Proceedings of the 5TH International Symposium on FSI, AE & FIV+N At the 2002 ASME Int’l Mechanical Engineering Congress & Exposition

17-22 November 2002, New Orleans, Louisiana

NCA-33378

ACOUSTIC VIBRATION IN A STACK INDUCED BY PIPE BENDS

Eisinger, F.L. and Sullivan, R.E.,

Foster Wheeler Power Group Inc., Clinton New Jersey 08809-4000 and

Feenstra, P. and Weaver, D.S., McMaster University

Hamilton, Ontario, Canada Phone: 908-713-2394

Fax: 908-713-2380 E-Mail: frank_eisinger@fwc.com

ABSTRACT Acoustic vibration in two stack liners located inside a stack downstream of two induced draft fans occurred at high loads. Measurements confirmed that an acoustic wave developed in the fundamental diametral mode of the cylindrical stack liners. It manifested itself as a pure tone traveling through the stack to surrounding residential areas. It was suspected that turbulent flow in the pipe bends upstream of the stack and downstream of the fans was the source of the excitation. Laboratory scale model tests confirmed that the bends indeed acted as the source. Two guide vane configurations placed inside the bends were tested experimentally. The tests showed that properly placed guide vanes would reduce the acoustic levels in the stack. The paper gives a description and evaluation of the problem. NOMENCLATURE c = speed of sound, m/s D = pipe diameter, m k = pressure drop coefficient, dimensionless M = v/c = Mach number, dimensionless ∆p = pressure drop, Pa P = acoustic pressure, Pa

p,q = acoustic mode orders for cylindrical pipe, diametral and

radial, respectively, dimensionless v = flow velocity, m/s (πα)p,q = acoustic frequency parameter for

cylindrical pipe, dimensionless ρ = mass density of gas, kg/m3

Subscripts: a = absolute i = inside or inlet o = outlet ac = acoustic INTRODUCTION Noise measurements in the residential areas in the vicinity of a power plant revealed the existence of a persistent 50dB strong single tone noise generated by an acoustic resonance condition which developed inside the 1.45m diameter 88m long vertical stack liners. As the upstream sections of the liners at their inlet consist of two 90 degree bends, it was suspected that the likely driving source of the acoustic resonance is the flow turbulence generated inside the bends. One fifth scale laboratory air flow model tests [1] confirmed the development of the acoustic waves.

The effect of two and three guide vanes installed in both upstream bends was tested successfully. The tests showed that the installation of guide vanes reduced the pressure drop through the bends substantially and also commensurably reduced the acoustic resonance peaks developed in the liners. This paper will provide the results of the experimental full scale and laboratory scale tests and their interpretations. A theoretical analysis of the noise reduction in the system due to the installation of guide vanes in the bends will also be given. BRIEF REVIEW OF PUBLICATIONS Predictions of acoustic pressures in a pipe based on heat-generated one-dimensional wave theory was published by Chu [2,3] and its analogy to a flow velocity and pressure drop-generated wave was shown and discussed by Eisinger et al. [4]. The theory of Mach number and pressure drop-generated acoustic waves was extensively utilized by Eisinger et al. [4] and Eisinger and Sullivan [5] in the prediction of acoustic vibration and its suppression in steam generator and heat exchange tube banks. Blevins and Bressler [6] published experimental data from cold air laboratory scale model tests relating the product of Mach number and pressure drop to the acoustic pressure levels in heat exchanger tube banks. Turbulence-induced acoustic waves generated in piping systems were extensively studied by Bull and Norton [7], Norton [8] and Fahy [9]. Carucci and Mueller [10] presented experimental evidence for a large number of full scale piping systems exposed to flow velocity and pressure drop related internal acoustic loading. Eisinger [11] and Eisinger and Francis [12] developed design guidelines against acoustic fatigue in piping systems utilizing the theory of the strength of the acoustic waves inside a piping system related to the flow Mach number and pressure drop through the system. DESCRIPTION OF PROBLEM AND EVALUATION Stack Liner Geometry and Flow Conditions The 96m high concrete stack contains two side-by-side 1.45m in diameter 88m long cylindrical liners through which the final boiler exhaust gases are released to the atmosphere. Two 90 degree bends placed in series are located at the upstream end of each liner. Figure 1 shows schematically the liner configuration and Figure 2 shows the geometry of the bends. Gas flow discharged from induced draft fans through silencers (one fan for each liner) enters the bend portions of the liners, continues through the

cylindrical portions and exits to the surrounding atmosphere at the top. Table 1 gives the representative gas flow parameters at the inlet and outlet at full load. It can be seen that the gas undergoes temperature, pressure and density changes over the length of the flow path. Full Scale Sound and Vibration Measurements Sound measurements conducted in the surrounding areas of the power plant have revealed the existence of a single tone 50dB (re: 2 x 10-5Pa) noise at a frequency of 144Hz. Figure 3 shows a typical sound spectrum taken in the vicinity of the plant. Structural vibration (acceleration) measurements were taken on the pipe bends at the accessible lower end of the stack liners. A single frequency response at a frequency of 172 Hz was measured in the bend area. Figure 4 shows a typical acceleration spectrum. Interpretation of Measurements. The frequency of acoustic waves (higher order acoustic modes) in a cylinder is given by [8]

( )i

iqp,qp, πD

cf

πα= (1)

where ci is the speed of sound in the medium inside the cylinder, Di is the inside diameter of the cylinder and (πα)p,q is a parameter representing the acoustic mode. Here p,q are the mode orders giving the number of diametral and cylindrical nodal lines, respectively. Using equation (1) and flow data in Table 1 for p = 1, q = 0, i.e. for the first diametral acoustic mode with (πα)1,0 = 1.8412 [8], we obtain for the acoustic frequencies the following values: fi = 172Hz at the stack inlet, and fo = 144Hz at the stack outlet (Table 1). These frequencies match those measured at the bends and in the plant surrounding areas, respectively, confirming the existence of the diametral acoustic mode inside the entire length of the stack liners. A gradual change of the acoustic frequency occurs, consistent with the variation of the temperature and pressure of the gas inside the stack liners. Scale Model Laboratory Tests with Cold Air Laboratory model testing of one simulated stack liner (one fifth scale) exposed to air flow at ambient atmospheric conditions was performed [1]. The main purpose of the test was to determine whether acoustic waves would be generated and if generated whether their strength could be reduced by inserting guide vanes in the bends. The motivation of utilizing

guide vanes to reduce pressure drop and thereby reduce the generated acoustic pressure levels was based on the past studies of piping systems [11], [12], where a relationship between acoustic pressure P and the product of Mach number M and pressure drop ∆p has clearly been established. The tests were designed to first obtain baseline data for the unmodified scale model and then data with two and three guide vanes inserted into both of the 90 degree bends. The recommended “optimum” arrangement of guide vanes [13] has been chosen for the tests. Figure 5 shows the arrangement of the guide vanes inserted into the larger 2.45m radius bend and the smaller 1.53m radius bend, respectively. The “optimum” vane arrangement based on the equal radius ratio concept is shown in Figure 6 for two and three guide vanes in the smaller 1.52m radius bend. A similar arrangement was devised for the larger radius bend. The scale model pipe system made of acrylic material was exposed to air flow generated by a centrifugal fan within a range of flow velocities. At each flow condition, average flow velocities, pressure drop through the bends, and acoustic resonant pressures generated in the straight pipe downstream of the bends, was measured. Table 2 gives the results for two sets of tests for three flow conditions for the unmodified and for the modified structure with two and three guide vanes installed. At each flow velocity v, the maximum acoustic pressure P, the pressure drop through the bends ∆p, and the product of Mach number M = v/c and pressure drop, M∆p, are given in Table 2 for a speed of sound of c = 346.9 m/s at 25oC. The results show that the pressure drop through the bends is reduced by an average of 32.5% with two guide vanes and practically is not further reduced by the three guide vanes. It can also be seen that the installed guide vanes reduce the generated maximum acoustic pressures significantly (here again, the three guide vanes did not improve the results over those of the two guide vanes). From the experimental data the numerical values of the pressure drop coefficients through the bends (excluding explicit friction effects)

2ρv21∆pk = (2)

can be evaluated at k = 0.728 for the two bends with no guide vanes, and k = 0.491 for the bends with two or three guide vanes, respectively.

In order to visualize the relationship between the acoustic pressures and the parameter (M∆p), the values in Table 2 for both the bends with no guide vanes and with two guide vanes have been normalized to atmospheric pressure po = 1.0135 x 105Pa and plotted in Figure 7. It can be seen that a clear relationship between P and M∆p for both conditions emerges in the form of ( ) ( )2.1oo p/p∆M721pP = (3) indicating a strong exponential relationship between the flow parameter M∆p in the bends and the generated maximum acoustic pressure P in the cylindrical pipe downstream. Prediction of Acoustic Pressures in Full Scale System Table 3 summarizes the flow parameters in the bend area in the full scale arrangement at full load. Two conditions are shown: 1) The original condition with no guide vanes and 2) The modified arrangement with two guide vanes installed in each of the upstream bends. Here the pressure drop data were calculated using the experimentally-determined pressure drop coefficients of k = 0.728 and 0.491 for the bends with no vanes and two guide vanes, respectively. Table 4 gives the acoustic parameters, again, for the two conditions of the bends without and with two guide vanes installed. The parameter M∆p represents a common link between the scale model tests with cold air and the full scale hot conditions. On this basis, the prediction of the reduction of acoustic pressures in the full scale system can be predicted. Based on Figure 7 and equation (3) the reduction in the predicted acoustic pressures in the full scale hot stack liners due to the installed guide vanes will be from 21.0 x 10-3 Pa or 60.4dB (re: 2 x 10-5Pa) to 9.17 x 10-3 Pa (53.2dB), or a total of 7.2dB. Considering that no additional losses will occur to the acoustic waves traveling through the stack liners, the stack noise emissions are thus predicted to be reduced by a minimum of 7.2dB (Fig. 7). DISCUSSION AND SUMMARY Based on experimental data corroborated with theoretical analysis, the full scale facility has provided clear evidence of the existence of an acoustic resonance condition in the upstream bends and of an acoustic wave traveling through the stack liners into the surrounding areas of the plant.

The laboratory scale model tests confirmed that the source of the acoustic wave propagating in the cylindrical portions of the stack liners was in the upstream bends. Here the turbulent flow conditions as measured by the input parameter M∆p give rise to the development of the acoustic wave in the downstream pipe with an acoustic pressure P which is exponentially proportional to this parameter. The guide vanes installed inside the bends have reduced the pressure drop through the bends by about one third and strongly (disproportionately) reduced the generated acoustic pressures and therefore the noise produced by the resonant condition at the same flows. Utilizing the experimentally derived relationship between acoustic pressure P and M∆p, given by equation (3) the noise produced in the full scale facility by the acoustic resonant condition can be reduced by 7.2dB by installing 2 guide vanes in each of the upstream bends. This significant reduction would eliminate the concern with the single tone noise emitted from the stack prior to the modification. CONCLUSIONS The results show that the upstream bends in the stack liners were the primary source of the single tone noise generated in the straight cylindrical liners which propagated into the surrounding areas of the plant. It has been shown that guide vanes installed inside each of the bends (two optimally placed vanes per bend) will reduce the pressure drop through the system by one third and substantially reduce the generated noise level by over 7dB. Thus, the installation of guide vanes in the upstream bends is a desirable feature as it makes the system more energy efficient and also much less noisy. It is therefore recommended that in systems of similar size the installation of guide vanes in the bends becomes a standard design feature. ACKNOWLEDGEMENT The authors gratefully acknowledge the permission of Foster Wheeler Power Group, Inc. to publish the results contained in this paper. REFERENCES [1] Weaver, D.S., Feenstra, P., Ewing, D., 1997,

“Scale Model Testing of Pipe Elbow Turbulence-Induced Acoustic Resonance in a Straight Circular Pipe”, Project Report, Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, Canada, November, 34 pages.

[2] Chu, B.T., 1955 “Pressure Waves Generated by Addition of Heat in a Gaseous Medium”, National Advisory Committee for Aeronautics. Technical Note 3411, pp. 1-47.

[3] Chu, B.T., 1956, “Stability of Systems Containing a Heat Source – the Rayleigh Criterion”. National Advisory Committee for Aeronautics Research Memorandum 56D27.

[4] Eisinger, F.L., Francis, J.T., and Sullivan, R.E., 1996, “Prediction of Acoustic Vibration in Steam Generator and Heat Exchanger Tube Banks”, ASME Journal of Pressure Vessel Technology, Vol. 118, pp. 221-236.

[5] Eisinger, F.L., and Sullivan, R.E., 1996 “Experience with Unusual Acoustic Vibration in Heat Exchangers and Steam Generator Tube Banks, Journal of Fluids and Structures, Vol. 10, pp. 99-107.

[6] Blevins, R.D., and Bressler, M.M., 1992 “Experiments on Acoustic Resonance in Heat Exchanger Tube Bundles”, ASME PVP-Vol. 243, Symposium on Flow-Induced Vibration and Noise, Vol. 4, pp. 59-79, also, 1993, Journal of sound and Vibration, Vol. 164 (3), pp. 503-533.

[7] Bull, M.K., and Norton, M.P., 1982, “On Coincidence in Relation to Prediction of Pipe Wall Vibration and Noise Radiation Due to Turbulent Pipe Flow Disturbed by Pipe Fittings”, International Conference on Flow Induced Vibration in Fluid Engineering, Reading, England BHRA fluid Engineering, pp. 347-368.

[8] Norton, M.P., 1989, “Fundamentals of Noise and Vibration Analysis for Engineers”, Cambridge University Press, Cambridge, U.K.

[9] Fahy, F.J., 1998, “Sound and Structural Vibration,” Academic Press, London, New York.

[10] Carucci, V.A., and Mueller, R.T., 1982, “Acoustically Induced Piping Vibration in High Capacity Pressure Reducing Systems”, ASME Paper No. 82-WA/PVP-8.

[11] Eisinger, F.L., 1997, “Designing Piping Systems Against Acoustically Induced Structural Fatigue”, ASME Journal of Pressure Vessel Technology, Vol. 119, pp. 379-383.

[12] Eisinger, F.L., and Francis, J.T., 1999, “Acoustically Induced Structural Fatigue of Piping Systems “, ASME Journal of Pressure Vessel Technology, Vol. 121, pp. 438-443.

[13] Blevins, R.D., 1984, “Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Company, New York, N.Y.

Table 1

Mean Gas Flow and Acoustic Parameters inside Stack Liner at Full Load

Parameter At Inlet At outlet T,oC ρ,kg/m3

pa,Pa ci,m/s fac,Hz

172 0.783 1.01 x 105

425 172

42 1.1 1.003 x 105

356 144

Table 2 Results of Scale Model Tests

With Cold Air at 25oC No vanes 2 Guide Vanes 3 Guide Vanes v

m/s P Pa

∆p Pa

M∆p Pa

P Pa

∆p Pa

M∆p Pa

P Pa

∆p Pa

M∆p Pa

21.5 0.408 0.538

202 199

12.52 12.2

0.1845 0.1885

130 131.8

8.06 8.09

0.173 0.1845

130 131.8

8.06 8.09

23.5 0.653 0.853

230 238

15.57 16.1

0.303 0.36

160 160.9

10.83 10.86

0.292 0.399

160 160.4

10.83 10.86

24.5 0.86 1.1

250 254

17.65 17.78

0.387 0.53

170 171.5

12.00 12.00

0.343 0.443

170 171.5

12.00 12.00

Table 3 Flow Parameters

In Upstream Bends of Stack Liners at Full Load

Pressure Drop Gas Flow W

kg/hr

Gas Temperature

T °C

Gas Density ρ

kg/m3

Gas Velocity v

m/s No vanes

∆p Pa

2 Guide Vanes ∆p Pa

76,950 172 0.783 16.55 75.00 50.625

Table 4

Acoustic Parameters in Upstream Bends Of Stack Liners at Full Load

Speed of Sound

C m/s

Mach Number

M

M∆p

Acoustic Pressure Px)

No vanes Pa

2 Guide Vanes

Pa

No Vanes Pa

(dB)

2 Guide Vanes

Pa (dB)

425 0.0389 2.92 1.969 21.0x10-3

(60.4) 9.17 x 10-3

(53.2)

x) See Equation (3) and Figure 7

Figure 1 Arrangement of cylindrical stack liner

Figure 2 Two ninety degree bends in upstream section of stack liner

Figure 3 Typical sound spectrum taken in vicinity

of power plant. Shown single tone sound of 50 dB at frequency of 144 Hz.

Figure 4 Structural vibratory acceleration spectrum

taken on outside surface of upstream bend. Shown single frequency response at 172 Hz.

Figure 5 Upstream bends of stack liner shown with two guide vanes in each bend

Figure 6 Arrangement of two and three guide vanes based on the equal radius ratio concept. Shown arrangement for bend with 1.52m Radius

Figure 7 Normalized diagram of acoustic pressure P versus flow parameter M∆p showing experimental data

from cold air tests and prediction for full scale system (see also Tables 2, 3 and 4)