Computation of aerodynamic noise of centrifugal fan using ...

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Computation of aerodynamic noise of centrifugal fanusing large eddy simulation approach, acoustic analogy,and vortex sound theoryQ Liu∗, D Qi, and H TangSchool of Energy and Power Engineering, Xi’an Jiaotong University, Shannxi, People’s Republic of China

The manuscript was received on 22 January 2007 and was accepted after revision for publication on 24 July 2007.

DOI: 10.1243/09544062JMES609

Abstract: Large eddy simulation is applied to solve the unsteady three-dimensional viscous flowin the whole impeller–volute configuration of a centrifugal fan. The results of the simulation areused to predict the impeller–volute interaction and to obtain the unsteady pressure, velocity,and vorticity fluctuations in the impeller and volute casing. The simulation at the design point iscarried out with the wall-adapting local eddy-viscosity subgrid-scale model and a sliding meshtechnique is applied to consider the impeller–volute interaction. The results show that a stronglyunsteady flow field occurs in the impeller and volute casing of the fan, and the flow is char-acterized with obvious pressure and vorticity fluctuations, especially at the tongue and at theblade wake region. The large pressure fluctuation at the tongue and the large fluctuation of theblade wake vorticity appear as the blade wake is passing the tongue. Acoustic analogy and vortexsound theory are used to compute the radiated dipole and quadrupole sound fields, which arein good agreement with the experiment. The sound results show that the vortex sound theoryis convenient for the broadband noise computation, and the dipole sound is much higher thanthe quadrupole sound. The dipoles, distributed over the volute tongue surface, are the dominantsound source of the fan.

Keywords: acoustic analogy, centrifugal fan, large eddy simulation, vortex sound theory

1 INTRODUCTION

The flows in centrifugal turbomachinery have been thesubject of experimental and theoretical studies sincethe last century. The knowledge of flows in centrifugalturbomachinery provides a useful insight for engi-neering design. In recent years, many authors haveworked in the numerical simulations of unsteady flowfield in centrifugal fans as a way to identify sourcesof aerodynamic noise. And the accurate predictionof the turbulent flow field in a centrifugal fan is veryimportant for the noise sources identification.

As it is known, the instantaneous flow variablessatisfy the Navier–Stokes equations. The methods for

∗Corresponding author: School of Energy and Power Engineering,

Xi’an Jiaotong University, Xi’an, Shannxi 710049, People’s Republic

of China. email: [email protected]

simulating turbulence are many: turbulence mod-els (educated guesses about the Reynolds stressesrequired), statistical theory of turbulence (to gainfundamental understanding), and direct numericalsimulation (DNS). The conventional Reynolds-averaged Navier–Stokes (RANS) solver has its limita-tions for simulating small scale eddies. It is possible,in theory, to directly resolve the whole spectrum ofturbulent scales using an approach known as DNS.However, DNS is not feasible for practical engineer-ing problems involving high Reynolds number flows.The cost required for DNS to resolve the entire rangeof scales is proportional to Re3, where Re is the tur-bulent Reynolds number. Clearly, for high Reynoldsnumbers, the cost becomes prohibitive. Thus, largeeddy simulation (LES) is one of the more promisingmodes of numerical simulation of turbulence. Thenumerical solutions for the viscous flow of centrifugalturbomachinery are made by the RANS calculationsfrom the 1980s [1–3]. More recently, LES techniques

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1322 Q Liu, D Qi, and H Tang

have been attempted to simulate unsteady flows ofturbomachinery [4–6].

Dealing with the turbulent flows in complexdomains by LES, such as flows in a centrifugal fan,requires good subgrid-scale models, a robust numeri-cal algorithm, and fast computer. In LES, large eddiesare resolved directly, while small eddies are modelled.LES thus falls between DNS and RANS in terms of thefraction of the resolved scales. Resolving only the largeeddies allows one to use much coarser mesh and largertimes-step sizes in LES than in DNS. However, LES stillrequires substantially finer meshes than those typi-cally used for RANS calculations. In addition, LES hasto be run for a sufficiently long flow-time to obtainstable statistics of the flow being modelled. As a result,the computational cost involved with LES is normallyorders of magnitudes higher than that for steady RANScalculations in terms of memory (RAM) and CPU time.Therefore, high-performance computing (e.g. paral-lel computing) is a necessity for LES, especially forindustrial applications.

The production of aerodynamic noise by turbo-machinery has been extensively studied in relationto aircraft engines. Important problems of turboma-chinery aerodynamic noise and vibration also occur,however, in applications of the industrial centrifugalfans, often with flow of very low Mach number, andthere is currently much interest in the developmentof numerical schemes for predicting the aerodynamicsound and vibration in these conditions. The rota-tion of the impeller and the asymmetric shape of thespiral volute and tongue make the flows highly three-dimensional and unsteady in nature. The generatedaerodynamic sound generally includes both discreteand broadband frequency components. The discretenoise is often dominated by tones at the blade pass-ing frequency (BPF) and its higher harmonics [7, 8],which are due to the strong flow interaction betweenthe rotating impeller and stationary volute casing. Theseparate flows, the secondary flows and the wake flowsresulting in flow losses in the passage form vortices,which not only introduce high degrees of unsteadi-ness into the mean flow but also generate broadbandnoise.

The numerical research on aerodynamic noise isusually based on the unsteady flow fields solvedby computational fluid dynamic methods or mea-sured by experimental techniques to obtain the noisesources. Then, the generalized Lighthill equation orits special form, such as FW-H equation, Lowsonequation, and Curle equation, is applied to pre-dict the acoustic field [9–12]. Recently, a numer-ical method to predict the noise of a centrifugalimpeller near a wedge was developed by Jeon andLee [13–15]. They introduced an incompressible andinviscid discrete vortex method (DVM) to describe thetwo-dimensional unsteady flow field and introduced

Lowson’s formulation to predict the noise generatedfrom the impeller blades. However, the unsteady flowfield of this wedge model is obviously different fromthe real centrifugal fan equipped with a volute casing.Langthjem and Olhoff [16, 17] used two-dimensionalDVM and boundary element method (BEM) to predictthe noise generated from a centrifugal pump within avolute casing. Moon et al. [18] used two-dimensionalunsteady Navier–Stokes equations and Curle equationto predict the noise generated from a cross flow fan.Since the exact information of the unsteady flow can-not be obtained from such a two-dimensional flowfield due to the lack of detailed modelling on the turbu-lence, a three-dimensional description of the unsteadyflow in the impeller–volute configuration could be ofgreat interest [19]. Liu et al. [20] performed a three-dimensional numerical simulation of the completeunsteady flow in the whole impeller–volute configu-ration to calculate the noise with FW-H equation. Allthe researchers mentioned above only considered thesound generated by a distribution of dipoles over theblades and neighbouring surfaces. The quadrupolesources within the flow, associated with turbulentReynolds stress fluctuations, were neglected.

In the current work, a numerical study on the aero-dynamic noise generation in an industrial centrifugalfan with forward swept blades is carried out. Three-dimensional numerical simulations of the completeunsteady flow field in the whole impeller–volute con-figuration are performed by LES approach to obtainthe dipole and quadrupole sources. Based on theunsteady flow information, the aerodynamic tonal andbroadband sounds are calculated by using the FW-Hequation and the vortex sound theory, respectively.

2 METHODOLOGY OF LES

2.1 Filtered Navier–Stokes equations

The governing equations employed for LES areobtained by filtering the time-dependent Navier–Stokes equations in either Fourier (wave number)space or configuration (physical) space. The filteringprocess effectively filter out the eddies whose scalesare smaller than the filter width or grid spacing used inthe computations.The resulting equations thus governthe dynamics of large eddies.

A filter of a function φ(X, t) with respect to the spacevariable can be defined by convolution

φ(X, t) =∫

Dφ(X ′, t)G(X − X ′) dX ′ (1)

where D is the fluid domain of concern, and G is thefilter function that determines the scale of the resolvededdies.

Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science JMES609 © IMechE 2007



Computation of aerodynamic noise of centrifugal fan using LES 1323

The box filter operation (also known as‘moving aver-age’ or ‘top hat filter’) is commonly used in practice forexperimental or field data

φ(X , t) = 1V

∫vφ(X ′, t) dX ′, X ′ ∈ v (2)

where V is the volume of a computational cell. Thefilter function, G(X − X ′), implied here is then

G(X ) =⎧⎨⎩

1V

, if X ′ ∈ v

0, otherwise(3)

Filtering of the incompressible Navier–Stokes equa-tions yield

∂

∂xi(ρvi) = 0 (4)

and

ρ∂ vi

∂t+ ρ

∂

∂xj(vi vj) = − ∂P

∂xi+ µ∇2vi − ∂τij

∂xj(5)

where τij is the subgrid-scale stress tensor defined by

τij = ρvivj − ρvi vj (6)

2.2 Subgrid-scale models

The subgrid-scale stresses tensor resulting from thefiltering operation are unknown, and require mod-elling. Most subgrid scale models are based on aneddy-viscosity assumption to model the subgrid-scaletensor

τij − 13τkkδij = −2µtSij (7)

where µt is the subgrid-scale turbulent viscosity, andSij is the deformation tensor for the resolved fielddefined by

Sij = 12

(∂ vi

∂xj+ ∂ vj

∂xi

)(8)

In the wall-adapting local eddy-viscosity (WALE)model, the eddy viscosity is modelled by

µt = ρL2s

(Sd

ijSdij

)3/2

(Sd

ij Sdij

)5/2 + (Sd

ijSdij

)5/4 (9)

where Ls and Sdij in the WALE model are defined,

respectively, as

Ls = min(κd, CwV 1/3) (10)

Sdij = 1

2(g 2

ij + g 2ji) − 1

3δijg 2

kk, gij = ∂ vi

∂xj(11)

where κ is the Von Kármán constant, d is the distanceto the closest wall, Cw is the WALE constant, V is the

volume of the computational cell, and the value of theWALE constant Cw is 0.325.

2.3 Inlet boundary conditions for the LES model

To generate a time-dependent inlet condition, a ran-dom two-dimensional vortex method is considered.With this approach, a perturbation is added on a spec-ified mean velocity profile via a fluctuating vorticityfield (i.e. two-dimensional in the plane normal to thestreamwise direction). The vortex method is based onthe Lagrangian form of the two-dimensional evolu-tion equation of the vorticity and the Biot-Savart law.A particle discretization is used to solve this equation.These particles or ‘vortex points’ are convected ran-domly and carry information about the vorticity field.If N is the number of vortex points and A is the area ofthe inlet section, the amount of vorticity carried by agiven particle i is represented by the circulation �i andan assumed spatial distribution η

�i(x) = 4

√πAk(x)

3N [2 ln(3) − 3 ln(2)] (12)

η(x) = 12πσ 2

(2e|x|2/2σ 2 − 1)2e|x|2/2σ 2(13)

where k is the turbulence kinetic energy. The parame-ter σ provides control over the size of a vortex particle.The resulting discretization for the velocity field isgiven by

v(x) = 12

N∑i=1

�i(xi − x) × z

|x − xi|2(1 − e|x−x|2/2σ 2

)e|x−x|2/2σ 2

(14)

In order to make this vortex method generally applica-ble, a local vortex size is specified through a turbulentmixing length hypothesis. σ is calculated from a knownprofile of mean turbulence kinetic energy and meandissipation rate at the inlet according to the following

σ = ck3/2

2ε(15)

where c = 0.16. In order to ensure that the vortex willalways belong to resolved scales, the minimum valueof σ in equation (15) is bounded by the local grid size.The sign of the circulation of each vortex is changedrandomly each characteristic time scale has passed.In the general implementation of the vortex method,this time scale represents the time necessary for a two-dimensional vortex convected by the bulk velocity inthe boundary normal direction to travel along n timesits mean characteristic two-dimensional size, where nis fixed equal to 100 from numerical testing. The vor-tex method considers only fluctuations in the plane





normal to the streamwise direction. By their interac-tion with the mean velocity field, these fluctuationsimpact streamwise fluctuations downstream from theinlet plane as well.

3 NUMERICAL SIMULATION OF THE UNSTEADYFLOW

A three-dimensional numerical simulation of the com-plete unsteady flow in the whole impeller–volute con-figuration of the centrifugal fan is performed with acommercial software package, FLUENT. The unsteadyflow is solved using a sliding mesh technique, which iscommonly applied to turbomachinery flows.

3.1 Grid system

The numerical simulation is made on an industrialcentrifugal fan with 12 forward curved blades drivenby a 3.0 KW AC motor rotating at 2900 r/min. It con-sists of an impeller, a vaneless diffuser and a volute.The volume flowrate at design point is 0.35 m3/s.Table 1 summarizes the main dimensions of thecentrifugal fan.

There are many difficulties related to the LES of flowsin a centrifugal fan. For example, the fine grid resolu-tion is required for the high Reynolds number flowfield. A geometrical discretization of the centrifugalfan is made for the numerical treatment. Structuredhexahedral cells are generated to define the flow zones(2 177 409 cells at total). Figures 1(b) and (c) show somedetails of the structured mesh in a plane perpendicu-lar to the axis of rotation and the mesh at impellerinlet, respectively. And mesh refinement zones aredefined at the trailing edge of the impeller blades andnear the tongue as shown in Fig. 1(d). The first gridpoint adjacent to the wall has the order of one wallunit, and Fig. 1(e) shows the details of the mesh nearthe tongue wall. Surfaces between inlet-impeller anddiffuser-volute define the grid interfaces needed forthe relative rotation of the impeller.

Table 1 Fan dimensions

Vaneless diffuser outlet diameter D3(mm) 460Impeller blade outlet diameter D2(mm) 400Impeller blade inlet diameter D1 (mm) 164Impeller inlet diameter D0 (mm) 155Impeller outlet width b2 (mm) 36Impeller inlet width b1 (mm) 70Blade thickness h (mm) 2.5Blade number Z 12Blade inlet angle β1A(◦) 38Blade outlet angle β2A(◦) 126Volute width b (mm) 64Impeller-tongue distance (mm) 40Impeller-tongue distance (% of D2) 10%

3.2 Numerical solution

The code solves the fully three-dimensional incom-pressible flitted Navier–Stokes equations, includ-ing the centrifugal force source inside the impellerand the unsteady terms. Turbulence is simulated withthe WALE subgrid-scale model. The time-dependentterm scheme is second of order, implicit. Thepressure–velocity coupling is calculated through theSIMPLE algorithm. Second order, bounded central-differencing scheme is used for convection and dif-fusion terms. In the two grid interfaces betweena stationary and moving mesh, inlet-impeller anddiffuser-volute, the overlapping faces in the inter-face zones are determined at each new timestep. Fluxes across each grid interface are calcu-lated proportionally to the areas of the superposedfaces.

Parallel implementation is simplified by a parallelcluster, which consists of four Intel XEON 3.4 GHzCPUs with a total of 8 GB of RAM. The time stepof the unsteady calculations has been set to t =5.747 × 10−5 s in order to get enough time resolutionfor the dynamic analysis. This time step is related tothe rotational speed of the impeller and is chosenin such a way that one complete impeller revolu-tion can be performed after each 360 time steps. Thenumber of iterations is adjusted to reduce the resid-ual below an acceptable value in each time step. Inparticular, the ratio between the sum of the resid-uals and the sum of the fluxes for a given variablein all the cells is reduced to the value of 10−6 (sixorders of magnitude). Initializing the unsteady cal-culation with the steady solution simulated by arealizable k − ε model, and 100 impeller revolutionsare used to achieve enough stable statistics solu-tion convergence. It costs 3 months to finish the LESsimulation.

3.3 Results and discussions

Based on the same grid system, the unsteady-stateRANS calculations are also performed using RNG k−ε

and realizable k−ε models. Figure 2 shows the vortic-ity comparison between LES and RANS at the midspanof the impeller outlet. The time intervals for the LESand RANS unsteady calculations are the same, and thenon-dimensional time steps, defined as

Nt = mod(

t t

, 360)

(16)

are also the same. The LES snapshot clearly shows theconvection of eddy structures. On the contrary, theRANS solver has its limitations for simulating smallscale eddies. The following discussions are all on thebasis of LES simulation.





Fig. 1 Details of the impeller and volute meshes: (a) sketch of the fan structured hexahedral mesh;(b) mesh at midspan of impeller outlet; (c) mesh at impeller inlet; (d) mesh at blade trailingedge and near the tongue; (e) details of the mesh near the tongue

The total pressure coefficient ψ , internal efficiencyη, and power coefficient λ curves are defined as

ψ = Pt

0.5ρu22

, η = Pt · Qv

Pw, λ = 4Pw

πρD22u3

2

(17)

respectively. The instantaneous values of ψ , η, and λ ina blade-passing event are computed as shown in Fig. 3.

From the figure, one can find that the relative locationbetween the impeller and the volute has a great effecton the performance. The root mean square valuesof these numerical instantaneous performances arecompared with the experiment as shown in Table 2.The calculated results are bigger than the experimentalones. However, the errors between the numerical and





Fig. 2 Vorticity comparison between LES and RANS at the same non-dimensional time step Nt = 0;(a) LES; (b) RNG k−ε; (c) realizable k−ε

Fig. 3 Numerical instantaneous performance curves

Table 2 Comparison of the numerical andexperimental performances

η ψ λ

Numerical value 0.74 1.69 0.067Experiment 0.73 1.63 0.062Error 1.37% 3.68% 8.06%

experimental values are small, indicating that, theunsteady flow simulations could be used to predictthe sound source for noise generation.

The unsteady calculation captures the interactionbetween the tongue and the blades. The static pressureis normalized using a dynamic pressure based on theimpeller outlet tip velocity

Cp = P − Pref

0.5ρu22

(18)

Figure 4 shows the contour plots of the static pressurecoefficient Cp near the tongue in the midspan ofthe impeller outlet at three different non-dimensionaltime steps. According to these pictures the tongue andthe blades are interacting strongly.

Fig. 4 Pressure coefficient near the tongue

Figure 5 shows the contours of the vorticitymagnitude of the blade wake at the midspan of theimpeller outlet at the same non-dimensional timesteps as in Fig. 4. In order to distinguish the vor-ticity strength, the minimum and maximum valuesof the colour scale of contours remain the same inall the time steps. It means contour level scales areconsistent among all time steps. The large amplitudeof the wake vorticity appears as blade wake is pass-ing the tongue. And as each blade wake approachesthe tongue, very strong pressure fluctuations in thevicinity of the tongue can be observed from Fig. 4.These reflect the strong interactions between the wakeflow and the tongue, which is well known as thedominant cause of the discrete noise of industrial fans.

Figure 6 shows the distribution of the pressure coef-ficient and secondary flow in A-A cross-sectional plane

Fig. 5 Contours of the vorticity magnitude of blade wake





Fig. 6 Pressure coefficient and secondary flow in theA-A cross-sectional plane of the volute casing:(a) pressure coefficient in the A-A cross-sectionalplane; (b) projections of the velocity vectors ontothe A-A cross-sectional plane

(shown in Fig. 7) of the volute casing. At differenttime steps the pressure fluctuates strongly (coloursvary strongly) in the cross-sectional plane, and sodoes the pressure gradients. These pressure gradientsare arising from the passage curvature and they arein combination with boundary layers responsible forthe secondary flows in the volute casing. Since thesepressure gradients vary with time, the secondary flowsvary too.

Since the dipoles over the blade and volute surfacesare the main source of the sound pressure, variationsof the surface dipoles will be of great interest. The sur-face dipole strengthen can be approximated by theroot mean square value of the time-derivative of thestatic pressure

Ps =√√√√ 1

N

N∑1

(∂P∂t

)2

(19)

which is shown in Fig. 8. It can be seen that the maindipole sources are located at the tongue.

Fig. 8 The dipole strengthen over the blade and volutesurfaces

Fig. 7 Location of the investigated cross-section





4 NUMERICAL CALCULATION OF FAN NOISE

4.1 Acoustic analogy

Different methods have been proposed for calculat-ing the sound generated by low Mach number flow. Inthese methods an inhomogeneous wave equation ofthe form

1c2

0

∂2p∂t 2

− ∂2p∂xi

= q (20)

is derived from the compressible hydrodynamic equa-tions. Different expressions for q have been derivedwhich can be shown to agree in the sound pressurefield obtained from equation (20). Lighthill showedthat q can be written as a quadrupole source

q = ∂2Tij

∂xi∂xj, Tij = ρuiuj + δij[(p − p0)

− c20(ρ − ρ0)] − eij (21)

In this case the stress tensor Tij acts as the soundsource. In 1965, Lowson gave the result for the soundfar field of a generally moving point acoustic stress∂2Tij/∂xi∂xj in arbitrary motion as

p(xi, t) = (xi − yi)(xj − yj)

4πc20 R3(1 − Mr)3

[ {∂2Tij

∂t 2

+ 31 − Mr

∂Tij

∂t∂Mr

∂t+ Tij

1 − Mr

∂2Mr

∂t 2

+ 3Tij

(1 − Mr)2

(∂Mr

∂t

)2}]

(22)

Here the square brackets imply evaluation at theretarded time τ = t − r/c0, where, t is the time ofobservation and r is the distance from source toobserver. Mr is the component of the instantaneousconvection Mach number in the direction r of theobserver, and

Mr = (xi − yi)

rMi (23)

where Mi is the component of the instantaneous con-vection Mach number M in the i direction; xi and yi

are the observer position and source position; and (1 −Mr) is the Doppler factor. ∂Mr/∂t is the component ofacceleration in the r direction

∂Mr

∂t= (xi − yi)

r∂Mi

∂t(24)

Ffowcs Williams and Hawkings extended Lighthill’sacoustic analogy by taking into account the displace-ment of a rigid surface placed in the flow as the

form

q = ∂Q∂t

− ∂Fi

∂xi+ ∂2Tij

∂xi∂xj(25)

where, Q is the mass flux per unit volume and Fi is theexternal force acting on the fluid.

The FW-H equation can offer acoustic scatteringsand reflections of turbulence over a solid wall bound-ary with simple shape, such as an infinite half-plane,by involving an acoustic Green’s function. However, itis not feasible to find an appropriate acoustic Green’sfunction for the geometry of a centrifugal fan unlessa numerical Green’s function is introduced by using aBEM. No such work has been reported to the author’sbest knowledge. Thus, the FW-H equation cannot takeinto account the possible acoustic reflections on theimpeller blades and the volute casing. Up to now,the radiated sound field from turbulence is calculatedby solving the acoustic equation with the free spaceGreen’s function.

4.2 Vortex sound theory

The formulation of a region of eddy motion as anacoustic source is a major step towards a physicalunderstanding of turbulence-induced noise. However,Lighthill’s theory does not identify the characteris-tics of vortex dynamics that are noise producing. Itseems that Lighthill was motivated towards a descrip-tion of sound intensity in terms of the statisticalcharacteristics of the turbulent source region.

Reformulating the theory of aerodynamic sound byLighthill, the sound source was identified with a termof the form

q = ∇ · L, L = ρ0(ω × u) (26)

at low Mach number M , first by Powell [21] and laterby Howe [22], where ω = ∇ × u denotes the vorticityvector and ρ0 is the undisturbed fluid density. Thus, thewave equation for the acoustic pressure p is written as

1c2

o

∂2p∂t 2

− ∂2p∂x2

i

= ∂Li

∂xi(27)

This can be derived as an approximation from theconservation equations of mass, momentum, andenergy. Vortex sound theory is very useful for analyt-ical studies, but there is little research for numericalsimulations.

Lowson’s method also gives the result for the soundfar field of a generally moving point dipole force q =−∂Fi/∂yi as

p(xi, t) = (xi − yi)

4πr2c0(1 − Mr)2

[∂Fi

∂t+ Fi

(1 − Mr)

∂Mr

∂t

](28)





Following the same arguments that led toequation (28), one can obtain the sound field from apoint vortex in motion as

p(xi, t) = − (xi − yi)

4πr2c0(1 − Mr)2

[∂Li

∂t+ Li

(1 − Mr)

∂Mr

∂t

](29)

4.3 Experimental facility

A test facility for the aerodynamic and acoustic char-acterization of the investigated fan is designed andbuilt following China Standards GB-2888-91: Methodsof noise measurement for fans, blowers, compressorsand roots blowers, and GB-12362-85: test methods ofaerodynamic performance for fans. Figure 9 shows asketch of this test facility with its main elements. Inorder to measure the sound pressure level (SPL), themicrophones manufactured by the PCB Corporation(Model 377A02) are selected. An LMS SCADASIII 305

digital data acquisition and analysis system is used toacquire and analyse the data.

4.4 Numerical results and discussions

The radiated dipole and quadrupole sound fieldsare computed using the time-dependent flow field.A fourth-order polynomial regression is applied to findtime derivatives of the sound source densities at eachretarded time.

The dipole sound, shown in Fig. 10, is calculated byusing FW-H equation with the assumption of the freefield at 1 m apart from the outlet of the volute cas-ing (the noise test point, seen in Fig. 9). In Fig. 10(a),the sound pressure fluctuation generated by sourceson stationary volute surface is much higher thanthat generated by sources on rotating blades, andthe sound pressure phases are almost inversed. Thus,the force acting on the volute casing is the domi-nant source of the aerodynamic noise. An SPL is then

Fig. 9 Test installation

Fig. 10 Dipole sound calculated by FW-H equation: (a) variations of the calculated soundpressures; (b) the calculated quadrupole SPL





Fig. 11 Quadrupole sound calculated by Lighthill stress tensor: (a) variations of the numericalsound pressures; (b) the calculated quadrupole SPL

determined by

SPL = 10 log10

(p

pref

)2

(30)

where pref (= 2 × 10−5 Pa) is a standard referencepressure. The SPL spectrum is obtained by a fast-Fourier transform (FFT) algorithm. The calculated SPLis shown in Fig. 10(b). The amplitudes at the BPF andits second harmonic are much higher than that of thebroadband noise because of the small gap distancebetween the impeller and the tongue.

Figure 11(a) shows the variations of the calculatedsound pressure generated by quadrupole sources Tij

both in the rotating impeller (including the vanelessdiffuser) and in the stationary volute. In the figure, thepressures vary periodically and the pressure phases areinversed, so the resulting sound field will be consistedof discrete components. Moreover, the sound pressurefluctuation generated by rotating flow zone is lowerthan that generated by stationary one. The calculatedquadrupole SPL obtained by FFT algorithm is shownin Fig. 11(b). It shows that the BPF tone and its highharmonic tones are dominant, and the values of theother frequencies are entirely under 35 dB.

In Fig. 12, the time variations of the sound pres-sures calculated by equation (29) are represented.One can find some differences between Figs 11(a)and 12(a). The amplitude of vortex sound pressureis higher than that computed by equation (22). Andthe vortex sound pressure has not only periodic com-ponents but also strong random ones, and so theresulting sound field has discrete and broadband com-ponents, which is shown in Fig. 12(b). By consideringFig. 12(b), it is obvious that the large amplitudes of SPLare distributed in a broadband range of frequency.

The total SPL calculated by FW-H equation andvortex sound theory is compared with the measuredone as shown in Fig. 13. The pattern of the cal-culated sound pressure is similar to the measuredone, but the level shows some deviation becausethe calculated method does not consider the effectsof the scattering and reflection due to the volutecasing. According to Figs 10 to 13, the quadrupolesound is found to be much weaker than the dipolesound. It can be concluded that the dipoles, dis-tributed over the volute tongue surface, which resultsfrom the unsteady force fluctuation, is the domi-nant sound source of the fan with low Mach numberflow. The simulated dipole SPLs versus radiation angle

Fig. 12 Vortex sound calculated by vortex sound theory: (a) variations of the calculated soundpressures; (b) the calculated quadrupole SPL





Fig. 13 Comparison of the calculated and measuredSPLs

Fig. 14 Noise directivity pattern computed by FW-Hequation

are made in Fig. 14 for an incidence angle of 10◦.The simulated result shows the maximum radiationalong the direction from the impeller centre to thetongue.

5 CONCLUSION

A hybrid approach for aerodynamic noise simulationsis proposed in the current paper. In first step, theunsteady flow of an industrial centrifugal fan withforward swept blades is carried out by LES to com-pute the dipole and quadrupole noise sources, andin second step the tonal and broadband noises arecomputed by using acoustic analogy and vortex soundtheory.

The calculation results show that the flow field inthe impeller and volute casing of the investigated cen-trifugal fan is strong unsteady. It is confirmed that dueto the interaction between impeller and volute casingthe flow is characterized with pressure and vorticity

fluctuations, which are strong especially at the tongueand at the trailing edge of the blade, respectively. Thelarge pressure fluctuation at the tongue region and thelarge fluctuation of the blade wake vorticity appear asthe blade wake is passing the tongue.

The radiated dipole and quadrupole sound fieldsare computed by using the unsteady pressure fluc-tuation on the blade and volute surfaces, velocityand vorticity fluctuations in the impeller, and volute,respectively. The vortex sound theory is convenientfor the broadband noise computation and the dipolesound is much higher than the quadrupole sound.The dipoles distributed over the volute tongue sur-face and raised from the unsteady force fluctuationare the dominant sound source of the fan. The pat-tern of the calculated sound pressure is similar to themeasured one, but the level shows some deviationbecause the calculated method does not consider theeffects of the scattering and reflection due to the volutecasing. It could be improved, for example, by usinga multi-domain direct BEM to calculate the soundfield [23].

REFERENCES

1 Dawes, W. N. Development of a 3D Navier–Stokes solverfor application to all types of turbomachinery. ASMEpaper 86-GT-70, 1986.

2 Hillewaert, K. and Van den Braembussche, R. A. Numer-ical simulation of impeller–volute interaction in cen-trifugal compressors. ASME, J. Turbomach., 1999, 121,603–608.

3 He, L. and Sato, K. Numerical solution of incompressibleunsteady flows in turbomachinery. ASME, J. Fluids Eng.,2001, 123, 680–685.

4 Conway, S., Caraeni, D., and Fuchs, L. Large eddy simu-lation of the flow through the blades of a swirl generator.Int. J. Heat Fluid Flow, 2001, 21, 664–673.

5 Kato, C., Kaiho, M., and Manabe, A. An overset finite-element large eddy simulation method with applicationto turbomachinery and aeroacoustics. J. Appl. Mech.,2003, 70, 32–43.

6 Lee, S., Kim, H. J., and Runchal, A. Large eddy simu-lation of unsteady flows in turbomachinery. Proc. InstnMech. Engrs, Part A: J. Power and Energy, 2004, 218,463–475.

7 Neise, W. Noise reduction in centrifugal fans: a literaturesurvey. J. Sound Vibr., 1976, 45, 375–403.

8 Neise, W. Review of fan noise generation mechanismsand control methods. In An International INCE Sympo-sium, Senlis, France, 1992, pp. 45–56.

9 Lighthill, M. J. On sound generated aerodynami-cally. I. General theory. Proc. R. Soc., 1952, A211,564–587.

10 Ffowcs Williams, J. E. and Hawkings, D. L. Sound gen-eration by turbulence and surfaces in arbitrary motion.Philos. Trans. R. Soc., 1969, A264, 321–342.

11 Lowson, M. V. The sound field for singularities inmotion. Proc. R. Soc., 1965, A286, 559–572.





12 Curle, N. The influence of solid boundaries on aerody-namic sound. Proc. R. Soc., 1955, A231, 505–514.

13 Jeon, W. H. and Lee, D. J. An analysis of the flowand sound source of an annular type centrifugalfan. In Proceedings of the 5th International Congresson Sound and Vibration, Adelaide, Australia, 1997,pp. 1333–1340.

14 Jeon, W. H. and Lee, D. J. An analysis of the flow andaerodynamic acoustic sources of a centrifugal impeller.J. Sound Vibr., 1999, 222, 505–511.

15 Jeon, W. H. and Lee, D. J. A numerical study on the flowand sound fields of centrifugal impeller near a wedge.J. Sound Vibr., 2003, 266, 785–804.

16 Langthjem, M. A. and Olhoff, N. A numerical studyof flow-induced noise in a two-dimensional centrifugalpump, part I: hydrodynamics. J. Fluid Struct., 2004, 19,349–368.

17 Langthjem, M. A. and Olhoff, N. A numerical studyof flow-induced noise in a two-dimensional centrifugalpump, part II: hydroacoustics. J. Fluid Struct., 2004, 19,369–386.

18 Moon, Y. J., Cho, Y., and Nam, H. S. Computation ofunsteady viscous flow and aeroacoustic noise of crossflow fans. Comput. Fluids, 2002, 32, 995–1015.

19 Suárez, S. V. and Tajadura, R. B. Numerical predictionof the aerodynamic tonal noise in a centrifugal fan. InProceedings of ASME’02 Engineering Division SummerMeeting, FEDSM 2002-31210, Montreal, Canada, 2002,pp. 1–8.

20 Liu, Q., Qi, D., and Mao,Y. Numerical calculation of cen-trifugal fan noise. Proc. IMechE, Part C: J. MechanicalEngineering Science, 2006, 220, 1167–1178.

21 Powell, A. Theory of vortex sound. J. Acoust. Soc. Am.,1964, 36, 177–195.

22 Howe, M. S. Contributions to the theory of aero-dynamic sound, with application to excess jet noiseand the theory of the flute. J. Fluid Mech., 1975, 71,625–673.

23 Tournour, M., Hachemi, Z. E., Read, A., Mendonca, F.,Barone, F., and Durello, P. Investigation of the tonal noiseradiated by subsonic fans using the aero-acoustic anal-ogy. In Proceedings of the Fan Noise 2003 InternationalSymposium, Senlis, France, 2003.

APPENDIX

Notation

c0 speed of sound (m/s)Cp static pressure coefficientD2 impeller blade outlet diameter (mm)

Fi external force acting on the fluid (N)G(X ) filter functionk turbulence kinetic energy (m2/s2)

L Lamb vectorMi Mach number in i directionMr the component of convection Mach

number in the direction r of the observerNt non-dimensional time stepp sound pressure (Pa)P static pressure (Pa)Pref , pref reference pressure (Pa)Ps root mean square value of the time-

derivative of the static pressure (Pa)Pt total pressure (Pa)Pw power of the centrifugal fan (W)q sound sourceQ mass flux per unit volume (kg)Qv flowrate (m3/s)r distance between the observer and

source (m)Re turbulent Reynolds numberSPL sound pressure level (dB)Sij deformation tensor (Pa)t time(s)Tij ρuiuj + Pij − c2

0ρδij, Lighthill tensor (Pa)u velocity vectoru2 velocity at the impeller outlet (m/s)vi velocity in i direction (m/s)V volume of the computational cell (m3)

xi Cartesian coordinates of theobserver (m)

X space variableyi Cartesian coordinates of the source (m)

t time step of the unsteady calculations (s)ε turbulent kinematic dissipation rate

(J/kg s)η internal efficiencyκ Von Kármán constantλ power coefficientµ turbulent viscosity (kg/m s)µt subgrid-scale turbulent viscosity

(kg/m s)ρ air density (kg/m3)

ρ0 undisturbed fluid density(kg/m3)

τij subgrid-scale stress tensor (Pa)ψ total pressure coefficientω vorticity vector




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