12th aiaa/ceas aeroacoustics conference, 8-10 may 2006 ... · analogy using acusolve and actran/la...

12th AIAA/CEAS Aeroacoustics Conference, 8-10 May 2006, Cambridge MA, USA

Validation of a CAA formulation based on Lighthill’s

Analogy using AcuSolve and Actran/LA on an

Idealized Automotive HVAC Blower and on an axial

fan

Robert Sandboge∗, Pioneer Solutions Inc.

143 Cadycentre #351, Northville, MI 48167, USA

Stephane Caro†, Paul Ploumhans Free Field Technologies SA – www.fft.be

Axis Park Louvain-la-Neuve, Rue E.Francqui 1, B1435 Mont-St-Guibert, Belgium

Raymond Ambs and Balthasar Schillemeit Visteon Corporation – www.visteon.com

Visteon European Corporate Office and Innovation Center

Visteonstrasse 4-10, 50170 Kerpen, Germany

Karl B. Washburn John Deere Construction and Forestry Division– www.johndeere.com

NVH, Machine Dynamics, and Instrumentation, Dept. 612 PO Box 538

18600 S. John Deere Rd. – Dubuque, IA 52004-0538, USA

Farzin Shakib, ACUSIM Software, Inc. – acusim.com

2685 Marine Way, Suite 1215, Mountain View, California 94043, USA

I. Introduction

The purpose of this work is to evaluate a Computer Aided Engineering (CAE) method in which com-putational aero acoustics (CAA) techniques are used to predict the noise level from automotive fans. Theengineering objective is to ensure that the noise level in an automotive cooling system or an air handlingsystem is sufficiently low for all operating conditions. In fact, automobile manufacturers are placing in-creased emphasis on the reduction of cabin noise level so that this noise reduction has become a criticaldesign consideration. This has resulted in more stringent noise requirements for air handling systems andother cooling systems. For most operating conditions, the blower is the major noise contributor for the cabinnoise level.

In this paper we use the extended version of the variational formulation of Lighthill’s analogy, as presentedin Caro et al.1 This formulation is ideally suited to the finite element method (FEM). It accounts foraerodynamic sources through two source terms. The first term accounts for volume sources; the second termaccounts for sources defined on control surfaces, i.e., surfaces where the normal flow velocity does not vanish.

An important contribution of the present work is an innovative approach for transferring informationfrom the CFD mesh to the CAA one. This problem has a significant practical importance because CFD

∗Contact: [email protected]†Corresponding author: [email protected] c© 2006 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with

permission.

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American Institute of Aeronautics and Astronautics Paper 2006-2692

http://www.fft.be

http://www.visteon.com

http://www.johndeere.com

http://www.acusim.com

and CAA normally use meshes of different extent and resolution. However, if the resolutions of the twomeshes differ greatly in the source region, care must be taken to ensure that aerodynamic sources are wellaccounted for in the CAA simulation. In the new approach, the CFD code directly computes the nodalforces appearing in the variational formulation of Lighthill’s analogy. We present results of tests which provethat this approach allows aerodynamic sources to be accurately accounted for in the CAA simulation, evenif the CFD and CAA meshes differ significantly.

We validate the combination of CFD and CAA on the problem of an idealized HVAC blower and on anaxial fan. Simulations are compared with measurements done in a hemi-anechoic room at Visteon’s NVHlaboratory in Kerpen for the idealized HVAC blower, and with experiments at ISU acoustic laboratory atIowa State University for the axial fan. Preliminary results indicate that acoustic spectra predicted bysimulations match quite well those measured experimentally.

In this effort, CFD and CAA simulations are done using two commercial codes, AcuSolve2- CFD codedeveloped by Acusim Software Inc. - and Actran/LA3 - CAA code developed by Free Field TechnologiesS.A. - respectively.

II. Simulation strategy

II.A. Acoustic formulation

The formulation of Actran/LA is based on Lighthill’s acoustic analogy, implemented in its variationalform, following the approach first proposed by Oberai et al.4 We here used the extended approach presentedin Caro et al.,1 that accounts for control surfaces.

II.A.1. Lighthill’s analogy

The starting point of our approach is Lighthill’s analogy, written as (see Lighthill5)

∂2

∂t2(ρ− ρ0)− a2

0

∂2

∂xi∂xi(ρ− ρ0) =

∂2Tij

∂xi∂xj, (1)

where ρ is the fluid density, ρ0 denotes the density at rest, a0 the speed of sound at rest and T is Lighthill’stensor defined as

Tij = ρvivj +((p− p0)− a2

0 (ρ− ρ0))δij − τij , (2)

where v is the velocity, p is the pressure and τ is the viscous stress tensor. For a Stokesian perfect gaslike air, in an isentropic, high Reynolds number and low Mach number flow, Lighthill’s tensor T is oftenapproximated by

Tij ' ρ0vivj . (3)

II.A.2. Variational formulation of Lighthill’s analogy

The variational formulation of Lighthill’s analogy was first derived by Oberai4,6 et al. The strong variationalstatement associated to Eq. (1) can be written:∫

Ω

(∂2

∂t2(ρ− ρ0)− a2

0

∂2

∂xi∂xi(ρ− ρ0)−

∂2Tij

∂xi∂xj

)δρ dx = 0 ∀ δρ (4)

where δρ is a test function. The spatial derivatives are integrated by parts using Green’s theorem, to obtainthe weak variational form:∫

Ω

(∂2

∂t2(ρ− ρ0) δρ + a2

0

∂

∂xi(ρ− ρ0)

∂δρ

∂xi+

∂Tij

∂xj

∂δρ

∂xi

)dx =

∫Γ

(a20

∂

∂xi(ρ− ρ0) ni +

∂Tij

∂xjni

)δρ dx . (5)

By substituting the right hand side of Eq. (2) for Tij in the surface integral, Eq. (5) becomes∫Ω

(∂2

∂t2(ρ− ρ0) δρ + a2

0

∂

∂xi(ρ− ρ0)

∂δρ

∂xi+

∂Tij

∂xj

∂δρ

∂xi

)dx =

∫Γ

∂

∂xj(ρvivj + (p− p0) δij − τij)ni δρ dx .

(6)

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If we define the total stress tensor

Σij = ρvivj + (p− p0) δij − τij , (7)

Eq. (6) becomes:∫Ω

(∂2

∂t2(ρ− ρ0) δρ + a2

0

∂

∂xi(ρ− ρ0)

∂δρ

∂xi

)dx = −

∫Ω

∂Tij

∂xj

∂δρ

∂xidx +

∫Γ

∂Σij

∂xjniδρ dx . (8)

This is the variational formulation of Lighthill’s analogy. There a two aerodynamic source terms on the righthand side: a volume term, and a surface term.

II.A.3. Treatment of boundary conditions

Solid boundaries If the surface Γ is fixed or vibrating in its own plane, then −ni∂∂t (ρvi) reduces to zero

and the right-hand side of Eq. (8) vanishes. This corresponds to the natural boundary condition associatedwith the weak variational problem. This boundary condition must be applied on the solid boundaries thatare in contact with the region where aeroacoustic sources are defined (see Figure 1).

Control surface Consider a blower with its rotating part, as shown in Figure 1, with the rotating partsenclosed in a control surface. Aerodynamic sources are defined on this surface, and account for the effect ofthe flow enclosed inside the control surface on the noise generation. Such a control surface is also termed aporous boundary condition. If the aerodynamic sources vanish, the control surface reduces to a solid boundary(i.e., a reflecting boundary if there are no aerodynamic sources defined in the volume).

Figure 1. Use of solid and porous boundary conditions (control surface) for simulating the noise of a blower.

Infinite elements for radiation boundary condition For applications to external aeroacousticproblems, the physical domain is unbounded and the pressure fluctuations must satisfy the Sommerfeldradiation condition at large distance from the aeroacoustic sources. This is enforced through the use ofinfinite elements. They are based on the multipole expansion of the solution of the wave equation. Theorder of the expansion directly governs the accuracy of the boundary condition. The infinite element (IE)method implemented in Actran is an extension of a variable order Legendre polynomial formulation whosenumerical performance has been extensively studied (Astley and Coyette7,8). More details on the numericalimplementation can be found in the Actran User’s manual.9

II.B. CFD solution methodology

The fluid flow is modeled using the Navier-Stokes equations combined with the detached eddy simulationmodel as explained in Spalart,10 which is a combination of a RANS turbulence model and large eddysimulation. The turbulent eddy viscosity is modeled using the Spalart-Allmaras RANS turbulence model11

close to the walls,and large eddy simulation away from the walls. The transition between the two models iscontrolled by comparing the distance d to the closest wall with the local element size ∆. The mesh spacing

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in the boundary layer close to the walls is of the same order as the boundary layer thickness, and d is smallerthan c ·∆, where c is a certain constant, leading to the RANS model dominating. Away from the wall, thelength scale c ·∆ is larger than d, and a Smagorinsky large eddy simulation model is dominating. For moredetails see Debus.12

The rotation of the fan is modeled using a rotational mesh motion of a cylindrical mesh block, whichencloses the solid fan geometry, while the surrounding mesh remains static. For more details on the slidingmesh approach, see the Acusim software command reference.13 The sliding interface surface is used as acontrol surface in the acoustic model where aeroacoustic sources are defined, see Section II.A.3.

The finite element method, the Galerkin method with a least-square operator to provide stability withoutsacrificing accuracy as detailed in Shakib,14 is used to solve the model.13

II.C. Coupling between CFD and CAA

II.C.1. Two approaches for computing aerodynamic sources

Assuming that all solid boundaries are fixed or vibrating in their own plane, Eq. (8) reduces to∫Ω

(∂2

∂t2(ρ− ρ0) δρ + a2

0

∂

∂xi(ρ− ρ0)

∂δρ

∂xi

)dx = −

∫Ω

∂Tij

∂xj

∂δρ

∂xidx . (9)

Two approaches can be used to compute aerodynamic sources. Thery are referred to hereafter as thesampling approach and as the integration approach.

The sampling approach consists in having the CFD code directly compute ∂Tij

∂xjat the nodes of the

acoustic mesh. The CAA code will then use these sampled values to compute the right-hand side of Eq. (9).In the integration approach, the CFD code directly computes the right-hand side of Eq. (9) numerically.

The numerical evaluation will require sampling the integrand at the positions of integration points. Thelarger the number of integration points, the more accurate the sampling. The integration approach can thusbe viewed as a way to aggregate the information available on a fine CFD mesh onto a coarser acoustic mesh.

II.C.2. Test problem definition

Consider a two dimensional problem in free field, with the following source definition (divergence of Lighthill’stensor)

∂Tij

∂xj(x, t) = Q

(cos

(nπx

a

)cos

(nπy

a

))(A cos (2πft)−B sin (2πft)) if |x| ≤ a/2, |y| ≤ a/2 and i = 1 ,

(10)∂Tij

∂xj(x, t) = 0 otherwise , (11)

where Q is the source amplitude, A and B are two parameters such that, in the frequency domain, thecomplex amplitude at frequency f be Q(A + ıB). The source wavelength is thus λs = 2a/n. Only oddvalues of n are considered valid, so that the source has compact support [−a/2; a/2] × [−a/2; a/2], and iscontinuous.

II.C.3. Acoustic model

Figure 2 shows a FE/IE acoustic model used in this study. The FE mesh is a Cartesian mesh that coversa 2R × 2R area, and that was mapped, outside the square source region, to a circle in order to obtain acircular FE/IE interface.

II.C.4. Numerical tests

Numerical tests have been conducted to evaluate the influence of the mesh size, and of the approach forcomputing aerodynamic sources. We consider a frequency f , corresponding to a wavelength λ = a0/f ,where a0 is the speed of sound (a0 = 340 m/s). The computational domain is a circle of radius R = 2λ.The support of the source is a square of side a = λ. We consider 4 different mesh resolutions, made of linear

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Figure 2. Mesh for the acoustic analysis, with element size h = a/8. The support of the source is made of the4 × 4 elements at the center of the domain.

quadrangles of size h = a/2m, with 2 ≤ m ≤ 5. Parameters describing the sources are: Q = 1, A = 1,B = 2. Moreover, we consider two values for n, n = 1 and n = 3. All simulations are done for f = 85. Atthis frequency, the coarsest mesh used has elements of size h = λ/8, which guarantees a fair accuracy of theacoustic propagation (a rule of thumb is thus use 10 linear elements per wavelength). Further refining themesh thus allows assessing the effect of the sampling of the of aerodynamic sources, but does not significantlyincrease the accuracy of the acoustic propagation (except for the switch from h = a/4 to h = a/8). Thenumerical integration is done using ng Gauss-Legendre integration points in each direction.

Radiated acoustic power Tables 1 and 2 report the radiated power for the two different values of theparameter n.

If the source has n = 1, Table 1 shows that the total radiated power is moderately affected by themesh size, even when using the sampling approach for importing aerodynamic sources. Indeed, going fromh = a/4 to h = a/32 increases the radiated power by 36%. This moderate sensitivity was to be expected,since the source has a wavelength λs = 2a, and is thus discretized by 8 linear elements per source wavelength.The sensitivity is even lower for the integration approach. For n = 1, the results are more sensitive to theresolution when the number of integration points increases. The reason is that using a smaller number ofintegration points induces a numerical error, which happens to compensate for the sampling error. However,this is a coincidence, and there are no grounds for extending this to more general cases.

If the source has n = 3, the sampled approach leads to very inaccurate results for h = a/4 and h = a/8.The integration approach behaves similarly when using only one integration point. However, as soon a 2integration points are used in each direction (hence a total of 4 integration points in 2D), the integrationapproach produces results that are much less sensitive to the mesh size. As soon as h is less than or equalto a/8, and the number of integration points ng is greater than or equal to 4, the error in the total radiatedpower is smaller than 6%. Moreover, even when h = a/4, the error is smaller than 8% (the error is greaterfor ng = 9 than for ng = 4, but it is coincidental as the integration error in part compensates the samplingerror, as was the case for n = 1).

Directivity plots As for the directivity, Figure 3 confirms that the sampling and integration approachgive close results for h = a/16 and h = a/32. However, the two approaches lead to significantly differentresults for h = a/4 and h = a/8, with the integration approach (with ng = 2) leading to results that aremuch more accurate than those of the sampling approach, even when h = a/4.

II.D. CAE simulation strategy

CAE is important in product development, but it is often too time consuming to perform complex analysis.As a consequence, the performance is evaluated by costly physical testing; and if CAE analysis is used after

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Figure 3. Pressure amplitude as a function of azimuthal position, at a distance r = 2 a from the center ofthe aerodynamic sources. Aerodynamic sources computed using both the sampling and integration (with 2integrations points in each direction) approaches. Sources have n = 3

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Model sampled, n = 1 integration, n = 1ng = 1 ng = 4 ng = 9

h = a/32 1.909 10−3 1.918 10−3 1.916 10−3 1.916 10−3

h = a/16 1.883 10−3 1.916 10−3 1.907 10−3 1.907 10−3

h = a/8 1.779 10−3 1.910 10−3 1.874 10−3 1.874 10−3

h = a/4 1.407 10−3 1.881 10−3 1.739 10−3 1.740 10−3

Table 1. Power radiated by an aerodynamic source, n = 1.

Model sampled, n = 3 integration, n = 3ng = 1 ng = 4 ng = 9 ng = 16

h = a/32 6.829 10−7 7.130 10−7 7.029 10−7 7.029 10−7 7.029 10−7

h = a/16 6.281 10−7 7.536 10−7 7.105 10−7 7.105 10−7 7.105 10−7

h = a/8 4.055 10−7 9.526 10−7 7.413 10−7 7.430 10−7 7.430 10−7

h = a/4 4.682 10−8 2.097 10−6 7.843 10−7 8.109 10−7 8.106 10−7

Table 2. Power radiated by an aerodynamic source, n = 3.

all, it is probably too late in the product development cycle to provide valuable feedback. To avoid thisscenario, it is important that the CAE evaluation methodology can directly process design proposals. Amajor obstacle is that the geometrical representation of a design proposal, usually in a CAD system, isincompatible with the geometrical representation required by the CAE analysis if a traditional approach isused. Moreover, the old traditional method of healing CAD data of a design proposal to create a CAE fittinggeometrical model by human labor is too slow and too expensive to be a viable method for complex models.

For a CAE approach to be efficient and useful in a development process, it is important to have thefollowing foundation:

• Efficient approach to create CAE fitting CAD geometry.

• Automatic discretization method of the CAD geometry.

• Accurate CAE numerical methods.

• Interoperability between the different software components.

The above aspects have carefully been managed in development design processes in automotive industryfor several products, where fluid dynamics has been used to evaluate performance characteristics; the softwarepackage used for that purpose is FluidConnection.15 FluidConnection integrates CAD interpretationwith CAE simulation definition and direct CAD meshing.15–19 This project adds the ability to performaccurate aero acoustic simulations for complex systems such as fans and blowers.

The software components used in this presentation to address the aspects stated above are the following:

• Pro/E CAD tool.20,21

• FluidConnection simulation manager.15

• AcuSolve CFD solver.2,13

• Actran/LA acoustics propagation solver.1,3, 22

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III. Example on an idealized HVAC blower

Simulations were performed using the methodology presented above on a simplified radial blower usinga blower wheel with 44 blades and no hub. The blower model consist of the blower wheel and a simplescroll only. The unit sits in a large room, representing the test chamber. Two tests were performed, a fluiddynamics test in a test chamber, where a box was attached to the scroll outlet for back pressure adjustments,and a acoustics test, where the blower unit was sitting on a test stand 1 m from the floor in a hemi-anechoicchamber with no obstructions upstream nor downstream. The first test and comparison with simulationswas documented in.23 The second test is related to aeroacoustic, and the preliminary findings are givenbelow.

III.A. Experimental setup for the acoustics measurements

The prototype blower scroll assembly used for the NVH test is made out of PMMA to provide a convenientoptical access. In the NVH test set-up, the blower is elastically supported on rubber strings for isolationpurposes. The blower axis is extended to minimize the influence of blower motor vibration on the measure-ment. Special attention was payed to ensure a smooth flow path; the number of obstacles like clips, screwsetc. was kept to the absolute minimum. The housing of the scroll was reinforced and prepared to avoidresonances and structure born noise influencing the sound pressure measurements. A hemi-anechoic roomis used for the sound pressure level measurements. Background sound pressure level is 17 dB(A), cut-offfrequency is 50 Hz. The blower is positioned 1m from the floor on a stand. There are no obstructions closeto the inlet or outlet of the scroll, ensuring an undisturbed in- and outflow. The blower speed was adjustedto 1500rpm (or 25 rev

s ). Four B&K 4190 microphones were used to measure the sound pressure level inlocations given in Table 3. One microphone is located upstream of the inlet, and three downstream of theoutlet ,see Figure 4. Data acquisition and postprocessing was done using HeadAcoustics SQLab2 equipmentand Artemis software.

Mic. x y z

[m] [m] [m]1 -0.27 0.40 -0.0652 1.230 -0.1 -0.0653 0.730 -0.1 -0.3654 0.730 -0.5 -0.065

Table 3. Microphone locations used in experiment and analysis. The coordinate system is centered at thecenter of the wheel, where the x direction of the flow through the scroll outlet, and the y direction is pointingupstream the blower inlet.

III.B. CFD results

The CFD has been performed using AcuSolve as explained above. The velocity field is represented at agiven time step on Figure 5; it gives an idea of the complexity of the vortex structures in the vicinity of theblades and near the cutoff. Clearly, the technique with the porous boundary gives an enormous advantagehere, as it allows not resolving the sources in the very vicinity of the blades.

III.C. Acoustic results

An acoustic prediction at the position of a microphone is presented in Fig. 6. The effects of the groundare accounted for using an observer image technique. The agreement between measurements and simulationis quite good; the same type of agreement is found for the other microphones. Moreover, the results wereobtained with a CAA model made of a 170,000 nodes, which is not much. As a next step, we will makeadditional tests using a finer CAA model. The CFD mesh is 2 millions nodes (11,5 millions tets); a meshrefinement could also be performed on the new cluster.

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(a) Zoom on the mock-up (b) Microphone positions

(c) Zoom on the mockup (d) Microphone positions

Figure 4. Experimental setup for sound measurements in the blower case

III.D. Conclusions

The numerical results show a good agreement with the experiments, although the experimental results do notclearly show peaks in the spectrum. This is surprising for a rotor-alone configuration. The cause could be thatthe rotational speed is varying with time, causing a widening of the peak in the experimental spectrum. Thisnon-constant rotational speed could be explained by the fact that the hemi-anechoic chamber is too little fora blower with no heat exchanger upstream: the flow is too high and there are recirculations, causing burstsand big vortex structures at the intake. This phenomenon is not present in the CFD computation due to lackof mesh resolution in that area, and the resulting sources are not well enough resolved. The non-constantrotational speed of the rotor has been confirmed by using a stroboscope during the experiment. Anotherlimitation of this study was the available computer hardware for the highly extensive CFD computation.

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Figure 5.

Figure 6. Sound pressure level at a monitoring point

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IV. Example on a John Deere axial fan

A fan with seven blades (Figure 7) has been analyzed using the approach described in Section II. Physicaltests have also been performed for this fan. The CAE model tried to mimic the test setup in as high detailas was considered to be necessary, see Figure 8.

Figure 7. CAD model of axial fan impeller

IV.A. Fan experiments

The fan was tested experimentally at ISU Acoustic Lab,24 using three different rotational speeds, 1000 RPM,1500 RPM, and 2000 RPM, and with three different porous screens types, upstream of the fan. The threedifferent screens give similar results, which shows that an exact description of the screen is not important.The sound pressure was measured at 8 microphones located 1.5 m from the center of the hub, see Table 4;however, the measured spectrum is not known for each microphone, only the average of the contributions tothe 8 microphones is known; it is thus decided to work with this quantity as well.

IV.B. Test chamber geometry and meshing

The geometry for the CFD simulation consists of solid parts representing a cylindrical air volume surroundingthe fan impeller, the air in the test chamber, and the porous screens in the test setup. The geometry foracoustics propagation consists of solid parts representing the air outside the cylindrical rotating air impellervolume restricted by a sphere of 0.8m radius, indicated in Figure 8, and the porous screens in the test setup.In addition, the air outside the sphere is represented by the sphere (surface).

Even though both codes are based on Finite Element Methods, the CFD mesh, see Figure 9, and theacoustic mesh have been built independently, which makes it possible to use optimal mesh sizes for eitheranalysis.

IV.C. CFD simulations

Several simulations were performed on the same impeller geometry. As discussed above, different mesheswere used, and in addition different number of time steps were used to sample data. The simulations have

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Figure 8. CAD model of test setup

Mic. x y z

[m] [m] [m]1 0.0 0.0 1.502 0.75 0.75 1.063 -0.75 0.75 1.064 -1.50 0.0 0.05 -1.06 1.06 0.06 0.0 1.50 0.07 1.06 1.06 0.08 1.50 0.0 0.0

Table 4. Microphone locations used in experiment and analysis. The coordinate system is centered at thehub, where the x direction is upstream of the fan, and the z direction is up.

been performed with porous screens, where the screen was modeled as a thin region with a porous mediummaterial property, which represent the heat exchangers of the experiment (same pressure loss). The CAEanalysis showed good agreement with test data if sufficient number of time steps is used, see Section IV.E.A rectangular filter was used for all fan simulations.

Here, the frequency range is limited to 40 Hz to 1000 Hz. A snapshot of magnitude of velocity |u| throughthe center of the impeller from the transient CFD simulation for the 2000 RPM case is shown in Figure 10.The snapshots show a lot of large scale turbulence downstream of the fan, and much less turbulence upstreamof the fan. This is even more visible on the 3D snapshots of figure 11 at 2000 RPM, and on figure 12 at 1000RPM.

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Figure 9. Plot of a subset of the CFD mesh

(a) Velocity (b) Pressure

Figure 10. Plot of velocity and pressure at 2000 RPM

IV.D. Acoustic simulations

The sources used for the acoustic computation are directly exported on the FEM acoustic mesh using thetechnique described above. A snapshot of the sources at a given time step is given on Figure 13. It gives anidea of the typical vortex sizes that exist in the system. However, thanks to the porous boundary conditionused by Actran/LA, the sources in the very vicinity of the blades (the smallest) do not need to be used

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Figure 11. 3D snapshots of velocity and pressure at 2000 RPM


Figure 12. 3D snapshots of velocity and pressure at 1000 RPM

by the acoustic code, which makes the acoustic computation much lighter.The sound pressure level was computed at the microphone locations, taking the ground into accounta.

The sound pressure field on a section cut through the middle of the fan, for a few frequencies, is shown onFigure 14. This gives an idea of the complexity of the acoustic pressure field in the vicinity of the sources;at a larger distance however, things are much smoother.

IV.E. Comparison between physical experiment and computer simulations

The comparison between physical experiment and CAE simulations are done at the 1000 RPM and 2000RPM test points. The results show good agreement at low frequencies, see Figures 15-16. The simulations

aThis is done by adding the contribution of the real microphones with the contribution of virtual microphones located atsymmetric positions with respect to the ground.

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Figure 13. Snapshot of the sources at a given time step

(a) 200 Hz (b) 220 Hz

(c) 240 Hz (d) 600 Hz

Figure 14. Sound pressure field in dB at a section cut through the middle of the fan

used a frequency sampling of ∆f = 20Hz, while the experiment used a frequency sampling of ∆f = 6Hz.In both cases, we observe an excellent agreement.

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Figure 15. Average sound pressure level of computed response at eight points located 1.5 m from the centerof the fan hub compared with test data, 1000 RPM

Figure 16. Average sound pressure level of computed response at eight points located 1.5 m from the centerof the fan hub compared with test data, 2000 RPM

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V. Conclusions

We have presented an aeroacoustic approach for predicting the noise level generated by an idealizedHVAC blower and an axial fan. It is based on a two steps procedure. In a first step an unsteady flow iscomputed using AcuSolve. This first step serves to predict aerodynamic sources of noise. In a second step,an acoustic computation is made using Actran/LA. The variational formulation of Lighthill’s analogy,extended to allow handling control surfaces, is used. This is a key ingredient for treating blower problems.

Two different approaches for importing aerodynamic sources have been investigated. An analytic aero-dynamic source of compact support has been used to study the relative performance of the two approaches.

In the first approach - the sampling approach - aerodynamic sources are sampled at the nodes of theacoustic mesh, and these sampled values are used in Actran, in the context of the variational formulationof Lighthill’s analogy. In order to produce accurate acoustic results, this approach requires that aerody-namic sources be sampled finely enough. Tests have confirmed that roughly 10 acoustic elements per sourcewavelength are required to produce accurate results.

In the second approach - the integration approach - aerodynamic sources are imported into Actranas nodal forces. This means that sources are sampled at a number of integration points in each element,are multiplied by derivatives of shape functions, and are integrated according to the variational formulationof Lighthill’s analogy. Tests have shown that, provided enough integration points are used, this secondapproach is much less sensitive than the sampling approach to the size of the elements of the acoustic mesh.In practice, this second approach allows using different meshes - with elements of significantly different sizes- for a CFD simulation (that produces aerodynamic sources) and for an acoustic simulation.

Experiments on a ventilating blower have been performed, and sound pressure levels have been measuredat four locations. CFD simulations of the ventilating blower have been done, and the resulting aerodynamicsources have been used in a CAA computation. Preliminary acoustic results have been obtained and showa pretty good agreement with experimental results.

Future work will include continuing higher-resolution computation for CAA and comparing the predic-tions with experimental results.

References

1Caro, S., Ploumhans, P., and Gallez, X., “Implementation of Lighthill’s Acoustic Analogy in a Finite/Infinite ElementsFramework,” AIAA Paper 2004-2891, 10th AIAA/CEAS Aeroacoustics Conference and Exhibit, 10-12 May 2004, Manchester,UK.

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place de l’Universite, 1348 Louvain-la-Neuve, Belgium, 2006.4Oberai, A., Ronaldkin, F., and Hughes, T., “Computational Procedures for Determining Structural-Acoustic Response

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