to be the reason for the cessation of periodic vortex shedding in the supercr i t ical regime. The local drag coeff icient varies along the span, as the bubble changes in shape, within a range shown in Fig. 2. The f luctuating l i f t CLI is due to the turbulent fluctuations in the nearwake. At the end of TrS3, the separation bubbles are ful ly obl iterated along the span but not simultaneously on both sides; hence the reappearance of C L.

TrBL is characterised by the reappearance of the periodic vortex shedding, as found by Roshko (1961). The transi t ion in boundary layers moves slowly upstream and away from the now stra ight separation l ines. The slow r ise in C D and CLI is caused by the shortening of the vortex formation region in the t ranscr i t i ca ] reg ime.

The f ina l tu rbu lent s ta te of f l ow i s reached when the wake, f ree shear and boundary layers are ful ly turbulent. Although no more transit ions are expected the postcr i t i ca l flow regime is not l i ke ly to be invarJant. The turbulent boundary layers are thinned with a further increase of the Reynolds number. The continuous thinning of the boundary and free shear layers wi l l affect the location of separation and subsequent ro l l up of free shear layers. This in turn wil l influence the width of the nearwake and Strouhal number, and presumably the length of the vortex formation region and C D, CL1 values. This is not known at present for the postcr i t i ca l regime.

An ultimate flow regime, when Reynolds number tends asymptotically to inf in i ty, has been theoret ical ly postulated by Batchelor (1956). However, real flows at high Reynolds numbers wil l inevitably bring new influencing parameters before Re ~ ~. For example compressibil ity effect for small diameter cylinder due to high velocity and even a small surface roughness wi l l interfere with extremely thin boundary layers. The c~,,~tet~on wi l l appear in l iquids at high

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4. EFFECT OF FREE-STREAM TURBULENCE

The free-stream is usually turbulent in most pract ical applications but most research has been carried out in almost turbulence-free wind tunnels. However, even small turbulence can affect strongly some transi t ion states. The dominating parameter is the intensity of turbulence T i and only for a few flow regimes the scale T s can become important (see Bearman and Morel, 1983).

The free-stream turbulence has the least effect on the t rans i t ion in wake. The appearance of irregular spanwise ' f ingers ' (see Gerrard 1978) in i t ia tes the t rans i t ion by d istort ing the vortex filaments during their formation. The ' f ingers ' are located between the laminar free shear layers and can hardly be disturbed by the free stream turbulence, i f at a l l .

Hussain and Ramjee (1976) confirmed that the transi t ion in wake is insensit ive to turbulence. Further downstream, however, t rans i t ion is triggered when velocity fluctuations induced by the decaying laminar vortex filaments become of the same order of magnitude as turbulent f luctuations in the free stream, The higher T i the nearer to the cylinder the transi t ion takes place along the wake.

The free-stream turbulence has the strongest effect on t rans i t ion in the free shear layers. The three flow regimes in TrSL are affected in a different extent. Least affected is TrSL1 because the laminar t ransi t ion waves are stable. However, the development of a row of t rans i t ion vortices in TrSL2 is s ign i f icant ly affected by the turbulence and this in turn shortens the vortex formation region (see 6errard 1966). Thus TrSL2 can be obl i terated by a high T i . For example, i f T i > 10% the drag coeff icient reaches 1.2 at Re = 2k and TrSL3 moves in the 103 < Re < 104 range.

The upper subcr i t ical regime TrSL3 is characterised wlth a rapid t ransi t ion to turbulence in free shear layers. The free stream turbulence has l i t t le effect on th is type of t rans i t ion unti l the transi t ion reaches the separation. This heralds a new transi t ion state TrS.

The t rans i t ion at separation TrS is the most strongly affected by the turbulence. Up to three flow regimes in this state can be obl i terated by turbulence. The precr i t i ca l regime TrSO is always triggered ear l ie r by the free stream turbulence. Fig. 3 shows the resemblance in shape of the drag coeff icient curves for a l l turbulent streams and the progressive displacements to lower Reynolds numbers as T i increases. The Strouhal number remains almost constant because the nearwake width is not affected. The turbulence, being a three dimensional phenomenon, reduces the spanwise correlation and extends the length of the vortex formation region. This, in turn, gradually decreases the drag coeff icient.

The free stream turbulence has a strong effect on the formation and obl i terat ion of the separation bubbles. The combined effect of three dimensional and randomly modulated f luctuations inhib i ts the laminar separation and single and two bubble regimes are suppressed, The part ia l and fragmented formation of separation bubbles on both sides presumably resembles the supercr l t ica l regime of the disturbance-free flow around the cylinder. This means that the precr i t i ca l regimes TrSO is d i rect ly followed by the supercr i t ica l regime TrS3.

At s t i l l higher T i , the fragmented separation bubbles are also destroyed. I t is expected that the extent of the supercr i t ica l regime wi l l gradually shrink unt i l i t eventually disappears. The la t te r has not yet been corroborated by experiments. If th is happens then vortex shedding does not cease at a l l and the precr i t i ca l regime is succeeded by the t ranscr i t i ca l regime TrBL4. The drag coeff icient undergoes less and less variat ion with increasing T i, see curves for H.4% and 9.1% in Fig. 3. The Strouhal number ref lects these changes in C D and reaches 0.38, 0.30 and 0.24 respectively. Fluctuating l i f t coeff icient CL 1 r ises inversely at Re = 0.4M, CLI = 0.05, 0.08, 0.12 respectively.

I t should be polnted out that the effect of the free stream turbulence cannot be thought of as a simple displacement of the t ranscr i t i ca l regime to lower Reynolds numbers. This has been noted by Fage and Falkner (1931) by

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