Mean and fluctuating forces on a circular cylinder in cross-flow near a plane surface

Mean and fluctuating forces on a circular cylinder in cross-flow near a plane surface

Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 639--650 Elsevier 639 Mean and fluctuating f o r c e s o n a c i r c u l a r c...

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Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 639--650 Elsevier

639

Mean and fluctuating f o r c e s o n a c i r c u l a r cylinder in cross-flow near a plane s u r f a c e G. Buresti and A. Lanciotti Department of Aerospace Engineering, University of Pisa, V. Diotisalvi 2, 56126 Pisa, Italy Abstract An experimental investigation for the measurement of the mean and fluctuating forces acting on a circular cylinder in cross-flow, placed near a plane surface parallel to its axis, is described. Tests were carried out with three different types of boundary layer on the plane, having relative thickness ~/D from 0.1 to 1.1, at Reynolds numbers from 0.86 to 2.77 x 105, a range in which the flow around an isolated cylinder is characterized by a progressive disappearance of r e g u l a r vortex shedding. The results showed that at subcritical Reynolds numbers periodic oscillating lift forces induced by regular vortex shedding are present at least down to relative distances from the plane, G/D, of 0.4, irrespective of the thickness of the boundary layer. The mean lift coefficient was found to rapidly decrease by increasing the gap size, whereas the mean drag coefficient showed non-monotonic trends with G/D, clearly dependent on the Reynolds number and significantly influenced by the thickness of the boundary layer on the plane. I. INTRODUCTION The knowledge of the forces acting on a circular cylinder in cross-flow placed near a parallel plane surface is of interest for many engineering applications, as for instance the design of submarine pipelines. Particularly important are the periodic fluctuating cross-flow (lift) and in-line (drag) forces connected to regular vortex-shedding, which may give rise to flow-induced non-linear oscillations of a cylindrical structure. Measurements of the mean pressures and forces acting on the cylinder and of the spectra of the velocity fluctuations have already clarified many of the features of the interference between cylinder and plane ([1] - [9]). In particular, it was ascertained that regular vortex shedding persists almost unaltered down to a critical relative distance from the plane, G/D, of 0.3 - 0.4 ([3], [4], [6], [7]), whereas the mean lift and drag forces were found to strongly depend on the gap size ([1], [2], [5], [8]). However, the effects of the thickness and of the characteristics of the approaching boundary layer on the plane are not yet completely understood ([7], [8], [9]), and only few data are available as regards the direct evaluation of the fluctuating forces, [10]. In this paper further measurements of the mean and unsteady forces will be presented, covering a 0167-6105/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

640 Reynolds number range which spans the interval between the subcritical and the critical flow for an isolated cylinder, corresponding to the progressive transition from regular to random vortex shedding in the wake. 2. EXPERIMENTAL EQUIPME~NT AND PROCEDURES The experiments were performed in a GSttingen type subsonic wind tunnel, with a circular open test section 1100 mm in diameter and 1480 mm in length, and a freestream turbulence level of = 0.9%. The tests were carried out at the following approximate values of the Reynolds number, referred to the cylinder diameter: 0.86, 1.4, 1.9, 2.35, 2.76 x 105. Acceptably two-dimensional conditions (with maximum variations of the base pressure coefficient below 5% along the central 85% of the test cylinder) were obtained by means of two lateral walls mounted in the test section 780 mm apart. A 20 mm thick plane with rounded leading edge was positioned at various distances from the cylinder (G/D = 0., 0.2, 0.3, 0.4, 0.8, 1.5). The plane was adjusted to assure that it was truly parallel to the main flow direction by minimizing the pressure difference between its upper and lower surfaces near the leading edge. Further information on the general layout of the tests may be found in [4] and [5]. The model was an aluminium alloy tube, 118 mm in diameter, having two 50 mm long sectors (active cells) supported by two-component semi-conductor strain-gage balances (Fig. 1), expressly designed for this application ([11]); these cells could be positioned at different mutual distances by the insertion of dummy portions of cylinder of different length, so that the correlation of the forces could be obtained for distances between the mid-sections of the cells of 1.2 D, 2 D, 3 D and 4 D. The effect of the small gap (0.1 - 0.2 mm) between the active cells and the remaining parts of the model was found to be negligible through preliminary pressure measurements on the model and in the wake; nevertheless, a labyrinth-shaped gap was used to avoid any significant leakage of air (Fig. 1). For G/D -- 0 a gap of_--0.1 mm was actually present below the two active cells and sealed elsewhere. The model was positioned at approximately 750 mm from the leading edge of the plane, crossed the lateral walls, and was rigidly supported by a special external fixture; the gap between the model and the lateral walls was accurately sealed. Three boundary layers on the plane were used. The first was that developing naturally, with a thickness 8 of_-- 0.1 D at the cylinder axis position, while the intermediate one, with 8/D -~0.45, was obtained by means of a 10 mm rod followed by superficial roughness. To produce the third boundary layer, approximately 1 D thick, a 150 mm grid with degrading meshes was added between the rod and the roughness. Thus a range of 8/D similar to that of [8]-[10], and sufficient for the analysis of the influence of this parameter, was obtained The mean velocity profiles of the boundary layers may be approximated with power laws having expcr~ents between 0.18 and 0.14, and are shown in Fig. 2 for various free-stream velocities. The relevant global, displacement and momentum thicknesses corresponding to the lowest test velocity are given in Table 1. The dynamic response of the whole equipment was accurately determined by sinusoidal excitation in the drag and lift directions both of the measuring sectors and of the basic cylinder; the first natural frequency was found to be of

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642 the order of 300 Hz, i.e. sufficiently larger t h a n the highest significant harmonic components of the fluid dynamic forces, which during preliminary tests were found to be approximately 50-60 Hz. Consequently, the balance signals were filtered at 150 Hz and then acquired at the rate of 512 Hz. The acquisition and processing equipment is sketched in Fig.3. The reference velocity for the tests was that at the cylinder axis position in absence of the model for the natural boundary layer on the plane, and the velocity just outside the boundary layer in correspondence to the same position for the other two boundary layers. The corrections to be given to the reading of the wind tunnel reference Pitot to obtain these velocities were derived during the preliminary tests. From the calibration data of ff balances the maximum errors in the force measurements were estimated to be lower than 3%, while, from the accuracy of the pressure gage, the maximum errors in the reference velocity values ranged from 3% to below 1% with increasing Reynolds number.

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Fig. 3. Sl:etch of the acquisition and processing system. 3. RESULTS AND DISCUSSION The first tests were carried out without the plane to check the adequacy of the experimental set-up by comparison of the results with those available from the literature, and also to increase the number of data on the qualitative and quantitative features of the unsteady forces acting on an isolated cylinder in the transition from the subcritical to the critical regime. The decrease of the mean drag coefficient with increasing Reynolds number was in very good agreement with available literature data for similar turbulence levels, [12]. Plausible results were also found as regards the oscillating lift force coefficients, which decreased from r.m.s, values around 0.5 to approximately 0.2, in connection with the progressive disappearance of the regular vortex shedding (which, as ascertained from spectral analyses, took place above Re = 1.9 x 10s).

643 The influence of the presence of the plane with the different types of boundary layers will now be analysed, with particular reference to the more significant boundary layers 1 and 3. One of the main points to be investigated was the effect of the plane on the existence of regular vortex shedding and on the characteristics of the consequent fluctuating lift forces.

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644 Fig. 4 shows the spectra of the lift forces measured at Re = 0.86 x 105 with the two boundary layers. As can be seen, clear peaks are present down to distances of the order of 0.4 D for both boundary layers, and the existence of regular vortex shedding down to this gap size is confirmed by the behaviour of the correlation coefficient between the lift forces acting on the two active cells at a mutual distance of 2 D (Fig. 5). It is apparent that the critical gap at which vortex shedding ceases does not increase with the thickness of the boundary layer. Conversely, a closer analysis of Figs. 4 and 5 shows t h a t with the thickest boundary layer (5/D -- 1.1 D) a small peak at the Strouhal frequency is present even at G/D = 0.3; the result for boundary layer 2 (8]D -- 0.45 D) was found to be intermediate between those of the other two boundary layers. |

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Fig. 5. Correlation coefficientsbetween the liftforceson active cells2D apart. A similar flow behaviour had already been documented in previous works by measuring the velocity fluctuations around the cylinder ([3], [4], [7], [9]), whereas from lift force measurements an increase of the critical gap with the thickness of the boundary layer has recently been suggested in [10]. The reason of the discrepancy between the results obtained in [10] and all other available data is at present not completely clear. Indeed, in [7] the critical gap was found to be G/D = 0.3 up to a 5/D of about 2.5, and only for a cylinder immersed in an extremely thick (8/]3 over 3.5) and highly turbulent boundary layer did this value raised to 0.5. The explanation of this behaviour, already suggested in [7], may be that the critical gap in a thick boundary layer is larger than that for uniform approaching flow only if the gradient of velocity at the cylinder location is greater than some limit value. In other terms, a significant parameter may be the ratio, AU/U, between the velocity difference between the top and bottom of the cylinder and the approaching center-line velocity; from the results of [7] one might argue that for values of this parameter larger than, say, 0.35 - 0.4, vortex shedding may be inhibited. As for the small decrease of the critical gap with increasing thickness of the boundary layer, found in the present research and arising also

645 from the results of [3] and [7], it might be due to the disappearance, induced by the turbulence in the boundary layer, of the separation bubble in front of the cylinder, already described and discussed in [7] and [9]. Another possible mechanism is the downward rotation of the velocity approaching the cylinder caused by the stagnation pressure gradient in the boundary layer. The Strouhal number data obtained in the present investigation from the peaks in the lift spectra are shown in Fig. 6 for the three boundary layers. As can be appreciated, the values are practically constant with decreasing G/D, save for a 5% variation at the lowest gaps, with an increase for the smallest boundary layer and a decrease for the other two. Although these variations are only slightly above the m e a s u r e m e n t accuracy, they are qualitatively in agreement with those found in [6] and [7], but quantitatively smaller. 0.22 0.2 S 0.18

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Fig. 8. Mean lift coefficients for boundary layers 1 and 3. As regards the mean forces, the lift force (always positive, i.e. directed away from the plane) was found to rapidly decrease by increasing G/D, as shown in Figs. 8 a) and b). This result is in agreement with previous findings ([1], [2], [5], [8]); in particular, it was shown in [5] that, at least for 8/]) = 0.1, the positive mean lift is mainly due to a rotatio~ ox"the stagnation point on the cylinder, whereas the pressure distribution remains fairly symmetrical with respect to a meridian plane passing through the stagnation point. Fig. 8 b) shows tha~ for boundary layer 3 the lift coefficient seems to decrease more rapidly, and this result may perhaps be explained with the already mentioned mechanisms of rotation of the approaching velocity and of inhibition of the formation of

648 separation bubbles on the plane. Probably the same mechanisms may contribute to the negative lift forces which were found in [8] (but only for a particular boundary layer produced through mesh wire) for values of G/D between 0.2 and 1. 1.4

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G/D Fig, 9. Mcan drag coefficients for boundary layers I and 3. Fig. 9 a) shows that for the smallest boundary layer the m e a n drag coefficient passes from the value corresponding to a cylinder resting on the plane to that of an isolated cylinder with a non-monotonic trend, clearly dependent on the Reynolds number; the results are in good agreement with other available data ([1], [2], [5]). The significant influence of the thickness of

649 the boundary layer arises from the comparison with Fig. 9 b), in which the data at the higher Reynolds numbers and G/D _< 0.4 show a larger reduction than might be explained by the reduced dynamic pressure inside the boundary layer. The high turbulence intensity in the inner layers, and the consequent shift of the flow regime towards conditions nearer to those corresponding to a minimum in the CDm - Re curve, might justify this result. 4. CONCLUSIONS The results obtained in the present investigation generally confirm most of the available informat'on on the aerodynamic features of circular cylinders in cross-flow n e a r a plane surface. In particular, for subcritical Reynolds numbers fluctuating forces induced by vortex shedding, with only slightly variable Strouhal numbers, were found down to a critical gap G/D = 0.4 for the thin boundary layer (8/D -- 0.1), and G/D = 0.3 for the thicker boundary layers (5/D _--0.45 and 1.1). Therefore, the persistence of vortex shedding and related phenomena, irrespective of the thickness of the boundary layer on the plane, seems to be a strong feature of the flow, at least unless the vertical velocity gradient becomes excessive. However, the high sensitivity of the transitional regimes to even small perturbations, yet again apparent from the results of the present investigation, may lead to a significant influence of the characteristics of the turbulent field inside the approaching boundary layers. For instance, the increased turbulence in the inner parts of the boundary layer may explain the slight increase in the critical gap found when the Reynolds number was varied from 0 . 8 6 x 105to 1.42 x 105. As for the mean forces, they appeared to be significantly affected by the value of the distance from the plane. In particular, the drag coefficient showed no clear trends as a function of the relative gap, and a dependence on the boundary layer thickness that may be a consequence both of the reduced dynamic pressure and of the increased turbulence intensity.

5. REFEPt'~CES 1

2 3 4 5

S . - The drag and lift coefficients of a cylinder placed near a plane surface, MSc. Thesis, Naval Postgraduate School, Monterey, Cal., 1975. Roshko A., Steinolfson A., Chattoorgoon V. - Flow forces on a cylinder near a wall or near another cylinder, Proc. 2nd US Conf. Wind Engineering Research, Fort Collins, 1975, paper IV-15. Bearman P.W. & Zdravkovich M.M. - Flow around a circular cylinder near a plane surface, Jnl. Fluid Mech., Vol. 89, 1978, pp. 33-47. Buresti G. & Lanciotti A. - Vortex shedding from smooth and roughened cylinders in cross flow near a plane surface, Aeronautical Quarterly, Vol.XXX, 1979, pp. 305-321. Buresti G. & Launaro F. - Pressure measurements around a circular cylinder in cross flow near a plane boundary, Institute of Aeronautics of the Univ. of Pisa, Report AIAA 80-1, 1980. GStkun

650 6 Angrilli F., Bergamaschi S., Cossalter V. - Investigation of wall induced modifications to vortex shedding from a circular cylinder, ASME Jnl. Fluid Engng., Vol. 104, 1982, pp. 518-522. 7 Grass A.J., Raven P.W.J., S t u a r t R.J., B r a y J.A. - The influence of boundary layer velocity gradients and bed proximity on vortex shedding from free spanning pipelines, ASME Jnl. Ener. Res. Techn., Vol. 106, 1984, pp. 70-78. 8 Zdravkovich M.M. - Forces on a circular cylinder near a plane wall, Appl. Ocean Res., Vol.7, 1985, pp.197-201. 9 Zdravkovich M.M. - A circular cylinder partly submerged in three boundary layers, presented at the 5th Into OMAE Symp., Tokyo April 1986. • 10 Taniguchi S. & Miyakoshi K. - F l u c t u a t i n g fluid forces on a circular cylinder and interference with a plane wall, Experiments in Fluids, Vol. 9, 1990, pp. 197-204. 11 Buresti G. & Frediani A. - Misurazione delle forze indotte da campi fluidodinamici su cilindri in galleria aerodinamica, Progettare, N. 41, 1983, pp. 49-55. 12 E.S.D.U. - Mean forces, pressures and flow field velocities for circular cylindrical s t r u c t u r e s : single cylinder with t w o - d i m e n s i o n a l flow, Engineering Science Data Unit, Item N ° 80025,1980 (amended 1986).