Vortex shedding from finned tubes

Journal of Sotmd and Vibration (1975) 39(3), 293-296

VORTEX SHEDDING FROM FINNED TUBES W. A.

MAIR,P. D. F. JONESAND R. K. W. PALMER

Enghteerhtg Department, Unirersity of Cambridge, Cambridge CB2 IPZ, England (Recei~'ed 7 August 1974) The frequency of regular vortex shedding from a finned tube of the kind used in heat exchangers has been measured for an isolated tube in a wind tunnel. A Strouhal number expressed in terms of an effective diameter, defined as the frontal area per unit length of tube, is found to be nearly constant and to depend only on the ratio of fin spacing to tube diameter. The addition of fins to a tube increases the sharpness of the peak in the power spectrum obtained from a hot-wire anemometer. 1. INTRODUCTION The flow of a gas through a heat exchanger may cause vibration of the tubes and this may sometimes lead to mechanical failure. There are several possible mechanisms by which the flow may generate vibrations but one important one is the regular periodic shedding of vortices from a tube. It has been shown in many experiments, e.g., those by Chen [1, 2], that this occurs not only for an isolated cylinder in a stream, but also for each tube o f a bank in a heat exchanger. T h e shedding of vortices alternately from the two sides of a cylinder generates an oscillatory transverse force (lift) on the cylinder. If the frequency of this is close to a natural structural frequency, or an acoustic one, severe vibrations may occur. Some experiments by Chen [I] have shown that when fins are added to the tubes of a heat exchanger, to increase the heat transfer, the effect of the fins on the frequency of vortex shedding is dependent on the spacing ratio of the tubes. Walker and Reising [3] obtained the surprising result that the frequency of audible vibrations produced by finned tube banks increased continuously with flow velocity, in contrast to the behaviour found with plain tubes. The flow past a bank of tubes in a heat exchanger is much more complex than the flow past an isolated cylinder but an understanding of the former cannot be expected unless the latter is reason~ibly well understood. There is extensive information available on the flow past a single smooth circular cylinder, but little is known about the flow past an isolated cylinder fitted with fins. The object o f the experiments to be described was to find how the frequency of vortex shedding from a cylinder was affected by the presence of fins, of the kind used on tubes in heat exchangers. 2. FINNED TUBES The various finned tubes were m a d e u p by sliding fins and spacers over an inner tube of outside diameter 28.6 ram. The spacers were all of outside diameter 31.8 ram, so that this was the actual tube diameter, D, between the fins. The tube spanned the shorter dimension of the working section of a wind tunnel, measuring 715 m m wide and 940 mm high, but the fins and spacers were added only over the central 180 mm of the span. The central, finned portion 293

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of the span was isolated from the remainder of the cylinder by thin end plates, 305 mm square. For the finned tubes most commonly used in heat exchangers the ratio of fin diameter, Ds, to tube diameter, D, is between about 1.1 and i'5. The fin thickness, t, and the spacing, c, between centres are usually such that t/D varies between about 0.02 and 0.07 and c/D between about 0-06 and 0.15. Two fin diameters were used in the experiments, 38.1 and 44.5 mm, giving DflD equal to 1.2 and 1.4. For the smaller fins only one thickness was used, giving riD --- 0.0224, but for the larger fins t/D varied from 0-0224 to 0.064. For both sizes of fin the spacing ratio, c/D, was varied from about 0.06 up to 0.8 or more, a inuch larger value than is used on tubes in heat exchangers. 3. HOT-WIRE MEASUREMENTS Measurements were made at wind speeds, U, from about 8 to 22 m/s, giving Reynolds numbers based on the diameter D from about 1.6 x 10~ to 4.6 x 10~, but for a given tube little variation of Strouhal number was found within this range of Reynolds number. The optimum position of a hot-wire anemometer for recording the periodic vortex shedding was found initially by using a circular cylinder without fins. The hot wire was placed at a distance o f a b o u t 6D behind the cylinder and moved transversely until a position was reached, outside the turbulent wake, where a clear sinusoidal signal o f maximum amplitude was seen on an oscilloscope. This position of the hot wire was then used in all the later experiments with finned tubes. The hot-wire signals were recorded in analogue form on magnetic tape and subsequently analysed digitally by means of a computer to obtain power spectral density. The frequency at the peak in the power spectrum was then taken to be the vortex shedding frequency, n. The blockage correction calculated by Maskell's method [4] for the cylinder without fins gave an increase ofvelocity of 2.9 ~o. In the absence of information about blockage corrections for finned tubes, this correction was applied to all the results. Since the fins were added only to the central portion of the span and never changed the total frontal area by more than 5 ~o, any error in blockage correction due to neglect of the fins is likely to be small. 4. RESULTS In Figure 1 the Strouhal number, So = nD/U, is plotted for a range of finned tubes. The spacing ratio plotted as abscissa is taken here as the ratio D/c rather than the reciprocal, because this allows the tube with no fins (D/c = 0) to be included. It is clear that all the curves must intersect at D/c = 0 and this fact has been used in drawing the curves. When c/D = t/D the clearance between adjacent fins is zero and the tube becomes a smooth one of diameter Ds. If effects of varying Reynolds number can be ignored, the Strouhal number So (based on the diameter D) must then be equal to DSoo/D s, where Soo is the value of So for no fins (D/c = 0). For the upper curve in Figure 1 this limiting value of So is 0.160 and occurs at D/c = 44.6, while for the three lower curves the limit of So is 0.1375 and occurs at D/c equal to 44.6, 26.0 and 15"6. Thus the curves in Figure I must become more nearly horizontal as the limiting condition is approached. The results of Figure I show a considerable variation of Strouhal number with Ds/D, t/D and c[D. In order to simplify the presentation of the results an effective diameter was defined as 1 DE = - [(c-- t) D + tDf]. c

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VORTEX StlEDDING FROM FINNED TUBF.S 0 2O

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Figure I. Strouhal number So vs spacing ratio Dic for finned tubes.

DIID

riD

1-2 1"4 1"4 1"4

0"0224 0"0224 0'0384 0-064

x 9 A El

This is the frontal area of the finned tube, per unit length. In Figure 2 the. results of Figure 1 are re-plotted in terms of the Strouhal number SoE, based on the effective diameter DE. When D/c = O, SoE and So are the same and the curve in Figure 2 has been drawn to be consistent with Figure 1 in this respect.

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Figure 2. Strouhal number SvE based on effective diameter DL. Notation as for Figure I.

Figure 2 shows that the use of the effective diameter DE to define the Strouhal number collapses the results approximately on to a single curve. Thus the shedding frequency for any specified finned tube within the range investigated may be found with reasonable accuracy from the curve of Figure 2. In the limiting case where c = t, DE = Dj. and the shedding frequency is n = USoE/D I. Any variation o f So~ with D/c, as shown in Figure 2 for the larger values of D/c, would then give a variation o f n with D, which cannot be correct for this case. Thus the curve of Figure 2 for large D[c should not be used for values oft/c much larger than those used in these experiments. The oscilloscope record of the hot-wire signal for the circular cylinder without fins showed some random variation of shedding frequency with time. When the fins were added there was a marked reduction of this variation of frequency and the peak in the power spectrum became correspondingly sharper. This effect of the fins is probably related to increasing two-dimensionality o f the flow, as suggested by Keefe [5].

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w . A . MAIR ET AL. REFERENCES

1. Y. N. CH EN 1967 Journal of the Royal Aeronautical Society 71, 211-214. Frequency of the K arman vortex streets in tube banks. 2. Y. N. CHEN 1968 Transactions of the American Society of Alechanical Engbteers Series B. Journal of Engineerblg for hldustry 90, 134-146. Flow induced vibrations and noise in tube bank heat exchangers due to von Karman streets. 3. W. M. WALKER and G. F. S. REISING 1968 Chemical and Proeess Engh~eering 49, 95-103. Flowinduced vibrations in cross-flow heat exchangers. 4. E. C. MASKELL1965 Aeronautical Research Council Reports and Memorandum No. 3400. A theory of the blockage effects on bluff bodies and stalled wings in a closed wind tunnel. 5. R.T. KEEFE1971 Uni~'ersltyof Toronto blstitute of Aerophysics, Report 76. An investigation of the fluctuating forces acting on a stationary cylinder in a subsonic stream and associated sound field.