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SAE TECHNICAL

PAPER SERIES

2005-01-2495

On Predicting Aeroacoustic Performance of

Ducts with Broadband Noise Source Models

Ashok D. Khondge, Sandeep D. Sovani and Sung-Eun KimFluent Inc

Steven C. Guzy and Ashraf A. FaragDelphi Thermal and Interio

SAE 2005 Noise and VibrationConference and Exhibition

Traverse City, MichiganMay 16-19, 2005

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Copyright 2005 SAE International

ABSTRACT

A numerical method of predicting aeroacousticperformance of HVAC ducts is presented here. Themethod comprises of two steps. First, the steady stateflow structure inside a duct is simulated usingcomputational fluid dynamics (CFD). A k-epsilon basedturbulence model is used. In the second step broadbandnoise source models are used to estimate the soundpower generation within the duct. In particular, modelsestimating dipole and quadrupole sound sourcestrengths are studied.

A baseline generic duct geometry was studied with 3additional design variations. The loudness rankings ofthese three designs were determined numerically.Simultaneously, the sound generated by these threedesigns was measured on a flow bench with amicrophone kept downstream of the duct outlet. Thenumerically predicted loudness rankings were comparedwith experimentally determined rankings and the two arefound to be in agreement, thus validating the numericalmethod.

INTRODUCTION

Noise generated in automotive HVAC ducts can often bevery loud and cause discomfort and distraction to thedriver and passengers. HVAC system manufacturerstherefore take significant efforts to optimize noisegenerated by ducts. To-date these efforts mostlycomprise of expensive experimental noise testing due tothe lack of practically usable numerical methods that canpredict aerodynamically generated noise in ducts. It ishighly desirable to have numerical methods of predictingduct acoustic performance for many reasons. First,numerical analysis is often quite inexpensive comparedto experimental testing. Moreover, numerical analysiscan be done in the early stages of the design process to

provide design direction even before prototypes are builtAlso, numerical analysis easily provides much greateinsight into the physics involved compared toexperimental measurement.

Numerical simulation of duct noise has received attentionfrom researchers

1, 2, 3, 4. Though these works provide

excellent methods of computing sound propagation, theylack detailed calculations of sound generation.

To determine the loudness of a duct, it is essential toaccurately simulate sound sources. Automotive HVACduct noise is almost exclusively aerodynamic noise, i.e

noise generated by fluid flow. It is typically caused by twoaspects, one, the rotating blades of the blower, and twogeometric complexities in the duct. Both these cause theflow to be unsteady and turbulent and generate noise.

There are four primary approaches of numericallymodeling aeroacoustic phenomena. In order odecreasing computational effort, these are (a)computational aeroacoustics (CAA)

5, 6, 7, 8, 9, 10, (b) the

coupling of CFD and a sound propagation solver11, 12

, (cintegral sound propagation models

13, 14, 15 and (d)

broadband noise source models. Details of theseapproaches are presented in other articles

11, 12, along

with examples5, 6, 7, 8, 9, 10, 13, 14, 15

.

Of these, the first three methods require well-resolvedtransient CFD simulations, since they aim to determinethe actual time-varying sound-pressure signal at thereceiver, and from that, the sound spectrum. In severapractical engineering situations, only the locations andrelative strengths of sound sources need to bedetermined rather than the sound spectra at thereceivers. If the sound is broadband (i.e. lacking anyprominent tones characterized by sharp peaks in thespectrum), the source strengths can be evaluated with

* Corresponding Author

2005-01-2495

On Predicting Aeroacoustic Performance of Ducts

with Broadband Noise Source Models

Ashok D. Khondge, Sandeep D. Sovani* and Sung-Eun Kim

Fluent Inc

Steven C. Guzy and Ashraf A. FaragDelphi Thermal and Interior

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reasonable accuracy from the time-averaged structure ofthe turbulent flow in the source regions.

Turbulence is the primary cause of sound inaeroacoustics, so in a broad sense, regions of the flowfield where turbulence is strong produce louder sourcesof sound. A number of analytical models referred to asbroadband noise source models synthesize sound atpoints in the flow field from local flow and turbulencequantities and estimate local sound source strengths.The key advantage of these models is that they requirevery modest computational resources compared to theother three methods. Broadband noise models only needa steady state flow solution, whereas the other methodsrequire well-resolved transient flow solutions. However,the drawback of the broadband noise source models isthat they are not able to predict sound spectra at receiverlocations. They can only qualitatively indicate whichsound sources are stronger than others.

One important practical aspect where broadband noisesource models can be used is in determining loudnessrankings of different design variations of an object. In the

present work two broadband noise models are used todetermine loudness rankings of five different ductdesigns. The computationally predicted noise rankingsare compared with experimentally measured rankings.

PROBLEM STATEMENT

The aim of the present study was to determine whetherbroadband noise models have the ability to correctlypredict loudness rankings of automotive HVACducts/modules. For this a generic duct design, whichcontains some of the basic characteristics of HVACmodule, is considered with two additional design

variations. The baseline design is presented in Figure 1.

The duct design is purposely kept generic so that it canbe widely used as a benchmark in the future. Threeimportant features prominently found in actuaautomotive HVAC ducts/modules are included in thisdesign. They are, a sudden expansion (accompanied bya change in cross-section shape from round torectangular), a bend, and a side cavity. Dimensionadetails of the baseline duct are shown in Figure 2.

The baseline duct is referred to as Design1 henceforward. Designs 2, 3, and 4 are exactly same as Design1, except they have a baffle immediately upstream of thecavity. In Designs 2, 3, and 4 the baffle height is 0.03 m0.07 m, and 0.11 m respectively. In all designs the baffle

Inlet

Outlet

Figure 1.Baseline duct geometry.

0.155

0.200

0.250

Figure 2. Dimensional details of the baseline duct (Design1). All dimensions are in meters.

0.200 0.150

0.150

0.050 0.100

0.100

0.100

0.200

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(a) Design2

(b) Design3

(c) Design4Figure 3.Cross-sections of the different designs.

Dimensions are in meters.

is 0.0016 m thick. See Figure 3 for cross-sections of

Designs 2 through 4.Noise rankings of these ductdesigns are calculated by conducting numericalsimulations and are compared with experimentallymeasured rankings to determine if the broadband noisemodels studied predict noise rankings accurately.

NUMERICAL METHOD

The numerical simulation method comprises of twosteps. First, a steady state CFD simulation of flowpassing through the duct is conducted. In the secondstage, the broadband noise models are used to estimate

acoustic source power from the results of the CFDsimulation. Both these steps are conducted with thecommercial CFD code FLUENT 6.2.16

16.

COMPUTATIONAL DOMAIN AND MESH

The computational domain comprises of the duct and alarge plenum at its outlet that represents the openatmosphere.

Various views of the mesh cross-section along thebaseline ducts center plane are shown in Figure 4. Thevolume mesh was composed of a total of 2 millionexclusively hexahedral cells. A fine mesh resolution ismaintained in regions where high gradients areexpected, such as the region in close proximity of theduct walls and the shear regions in the suddenexpansion and in the cavity mouth. The mesh wascreated using the commercial meshing software packageGAMBIT2.1

17

SOLVER SETTINGS, TURBULENCE MODEL, ANDBOUNDARY CONDITIONS

The commercial CFD code FLUENT6.2.1616

used toconduct the simulations is based on the finite volumemethod and provides a choice of solvers and solvesettings. The settings chosen for this study are listed inTable 1.

Turbulence was modeled using RNG (Renormalization

Group Theory) k- model. In this model the turbulentviscosity is computed using the relation,

2k

Ct = (1

where the value of the constant C is derived to be0.0845 from RNG theory. Non-equilibrium wall functionsare used. These functions are similar to those proposedby Launder and Spalding

18but the log-law is sensitized

to pressure-gradient19

. Further details are seen inFLUENT documentation

16.

The boundary conditions used in the simulation are listedin Table 2. A constant velocity boundary condition waschosen for the inlet corresponding to a 300 cfm flow rateof air which is typical of an automotive climate controsystem. Since we assume the flow to be incompressiblean arbitrary value of pressure can be assigned to the

pressure outlet without any effect on the flow field, so it iskept at 0 Pa (gage). The boundaries of the duct and theplenum were kept as no-slip walls while the duct outletwas kept as an interior so air can pass freely from theduct into the plenum.

BROADBAND NOISE SOURCE MODELS

Two broadband noise source models are considered inthis work, a model estimating the contribution ofquadrupole (volume) sources and the other indicating the

0.03

0.11

0.07

Inlet

Outlet

Cavity

Baffle

SuddenExpansion

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(a) Entire computational domain.

(b) Mesh in the duct.

(c) Mesh in the sudden expansion.

(d) Mesh in the cavity mouth.Figure 4.View of the central cross section of the

baseline case mesh.

Table 1. Solver settings used in the simulations.

Function Setting

Solver

Precision

Pressure discretization

Momentum discretization

Pressure-velocity coupling

Fluid

Steady state,Segregated ImplicitDouble Precision2

ndorder

2nd

order upwindSIMPLEC

Air (incompressible)

Table 2. Boundary conditions

Boundary Boundary Condition Value

Duct Inlet

Duct Outlet

Duct boundaries

Plenum Outlet

Plenum boundaries

Constant Velocity

Interior

No slip wall

Constant Pressure

No slip wall

7.507 m/s

(=300 cfm)

0 Pa (gage)

contribution of dipole (surface) sources. Both have theirfoundation in Lighthills acoustic formulation. Lighthill

20

showed that at distances large compared with thedimension of the flow, the density fluctuation due tosound wave can be computed from:

(2)

where Tijis Lighthills stress tensor defined by

(3)

where ijis the viscous tensor.

Quadrupole Source Model

Proudman21

, based on Lighthills acoustic analogyoriginally derived a formula for acoustic power generatedby isotropic turbulence without mean flow. More recentlyLilly

22 re-derived the formula by accounting for the

retarded time difference which was neglected inProumans original derivation. Both derivations yieldacoustic power due to unit volume of isotropic turbulence

as:

(4)

where uand are turbulence velocity and length scalesrespectively, and a0is the speed of sound. The value of

the numerical constant in eqn. (4) varies depending onthe specific methods of derivation. In Proudmans

original derivation, 13. Lilly found 10.96. In terms

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of k and and using u2 = 2k/3, = 1.5u3/l and Mt =

0/2 ak , eqn. (4) can be written as:

(5)

The rescaled constant , is approximately 0.5 for the

Proudmans constant ( 13). Sarkar and Hussaini23

,based on their DNS (Direct Numerical Simulation) for

isotropic turbulence, found that = 0.1 best fits the DNSdata. FLUENT adopts = 0.1. Eqn. 5 thus provides thelocal sound power contribution per unit volume due toisotropic turbulence (quadrupole sound source) at everypoint in the computational domain.

Dipole Source Model

Far-field sound generated by turbulent boundary layerflow over a solid body at low Mach numbers is often ofpractical interest. The Curle's integral

24 based on

acoustic analogy can be used to approximate the localcontribution from the body surface to the total acoustic

power. To that end, one can start with the Curle's:

(6)

where denotes the emission time ( = t - r/a0), and Stheintegration surface.

Using this, the sound intensity in the far field can then beapproximated by,

(7)

where Acis the correlation area, , and cosis

the angle between and the wall-normal direction. The total acoustic power emitted from the entire body

surface can be computed from

(8)

where

(9)

which can be interpreted as the local contribution per unitsurface area of the body surface to the total acousticpower. The mean-square time-derivative of the surfacepressure and the correlation area are further

approximated in terms of turbulent quantities liketurbulent kinetic energy, dissipation rate, and wall-shear.

FLUENT reports the acoustic surface power defined byEquation (9) both in physical (W/m

2) and dB units.

SIMULATION PROCEDURE

A steady state CFD simulation was conducted for eachdesign. The solution was initially converged with firstorder discretization schemes and finally with secondorder schemes. After obtaining converged CFDsolutions, acoustic post-processing was done with thebroadband noise source models. This included twocalculations. The first was calculation of the volumeintegral of PA from Eqn. (5) on the volume containedinside the duct. Here, PA is an estimate of the locaquadrupole acoustic power contribution per unit volumeTherefore the volume integral of PA is indicative of thetotal acoustic power emitted by the entire duct due toquadrupole sources. The second was a calculation of thesurface integral of I from Eqn. (9) on all internal wal

surfaces of the duct. Here, I is an estimate of the locadipole acoustic power contribution per unit areaTherefore, the surface integral of Ion all inner surfacesof the duct is indicative of the total acoustic poweemitted by the duct due to dipole sources.

RESULTS

FLOWFIELD STRUCTURE

All designs were experimentally tested as well assimulated at a flow rate of 300 cfm corresponding to aninlet velocity of 7.507 m/s. Flow structure for the baseline

geometry is presented in Figure 5 via contour plots ovelocity magnitude, pressure, turbulent kinetic energyand dissipation rate. Velocity contours show that the flowenters the duct at a constant velocity and forms aboundary layer on the circular pipe section immediatelydownstream of the inlet. Upon encountering the suddenexpansion further downstream, the flow separates fromthe walls and forms a jet. The boundaries of the jet donot reattach with the walls until the jet enters the 90degree turn and impinges on the far wall. The bend turnsthe flow vertically upward and flattens the jet into athinner, high velocity jet with a large separated region toits left. The jet forms a shear layer in the cavity mouth

and creates a rotational flow inside the cavity.

Wherever the velocity gradient is large, high values ofturbulent kinetic energy are seen to occur in the contouplot of turbulent kinetic energy. Locations of highturbulence include the region downstream of the suddenexpansion as well as on the outer (left) boundary of thehigh velocity jet in the vertical section of the duct. Theseregions of high turbulence are expected to be strongsources of noise.

The flow structure in the other 3 designs is presented inFigure 6 using velocity contour plots. The 0.03 m baffle

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at the leading edge of the cavity in Design 2 lifts thevertical jet off from the cavity mouth. As a result therotation in the cavity of Design 2 is much milder than thatin the baseline case. The vertical jet also becomesthinner and faster than in the baseline case. When thebaffle height is increased to 0.07 m in Design 3 the jetvelocity increases further and a strong separation regionis seen behind the baffle. In Design 4 where the baffleheight is increased to 0.11 m, there is only a smallopening left for the flow and the vertical jet has a even

higher velocity. The separation region behind the baffle isfurther pronounced.

NOISE CHARACTERISTICS

As the vertical jet becomes progressively faster fromDesign1 through 4 and the separation region behind thebaffle becomes more pronounced, it is expected that theoverall turbulence in the flow field will increase causingan increase in the broadband noise level. Experimentalmeasurements confirm this trend. Figure 7 shows thesound spectra measured at a point 1 m directlydownstream of the centroid point of the duct outlet. The

spectra extend from 20 to 20,000 Hz. Over most of thisextent the SPL for all four ducts is the same, except inthe region from about 150 to 400 Hz. Therefore, theperceived difference in loudness of these ducts arisesfrom this frequency band. Here, Design 2 is seen to belouder than Design 1 by roughly 2 to 3 dBA. Design 3 islouder than Design 2 by about 3 to 4 dBA, and likewiseDesign 4 is louder than Design 3 by 3 to 4 dBA.

Sound power estimates made using broadband noisesource models in the CFD simulations are shown inTable 3. Both the dipole source power as well as thequadrupole source power are seen to increase from

Design 1 through 4.

In conclusion, the two broadband noise source modelsconsidered here correctly predict the same noise rankingbetween the 4 designs studied as observed inexperiments.

Table 3. Acoustic power generated inside the ductas estimated from the simulations.

Design QuadrupoleSource Power in

Watts

Volume Integral ofPAin Eqn. (5)

DipoleSource Power in

Watts

Surface Integral of IinEqn. (9)

Design1 7.31e-13 2.44e-09

Design2 1.63e-12 3.56e-09

Design3 9.48e-12 8.64e-09

Design4 2.94e-10 1.24e-07

CONCLUSION

Broadband noise source models are an attractive optionto quickly and inexpensively evaluate the acousticperformance of devices. Broadband noise modelsrequire inexpensive steady state simulations to estimatenoise where as other methods such as computationaaeroacoustics and integral sound propagation methodsrequire expensive transient simulation. Howeverbroadband noise source models cannot provide accuratesound spectra unlike the other methods.

One possible practical use of the broadband noisesource models is studied in this paper. The broadbandnoise models have been used to determine the noiseloudness rankings of a generic HVAC duct with 4 designvariations. The rankings are computed with a dipole anda quadrupole source power model. The computedrankings are compared to experimentally determinedrankings and the two are found to be in excellenagreement. In conclusion, the broadband noise modelsare a valuable and relatively inexpensive practical tool fodetermining noise loudness rankings of HVAC duc

designs.

REFERENCES

1. Reichert R.S. and Birigen S., Time domain

simulation of acoustic propagation in lined duct,Applied Acoustics, vol. 62, pp. 1049-1068 (2001)

2. Joseph P., Morfey C.L., and Lowis C.R., Multi-mode

sound transmission in ducts with flow, Journal oSound and Vibration, vol. 264, pp. 523-544 (2003)

3. Ju H. and Fung K.-Y., A time domain method foduct acoustics, Journal of Sound and Vibration, vol

237(4), pp. 667-681 (2000)4. Boudoy M. and Martin V., Prediction of acoustic

fields radiated into a damped cavity by an N-portsource through ducts, Journal of Sound andVibration, vol. 264, pp. 499-521 (2003)

5. Ambs R., Ayar A., Capellmann, C. and Matthes M.Computational aeroacoustics and the developmen

of climate control systems, VDI-Berichte Nr. 18462004

6. Hendriana, D., Sovani, S.D., and Schiemann M.K.On simulating passenger car side windowbuffeting, Society of Automotive Engineers

International, Paper 2003-01-1316 (2003)

7. An, C.-F., Alaie, S.M., Sovani, S.D., Scislowicz M.Singh, K., Side window buffeting characteristics of aSUV, Vehicle Aerodynamics, Vol. SP1874, pp. 43 -

53, SAE International Paper 2004-01-0230 (2004)8. Sovani, S.D. and Hendriana, D, Predicting

passenger car side window buffeting with transient

external aerodynamics simulations, Tenth annuaconference of the CFD society of Canada, June 9-

11, 2002, Windsor, Canada. (2002)9. Sovani, S.D., Reducing wind fatigue and summe

headaches, Desktop Engineering, Dec. (2004)

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10. Kannan, V., Sovani, S.D., Greeley, D., and Khondge,A.D., Computational Aeroacoustics Simulation of

Whistle Noise in an Automotive Air-Intake System,submitted to SAENVH conference(2005)

11. Seibert W., Elhen M., Sovani S.D., Simulation of

transient aerodynamics - Predicting buffeting, roaringand whistling using CFD, Sixth Motor Industries

Research Association (MIRA) International VehicleAerodynamics Conference, October 13-14, 2004,

Warwick, U.K.12. Sovani, S.D., Leading Edge Aeroacoustics

Simulation, Fluent News, Vol. 13, no. 2, pp 30-31

(2004)13. Kim, S.-E., Dai, Y., Koutsavdis, K., Sovani, S.D.,

Kadam, N.A., and Ravuri, K.M.R., A versatileimplementation of acoustic analogy based noise

prediction method in a general-purpose CFD code,American Institute of Aeronautics and Astronautics,Paper no. 2003-3202 (2003)

14. Lokhande, B.S., Sovani, S.D., and Xu, J.,Computational aeroacoustic analysis of a generic

side view mirror, Transactions of the SAE: Journal

of Passenger Cars - Mechanical Systems, pp. 2175-2184, SAE Paper 2003-01-1698 (2003)

15. Sovani, S.D. and Chen, K.-H., Aeroacoustics of anAutomotive A-Pillar Raingutter: A Numerical Study

with the Ffowcs-Williams Hawkings Method,submitted to SAE-NVH conference (2005)

16. Fluent 6.2 Users Guide, Fluent Inc., Lebanon NH(2005)

17. Gambit 2.1 Users Guide, Fluent Inc., Lebanon NH(2003)

18. Launder, B.E. and Spalding, D.B., The numericacomputation of turbulent flows, Computer Methods

in Applied Mechanics and Engineering, Vol. 3, pp269-289 (1974)

19. Kim, S.-E. and Choudhury, D., A near-wal

treatment using wall functions sensitized to pressuregradient, in Separated and Complex Flows, ASME

FED, Vol. 217 (1995)20. Lighthill M.J., On sound generated aerodynamically

I General theory, Proceedings of the RoyaSociety A, vol. 211, pp. 564 (1952)

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turbulence, Proceedings of the Royal Society A, vol214, pp. 219 (1952)

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CONTACT

Sandeep Sovani, Ph.D.,Senior Consulting Engineer, Fluent Inc.,220 E. Huron St. Suite 470, Ann Arbor MI 48104sds@fluent.comTel: 734-213-6821 x235 FAX: 734-213-0147

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(a) Velocity magnitude (m/s)

(b) Static pressure (Pa)Figure 5.Contour plots on the central cross-section showing flow structure in the baseline design.

FLOW FEATURES

Vertical Separation Region

Vertical Jet Rotational Flow in Cavity

Shear Layer

Jet Impingement

Horizontal Separation Region

Horizontal Jet

Boundary Layer

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(c) Turbulent kinetic energy (m2/s

2)

(d) Turbulence dissipation rate (m2/s

3)

Figure 5.Contour plots on the central cross-section showing flow structure in the baseline design.

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Figure 6. Velocity magnitude contours on the central cross section for different designs.

(a) Design 2

(b) Design 3

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Figure 7. Experimentally measured sound spectra at a point 1m directly downstream of the centroid of the duct outlet.

(c) Design 4

Figure 6. Velocity magnitude contours on the central cross section for different designs.