Numerical and Experimental Analysis of Sound

Generated by an Orifice

Renzo Arina∗

Politecnico di Torino, Torino, Italy

Riccardo Malvano†, Aline Piccato † and Pier Giorgio Spazzini †

Istituto Nazionale di Ricerca Metrologica, Torino, Italy

The present paper deals with noise produced by an orifice placed in a circular duct. Suchnoise is mainly generated by the orifice itself and by the unsteady flow and turbulencein the orifice wake. The main objective of the present work is to develop a numericalprediction tool for the acoustic energy level produced by the orifice placed in a ducted flow.The model is based on the solution of the Navier-Stokes equations, for the compressibleturbulent flow, inside the duct and in the near-region outside the duct termination, and onthe Ffowcs Williams-Hawkings surface method for the evaluation of the far-field acousticradiation. Experimental measurements were also performed; such data are used to validatethe numerical model. The measured and computed sound pressure level directivities are ingood agreement, and show the influence of the orifice on sound generation. The numericalresults are in good agreement with the law, relating the fluctuating drag force acting onthe orifice and the steady drag force, proposed in the theory of Nelson and Morfey.1

I. Introduction

The flow noise generated in ducts by obstructions can be a significant component of noise in manypractical applications. In this work we focus on the problem of the noise radiated down to the unflangedtermination of a semi-infinite duct, the noise is produced when an orifice is placed in a circular duct. Orificesare commonly used in ducts for absorbing the noise traveling inside the duct and produced by fluid handlingequipment (ventilation system fans, etc...). Moreover, the most commonly used device for regulating the fluidflow in pipes is the reducing valve, which provides a mechanical constriction in the duct, much as an orificereduces the cross-sectional flow area. The orifice generates noise as well as absorbing it: the generated noiseresults mainly from unsteady flow and turbulence in the orifice wake. Knowledge of the level of flow-inducednoise is clearly of importance in the optimum design of attenuators and regulation valves.

The main objective of the present work is to develop a numerical prediction tool of the acoustic energylevel produced by the orifice placed in a ducted flow. Experimental measurements are also provided, in orderto validate the proposed numerical model.

A fundamental work on aerodynamic sound production in low-speed flow ducts when a cross-sectionalrestriction is present, is the analytical model developed by Nelson and Morfey.1 The model predicts level andspectral distributions of the additional acoustic energy produced by the obstruction for low Mach numberflows, deriving scaling laws which relate the sound power radiated to the geometrical and flow parameters.The scaling laws relate the radiated sound power to the total fluctuating drag force acting on the orifice.In the model, it is assumed that sound reflected back upstream from the open end is not subsequentlyre-reflected to any significant extent from the obstruction. The model is based on the extended Lighthill’sacoustic analogy. The sound produced by the flow obstruction in the duct is treated by replacing the orificeand the turbulence by a distribution of dipole sources radiating into the duct filled with fluid at rest. The

∗Associate Professor, Dipartimento di Ingegneria Aeronautica e Spaziale, Corso Duca degli Abruzzi 24, 10129 Torino,renzo.arina@polito.it, Member AIAA.

†Unita Staccata Dinamica dei Fluidi, C/o Politecnico di Torino, Dipartimento di Ingegneria Aeronautica e Spaziale, CorsoDuca degli Abruzzi 24, 10129 Torino.

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strengths of these equivalent dipole sources are determined by the fluid forces acting on the orifice in thereal flow. The model evaluates the sound power radiated by a dipole distribution, and it is obtained assolution of the inhomogeneous wave equation. At frequencies below the cut-off frequency fcut−off of thefirst transverse duct mode, when only plane waves propagate, the model provides a sound power radiatedwith U4 velocity dependence, like a free-field monopole. For frequencies above the cut-off frequency thesound power radiated approaches a U6 velocity dependence, like a free-field dipole. The transition from U4

to U6 occurs very rapidly as the frequency is increased above the cut-on frequency of the first transversemode. As pointed out by Nelson and Morfey,1 for f > fcut−off when transverse modes can propagate in theduct, the source exhibits a free field type behavior because the duct has dimensions very much larger thanthe acoustic wavelength.

More recently Guerin at al.2 have applied the above model to predict the noise generated in automotivevents in the case of plane wave propagation. The experimental data are in quite good agreement with thetheoretical results. The problem of noise generation, always in the case of frequencies below the cut-offfrequency of the first transverse mode, has also been addresses by Abom et al.3 in the case of circular ducts.In their experimental work on orifices in circular ducts, the authors found that the sound on the upstreamside is slightly higher than the noise propagating on the downstream side of the orifice. This implies thatthe simple dipole model proposed by Nelson and Morfey is not sufficient.

The analytical model of Nelson and Morfey is limited to very low Mach numbers and based on severalsimplified hypothesis limiting its range of applicability. Therefore it is worth to develop a more generealmathematical model, applicable from low to moderate Mach numbers, taking into account all the involvedphysical processes, and able to deal with generally shaped ducts (arbitrary cross sections), curved pipes andwith an arbitrary number of obstructions.

In the present work, we intend to further investigate the problem of the orifice in a circular duct with amoderate Mach number flow. The work is the continuation of a ongoing research.4 The research consistsof an experimental analysis of the radiated sound from the duct termination and the development of anumerical model for the prediction of the radiated sound. The numerical model consists into the solution ofthe Navier-Stokes equations, by the Detached-Eddy Simulation technique, to reproduce the turbulent flowinside the duct and in the near region outside the duct termination, and the evaluation of the radiated noisein the far field by means of the Ffwocs Williams-Hawking surface technique to solve the inviscid, linear waveequation in the domain exterior to the Navier-Stokes calculation. Moreover the numerical evaluation of theduct flow, enables us to assess the applicability of the Nelson-Morfey theory in the present case (ducts withcircular cross section), by confirming the fundamental hypothesis that the fluctuating drag force acting onthe orifice is directly proportional to the steady state drag force.

In the next Section, the relevant physical aspects of the problem under study are described. In SectionsIII and IV the numerical model and the experimental procedure are presented. In Section V the experimentaland numerical results are reported.

II. The Physics of the Problem

In this Section the relevant phenomena involved in the sound generation and radiation from the termi-nation of the duct with an orifice are briefly summarized.

For high speeds, the radiated sound is mainly originated by the free turbulence in the mixing region ofthe jet exhaust. The classical theory of Lighthill demonstrates that the sources of noise are equivalent toacoustic quadrupoles and that the noise generated increases in intensity according to the eighth power ofthe exhaust velocity. Under the conditions of high turbulence in the duct flow and low exhaust velocity, afundamentally different mechanism dominates the sound field. It is observed that when an obstruction, suchas an orifice, is inserted upstream the duct exit, the broad-band noise is radiated from the exit plane, andthe dependence of the sound power upon flow velocity changes from one having an exponent of eight to onehaving an exponent varying between four and six, depending if the frequency of the signal is below or abovethe first transverse duct mode cut-off frequency.1

For low exit velocities, the dominant noise sources are located at the duct obstruction and behind it.The obstruction is equivalent to a distribution of dipole sources radiating into the duct. The strengths ofthese equivalent dipoles are determined by the fluid forces acting on the orifice. The turbulent region behindit is equivalent to a distribution of quadrupoles. When sources generate sound in acoustic enclosures, theradiated sound intensity depends on the coupling of the acoustic modes of the enclosure and the spatial

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distribution of the sources. Acoustic sound propagation in ducts is further complicated by the finite crosssection, which forces the sound to exist as standing waves across the duct cross section. Only some of thesemodes propagate along the axis, while the others decay exponentially with axial distance from the sources.The frequency above which a mode propagates is called cut-off frequency. Higher is the order of the mode,and higher is its cut-off frequency. However, there is an exceptional mode for which propagation alwaysoccurs, the plane wave. In the case of a circular duct, with radius r and uniform sound speed c0, below thefrequency of the first transverse duct mode5

fco =1.84118

2π

c0

r,

all modes are cut-off except for the plane wave.An important consequence on the duct acoustics at low frequencies (f < fco), preventing propagation of

higher modes, is that only dipoles and quadrupoles which are axially oriented will radiate. This is becauseonly the plane wave propagation down the duct may occur at low frequencies. All other orientations willnot produce radiation far from the source. The net effect is like a free field monopole (radiated sound powerproportional to U4). At higher frequencies, high order propagating modes contribute to the sound power.As the number of propagating modes increases, the radiated noise approaches the U6 velocity dependence,like a dipole in free field.

This scenario is no more valid when the obstruction is located within a distance L of the end, smaller thana characteristic cross-sectional length (the diameter in the case of circular sections). With the obstructionnear the opening, but still inside the duct, the radiated power is influenced by interferences due to thescattering from the edges of the opening.

III. Numerical Model

Various prediction models have been developed for the aeroacoustic analysis of the low frequency responseof ducts with an obstruction, assuming plane wave propagation. Focusing on the sound scattering (Durries etal6), or on the sound generation (Nelson and Morfey,1 Guerin et al.,2 Oldham and Upkoho7), or both (Abomet al.3). The methods are based on the assumption that the flow field around the obstruction resembles thatof an orifice plate. The flow streamlines converge downstream of the orifice owing to a minimum cross-section of the flow, the vena contracta, where the minimum static pressure and the maximum mean velocityof the fluid are attained. It is assumed that lossless flow occurs between the upstream region and the venacontracta. This assumption enables the development of analytical models, however much of the turbulentflow mechanisms is missing.

The purpose of the present work is to develop a more general model accounting for most of the physicalphenomena involved in the noise production. Moreover the model should deal with any kind of obstruction(valve, orifice, etc...) and cross-section shape. The Navier-Stokes equations are solved in the near-fieldregion, inside the duct and in the near region outside the termination. In principle it is possible to includethe acoustic far-field with the turbulent near-field in a single computational domain. Practically, however,such a calculation is beyond the today available computational resources. Therefore a projection techniqueis used, wherein the mid-acoustic field is projected onto the true acoustic far-field. The far-field propagationregion is assumed to be governed by the inviscid linear wave equation, solved by the Ffowcs Williams-Hawking(FW-H) surface technique.8

The Navier-Stokes equations, for a compressible flow, are solved with the Detached-Eddy Simulation(DES) technique proposed by Spalart and Allmaras.9 The DES technique is a hybridyzation of the Large-Eddy Simulation (LES) technique. The general idea of DES is to combine a fine-tuned solution of theReynolds-Averaged Navier Stokes (RANS) equations, in the near wall region, composed by attached eddies,with a Large-Eddy Simulation (LES) solution in the exterior region populated with relatively large andgeometric-specific detached eddies, whose representation is beyond the capabilities of traditional RANSmodels. The STARCCM+ code of CD-ADAPCO has been used for the near-field calculations. The numericalsimulations have been performed on a 30 degrees section of a cylindrical domain, assuming periodic symmetryon the lateral boundaries.

The FW-H surface method is a rearrangement of the Navier-Stokes equations, as proposed by Lighthill,in an integral form. The integral method can predicted the far field signal based solely on near-field data.In the case of the FW-H method the time histories of all flow variables are needed on a surface placed in the

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Figure 1. Schematic of the joint with the orifice.

near-field. The solution of the FW-H equation requires a surface and a volume integral, but the solution isoften well approximated by the surface integral alone. The FW-H surface approach has several advantagesover the Kirchhoff surface approach.The FW-H surface can be placed, in principle, anywhere within the nearfield, even in the nonlinear region of the flow. Singer et Al.10 have shown that when the surface is in thenon-linear near field, the FW-H approach correctly filters out the part of the solution that does not radiateas sound. Assuming a time harmonic dependence of the solution on the surface, the problem is transformedin the frequency domain. The method is an extension to three-dimensional domains of the method proposedby Lockard11 for two-dimensional geometries.

IV. Experimental Rig

IV.A. Design of the experimental rig

The experiments were conducted in the I.N.Ri.M.a anechoic chamber, which is provided with a muffled airinlet. The inlet is powered by a centrifugal blower positioned outside the building and is supported bya concrete base independent of the building structure. The tubing driving air to the inlet includes noisedampers and flexible parts in order to avoid transmission of sound and/or mechanical vibrations. At theentrance of the anechoic chamber building the tube has a diameter φ = 150 mm. The tube can be terminatedeither with a straight termination (φexit = 150 mm) or with a smooth convergent which halves the diameter(φexit = 75 mm).

A pipe for aeroacoustic tests was designed to be connected to the low-diameter exit. The pipe consistsof two Plexiglas tubes with inner diameter φp,in = 74 mm and outer diameter φp,out = 80 mm. Each tubeis 1 m long and is held by an adjustable support.

The pipe inlet is placed at the exit of the convergent, to which it is fitted with a smooth junction.The (radial) reference system has its origin at the center of the pipe inlet section, the positive x-axis isdirected along the pipe centerline and the r-axis is along a radius of the pipe. At a distance x = 1000 mm(i.e. ≈ 13.5 pipe diameters) downstream the inlet, the first Plexiglas tube is connected to an aluminum part(joint); the latter is carefully machined so that the junction with the Plexiglas parts is very smooth. Twojoints were built, one of them with a smooth inner wall and one including a orifice. The orifice is 3 mmthick; its inner hole has a diameter of 37.5 mm and the hole profile is inclined at 45o with respect to thex-axis. Figure 1 displays a schematic of the joint with the orifice and the mounting system.

After the joint, the second Plexiglas tubing is mounted. This last part maintains the diameter of the firstpart. Before the joint, at approximately 3 diameter upstream of the orifice, a radial hole in the Plexiglastube allows insertion of a probe for velocity profile measurements. On the opposite side, at the abscissa ofthe total probe mouth, a static probe is mounted. Figure 2 reports a schematic of the overall system.

IV.B. Experimental setup

In a first phase, profiles of average velocity were measured by means of a miniature total pressure probetransversed across the tube. Velocity was computed through Bernoulli’s theorem from the difference between

aIstituto Nazionale di Ricerca Metrologica, the Italian Institute for Metrological Research.

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Figure 2. Schematic of the overall experimental setup.

the measured total pressure and the static pressure at the static probe. Measurements are performed by aSchiltknecht ManoAir 500 differential pressure transducer which directly measures the pressure differencebetween the total and static probes. These flow profiles were employed as inlet boundary conditions for thenumerical computations.

The acoustic experiment consisted of measurements of the noise radiated at the duct exit. A micro-phone was moved a on circular path centered on the axis of the tube at the exit section. Because of theaxial symmetry of the setup, measurements of SPL on this path are considered to be representative of themeasurements that could be obtained on the whole sphere.

Data were acquired by means of a Ono-Sokki DS-2000 spectrum analyzer connected to a PC, and are inthe form of narrowband spectra in the range 0-20000 Hz, with a frequency separation of 25 Hz.

V. Results

The experimental and numerical tests were conducted for fix inlet conditions: mean velocity U0 = 39.0m/s, static temperature T0 = 300 K. The Reynolds number, based on inlet conditions, is Re0 ≈ 190, 000 andthe inlet sound speed is c0 = 347.4 m/s, with a Mach number M0 = 0.11.

The ratio of the orifice area over the duct cross-section area Aorifice/Aduct = 0.257. This leads to anabrupt acceleration of the flow just downstream the orifice. The Mach number approaches unity in theaccelerated region.

V.A. Experimental Results

Sound Pressure Level (SPL) spectra were measured over an arc ranging from -20o to 100o, being 0o the ductaxis direction, at distances of 2.5 m, 3 m and 3.5 m. The results over the three arcs were compared and werefound to be similar, the difference being the expected reduction in intensity when increasing the distance.

The measurements performed at the -10o, 0o and 10o angles were inaccurate because in that case themicrophone was within the jet flowfield; as the microphone was not shielded, an higher SPL was measuredat this location; this higher SPL was interpreted as due to pseudosound effects and therefore discarded asnon reliable. All other positions were found to be outside the motion field and therefore acceptable.

The results without orifice were observed to be essentially featureless spectra, with a constant decreaseof energy content with increasing frequency. The overall SPLs were obtained from an integration of thespectra. The level was of the order of 60 dB. Such levels are not very much higher than the backgroundnoise, therefore the uncertainty associated to these measurements is quite high. Essentially no directivityof the SPL was observed. The measurements of the sound generated by the tube with the orifice, on the

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Figure 3. Measured SPL spectra:red line, with orifice; black line, without orifice (shifted 40 dB upwards for ease ofcomparison). Angle = 40o, distance = 3 m.

other hand, displayed more peculiarities. First of all, an increase of the energy associated with increasingfrequencies up to about 2000 Hz was observed. This increase was followed by a plateau of energy extendingto approximately 6000 Hz, and then by the expected decrease. On the side of the overall SPL, a remarkabledirectivity was observed, with a maximum at around 40o. This directivity was observed also when comparingthe single frequencies, and was found to become more pronounced as the frequency was increased. The totallevels were of the order of 85 dB, i.e. much higher than in the case without orifice. Notice that this impliesthat the uncertainty associated to these results is lower than in the case without orifice.

As an example of the results, figure 3 reports the measured spectra in the two cases, with and withoutorifice, for the angle of 40o and a distance of 3 m. It can be noticed that the sound levels in the case withthe orifice are much higher than in the baseline case at all frequencies. The picture clearly displays thepeculiarities described earlier. It is also possible to observe that, in the case with orifice, a sequence of peaksare present in the spectrum. These peaks are spaced quite regularly, with an average spacing of about 125Hz. These peaks can be attributed to standing waves within the tube, at the typical resonant frequenciesof the tube and its harmonics. Notice that the resonant frequency of the tube section downstream theorifice would lead to a frequency of 170 Hz. Though, this is what would happen in the case of negligiblefluid speed in the tube. The difference can be explained by flow effects (variable convection speed, shear,nonuniformities, ...).

V.B. Numerical Results

The computational grid shown in figure 4 is made up of 227, 989 polyhedral cells, and 1, 375, 824 nodes. Thenodal points are clustered around the orifice, in the wake region behind the restriction, and in the externaljet region. Moreover along the duct walls, few layers of prismatic cells are introduced. A structured grid inproximity of the wall is an essential prerequisite for the low-Reynolds RANS model to perform optimally.The computations have been done on a cluster of 2 Dual-Opteron processors, the solution is quasi-periodicand it takes 6 hours of CPU-time to compute a cycle.

The inlet velocity profile is provided by the experiments, non-reflecting conditions are imposed on thefar-field boundaries, and periodicity conditions on the side planes.

In figure 5, the instantaneous Mach number distribution is reported. It is possible to remark that thejet remains confined in a narrow region around the axis, and the coherent structures mainly develop alongthe streamwise direction. Just downstream the orifice the flow field attains the maximum velocity, the Machnumber reaches the value of 0.94. In the enlargement around the orifice (figure 6), it is possible to verifythat the mean flow field recovers the duct behavior within 5 diameters downstream the orifice.

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Figure 4. Computational grid: complete domain (below), enlargement near the orifice region (above).

These remarks are confirmed observing the instantaneous pressure field. In figure 7, the range of thepressure countour levels has been narrowed in order to put in evidence the pressure fluctuations in the jetregion associated with the vortical structures. However, these fluctuations are not the main source of noisein the presence of the orifice, the main contribution coming from the duct. In figure 8, the enlargement ofthe region downstream the orifice shows that the pressure recovery, after the obstruction, is completed after5 diameters in the axial direction. At this station, the mean static pressure is practically constant on thecross section, and varies only along the axial direction.

Figure 5. Instantaneous Mach number distribution.

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Figure 6. Instantaneous Mach number distribution (enlarged region around the orifice).

Figure 7. Instantaneous pressure field.

Figure 8. Instantaneous pressure field (enlarged region around the orifice.

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100 1000 1000020

40

60

80

f_co=1374

f [Hz}

K^2

U^6

U^4

Figure 9. Relation K(ω): K2 in dB with reference value 10−12.

The prediction model developed by Nelson and Morfey1 is based on the hypothesis that, for low Machnumber flows, the sound power radiated can be related to the total fluctuating drag force D acting on theorifice, as follows

Drms(ω) = K(ω)D ,

where D is the mean steady drag force. By an inverse method, Nelson and Morfey deduced values of K(ω)from the radiation outside the duct with various spoilers. No universal curve K(ω) exists, however otherexperiments on different obstructions (such as the work of Guerin et al.2) support the hypothesis that similarcurves exist for a wide range of components. Moreover, Nelson and Morfey found that the K(ω) law changesat the cut-off frequency fco from U4 to U6 velocity dependence, and the change is quite abrupt. In figure 9the relation K(ω) obtained for the case with the orifice is reported. Across the cut-off frequency the datapresent a change in slope. The continuous lines are the slopes for a law with U4 and U6 velocity dependence,respectively. It can be argued that also for duct flows characterized by a relative high Mach number, a curveK(ω) similar to those valid in the limit of small Mach numbers exists.

V.C. Comparisons of Numerical and Experimental Results

The experimental directivity measurements have been compared with the numerical computations. Thenumerical directivities have been evaluated by applying the FW-H surface method. The FW-H surface is acylindrical surface of radius R ≈ 10rduct, well outside the near-field region. Both cases, with and withoutorifice, are considered. In figure 10 the numerical and experimental directivities along a circular path centeredon the axis of the tube at the exit, of radius 3 m are compared. The agreement is extremely good in thecase of the orifice, while for the simple duct test, some disagreement is evident. Being the sound level muchlower, the experimental and numerical accuracies are more critical and may easily bring to some differencesin the results.

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40

20

0

20

40

60

80

100

20 0 20 40 60 80 100

SPL

* s

in(α

) [d

B]

SPL * cos(α) [dB]

Numerical ResultsExperimental Data

40

20

0

20

40

60

80

20 0 20 40 60 80

SPL

* s

in(α

) [d

B]

SPL * cos(α) [dB]

Numerical ResultsExperimental Data

Figure 10. Comparison of the experimental and numerical sound directivities: r = 3. m, with orifice (left), withoutorifice (right)

VI. Conclusion

In the present work, the sound generated by a pipe including an obstruction was studied experimentallyand numerically. The obstruction consisted of an orifice 1 m upstream of the pipe termination.

The results obtained showed a satisfactory coincidence of the computed results to the measurements.In particular, it was possible to reproduce numerically the sound directivity and intensity measured in theexperiment. The SPL directivities obtained in the two cases were found to be in good agreement.

Moreover, it was possible to show a scaling law similar to the one forecast by the theory of Nelson andMorfey,1 which is rigorous for flow velocities much lower than the ones studied here, indicating that thetheory might be extended to higher velocities.

This work can be considered as a step towards the development of a reliable numerical tool for theprediction of aeroacoustic sound generation/propagation.

Acknowledgments

The work described in the present paper was partially supported by DENSO Thermal Systems, Italy.The Authors wish to thank Mr. I. F. Cozza and Mr. A. Iob, PhD candidates, for their help in developing

the numerical model and performing the computations; thanks go also to Dr. C. Guglielmone for putting atdisposal the experimental facility used for the measurements.

References

1Nelson P.A. and Morfey C.L., Aerodynamic Sound Production in Low Speed Flow Ducts, J. Sound and Vibration, 79-2,pp. 263-289, 1981.

2Guerin S., Thomy E. and Wright M.C.M., Aeroacoustics of Automotive Vents, J. Sound and Vibration, 285, pp. 859-875,2005.

3Abom M., Allam S. and Boij S., Aero-Acoustics of Flow Duct Singularities at Low Mach Numbers, 12th AIAA/CEASAeroacoustics Conference, AIAA 2006-2687, 2006.

4Arina R., Barone F., Carena F. and Durello P., Aeroacoustic Analysis of Car Ventilation Systems, Proceedings EFMC6,Stockholm, Sweden, June 2006.

5Pierce A.D., Acoustics - An Introduction to Its Physical Principles and Applications, Acoustical Society of America,1991.

6Durrieu P. et al, Quasisteady Aero-acoustic Response of Orifices, J. Acoustical Soc. Am., 110-4, pp. 1859-1872, 2001.

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7Oldham D.J. and Ukpoho A.U., A Pressure Based Technique for Predicting Noise Levels in Ventilation Systems, J.Sound and Vibration, 140-2, pp. 259-272, 1990.

8Ffowcs Williams J.E. and Hawkings D., Sound Generation by turbulence and Surfaces in rbitrary Motion, Phil. Trans-actions of the Royal Society of London, A 342, pp. 264-321, 1969.

9Spalart P.R., Strategies for Turbulence Modelling and Simulations, Int. J. of Heat and Fluid Flow, 21, pp. 252-263, 2000.10Singer B.A., Brenter K.S., Lockard D.P. and Lilley G.M., textit Simulation of Acoustic Scattering from a Trailing Edge,

AIAA 99-0231, 1999.11Lockard D.P., An Efficient, Two-Dimensional Implementation of the Ffwocs Williams-Hawkings Equation, J. Sound and

Vibration, 229-4, pp. 897-91, 2000.

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