ncej-2012-AcOpt

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Acoustic optimization for centrifugal fans Esra Sorgüven a) and Yılmaz Doğan b) (Received: 16 January 2012; Revised: 10 May 2012; Accepted: 10 May 2012) The aim of this study is to perform a multi-objective optimization in order to re- duce the noise level of a centrifugal fan in early design stages. The main goal is to minimize the ow-induced noise while providing the required pressure rise at the operating ow rate. The design procedure begins with a baseline fan. An optimi- zation surface around the baseline design is formed by using the design of experi- ments method. Accordingly, geometric parameter sets and the corresponding CAD models are generated. Flow through these fans is simulated via Reynolds averaged Navier-Stokes equations. Flow data are evaluated to predict the noise level and the fan performance. Neural network method is employed to determine the family of optimum points. Two of the Pareto designs are manufacturedwith rapid prototyping in order to validate the numerical optimization procedure via aerodynamic and aeroacoustic experiments. Experiments show that both designs satisfy optimization goals. © 2012 Institute of Noise Control Engineering. Primary subject classication: 11.4.2; Secondary subject classication: 75.3 1 INTRODUCTION Fan noise is one of the major concerns in a large va- riety of industrial applications. It is essential to integrate noise emission as a design criterion in the early design stage in addition to aerodynamic performance and pro- duction cost in order to decrease the time and money spent to design and produce fans. In fan systems noise is generated aerodynamically, mechanically and electromagnetically. This paper fo- cuses only on the aerodynamically generated noise in centrifugal fans, which can be classied as follows 1 : 1. Interaction between the rotor blades and distor- tions in the inow or stationary obstacles (like diffuser blades, tongue etc.) (Fig. 1(a)) 2. Relative circulation in blade passages (Fig. 1(b)) 3. Boundary layer separation due to increased inci- dence at high ow rates or due to decreased inci- dence at low ow rates (Figs. 1(c) and (d)) 4. Recirculation at the intake opening and in the blade row (Fig. 1(e)). The rst noise source arises periodically at the blade passing frequency (BPF), which is called a tone. The rest of the sources are non-periodic and provoked by random force excitations. These contribute to the broadband noise. In most industrial applications with small centrifugal fans, both tonal and broadband com- ponents are perceived as annoying. All components of the aerodynamically generated noise can be predicted via computational aeroacoustics (CAA). Modern CAA methods are based on the Light- hills analogy 2,3 , which is enhanced among others by Curle 4 , Ffowcs Williams and Hawkings 5 , Farassat and Myers 6 and Brentner and Farassat 7 . An important prob- lem arises in the aeroacoustic computation due to the large difference between the aerodynamic and acoustic scales. Acoustic waves inherit lesser amplitudes and higher frequencies than the aerodynamic pressure waves, which can be resolved with traditional computa- tional uid dynamics (CFD) methods. The usual discre- tisation methods of CFD are too dissipative for the computation of acoustic waves. A solution for this problem is the hybrid CAA methods, which predict ow and acoustic elds separately (Fig. 2). In the rst step the unsteady turbulent ow eld is simulated to de- termine the acoustic sources. In the second step the propagation of the acoustic sources in near and far acoustic elds is computed. In the literature, a great number of models exist to solve the wave propagation. Most of these models are based on linearizing the governing uid dynamics equations. Some of these methods are uid-acoustic decomposition 811 , acoustic perturbation equations (APE) 12,13 , acoustic-viscous splitting 14,15 and expansion about incompressible a) Yeditepe University Mechanical Engineering Department, 34755 Istanbul TURKEY; email: sorguven@yeditepe. edu.tr. b) Arcelik A.S., R&D Department, Vibration & Acoustic Technologies, 34950 Istanbul TURKEY; email: yilmaz. [email protected]. 379 Noise Control Engr. J. 60 (4), July-August 2012

Transcript of ncej-2012-AcOpt

  • Acoustic optimization for centrifugal fansEsra Sorgvena) and Ylmaz Doanb)

    (Received: 16 January 2012; Revised: 10 May 2012

    The aim of this study is to perform a multduce the noise level of a centrifugal fan in eminimize the ow-induced noise while pro

    uren ic pughw detwhee thper12

    sub

    1. Interaction between the rotor blades and distor-tionsdiffu

    2. Rela3. Boun

    dencdenc

    4. Reciblad

    The rstpassing fre

    Myers and Brentner and Farassat . An important prob-

    scales. Acoustic waves inherit lesser amplitudes andpressure

    l computa-ual discre-ve for then for thisch predictIn the rstated to de-d step thear and farre, a greatopagation.rizing thee of these1

    a) Yeditepe U34755 Isedu.tr.

    b) Arcelik ATechnologdogan@a379Noise Control Engr. J. 60 (4), July-August 2012methods are uid-acoustic decomposition , acousticperturbation equations (APE)12,13, acoustic-viscoussplitting14,15 and expansion about incompressible

    .S., R&D Department, Vibration & Acousticies, 34950 Istanbul TURKEY; email: yilmaz.rcelik.com.in the inow or stationary obstacles (likeser blades, tongue etc.) (Fig. 1(a))tive circulation in blade passages (Fig. 1(b))dary layer separation due to increased inci-e at high ow rates or due to decreased inci-e at low ow rates (Figs. 1(c) and (d))rculation at the intake opening and in thee row (Fig. 1(e)).

    noise source arises periodically at the bladequency (BPF), which is called a tone. The

    higher frequencies than the aerodynamicwaves, which can be resolved with traditionational uid dynamics (CFD) methods. The ustisation methods of CFD are too dissipaticomputation of acoustic waves. A solutioproblem is the hybrid CAA methods, whiow and acoustic elds separately (Fig. 2).step the unsteady turbulent ow eld is simultermine the acoustic sources. In the seconpropagation of the acoustic sources in neacoustic elds is computed. In the literatunumber of models exist to solve the wave prMost of these models are based on lineagoverning uid dynamics equations. Som

    81

    niversity Mechanical Engineering Department,tanbul TURKEY; email: [email protected] arises in the aeroacoustic computation due to thelarge difference between the aerodynamic and acousticcentrifugal fans, which can be classied as follows1:operating ow rate. The design procedzation surface around the baseline desigments method. Accordingly, geometriCAD models are generated. Flow throaveraged Navier-Stokes equations. Flolevel and the fan performance. Neural nthe family of optimum points. Two of trapid prototyping in order to validatvia aerodynamic and aeroacoustic exdesigns satisfy optimization goals. 20

    Primary subject classication: 11.4.2; Secondary

    1 INTRODUCTION

    Fan noise is one of the major concerns in a large va-riety of industrial applications. It is essential to integratenoise emission as a design criterion in the early designstage in addition to aerodynamic performance and pro-duction cost in order to decrease the time and moneyspent to design and produce fans.

    In fan systems noise is generated aerodynamically,mechanically and electromagnetically. This paper fo-cuses only on the aerodynamically generated noise in; Accepted: 10 May 2012)

    i-objective optimization in order to re-arly design stages. The main goal is toviding the required pressure rise at thebegins with a baseline fan. An optimi-s formed by using the design of experi-arameter sets and the correspondingthese fans is simulated via Reynoldsata are evaluated to predict the noiseork method is employed to determinePareto designs are manufactured withe numerical optimization procedureiments. Experiments show that bothInstitute of Noise Control Engineering.

    ject classication: 75.3

    rest of the sources are non-periodic and provoked byrandom force excitations. These contribute to thebroadband noise. In most industrial applications withsmall centrifugal fans, both tonal and broadband com-ponents are perceived as annoying.

    All components of the aerodynamically generatednoise can be predicted via computational aeroacoustics(CAA). Modern CAA methods are based on the Light-hills analogy2,3, which is enhanced among others byCurle4, Ffowcs Williams and Hawkings5, Farassat and

    6 7

  • formulation (EIF)16,17. The accuracy of noise predictiondepends basically on the modeling errors in owsimulation, where the acoustic sources are computed.Sophisticated ow simulations, which involve lessmodeling errors, result in accurate acoustic sourceterms; however, they increase the computational costdrastically. For example a large eddy simulation(LES) based noise source prediction for a centrifugalfan may take months of pure computation time withstate-of-art parallel computers18. Such simulations canonly be performed in order to gain physical insightand understand general noise generation mechanisms.In order to implement noise prediction into early de-sign stage, one needs to shorten the computationalrequirements.

    During the design stage usually several geometriesare proposed and these are compared to each other todetermine a geometry which satises the design crite-

    is a time-consuming process, which requires accurateow simulation and acoustic computation, comparisonof noise levels of different geometries can be performedwithin reasonable time requirements with less sophisti-cated computational methods.

    This paper proposes a multi-objective aeroacousticoptimization method for fans, which can be easily per-formed in early design stages. Multi-objective optimi-zation problems have been studied over three decadesusing diverse techniques and providing successful solu-tions to a variety of problems1921. However, it has notbeen applied to noise reduction yet.

    The design procedure begins with an initial baselinedesign. The baseline can be a new fan designed accord-ing to the traditional turbomachinery design correla-tions, or an existing fan, which is to be improved.With the design of experiments (DoE) method, geomet-ric parameters of the baseline are varied systematically.

    Fig. 1Noise generation mechanisms in a centrifugal fan.ria. Hence, during the early design stage it is enoughto determine the design with the lowest noise emissionrather than to determine the exact noise level of eachproposed design. Although accurate noise predictionFig. 2An overview of modern CAA methods ( racoustic pressure).

    380 Noise Control Engr. J. 60 (4), July-August 2012Reynolds averaged Navier-Stokes (RANS) simulationsare performed for each of the proposed fan geometries.Flow data, which provide an indication on aerodynamicand acoustic performance, are extracted from theepresents any ow variable and rac is the

  • simulations. The extracted ow data are modeled asfunctions of the geometric parameters. These functionsare minimized or maximized to achieve the optimiza-tion goals. Finally, a family of fan geometries, whichprovide the best aerodynamic and aeroacoustic proper-ties is determined. The proposed method is demon-strated for a backward curved centrifugal fan. Withthis strategy, sound power level is reduced by 6 dB onthe average over the whole operation range.

    2 ACOUSTIC PREDICTION BASED ONFLOW DATA

    The direct numerical simulation (DNS) is the mostaccurate ow prediction method, since it solves theNavier-Stokes equations without any modeling. Thewhole range of time and length scales (from integralscales to Kolmogorov scales) is resolved. Thus, theacoustic scales are directly resolved, i.e. an additionalcomputation of acoustic sources and wave propagationis redundant (Fig. 2). Unfortunately, it is only appliedin low Reynolds number ows because of the practicallyunaffordable discretisation requirements (numerical

    effort of DNS-Re4). Large eddy simulation (LES) isthe second most accurate method, which resolves thelarge and energetic scales of turbulence and modelsthe small and dissipative scales. Although computa-tional requirement of LES is considerably lower thanDNS, it is still high for industrial applications. Reynoldsaveraged Navier Stokes (RANS) method is based on av-eraging the ow variables over a large time range.RANS is the fastest ow simulation method; however,it fails in accuracy mainly due to the deterministic ap-proach of its formulation. The decomposition of the tur-bulent energy spectrum with different turbulencemodels is symbolically represented in Fig. 3. RANSresults do not contain any information on acousticwaves because of the inherent modeling errors. Still,any other method cannot be chosen in the design stagebecause of the time limitations. One approach to over-come this deciency is to employ empirical methods,which estimate turbulent uctuations based on the aver-aged ow eld2224. These stochastic methods can becombined with a RANS solution in order to estimate un-steady turbulent uctuations, which can then be used tocompute acoustic sources generated in the ow eld.

    seny RFig. 3Kinetic energy decomposition in the premiddle: with LES, bottom: with unstead

    Noise Control Engr. J. 60 (4), July-August 2012ce of a predominant frequency, top: with DNS,ANS formalismus.

    381

  • Although there are well evolved models for stationary pressure distribution on the OSPL. Figure 4 shows the

    Fig. 4Instantaneous vorticity distributions a) Fan I, b) Fan II.blunt bodies such as airfoils25, a stochastic model for ro-tating blades does not exist.

    The approach followed in this study is to employRANS simulations to compare the overall sound powerlevel (OSPL) of different fan geometries, rather than topredict the exact noise level of each fan. For this pur-pose, a preliminary investigation is performed in orderto determine the ow variables, which can be computedwith RANS simulations and also provide a good indica-tion for the OSPL of a fan. In a preliminary study18,two fans are investigated via aerodynamic and acousticexperiments, as well as via LES and RANS. Both fansare centrifugal fans with similar dimensions, perfor-mance curves and operating points. Nevertheless, oneof the fans has much lower OSPL than the other. Theaerodynamic and acoustic elds are compared to deter-mine a correlation between the powerful acousticsources and ow variables. Two ow variables, vortic-ity and pressure distribution are found to be stronglycorrelated with the acoustic properties.

    Results of the preliminary study are summarized inFigs. 4 and 5 to demonstrate the effect of vorticity andFig. 5Instantaneous pressure distributions a) Fa

    382 Noise Control Engr. J. 60 (4), July-August 2012instantaneous distribution of the vorticity magnitudeextracted from LES on a cross-section across the impel-ler for both fans. In both fans vorticity is producedmainly around the blades, especially on the trailingedge. However, in the louder fan vorticity is not dissi-pated immediately, but transported further with the owthrough the volute. Furthermore, large vorticity magni-tudes indicate a strong tongueblade interaction andpoor ow conditions through the volute. Hot spots up-stream the blades indicate that inow is not axisymmet-ric, which causes an unbalanced loading on the blades.Comparison of LES results shows that large vorticitymagnitudes indicate large OSPL values. Therefore theaverage vorticity magnitude on a cross-section acrossthe impeller is chosen as an indicator for OSPL.

    Figure 5 shows the instantaneous pressure distribu-tion. Pressure contours exhibit a high spatial gradient inthe neighborhood of the tongue. In both fans, as the ra-dius of the volute increases, the gap between the bladesand the volute increases and the effect of the pressurewaves due to blade motion on the volute surfacedecreases. Spatial pressure gradients on the voluten I, b) Fan II.

  • p 1XN

    p p 2 1

    which can be used for surface tting. As a result,24 combinations of the investigated parameters aredetermined (Table 1) and corresponding impeller ge-ometries are generated. The new impellers have allother geometric variables (such as volute shape, bladeheight, thickness etc.) the same as the baselinedesign.

    : side view, right: cross-sectional view.

    Table 1Geometric variables of the simulatedfans.

    Number ofgeometries r1 (mm) r2 (mm) b1 () b2 ()

    1 32 63 85 382 32 67 85 383 42 63 85 384 42 67 85 38stdN 1

    i1i

    where N is the total number of nodes, pi is the pressure atthe node i and pis the surface-averaged pressure value.Large values of pstd indicate powerful sound sourcesand a high OSPL.

    In summary, two variables are chosen as indicators ofthe OSPL: the average vorticity on a cross-sectionacross the impeller and the standard deviation of pres-sure on the volute. Since RANS provides a fair predic-tion for average ow variables, both of these owvariables can be predicted accurately with RANSsimulations.

    3 DESIGN OF EXPERIMENTS

    A centrifugal fan, which is shown in Fig. 6, isselected as the baseline. Reynolds number based onthe blade tip diameter is Retip = 1.7106 and Machdecrease in rotational direction. In the louder fan, magni-tude of the pressure gradients on the volute is higher. Toquantify this phenomenon, the standard deviation of thepressure on the casing, pstd, is computed. !

    Fig. 6Schematic view of the baseline fan, leftnumber at the tip is Matip = 0.06.Aerodynamics and aeroacoustics of a fan is affected

    by a number of geometrical parameters, such as theshape of the volute, inlet and exit areas, number ofblades, blade thickness, length, height and angles. Inorder to keep the calculations simple and focus on theoptimization strategy, the effect of only four geometricvariables on the OSPL is investigated. These are theblade inlet and outlet angles (b1 and b2) and the bladeinlet and outlet radii (r1 and r2).

    With the help of the DoE method the number ofcombinations to be tested is reduced. The DoEmethod provides a well-distributed set of parameters,

    Noise Control Engr. J. 60 (4), July-August 20125 37 65 80 336 37 65 80 437 37 65 90 338 37 65 90 439 32 65 85 3310 32 65 85 4311 42 65 85 3312 42 65 85 43

    13 37 63 80 3814 37 63 90 3815 37 67 80 3816 37 67 90 3817 32 65 80 3818 32 65 90 3819 42 65 80 3820 42 65 90 3821 37 63 85 3322 37 63 85 4323 37 67 85 3324 37 67 85 43

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  • 4 COMPUTATIONAL METHODS

    averaged values are denoted with an overbar. The clo-sure problem, which arises due to the emergence ofthe Reynolds stress tensor, is solved with the Boussi-nesq approximation by dening the eddy viscosity mt.

    rui0uj 0 mt@ui@xj

    @uj@xi

    23dijrk 3

    The k-e turbulence model calculates the eddy viscos-ity as a function of the turbulent kinetic energy k and theturbulent dissipation e.

    mt rCmk2

    e4

    Here r is density and Cm is a constant with the value0.09. The transport of k and e is calculated with thefollowing partial differential equations.

    @ rkui @xi

    @@xj

    m mtsk

    @k

    @xj

    Fig. 7Computational mesh.4.1 Computational Fluid Dynamics

    Steady RANS simulations are performed for alldesigns with the commercial software Fluent26. Thecontinuity and the RANS equations are given below.

    @ui@xi

    0 2

    @ ruiuj @xi

    @p@xj

    @tij@xi

    @ rui0uj 0

    @xi

    rgj 3

    Here, ui is the ow velocity in i direction, p is pres-sure, tij is the shear stress, g is the gravitational acceler-ation and rui0uj 0 is the Reynolds stress tensor. The timeFig. 8Vorticity distributions.

    384 Noise Control Engr. J. 60 (4), July-August 2012 Gk Gb re Ym Sk 5

    @ reui @xi

    @@xj

    m mtse

    @e@xj

    C1e ek

    Gk C3eGb C2er e2

    k Se 6

    Where Gk is the generation of turbulence kinetic en-ergy due to the mean velocity gradients (Gk = mt 2jSij Sijj,where Sij is the strain tensor),Gb is the generation of tur-bulence kinetic energy due to buoyancy, Ym is the contri-bution of the uctuating dilatation in compressibleturbulence to the overall dissipation rate. C1e, C2e andC3e are constants and sk and se are the turbulent Prandtl

  • numbers for k and e, respectively. Sk and Se are sourceterms. In this study, since the ow through the fanis isothermal and incompressible, the terms Gb, Ym,Sk and Se are zero. The values of the model constantsare: C1e = 1.44, C2e = 1.92, sk = 1.0 and se = 1.3.

    In order to assure grid-independent results, meshingis performed in two steps. First the coarsest meshresulting grid-independent ow data is determined byrepeating the ow simulation of the baseline designwith meshes of varying renement levels, and compar-ing their results. At the second step all CAD models aremeshed systematically with the predetermined meshingparameters. Parameters that are kept constant for eachcomputational grid are the normal wall distance (y+),growth rate, boundary layer thickness and mesh sizeson the boundaries. The volume mesh around the impel-ler is then generated with hexahedral control volumes(Fig. 7). The stationary part is meshed with unstruc-tured tetrahedral cells. As a result of this procedure,regions where large derivatives occur (e.g. boundary

    Fig. 9Streamlines of relative velocities.layer) are represented with similar meshes. However,some variations in the total number of control volumesoccur. The mean number of control volumes is 2106.

    The computational domain is divided into two zones,one surrounding the rotating impeller and the other sur-rounding the stationary volute. Zones are coupled via asliding interface and mass balance is forced across thesliding interface. In order to minimize interpolationerrors, the ratio of the control volumes across the slid-ing interface is kept below 4:1. The employed boundaryconditions are no-slip on the walls, constant mass owrate on the inlet and constant static pressure on the out-let. In all simulations the ow rate and the rotationalspeed are kept constant at 65 l/s and 2900 rpm, respec-tively. Spatial discretisation is performed with 2nd or-der central differencing scheme.

    Noise Control Engr. J. 60 (4), July-August 20124.2 Acoustic Optimization

    Optimization is performed to enhance the aeroacous-tic properties of the baseline fan, i.e. to decrease itsOSPL. For this purpose two optimization objectivesare formulated:

    Minimize the average vorticity on the cross-section across the impeller.

    Minimize the standard deviation of pressure onthe volute.

    An important point is that the aerodynamic perfor-mance should not be affected adversely by loweringthe OSPL. A fan performance curve represents thepressure rise developed versus ow rate at a constantrotational speed. In order to predict the performancecurve numerically, several CFD runs at varying owrates have to be performed for each fan. However, thenumber of simulations required for a successful opti-mization process is already so large at to forbid an ex-

    tensive numerical study. Considering the requiredcomputation time and the data processing effort, owis simulated only at the operating point for each fan. Itis assumed that the performance curve is characterizedby the pressure rise developed at that ow rate. In orderto guarantee that the required aerodynamic performance

    Table 2Correlations between the ow and geo-metrical variables.

    r1 r2 b1 b2

    P 0.252 0.823 0.008 0.260oave 0.192 0.237 0.106 0.451pstd 0.224 0.757 0.044 0.312

    385

  • Fig. 10Response surface for the pressure rise P.

    Fig. 11Response surface for the average vorticity oave.

    386 Noise Control Engr. J. 60 (4), July-August 2012

  • iatFig. 12Response surface for the standard devis achieved, the minimum pressure rise that the fan hasto provide at the operating point is set as an optimizationconstraint:

    At the operating point (i.e. 65 l/s at 2900 rpm)the pressure rise should be at least 160 Pa.

    Response surface methodology is used to explore therelationships between the extracted ow variables andthe geometric parameters. A surface is interpolated torepresent each of the ow variables as a function ofb1, b2, r1 and r2. Since the relationship between theexplanatory and response variables are complicated,simple techniques such as single value decompositionor polynomial responses did not provide satisfactoryresults. Neural network method is used to generate theresponse surfaces. The present optimization requiressimultaneous minimization of two ow variables. Incontrast to single objective optimization problems, thesolution of this multi-objective optimization is not asingle point, but a family of points referred to in the lit-erature as Pareto points or Pareto front27. An exampleto explain the theory of Pareto front is the 1-variable2-objectives problem used in Ref. 28. Objectives of thisproblem are:

    Noise Control Engr. J. 60 (4), July-August 2012ion of pressure pstd. Minimize f11 = x2

    Minimize f12 = (x 2)2

    Any point between 0 and 2 can be a solution for thisproblem. So, here the Pareto front is {xj0 x 2}.

    5 NUMERICAL RESULTS

    One of the optimization objectives is to minimizevorticity. Simulation results show that the generationand transport of vorticity vary greatly with the geomet-ric parameters of the impeller. Figure 8 presents thecomparison of vorticity distributions in two of the in-vestigated impeller geometries. In the impeller #22,vorticity generation is limited in the near vicinity ofthe blades. However, in the impeller #23, even at the in-let large vorticity magnitudes are visible. The blade ge-ometry causes an unbalanced blade load, which triggersreverse ows and vorticity generation.

    Figure 9 shows the comparison of streamlines of rel-ative velocity in two impeller geometries. Reverse owthrough the blades in the upwind of the tongue is notuncommon in centrifugal fans. Here, such a reverseow region is visible in all of the impeller geometries.However, the extent of the reverse ow varies. Since

    387

  • the reverse ow region obstructs the outlet area, magni- where w is the work done on the uid per unit mass, U

    Fig. 13Relative velocity vectors and vorticity distribution of the rst Pareto design.tude of the outlet velocity increases locally. This causesan increase in the OSPL and also a decrease in the aero-dynamic performance. In an optimized fan, reverse owregion should be minimal.

    Pressure rise, average vorticity and standard devia-tion of pressure are extracted from RANS simulations.The correlations between the ow and the geometricvariables are summarized in Table 2. The blade outletradius r2 has a large effect on all ow variables. Thecorrelation between r2 and P is the largest, which isa direct result of the Eulers turbomachinery equation:

    w U2c2 U1c1 7Fig. 14Relative velocity vectors and vorticity dis

    388 Noise Control Engr. J. 60 (4), July-August 2012is the blade circumferential speed and c is the absolutetangential ow velocity and 1 and 2 represent the bladeinlet and outlet, respectively. Work is pressure rise, p,over density (w = p/r). Eulers turbomachinery equa-tion assumes the following form, if it is applied to acentrifugal fan with no whirl at the inlet (c1 = 0):

    pideal rr2c2 r U22 U2

    Q

    2pr2b2

    cot b2

    ; 8

    where pideal is the ideal pressure rise, is the angularvelocity ( = pn/30, where n is the rotational speed intribution of the second Pareto design.

  • min-1), Q is the volumetric ow rate and b2 is the rotorblade outlet width. In the ideal case the correlation be-tween the pressure rise and the outlet blade radius r2 is

    surfaces are shown in Figs. 10 through 12. In the pro-jections x- and y-axes are chosen as r2 and b2, sincethese geometric parameters have the largest effect onthe investigated ow variables.

    The objectives of the optimization procedure are tominimize both pstd and oave. As the response surfacesdemonstrate, these objectives are competitive. The localminimum and maximum of pstd and oave surfaces are atdifferent locations. Furthermore the optimization con-straint (i.e. p should be at least 160 Pa) eliminatesa number of points in the optimization space, whichwould lead to low pstd and oave values. With these goalsand the constraint, optimization procedure results inseveral Pareto designs. Two of the Pareto designs,which have the longest and the smallest blade chordlengths, are chosen for further study. These designsare investigated both numerically and experimentally.Both Pareto designs are manufactured via rapid proto-

    Fig. 15The experimental setup.1, since these are in a linear relationship. Here, the cor-relation decreases to 0.82 due to losses, reverse owsand leakage.

    Second important geometric variable is the outletblade angle b2. Negative correlations show that anincrease in b2 decreases the listed ow variables(Eqn. (8)). The average vorticity, which is the mainindicator of OSPL is mostly affected by b2.

    The inlet blade angle and radius have only a limitedinuence on the ow variables. Since there is no pre-whirl (c1 = 0), the second term in Eqn. (7) disappearsand the dependence of pressure rise on inlet blade angleand radius vanishes.

    The data extracted from RANS are fed into the opti-mization procedure, where the neural network methodis employed to t a surface for each ow variable as afunction of the geometric variables. The response sur-faces are created in a 5-dimensional space, where eachow variable is represented as a function of r1, r2, b1and b2. 3D and 2D projections of the tted responseFig. 16OSPL of the baseline and Pareto designs

    Noise Control Engr. J. 60 (4), July-August 2012typing and tested to determine the OSPL values.Average vorticity distribution and the relative veloc-

    ity vectors of the Pareto designs are presented inFigs. 13 and 14. In both Pareto designs no reverse owthrough the blades is visible and large vorticity magni-tudes are limited in the near vicinity of the blades.

    6 EXPERIMENTALVALIDATION

    Prototypes of both Pareto designs are manufacturedwith rapid prototyping and OSPL values are measuredover the whole operating range. Acoustic measurementsare performed in a semi-anechoic room, which has abackground noise level of less than 20 dB. Dimensionsof the semi-anechoic room are 4 4 5 m, so thatthe minimum measurable frequency is 125 Hz, whichis below the frequency range of interest in this study.Experiments are performed according to the ANSIstandards29. In the experimental setup (Fig. 15) mylar,an acoustically transparent material, is used to obtain a

    with respect to pressure rise.

    389

  • control volume for mass ow and a free eld boundary 2. J.M. Lighthill, On sound generated aerodynamically. I. Generaltheory, Royal Society of London (A), 211, 564587, (1952).for acoustic waves. The maximum limits of the exper-

    imental setup are 1 m3/s and 750 Pa for ow rate andpressure rise, respectively. OSPL is measured with re-spect to pressure rise, which is chosen as the controlvariable in the experiments. Pressure rise through thefan is controlled by adjusting the air outow area. Adifferential pressure sensor with 1% accuracy is usedto measure the pressure rise. Reproducibility and re-peatability of the experiments are ensured before eval-uating the experimental results. Figure 16 shows thecomparison of OSPL curves of the baseline and Paretodesigns. Both Pareto designs are acoustically betterthan the baseline.

    7 CONCLUSION

    In the frame of this work, a multi-objective acousticoptimization of a centrifugal fan is performed. The ob-jective functions are identied by comparing detailedow data obtained via LES with acoustic measurementsand RANS simulations. With this strategy we foundthat for small centrifugal fans pstd and oave should beminimized to minimize the OSPL. These objectivefunctions should be valid for any fan having low pres-sure rise and low ow rate. This optimization strategycan be applied to axial, centrifugal and mixed type fans.But, if the operating conditions change dramatically, sothat the noise generation mechanisms change, then theobjective functions may not be valid any more. Never-theless, the main strategy, i.e. comparing detailed owdata with OSPL and identifying ow variables, whichinuence OSPL and trying to optimize these ow vari-ables, can help to reduce ow-induced noise in a varietyof applications including but not limited to fans.

    To evaluate the acoustic performance of the optimizedfans the OSPL of a set of commercially available fanswith similar pressure rise and ow rate is measured withthe same experimental setup and procedure. At the oper-ating point the OSPL values for the commercial fans aremeasured between 76 and 81 dB. At the operating pointOSPL of the optimized fans is 74.5 and 76.5 dB.

    The sole input of the optimization procedure is theow data extracted from steady RANS simulations.Since hardware and computation time requirementsfor steady RANS simulations are low, optimizationcan be performed with reasonable resources. Thismakes the integration of acoustic optimization into theearly design stage possible.

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