SoundDuctFlow: A Modelica Library for Modeling Acoustics and … · 2009-10-02 · SoundDuctFlow : A Modelica Library for Modeling Acoustics and Flow in Duct Networks Helmut Kühnelt

SoundDuctFlow: A Modelica Library for ModelingAcoustics and Flow in Duct Networks

Helmut Kühnelt Thomas Bäuml Anton HaumerAustrian Institute of Technology, Mobility Department

Giefinggasse 2, A-1210 Vienna, Austria{helmut.kuehnelt,thomas.baeuml,anton.haumer}@ait.ac.at

Abstract

SoundDuctFlow, a Modelica library for the jointcalculation of acoustic and flow quantities inHVAC (Heating, Ventilation and Air Condition-ing) ducts is presented. Modeling the sound prop-agation in ducts by one dimensional acoustic two-port methods is a well-established technique forthe acoustic characterization of large HVAC ductnetworks. Two different approaches of acousticmodeling will be considered in the framework:When resonant phenomena are insignificant, it isoften sufficient to apply band-averaged models topredict the sound power level and the transmissionloss within the individual components of the ductnetwork. For the low frequency range where linearplane wave propagation is valid, acoustic two andmulti-port models based on a transmission matrixformulation of the sound pressure can be appliedfor high frequency resolution and phase accuratecalculations. For the prediction of the mean airflow in the duct network pressure loss modelsare applied. The coupling of acoustic and flowelements permits the simulation of flow acousticphenomena.For setting up large networks a smooth workflow is vital for the user: The simulation iseasily set up using the GUI provided by Dymola.External parameterisation ensures persistent datamanagement. The resulting system of equationsis automatically pre-processed and solved by Dy-mola.In this paper an overview of this new library isgiven together with exemplary applications.

Keywords: acoustics; flow; ducts; flow noise;HVAC; modeling; simulation; Modelica library

1 Introduction

The joint calculation of sound level, air flow rateand pressure loss in large HVAC duct networks aswell as the prediction of the noise level in the pas-senger compartment gains more and more in im-portance in the early phase of design. The unifiedModelica framework for one-dimensional acousticand flow simulation introduced here serves as atool for concept modeling. Used by the designengineer in an early design phase, it has to meetseveral requirements: The prediction method hasto be fast and computational efficient. All kindsof available data should be used, from analyticand (semi)empiric models to data obtained frommeasurements and three-dimensional acoustic andfluid dynamics computer simulations to charac-teristic diagrams and sparse point data providedby component manufacturers. It also should beextendable to add physical phenomena like heattransfer or transport of humid air and complexflow-acoustic interactions. Finally the frameworkshould be open for integration into a completesystem simulation.

2 Modeling acoustics in ductnetworks

In modeling acoustics of duct networks usuallyfollowing assumptions are made: Only the steadystate of the system has to be regarded. Thedimensionality of the systems often can be reducedfrom 3-D to 1-D. The acoustic properties of eachcomponent can be characterized by an acousticaltwo-port (or a multi-port in the case of a branch-ing), a grey box whose transfer behavior can becalculated by means of 1-D to 3-D methods, like fi-nite (FEM) or boundary element methods (BEM),

Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009

© The Modelica Association, 2009 519 DOI: 10.3384/ecp09430115

independently from each other. Two standardone-dimensional approaches are available:

First, the sound power-based description hasbeen widely used and forms the basis of the moststandards and guidelines for the analysis of soundin ducts, e.g. see ASHRAE [1, 2] or VDI [3].It can be applied for frequencies well above theplane wave cut-off. The sound power level withina duct network can be determined by summationof the losses and gains in sound power level at theconnecting interfaces of the components from thefan towards the terminal sections of the network.All contributions resulting from wave reflectionsare neglected in this approach. This makes theprediction procedure very simple, but reduces thereliability considerably.Second, the plane wave based description of

ducts, mufflers and networks [4, 5, 6] covers thelow frequency range. A variety of analyticalplane wave two-port models is available in theliterature. The acoustical transmission matrix ofnon-standard components can be determined by3-D FEM/BEM or unsteady CFD simulations incase of non-zero mean flow. In HVAC duct net-works with their large lateral dimensions, however,the frequency range of plane wave propagation israther limited. Nevertheless, accurate sound pre-diction at lower frequencies below a few hundredHz is quite important, since absorbing liners areineffective at those frequencies. In Table 1 theplane wave cutoff frequency, fc, is given for someexemplary circular ducts.

Table 1: Plane wave cutoff frequencies for circularducts.

diameter fc typical usage10 mm 20 kHz brass wind instrument50 mm 4 kHz car exhaust pipe300 mm 670 Hz HVAC ducts

2.1 Sound power-based description

The sound power-based description of soundtransmission in ducts is valid for frequencies wellabove the plane wave cut-off. Wave reflectionsare neglected. The transmission loss of a ductelement is considered. The variable of state thenis the sound power level LW :

LW = 10log10

(PacP0

)dB (1)

with a reference sound power level P0 = 10−12

Watt. Typically LW is specified for octave or 1/3-octave frequency bands. The summation of levelsLi obeys the following rule:

Lsum = 10log10

n∑i=1

10Li/10 (2)

The acoustic elements based on the sound powerdescription are extended from one, two or multi-ports. Each port is represented by a signal-based connector holding two arrays of incomingand outgoing LW in N frequency bands. Sincethere are no reflections considered, in passiveelements like silencers, each incoming LW signalis mapped onto the outgoing LW independentlyof its counterpart:

LWioutA = LWi

inB −∆LWiB→A

LWioutB = LWi

inA −∆LWiA→B

(3)

with ∆LWi the reduction of the sound power levelat the ith band. This allows bidirectional usage ofthe components.In-duct sources, like fans or bends contributing

regenerated flow-noise, add their forward andbackward contribution to the total sound pressurelevel according to eq. (2)Figure 1 gives some examples of acoustic com-

ponents already included in SoundDuctFlow, likedifferent types of pipes, bends, silencers, fans.

2.2 Plane wave description

In the wave based description the steady state,frequency dependent plane wave solution of thewave equation is regarded. This approach is validonly for the low frequency region below the planewave cut off. Although this region is ratherlimited because of the large lateral dimensionsusually found in HVAC duct networks, an accu-rate calculation is nevertheless important, sinceabsorbing materials are rather ineffective at thosefrequencies. Two physically equivalent methodscan be applied to characterize the individual ductelement.In the scattering matrix method the sound pres-

sure p is decomposed into forwards and backwardstraveling plane waves:

p(x,t) = p̂(x)expiωt = p+ expi(ωt−kx) +p− expi(ωt+kx)

(4)


© The Modelica Association, 2009 520

Figure 1: Examples of acoustic elements.

where k = ω/c0, p+ and p− are the amplitudesof forwards and backwards traveling waves. Theacoustic particle velocity then is:

v̂ = 1ρ0c0

(p+ exp−ikx−p− expikx

). (5)

A four pole scattering matrix S maps the for-ward and backward propagating sound pressuresof one port onto the second port:(

p+1p−1

)=(S11 S12S21 S22

)(p+

2p−2

)(6)

This formulation is preferred in connection withthe experimental determination of the acousticreflection coefficient R = p−/p+ at the interfacesof duct elements.The transmission matrix method describes the

relation between acoustic pressure, p, and acousticvolume flow, q, in forward and backward sectionsof the single element by the matrix T :(

p1q1

)=(T11 T12T21 T22

)(p2q2

)(7)

This formulation is preferred for modeling inModelica since the potential variable p and theflow variable q directly can be used to constitutethe physical connector.A collection of plane wave models will be in-

cluded into the SoundDuctFlow library.

2.3 Modeling of junctions

In the sound power-based description, at junctionsthe incident sound power is distributed over thetotal of all outgoing duct sections. By definitionthere are no reflections. The proportion of the

sound power transmitted from section i to sectionj, Wi→j , then is

Wi→j =WiSj

Stot−Si(8)

where Wi is the sound power incident at the ductsection i, Si, Sj and Stot are the incident, outgoingand total cross-sectional areas.In the plane wave model, the reflection of

waves at a multiple junction is considered. Asan example a T-shaped junction between threepipes of cross-sectional surfaces A1, A2 and A3 isexamined here. From the equation of Bernoulli wefind that the acoustic pressures p1 and p2 in theduct just before and after the side-branch have tobe the same as the pressure p3 at the mouth of theside-branch:

p1 = p2 = p3 (9)

The conservation of mass yields that the sum ofthe acoustic volume flows at the junction is zero:

q1 + q2 + q3 = 0 (10)

3 Modeling flow and pressureloss in duct networks

The 1-d modeling of air flow in HVAC ducts andother components is based on several approxi-mations: The air flow in HVAC ducts with itslow Mach number is regarded as incompressible,steady state and fully stabilized. In most cases itis also turbulent. The state variables for fluid floware the static pressure as the potential variableand the mass flow rate as the flow variable. Thepressure loss coefficient K = ∆P

ρU2/2 relates thepressure difference ∆P between the two portsof an flow duct element to the kinetic energydensity of the flow. It depends on the Reynolds



Figure 2: Examples of flow elements.

number, on the relative roughness and on thecross-sectional shape of the duct.Analytic models, like the Colebrook-White

equation, as well as measurement data, given ascharacteristic diagram or interpolated formula[7, 8, 9] or tabulated manufacturer data servesas input for the various flow models. Effectsby turbulence, adverse velocity gradients, cross-sectional shape, surface roughness, curvature,interaction between elements in not fullydeveloped flow regions result in corrective terms.Within the Modelica library flow elements forstandard duct components are available (Fig. 2).

4 Complex duct components

Complex compound flow-acoustic duct compo-nents (see Fig. 3) can be assembled from simpleelements representing either the acoustic or theflow part of a duct element using a special con-nector that combines the acoustic and the flowconnector. This allows the modeling of non-standard components.

Figure 3: Complex compound flow-acoustic ductcomponent utilizing a combined flow-acousticconnector.

5 Flow-acoustic interactionFlow-acoustic coupling can also be modeled onthis basis. Inside duct elements, like bends ororifices, the high Reynolds number flow triggersflow noise. In most cases the back-reaction ofthe sound field on the flow is negligibly weak.This effect can be modeled by extracting thestate of the fluid flow and feeding it into theacoustic element. There the additional flow noiseis calculated by (semi)empirical models, as givenin [3, 10] for instance. An example of a complexcompound pipe component with flow noise is givenin Fig. 4.

Figure 4: Compound flow-acoustic duct compo-nent in which the mean flow velocity generatesflow noise at the bend.

6 Work flow and practical issuesWhen dealing with large models, the parameter-isation of each component in the Dymola GUI iserror-prone and not very convenient for the user,



Figure 5: Acoustic representation of of a ventilation unit.

(a) (b)

Figure 6: A-weighted LW in third octave bands at the suction side (a) and pressure side (b) componentsof a ventilation unit.

especially when the parameters are varied repeat-edly within the design process. Therefore we usean external parameterisation procedure to ensureconsistent data handling and a smooth work flow:After setting up the model in the Dymola GUI, allmodel parameters and connections are extractedinto an XML structure. This XML structure thenis filled in with the parameters’ numerical valuesand read in at the run time of the simulation. Allresults are also written to an XML file for externalpostprocessing procedures like report generation.

7 Examples

As a first example, the acoustic representation ofa ventilation unit is presented in Fig. 5. Here itit is not connected to the duct network but ina configuration for measuring the radiated soundpower from its exits. Therefore the nozzle reflec-tions at the intake and exhaust pipe terminationshave to be included. The predicted A-weightedLW at each element is shown in Fig. 6. Prediction

and measurement of the A-weighted LW at theexits (Table 2) agree quite well.

Table 2: Measured and predicted A-weightedsound power level of a ventilation unit.

Position Sound power level LwAMeasurement Prediction

Pressure Side 52 dB(A) 50.4 dB(A)Suction Side 54 dB(A) 51.9 dB(A)

The ventilation unit is then installed in a smallduct network (Fig. 7). The predicted third bandSPL at each element is shown in Fig. 8.

8 Conclusions and perspectives

The concepts of sound propagation in HVACsystems together with modeling of the air floware realized in the new Modelica library Sound-DuctFlow, providing a joint prediction of the noiselevel and the pressure loss in the duct network.The concept of acoustical connectors based either



Figure 7: Acoustic representation of a ventilation duct network.

(a) (b)

Figure 8: A-weighted LW at each element of a ventilation duct network along two paths from the fanto a listener, (a) at the suction side and (b) the pressure side.

on a sound power level description or a planewave description was discussed. The effects ofthe geometric conditions on the mean air flowis modeled by 1D pressure loss models. Thetriggering of noise by flow effects is also modeled.The modeling of the emitted noise level of aventilation unit agrees quite well with acousticalmeasurements.

SoundDuctFlow will be extended to incorporatealso heat transfer, transport of humid air andcomplex flow-acoustic interactions. For the lastpoint, however, there will be the need for newmodels deduced from complex 3D computationalaeroacoustic simulations.

9 AcknowledgmentsWe are very grateful to Gerhard Karlowatz,Liebherr-Transportation Systems, Austria,for providing real life network examples andmeasurement results.



References[1] Reynolds, D. D. and Bledsoe, J. M.,

Algorithms for HVAC Acoustics, ASHRAEInc., Atlanta, 1991.

[2] ASHRAE, Sound and Vibration Control,2007 ASHRAE Handbook – HVAC Applica-tions, ASHRAE Inc., Atlanta, 2007 (Chapter47).

[3] VDI, Association of German Engineers, VDIGuideline 2081, VDI, Düsseldorf, 2001.

[4] Munjal, M. L., Acoustics of Ducts andMufflers, Wiley, New York, 1987.

[5] Boden, H. and Abom, M., Modelling of FluidMachines as Sources of Sound in Duct andPipe Systems, Acta Acustica, 3 (1995), 545-560.

[6] Boden, H. and Glav, R., Exhaust and IntakeNoise and Acoustical Design of Mufflersand Silenecers, in Handbook of Noise andVibration Control, ed. by Crocker, M. J.,John Wiley & Sons, 2007.

[7] Miller, D. S., Internal Flow Systems, BHRGroup Limited, Cranfield, UK, 1996 (2nded).

[8] Idelchik, I.E., Handbook of Hydraulic Resis-tance, Begell House, 1996 (3rd ed).

[9] Recknagel, Sprenger, Schramek, Taschenbuchfür Heizung und Klimatechnik. R. OldenbourgVerlag, München Wien, 1999 (69th ed).

[10] Nelson, P. A. and Morfey, C. L., Aero-dynamic sound production in low speedflow ducts, Journal of Sound and Vibration,79(1981), 263–289.



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SoundDuctFlow: A Modelica Library for Modeling Acoustics and … · 2009-10-02 · SoundDuctFlow : A Modelica Library for Modeling Acoustics and Flow in Duct Networks Helmut Kühnelt