An integrated performance analysis for a backward-inclined centrifugal fan

Computers & Fluids 56 (2012) 24–38

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Computers & Fluids j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d

An integrated performance analysis for a backward-inclined centrifugal fan Sheam-Chyun Lin, Ming-Lun Tsai ⇑ Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43, Sec. 4, Keelung Road, Taipei 10672, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 16 April 2010 Received in revised form 16 August 2011 Accepted 18 November 2011 Available online 8 December 2011 Keywords: Centrifugal fan Computational fluid dynamics Efficiency Noise

a b s t r a c t Recently, the requirement for developing high-performance centrifugal fans exists due to increasing system resistance and space limitation on computer devices. Also, performance evaluation of fan design under different operating conditions is evidently in great demand for practical engineering applications. Therefore, this comprehensive investigation is aimed at offering the overall technical information for thoroughly evaluating fan performance. An 80 mm-diameter backward-inclined centrifugal fan is chosen to serve as the research subject for demonstration purposes. Numerical results are utilized to perform detailed flow visualization, torque calculation, efficiency estimation, and noise analysis. The results indicate that the fan performance curve and the sound pressure level (SPL) spectrum of the experiment agree with those of numerical simulations. In addition, this study proposes two modification alternatives based on the flow visualization at each operating point, having verified the successful enhancement of fan performance via numerical calculation. Consequently, this study establishes an integrated aerodynamic, acoustic, and electro-mechanical evaluation scheme that can be used as an essential tool for fan designers. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction While the industrial technology develops along with time, the computer’s efficiency and power consumption also keep enhancing continuously. In order to maintain the stable status and avoid the overheating problem, the system’s cooling design becomes an important and challenging task. At present, the cooling fans play the vital role in the thermal design and are designed in diversified specifications for meeting different demands of heat dissipation. Among them, centrifugal fans are commonly used in the cooling system to generate sufficient airflow rate and static pressure to overcome the high-resistance characteristics and space limitation of the small-size desktop and notebook computers. In the case of thermal module for VGA card or CPU, the airflow system usually consists of a cooling fan and various elements through which the airflow can pass. Computer case and heat sink along the air stream passage are two of the most essential elements. The computer case at the upstream of fan will result in the decrease of fan airflow, which is referred as the blockage effect [1]. The corresponding reductions on the fan flow rate and thermal dissipating capability of thermal module are investigated systematically in previous researches [1,2]. Those studies indicated that the blockage effect and heat sink assembly can induce system resistance and diminish fan flow rate. The decrease in air delivery ⇑ Corresponding author. Tel.: +886 2 27376453; fax: +886 2 27376460. E-mail addresses: [email protected] (S.-C. Lin), [email protected]. edu.tw (M.-L. Tsai). 0045-7930/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compfluid.2011.11.009

of a fan definitely causes less heat dissipation from the critical components. Consequently, the fan performance should be evaluated under different system resistances for meeting the need of practical application. Even though many evaluation approaches for fan design were developed, fan designers are still searching for an effective evaluation method from several perspectives, including flow-field visualization, torque calculation, efficiency estimation, and noise spectra analysis. Consequently, meeting the requirements of thermal management under different operating conditions and acquiring detailed information are very important and become the goal of this integrated experimental and numerical analysis. The performance evaluation and the flow-field investigation for centrifugal fans begun in 1970s. Raj and Swim [3] used a smoke technique to visualize the flow pattern at the inlet region of a forward-curved (FC) centrifugal fan. Their work indicated that the flow entering the fan changes from axial at the inlet mouth to radial at the back plate. A resulting ‘‘inactive’’ separation zone exists between the entry point and the shroud and can be expressed as a function of circumferential location for a range of flow rate. In general, the extent of separation is maximized just past the cut-off and minimized at the discharge area of the housing. The separation zone tends to expand with increasing flow rate. Moreover, the velocity measurements demonstrated the presence of a jet-wake velocity profile at the rotor exit. The ratio of the jet area to the wake area increases with a higher velocity at the rotor inlet. In 2002, Lin and Huang [4] conducted preliminary experimental and numerical study of FC centrifugal fan. A small centrifugal fan is

S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

25

Nomenclature Notation 2D 3D cfm t u  u M Mr P RMS

two-dimensional three-dimensional cubic feet per minute represents time absolute velocity tensor mean velocity tensor Mach number Mach number at which the source approaches the field point pressure root mean square

successfully designed for the thermal task of cooling laptop computers by utilizing an integrated scheme, which consists of fan design, mockup manufacture, experimental verification, and numerical simulation. In this research, a cooling fan (45  45  7 mm3) is designed under the space limitations of notebook computers. Prototypes are manufactured by the computer numerically controlled (CNC) machine to carry out the corresponding experimental verifications. By comparing the experimental and numerical results, a good agreement between them indicates a great potential to reduce expensive experimental work by using CFD tools. Later, Han and Maeng [5] executed the cut-off optimization in a multi-blade rotor/scroll system by using two-dimensional CFD analysis and neural network. In this study, two-dimensional CFD calculation was utilized instead of the complicated threedimensional analysis in a FC centrifugal fan. Experiments for various angles and curvatures of cut-off geometry were performed to obtain the proper input data for numerical calculations. Then the neural network was applied to optimize the angle and curvature of cut-off. As a result, the optimal angle and radius of cut-off were determined as 71° and 0.092 times the outer diameter of impeller, respectively. Although the optimal results using neural network agree well to the 2D numerical outputs; unfortunately, obvious discrepancies still occur between numerical calculations and experimental measurements. Besides the aerodynamic performance, low acoustic emission has become a highly competitive factor for the purchase of fan and the low-noise fan design is in great demand by consumers. In recent years, Liu et al. [6] used the unsteady three-dimensional numerical simulation to calculate the aerodynamic noise generated by an industrial centrifugal fan. A comparison between the acoustic simulation and experimental measurement shows that the trend of calculated sound pressure level (SPL) spectra agrees to the test results. However, the predicted noise levels are obviously underestimated compared to test data at a low frequency range. This is because the turbulence model used here is based on the time averaged method and is not capable to simulate the tiny unsteady variation in the flow field of a centrifugal fan. Later, Rafael [7] carried out the numerical calculation of wall pressure fluctuations at the volute of an industrial centrifugal fan. The power spectra of these fluctuations demonstrate an apparent peak at the blade passing frequency (BPF). The amplitude of this peak reaches its highest value near the volute tongue, which agrees with the experimental result. A more detailed analysis on fan performance and aerodynamic tonal noise evaluation has been carried out by Sandra et al. [8]. They performed a comprehensive experimental effort to investigate the influences of important geometric parameters on the acoustic behavior of a squirrel-cage fan which is used in the automotive air conditioning unit. The geometric parameters considered

Greek d

l q s

shear strain tensor dynamic fluid viscosity fluid density stress tensor

Subscripts i, j, k directions t turbulent

here include the shape and the position of the volute tongue of the FC centrifugal fan. First of all, the performance curves were measured in a standardized test facility. Then, the acoustic behavior of the fan was characterized by means of acoustic pressure measurements near the fan inlet. The comparison of the test results indicated a great influence of both the shape and the position of the volute tongue on the noise generation. Some geometric configurations of the volute tongue were able to reduce the fan noise generation without reducing the fan operating range. Through an extended literature survey about noise prediction, it is clear that the qualitative validity of acoustic numerical simulation can be further improved. A reliable and rational noise spectrum prediction is still in demand nowadays. In addition, the forgoing investigations are deficient in aerodynamic torque prediction, numerically estimated efficiency, legitimate acoustic prediction, and numerical flow-field visualizations for different operating points of a specific fan. To supplement the lack of providing technical information in previous researches, this work integrates the experimental and CFD tools to perform the flow-field analysis, efficiency estimation, and noise prediction for an in-depth evaluation on a centrifugal fan. Noticeably, the torque calculation is essential in determining the motor specification for fan manufacturers. Also, the detailed aerodynamic and acoustic information over the entire performance curve provide a complete technical background for fan users and engineering applications. This study chooses a commonly used 80 mm-diameter backward-inclined (BI) fan for demonstrating this integrated investigation. Experimentally, the fan’s performance and noise tests are executed in a test chamber established in accordance to Air Movement and Control Association (AMCA) code-210-99 [9] and in a semi-anechoic chamber following CNS-8753 code [10]. The numerical calculation and visualization analysis are carried out using the CFD software Fluent [11]. Also, the numerically calculated efficiencies and noise spectrum are validated by comparing them with the corresponding experimental measurements. Fig. 1 illustrates the flow chart of this integrated fan performance analysis, which includes the determinations of P–Q (static pressure versus airflow rate, i.e., fan performance) curve, torque estimation, efficiency calculation, and noise analysis. As for the P–Q curve determination, not only the predicted result is compared with the test measurement, but also the flow-field visualization at each operating point is conducted with the aids of numerical simulation. Based on the flow visualization results, two modification strategies are performed to enhance the fan performance. Besides, CFD calculation in this study yields the fan’s aerodynamic torque, which can be used to evaluate its efficiency. Therefore, the motor efficiency can be identified by comparing the numerically calculated and experimentally tested efficiencies. Furthermore, the SPL is predicted via numerical simulation, and compared with

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S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

Fan design Efficiency evaluation

Performance analysis CFD P-Q prediction and flow visualization

AMCA chamber test

Flow-field analysis at various operation conditions

CFD predictions of torque and efficiency

Noise analysis

AMCA chamber test

CFD SPL calculation

Motor efficiency identification

Measurements following CNS-8753 code

Qualitative acoustic investigation

Integrated fan evaluation Fig. 1. Flow chart of the integrated fan performance analysis.

experimental measurements. Consequently, an integrated aerodynamic and electro-mechanical evaluation procedure is constructed to serve as an evaluation reference for fan designers.

12 3

4

5

Multiple nozzles

Auxiliary fan

Test fan 2. Experimental apparatus To validate the numerical results, this study measures the performance and noise characteristics of a centrifugal fan via the standard test procedures following AMCA 210-99 [9] and CNS-8753 codes [10], respectively. As illustrated in Fig. 2, the test fan is an 80 mm-diameter backward-inclined centrifugal fan with a rotational speed at 1650 rpm. The related measurement setups are explained in the following subsections.

Power supply Pressure tap + Pressure transducer A Dry and wet bulb thermometer

Pressure transducer B

+

PC

Controller

Fig. 3. Sketch of AMCA outlet test chamber and instrument setup.

measuring plane. Besides, the fan airflow at each operating point is controlled by a throttling device and an auxiliary fan at the end of the test chamber. Thus, the fan P–Q curve can be measured through such a experimental setup. In addition, the fan totalto-static (static) efficiency gStatic;Exp is herein determined to assess the fan performance, which is expressed as

gStatic;Exp ¼

Fig. 2. Mockup of the 80 mm-diameter backward-inclined centrifugal rotor.

Pressure Pressure tap tap Invertor

2.1. Performance measurement setup In this work, the pressure and flow rate under various system resistances are measured by the extensively used and accepted fan test code AMCA 210-99 [9]. Fig. 3 schematically plots the outlet chamber and its instruments. The test setup includes the chamber, flow setting means, multiple nozzles, throttling devices, and auxiliary fan. Flow settling means are installed inside the chamber to provide proper flow patterns for measurement. For a measuring plane located upstream of the settling means, the settling screen absorbs the kinetic energy of the upstream jet, and allows the flow to undergo a normal expansion. The measuring plane after the settling screen ensures a substantially uniform flow ahead of the

M

Ps  Q Fan Power Input

ð1Þ

where Ps is the fan static pressure, and Q is the fan volumetric flow rate. The static efficiency is expressed as the ratio of the static power transfer to the fluid from rotor to the actual power applied to the fan. In this experiment, the fan speed is measured by a non-contact photo tachometer, which is accurate to 0.05% with a resolution of 1 rpm. The discharge static pressure is measured using a pressure transducer in plane 3 (see Fig. 3). The flow rate can be calculated with the aids of differential pressure measured across multiple nozzles (planes 4–5 in Fig. 3). Therefore, the measurement uncertainty of discharge flow rate and static pressure are mainly affected by the accuracy and calibration of the pressure transducer. Since the static pressure is very small for a typical cooling fan, this study chooses a

27

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pressure transducer designed for exceedingly low differential pressure measurement applications. With full ranges below 56 mm H2O, the accuracy of this instrument was estimated to be within 0.25% full scale. This experiment also uses a pressure calibration system to calibrate this ultra-low-range pressure transducer with a resolution of 0.05 mm H2O and an accuracy of 0.5% of the readings. The uncertainties in the measurements are expressed in two parts [9,12], one is called characteristic uncertainty which deals with the static pressure versus airflow rate, and the other is efficiency uncertainty which deals with the static efficiency versus airflow rate. As a result, the characteristic uncertainty and efficiency uncertainty of the performance measurements are estimated to be around 1–3% and 3–6%, respectively. 2.2. Noise measurement setup This experiment measures sound pressure levels using a RION NL-14 portable sound level meter (SLM) and an AND AD-3524 FFT frequency analyzer. The sound pressure creates analog electric signals in SLM microphone; these signals were then fed into the FFT analyzer to generate the noise characteristics. Additionally, the consistency and calibration of these devices are verified by a transducer-type calibrator (94 dB at 1 k Hz) both before and after each measurement. The noise at fan outlet is measured by employing the CNS-8753 standard. As shown in Fig. 4, the semi-anechoic chamber offers an appropriate test environment with the following specifications (1) The background noise is 18 ± 2 dBA. (2) The valid measuring size of the chamber is 2.8 m  2.3 m  2.05 m. (3) The lowest cut-off frequency is 125 Hz. (4) The absorption rate of sound pressure for wedge is greater than 99%. (5) The reflection of sound pressure for wedge is less than 10%. (6) The inverse square law is valid between 125–20 k Hz, and the deviation is ±1.5 dB. (7) The transmission decay is greater than 35 dBA. 3. Numerical scheme Generally speaking, a laminar airflow seldom appears in fan engineering. The airflow inside a fan is turbulent for most cooling systems. In this study, the Reynolds number [13] based on the fan radius and average air velocity of 4–7 m/s for the centrifugal fan is approximately 10,956–19,173. This is far above the critical value of

2000 in duct flow, and indicates a very turbulent flow. Therefore, this study simulates the complex flow patterns inside the BI centrifugal fan by utilizing the commercial computational fluid dynamics (CFD) software Fluent [11] to solve the fully threedimensional incompressible Navier–Stokes equations with the standard k  e turbulence model. The steady k  e simulation is executed with the moving reference frame (MRF) model to deal with the rotating fluid inside a centrifugal fan. The flow-field visualization at each operating point is performed by the steady k  e computation. The predicted outlet static pressures with the various airflow rates on operating points can be used to determine the performance curve. Based on the calculated torque for each operating point, it is then possible to calculate the fan efficiency for the entire performance curve. Regarding the acoustic analysis, the numerical simulation in this study solves the unsteady flow field using the sliding mesh technique. This approach captures the instantaneous pressure fluctuation and plots it to the frequency domain. This study adopts the LES turbulence model to calculate the sound effects of the small eddies enhanced pressure fluctuation. The following subsections describe the mathematical models, boundary conditions, and grid verification used in this numerical approach. 3.1. Mathematical models This study uses Fluent [11] to solve the incompressible 3D Navier–Stokes equation using an unstructured finite-volume method. For pressure–velocity coupling algorithms, the modified SemiImplicit Method for Pressure-Linked Equations (SIMPLE) method and Pressure-Implicit with Splitting of Operators (PISO) coupling method are implemented to enhance the efficiency of the pressure calculation for both steady and unsteady cases. The PISO algorithm adopts additional corrections to satisfy the momentum balance more accurately, especially for transient problems. For the discretization of momentum equations, this study adopts the second-order upwind scheme for k  e calculations, and adopts the bounded central differencing scheme for LES calculations. The bounded central differencing scheme based on the normalized variable diagram approach together with convection boundedness criterion is an ideal choice for the LES model because of its low numerical diffusion [14]. Table 1 summaries related numerical schemes. The following subsections summarize the governing equations, turbulence, and acoustic model. 3.1.1. Governing equation and turbulent model The continuity and momentum equations in conservation form are expressed as follows: Continuity equation:

@ui ¼0 @xi

ð2Þ

where ui is the velocity tensor. Momentum equation:

q

@ui @ðui uj Þ @p @ ¼ þ þq @xj @xi @xj @t

   @u @u l iþ j @xj @xi

ð3Þ

Consider a coordinate system that is rotating at a steady angular velocity with respect to the stationary reference frame. When the equations of motion (continuity and momentum equations) are solved in a rotating frame, the acceleration of the fluid is augmented by additional terms in the momentum equations [15]. The relative * * velocity u r and absolute velocity u are related by * ur

Fig. 4. Measuring position of microphone inside the semi-anechoic chamber.

*

*

*

¼ u ðx  r Þ *

where x is the angular velocity vector.

ð4Þ

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S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

Table 1 Summary of numerical scheme. Demonstration purpose

Turbulence model

Pressure–velocity coupling method

Discretization of the momentum equations

Flow visualization and performance evaluation Acoustics prediction

ke ke LES

Simple PISO PISO

Second-order upwind scheme Second-order upwind scheme Bounded central differencing scheme

With respect to the steadily rotating reference frame, the governing equations of fluid flow are *

r  ur ¼ 0

( 0

Gðx; x Þ ¼

ð5Þ

* * * * * * * @ * r ðq u r Þ þ r  ðq u r u r Þ þ qð2 x u r þ x  x  r Þ ¼ rp þ r  s @t ð6Þ *

* u r Þ

q

i i u j Þ @u @ðu @ ¼ þq @xj @xj @t

   @ @ @p @ @u @u 2 @u ðqui Þ þ ðqui uj Þ ¼  þ l i þ j  dij l @t @xj @xi @xj @xj @xi 3 @xl

and

Eq. (7) is called the Reynolds-averaged Navier–Stokes (RANS) equation, where the Reynolds stress qu0i u0j is modeled by the Boussinesq hypothesis [16] and related with turbulent viscosity lt.

qu0i u0j ¼ lt

    @ui @uj 2 @u  þ qk þ lt i dij 3 @xj @xi @xi

ð8Þ

The k  e model computes the turbulent viscosity as a function of turbulence kinetic energy (k) and turbulence dissipation rate (e):



@ @ @ ðqkui Þ ¼ ðqkÞ þ @t @xi @xj

lþ



@ @ @ ðqeÞ þ ðqeui Þ ¼ @t @xi @xj

lt ¼ q C l

k





lt @k þ Gk  qe rk @xj 

ð10Þ

2

ð11Þ

e

where Gk (¼ lt



@uj @xi

i þ @u @xj



@uj ) @xi

is the turbulent kinetic energy gener-

ated by the mean velocity gradients. Cl, C1e, C2e, rk, and re are model constants with the following empirically derived values: Cl = 0.09, C1e = 1.44, C2e = 1.92, rk = 1.0 and re = 1.3, respectively [17]. In addition to the k  e model, this study adopts the LES turbulence model to solve the large eddies in this unsteady flow field to calculate sound pressure. The LES model solves large eddies directly by filtering the time-dependent Navier–Stokes equations. A filtered variable is defined by

uðxÞ ¼

Z

uðx0 ÞGðx; x0 Þdx0

ð12Þ

D

where D is the fluid domain, and G is a filter function that determines the scale of the resolved eddies. Through finite-volume discretization, the filtering operation can be represented as

 ðxÞ ¼ u

1 V

Z

uðx0 Þdx0 ; x0 2 m

l

  @ sij @ rij @p   @xi @xj @xj

ð16Þ

   i @ u j l @u 2 @u  l þ dij    3 @ xl @ xj @ xi

ð17Þ

sij is the subgrid-scale stress defined by ð18Þ

Since the subgrid-scale stresses resulting from the filtering operation are unknown, and therefore require modeling, the subgrid-scale turbulence model employs the Boussinesq hypothesis as in the RANS model, computing subgrid-scale stress from

1 3

sij  skk dij ¼ 2lt Sij

ð19Þ

where lt is the subgrid-scale turbulent viscosity, and  Sij is the rateof-strain tensor defined by

  1 @ui @uj þ 2 @xj @xi

ð20Þ

This study employs the Smagorinsky–Lilly model [18] to model the eddy-viscosity by



l @e e e2 þ C 1e Gk  C 2e q lþ t re @xj k k



rij ¼ l

Sij ¼ ð9Þ

ð15Þ

rij is the stress tensor due to molecular viscosity expressed

sij  qðui uj  ui uj Þ ð7Þ

ð14Þ

0; x0 R v

Filtering the Navier–Stokes equation leads to

where as

@ ðqu0i u0j Þ @xj

; x0 2 v

i @u ¼0 @xi

r is the viscous stress. where 2qðx is the Coriolis force and s When the fluid inertia affects the flow field more significantly than the fluid viscosity, the flow develops into a turbulent flow. Turbulent flows exhibit fluctuating velocity fields, which in turn cause many eddies. This study utilizes the k  e turbulence model to solve the Navier–Stokes equations.

þ

1 V

ð13Þ

t

where V is the volume of a computational cell. The filter function Gðx; x0 Þ determines the filter scale and executes the filter process

lt ¼ qL2S jSj

ð21Þ

LS ¼ minðjd; C S V 1=3 Þ

ð22Þ

qffiffiffiffiffiffiffiffiffiffiffiffi where LS is the mixing length for subgrid scales and jSj ¼ 2 Sij Sij . LS is computed using

where j is the von Karman constant, d is the distance to the closet wall, CS is the Smagorinsky constant of 0.1 for a wide range of flows. V is the volume of the computational cell. 3.1.2. Acoustic sound model Computational techniques for flow-generated sound can be classified as direct, indirect, or hybrid computation. The direct approach computes the sound together with its fluid dynamic source by solving the flow equations, which incurs a high computational cost. The hybrid approach decouples the flow calculation from the sound calculation, which is possible in aeroacoustic theory with less computational cost than the direct approach [11,19]. This study employs a hybrid approach in which the far-field sound is obtained by integral solutions to wave equations [20]. A fundamental assumption for acoustic analogy-based prediction is the one-way coupling of flow and sound. In other words, the unsteady flow generates sound and its propagation, while the sound waves do not significantly affect the flow. The principal application of the hybrid approach lies in flows with low fluctuating Mach numbers. Time-accurate turbulence simulation tools, such as LES and

S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

unsteady RANS methods, can be used to compute the space–time history of the flow field, from which acoustic source functions are extracted. At low Mach numbers, incompressible flow solutions can be adequate for approximating acoustic source terms [19]. The approximation applies to this study well since the maximum velocity does not exceed in 10 m/s (Mach number = 0.029). To calculate aerodynamically generated sound, the prediction of the radiated sound follows the Ffowcs Williams and Hawkings (FW–H) Model [21], which is capable of predicting the sounds generated by a moving surface. This model is essentially a wave equation derived by manipulating the continuity equation and the Navier–Stokes equations. The FW–H equation can be written as 2 0

2

1 @ p @ @  r2 p0 ¼ fT ij Hðf Þg  f½Pij nj þ qui ðun @xi @xi @xj a20 @t 2 @  v n Þdðf Þg þ f½q0 v n þ qðun  v n Þdðf Þg @t

ð23Þ

where ui is the fluid velocity component in the xi direction, and un is the fluid velocity component normal to the surface f = 0. vi is the surface velocity component in the xi direction, vn is the surface velocity component normal to the surface, and k (f) and H(f) represent the Dirac delta function and Heaviside function, respectively. p0 is the far field sound pressure (p0 = p  p0). f = 0 denotes a mathematical surface introduced to embed the exterior flow problem (f > 0) in an unbounded space, which uses the generalized function theory and the free-space Green function to obtain the solution. ni is the unit normal vector pointing toward the exterior region, a0 is the far field sound speed, whose expression of Tij is the Lighthill stress tensor. Concerning fluid dynamics, the approximation of a compressible fluid field through an incompressible one requires the splitting of the pressure fluctuations into incompressible pressure fluctuations (called pseudo-sound pressure) and the actual far-field acoustic pressure [22]. The density perturbation can be expressed in the integral representation and evaluated at retarded time [21]. The complete solution to the above wave equation includes both surface and volume integrals. The surface integrals represent the contributions from monopole and dipole acoustic sources, and partially from quadrupole sources. The volume integrals represent quadrupole sources in the region outside the source surface. Since the contribution of the volume integrals is not significant, they are excluded from the numerical scheme. Thus, the solution becomes

P0 ð~ x; tÞ ¼ p0T ð~ x; tÞ þ p0L ð~ x; tÞ 4pp0T ð~ x;tÞ ¼

"

Z

ð24Þ #

q0 ðU_ n þ U n_ Þ rð1  Mr Þ2

f ¼0

dS þ

Z

"

q0 U n frM_ r þ a0 ðMr  M2 Þg r 2 ð1  M r Þ3

f ¼0

# dS

ð25Þ p0L ð~ x; tÞ

4p

1 ¼ a0

Z

"

L_ r

#

Z

"

Lr  LM

#

dS þ dS 2 rð1  Mr Þ2 f ¼0 r 2 ð1  M r Þ # Z " _ r þ a0 ðM r  M 2 Þg 1 Lr fr M dS þ a0 f ¼0 r2 ð1  M r Þ3 f ¼0

ð26Þ

q U i ¼ v i þ ðui  v i Þ q0

ð27Þ

^ j þ qui ðun  v n Þ Li ¼ Pij n

ð28Þ

P0T

P0L

where and are the thickness and loading terms, respectively. Pij is the compressive stress tensor. S is the source surface, which moves at an outward normal velocity of Un. This study treats the surfaces of blades, hub, and fan frame as acoustic sources in the FW–H model. An acoustic receiver is set in this model at a location of 50 cm from the fan outlet along the

29

axial direction to record the radiated sound pressure. The relative position between the sound receiver and fan is the same as the experimental measurement. 3.2. Boundary conditions This study makes several appropriate assumptions and sets various boundary conditions to simulate the actual flow patterns inside the fan. These assumptions and conditions are described as follows: (1) Pressure outlet boundary condition. The atmosphere is set at the flow inlet boundary to define a free external flow, at the flow outlet boundary to calculate the maximum airflow rate under the free-delivery condition. (2) Mass flow outlet boundary condition. The mass flow rate of each operating point at the flow outlet boundary is set to calculate the corresponding static pressure. (3) Wall boundary condition. This numerical model sets the no-slip boundary condition on the solid surfaces of the fan. (4) Moving reference frame (MRF). This study deals with the rotating flow in a fan via the MRF in the CFD codes. The rotating wall surfaces are treated as stationary boundaries relative to the rotating frame. When the equations of motion are solved in this rotating reference frame, the acceleration of the fluid is supplemented by additional terms that appear in the momentum equations. (5) Sliding mesh boundary condition. This study employs the sliding mesh model to compute the unsteady flow feature when a sound pressure solution for rotor–stator interaction is considered. This technique divides the mesh domain into rotating and static zones. Each zone is bounded by the interface boundary, and the adjacent two mesh zones between rotor and stator move relative to each other along the grid interface [11]. Thus, the grid faces do not need to be aligned on the grid interface. This situation requires a means of computing the flux from velocity field across the two non-conformal interfaces that comprise the boundary of rotator and volute zones. To calculate the interface flux, the intersection between the interface zones is determined at each time step. The resulting intersection produces an interior zone in which the two interface zones overlap to transfer the node information. The static pressure and hub torque at each operating point can be calculated using the numerical procedure above. The calculated static efficiency can be therefore determined by:

gStatic;CFD ¼

Ps  Q T hub  x

ð29Þ

where the product of calculated hub torque (Thub) and rotational speed (x) is the fan input energy applied to the fluid. 3.3. Numerical model and grid verification The grid system of a fan can be divided into the inlet region, rotor, volute, and outlet region (Fig. 5). The inlet and outlet regions simulate the outside space, and must be large enough to avoid the boundary effect and ensure the validity of the numerical

S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38 Table 2 Grid distribution for each flow region (unit: million). Total grids number

Rotor

Volute

Inlet

Outlet

0.594 0.799 0.984 1.184

0.225 0.276 0.341 0.392

0.101 0.134 0.186 0.231

0.124 0.181 0.223 0.277

0.144 0.208 0.234 0.284

(a)

Coarse mesh

Refined mesh

(b) 3.1

9.7 Max. Static Pressure

3

9.6

Max. Airflow rate

9.5 9.4

2.9

9.3 2.8

9.2 9.1

2.7

Airflow Rate (cfm)

outcome. To allow the full expansion of the external flow field, the size of outlet chamber was set as 510 mm  200 mm  300 mm, and the length along the flow direction was set as 200 mm for a 100 mm-diameter inlet region. Even though the flow regions in the fan inlet and outlet are significantly larger than those in the fan itself, acute flow motions occur in the rotor region and must be carefully examined. This is because the physical phenomenon becomes very complex after the flow enters the fan rotor, as the energy transfer to the fluid occurs mainly within the blade passage. Thus, many grid points are necessary to obtain detailed information on the flow field in the rotor region. The rotor region uses a finer grid distribution, while the inlet and outlet zones use relatively coarser grids. This study also presents a grid independence test to identify the optimal grid system. Computations for steady RANS with various grid-density systems were performed to ensure the validity of the numerical calculations in this study. Table 2 lists the grid distribution for each flow region, while Fig. 6a displays the coarsest and refined grid points. Fig. 6b illustrates the calculated maximum static pressure and airflow rate for several grid systems with different grid numbers. The results of the 0.98 M-grid system are sufficient to yield the detailed flow characteristics inside the centrifugal fan and almost identical to those of 1.18 M-grid system. However, to ensure precise numerical calculation in the LES simulation, this study utilizes a 1.18 M-grid system to perform the related CFD simulations of the centrifugal fan. For the transient simulation, the size of time steps was set to be 0.0001 (363.6 time steps per revolution), and acoustic data were extracted from 8th to 10th revolution. Fig. 7a illustrates the resulting wall y+ of the fan rotor, which is around 3–5 for most of the rotor surface and 7–9 close to the fan outlet region. As the rotor mesh number was increasing to 0.79 M (1.58 M in total), the resultant y+ is less than 4 for most of the hub surface, and 5–6 near the blade tip close to the fan outlet (Fig. 7b). The resulting overall SPL and SPL values at the BPF are 29.3 dB and 12.5 dB, respectively, which are almost identical to the results of the 1.18 M-grid system. Therefore, the predicted SPLs are acceptable for the 1.18 M-grid system. The validity of this grid refinement can be confirmed by referring to the modeling errors of LES applying the standard Smagorinsky model in a turbulent plane Poiseuille flow [23]. When the y+ in the grid resolution is close or below 10, the errors in the mean

Static Pressure (mm-Aq)

30

9 2.6 0.6

8.9 0.8

1

1.2

Mesh number (millions) Fig. 6. Grid refinements and independence test. (a) Various grid densities and (b) calculated results.

Inlet region

velocity are within 3% in comparison with the results of related theories and direct numerical simulation (DNS) [24].

Fan 4. Results and discussions

Outlet region

(a) Overall Volute

Rotor

(b) Rotor and volute regions Fig. 5. Grid system of a 80 mm-diameter centrifugal fan. (a) Overall mesh and (b) rotor mesh.

The above mentioned experimental work on centrifugal fan provides the P–Q curve, brake horsepower, static efficiency, and SPL spectrum characteristics, which can be used to validate CFD results. Also, the complete performance behavior of a BI centrifugal fan at various operating points is analyzed with the aids of this integrated experimental and numerical effort. This comprehensive approach makes it possible to appraise a centrifugal fan in a thorough and detailed manner, which supplements the insufficiency of previous work. Moreover, according to the flow-field analysis at various operating points, modification alternatives are proposed and implemented to enhance the fan performance. The following subsections discuss the performance evaluation, efficiency estimation, noise spectrum analysis, and modification alternatives, respectively.

31

Static Pressure (mm-Aq)

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(a)

4

Exp. CFD

3 2 1 0

0

2

4

6

8

10

Airflow Rate (cfm)

45 40 35 30 25 20 15 10 5 0

P-Q curve (CFD)

3

Static Eff. (CFD)

A

2

B

1

C

0 0

2

4

6

8

Efficiency (%)

(b)

Static Pressure (mm-Aq)

Fig. 8. Performance comparison between experimental and numerical results for the centrifugal fan operating at 1650 rpm.

10

Airflow Rate (cfm) Fig. 9. Calculated performance and efficiency of the centrifugal fan operating at 1650 rpm.

Fig. 7. Contour of wall y+ at the first grid point. (a) 1.18 M-grid system and (b) 1.58 M-grid system.

4.1. Performance evaluation For comparing fan performance under the same criterion, the rotational speed is set at 1650 rpm at each operating point for both numerical simulation and performance measurement. Then, the steady RANS simulations are conducted to visualize the related flow fields and determine the fan performance curve. Fig. 8 illustrates a good agreement between experimental and numerical P– Q curves. The calculated deviations on maximum volumetric flow rate and static pressure are approximately 3% and 5% lower than the measuring data. For demonstration purpose, three operating points are selected to evaluate the influences of various system resistances on fan performance. Fig. 9 shows that these points are denoted as point A (1.1 cfm), point B (4.5 cfm), and point C (7.9 cfm) to represent three cases of high, medium, and low system resistances, respectively. In addition, to obtain an overall understanding, flow visualization is carried out numerically at several important cross sections, such as the fan inlet, blade passage, blade outlet, and fan discharge, to reveal the distinctive flow patterns under different system resistances. These visualization results can serve as the important references to modify fan configuration for improving its aerodynamic performance. When air flows into the fan, part of the fluid enters into the fan along axial direction at the inlet region as shown in Fig. 10. Clearly, a substantial reverse flow appears near the volute-tongue region

and results in a severe spilling phenomenon (see Fig. 11), especially for the case of high system resistance (point A). Consequently, these spilling flows from the fan casing to outside region lead to energy loss and poor performance. However, this reverse flow diminishes significantly for the lower resistance conditions (points B and C). Fig. 12 shows the velocity distributions inside the blade passage. In the region near volute-tongue, high-resistance condition (point A) induces a severe reverse flow along the axial direction. Also, this reverse flow pattern turns into weak circulation for the mid-resistance condition (point B) and smoothes out for the low-resistance condition (point C). In addition, the circulation flows inside the blade passages are obvious under the high system resistance (Fig. 13a) and becoming moderate for the lower resistance conditions (Figs. 13b and c). The exit velocity distributions at the blade outlet are plotted in Fig. 14 for different operating points. Apparently, the low-velocity flow patterns exist near the cut-off; thus, instead of flowing outward, part of the airflow is suppressed into the cut-off clearance to generate a lower volumetric flow rate. However, the higher velocity from rotor blades to fan outlet are observed for the lower system-resistance condition (see Fig. 14c). Furthermore, it is instructive to observe this phenomenon from the flow pattern in the fan discharge. As illustrated in Fig. 15, the stagnated and circulation flows appear over most of the discharge area at operating point A. For the case of decreasing system resistance, the outward velocity component reinforces gradually and enables more airflow flowing outward through the volute tongue (Figs. 15b and c). In summary, the suppressed and reverse flow patterns exist inside the fan via a thorough flow-field analysis for a higher downstream static pressure. Such a high system resistance induces circulation and reverse flows at the regions, such as fan inlet (Fig. 10), blade passage (Figs. 12 and 13), cut-off, and fan discharge (Figs. 14 and 15). The locations of severe reverse flows and separated circulations which cause losses are schematically illustrated in Fig. 16. Evidently, these reverse flows and circulations lead to a diminished fan performance.

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(a)

(b)

Unit: m/s

(c)

Fig. 10. Velocity distributions at the fan inlet for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

(a)

(b)

(c)

Fig. 11. Reverse flow areas (black region) at the fan inlet for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

4.2. Efficiency estimation Besides the P–Q curve, another vital parameter in assessing the fan design is the static efficiency, which represents the ratio of the static energy transfer to the fluid to the total power input. As listed in Eq. (29), the torque is needed for determining the static efficiency. In this work, the torque variation for different flow rates is calculated via CFD simulation and plotted in Fig. 17a. Noticeably, since the measured input powers are only 0.6–1.2 watts for a small

DC motor installed in this fan, the corresponding torques can be estimated in the range of 0.0035–0.0069 N m for a perfect motor running at 1650 rpm. Thus, it is rational that an extra low torque is observed over the entire operating range. From Fig. 17a, the torque enlarges with an increasing flow rate and reaches its maximum value at the free-delivery condition. Such a torque variation is due to that the increasing system resistance suppresses the fluid and causes reverse flows, circulations, and low-velocity regions inside the centrifugal fan.

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(a)

33

Cut-off

(b)

Hub Unit: m/s

(c)

Fig. 12. Lengthwise velocity inside the blade passage for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

(a)

(b)

Unit: m/s

(c)

Fig. 13. Transverse velocity inside the blade passage for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

A similar trend is found from the static-efficiency comparison between numerical and experimental results (see Fig. 17b). Starting from the no-delivery point, the calculated static efficiency continues to enlarge and reaches the maximum value at Q = 3.4 cfm due to the increasing volumetric flow rate, thereafter the efficiency curve declines with the decreasing static pressure. Besides, the experimental efficiency is under-estimated compared to the numerical predictions. For example,

the maximum static efficiency obtained from simulation and measurement are approximately 26% (Q = 3.37 cfm) and about 4.1% (Q = 3.41 cfm), respectively. This is because the experimental data (gstatic,Exp) adopts the measured fan power to compute the static efficiency, while the numerical prediction (gstatic,CFD) utilizes the product of calculated hub torque and rotating speed as the fan input power, which is not taking the motor efficiency into account.

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S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

(a)

Cut-off

Blades

(b)

Unit: m/s

(c)

Fig. 14. Velocity distributions at the blade outlet for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

(a)

(b)

Unit: m/s

(c)

Fig. 15. Velocity distributions at the fan outlet for various operating points. (a) Operating point A, (b) operating point B and (c) operating point C.

The motor efficiency is expressed as

gmotor ¼

T hub  x gstatic;Exp ¼ Hp gstatic;CFD

ð30Þ

where Thub represents the applied torque to airflow by hub, and Hp is the brake horsepower. From experiences, the DC motor efficiency for a small centrifugal fan is usually very low. For demonstration purpose, the motor efficiencies under various operating conditions are obtained straightforwardly by following Eq. (30). These estimated results present the motor efficiency is within the range of

15–20% for the centrifugal fan, as illustrated in Fig. 17c. By realizing the loading characteristic of fan motor, fan designers can accordingly choose an appropriate motor allocated inside the fan to offer more operating power and less energy consumption. In this study, the torque output of fan rotor is calculated with the aids of numerical simulations. Thereafter, the brake horse power and static efficiency can be determined and analyzed according to the corresponding flow-field phenomenon. In conclusion, with the comparison of experimental and predicted static efficiencies, this work successfully decides the corresponding motor efficiency of centrifugal fan for fan user and designer.

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Fig. 10a Fig. 12a Fig. 13a Fig. 14a

Fig. 16. Schematic locations of circulation and reverse flows.

(a) 0.0012 0.0010 0.0008 0.0006 0.0004 0

2

4

6

8

10

Exp. Efficiency (%)

(b) 15

45 40 35 30 25 20 15 10 5 0

Static Eff. (Exp.) Static Eff. (Num.)

10

5

0 0

2

4

6

8

Cal. Efficiency (%)

Airflow Rate (cfm)

10

Airflow Rate (cfm)

Efficiency (%)

(c)

40 30 20

4.4. Modification alternatives

10

According to the above analysis and discussion on the flow-field visualization inside the centrifugal fan, the overall understanding of flow mechanism at each operating point has been introduced. The undesirable flow patterns can be clearly identified in this

0 0

2

4

6

8

10

Airflow Rate (cfm) Fig. 17. The calculated fan characteristics for different operating points. (a) Calculated torque, (b) static efficiency and (c) motor efficiency.

4.3. Acoustic noise evaluation In this study, not only the noise frequency spectrum at the fan outlet is measured in the semi-anechoic chamber, but also the aerodynamic noise is calculated via CFD codes. In numerical simulation, the acoustic receiver is placed at the same location as that of experimental work. Also, the unsteady sliding mesh is employed to calculate the radiated sound pressure. After the calculation is stable and converged, this sound pressure is recorded and converted into a spectrum pattern by fast Fourier transformation. Fig. 18

Sound Pressure Level (dB)

Torque (N-m)

0.0014

plots the measured SPL and two calculated SPLs, which are calculated by using k  e and LES turbulent models under maximum airflow rate condition, respectively. Apparently, the experimental SPL is higher than two numerical results because only the aerodynamic acoustic source and its radiation to free field are captured in the numerical calculation. In fact, the numerical prediction excludes some actual effects, such as the mechanical vibration and motor noise. Therefore, with the similar SPL pattern, the underestimation of numerical results is reasonable and can be expected. As regards the CFD outcomes, since k  e turbulence model is based on a semi-empirical and time-averaged relation, detailed eddies are missing in this model and thus revealed a general underestimation in the SPL compared with the experimental measurement. On the contrary, LES turbulent model can capture the grid-scale eddies if the mesh is sufficiently refined. Fig. 19 compares the flow characteristics of two turbulence models. Obviously, the velocity field inside the fan rotor of the LES model fluctuates more than that of the k  e model, especially within the blade passages near the volute tongue (Fig. 19a). Also, the LES model reveals some small circulations in this region. However, these circulations disappear in the k  e model, with the airflow moving smoothly outward. A comparison of these results reveals higher-velocity airflow near the blade surface for the LES turbulence model (see Figs. 19a and b). These small circulations and partial higher-velocity airflow near the blade surfaces may increase noise generation and pressure fluctuations within the rotor (Fig. 19c). Hence, as indicated in Fig. 18, the LES model calculates tiny pressure fluctuations and yields more accurate acoustic result compared to the k  e model. Additionally, evident peaks on spectrum are illustrated clearly at the blade passing frequency (BPF). As illustrated in Fig. 18, the experimental and numerically predicted SPLs at the BPF are 13.5 dB, 12.9 dB, and 10.2 dB for measured, LES, and k  e results, respectively. This comparison demonstrates that the predicted noise level of LES model agrees well to the experimental measurement. In addition, the non-weighted overall SPLs for experimental spectra, LES, and k  e calculations are 31.2 dB, 29.2 dB, and 24.9 dB, respectively. Consequently, in this study, a qualitatively agreeable prediction on sound pressure level is attained via the numerical simulation of LES turbulent model. The underestimation of calculated result is rational since the motor noise and effect of structural vibration are excluded in the CFD simulations. Therefore, fan designer can utilize the noise simulation as a useful analysis tool to obtain the noise fluctuation information and evaluate the fan acoustic behavior in a thorough manner.

50 40 30 20 10 0 -10 -20 -30 -40 -50 200

Exp. CFD (LES) CFD (k-e)

400

600

800 1000 1200 1400 1600 1800 2000

Frequency (Hz) Fig. 18. SPL comparison between experimental result and numerical calculations.

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S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

(a)

Cut-off

Hub

Unit: m/s

k − ε model

LES model

(b) Cut-off

Hub

LES model

k − ε model

LES model

k − ε model

(c)

Fig. 19. Flow-field comparison of different turbulence models (at 0.405 s). (a) Transverse velocity field inside the blade passage, (b) lengthwise velocity field inside the blade passage and (c) RMS value of the time-derivative of static pressure.

investigation. From the viewpoint of improving fan performance, this study proposes two modifications on fan geometry to smooth out these reverse flow patterns. One of them is to utilize an additional inlet bell design (see Fig. 20a), which is aimed to reduce the reverse flow at the inlet region. Another alternative is to adjust the cut-off clearance for decreasing the reversed flow rate through volute-tongue (Fig. 20b). Through the numerical simulations on these modified fans, the results indicate that the inlet bell design effectively reduces the flow rate (Table 3a) and the area ratio (Table 3b) of reverse flow at each operating point. Also, a small cut-off clearance successfully diminishes the reverse flow and generates more outward airflow at the fan discharge (Table 4). As illustrated in Fig. 21a, both modified fan designs result in a superior performance curve compared to the original fan’s performance. Additionally, the static efficiency is predicted to appraise the fan performance via the numerical simulation. Fig. 21b compares the calculated static efficiencies of original and modified models for various operating points. As expected, these modified designs yield the higher fan efficiency because the reverse airflow at the regions near fan inlet and cut-off

are effectively reduced. Therefore, more airflow can pass through the fan rotor and obtain more static energy from fan blades. As a result, these modified designs improve the fan efficiencies over the entire performance curve. In summary, this study utilizes the flow visualization results inside the centrifugal fan as a design reference to enhance its performance. Proper modification alternatives are thus proposed to smooth out the reverse flow patterns inside the fan, especially for the high system-resistance condition. Moreover, the obvious enhancements on fan performance and static efficiency are verified by means of numerical simulations. It is concluded that, with the understanding of flow phenomenon for various system resistances inside the centrifugal fan, fan designers can accordingly conduct the feasible modifications to improve the fan performance and efficiency. 5. Concluding remarks In this study, a comprehensive performance analysis for a BI centrifugal fan is carried out through a combined experimental

37

(a)

(a)

Inlet bell

Static Pressure (mm-Aq)

S.-C. Lin, M.-L. Tsai / Computers & Fluids 56 (2012) 24–38

3 Original Model Inlet Bell Design Reduced Cut-Off Clearance

2 1

0

0

2

4

6

8

10

Airflow Rate (cfm)

(b) (b) Static Efficiency (%)

Original cut-off

Modified cut-off

45 40 35 30 25 20 15 10 5 0

Original Model Inlet Bell Design Reduced Cut-Off Clearance

0

2

4

6

8

10

Airflow Rate (cfm) Fig. 20. Modification alternatives for the centrifugal fan. (a) Inlet bell design and (b) modified cut-off design.

Table 3 Comparison of reverse airflow at the fan inlet for various operating points. Point A (a) Reverse airflow rates Original model 1.96 cfm Inlet bell design 1.76 cfm (b) Area ratios of reverse flow Original model 36.1% Inlet bell design 30.1%

Point B

Point C

0.64 cfm 0.43 cfm

0.41 cfm 0.27 cfm

16.9% 13.4%

10.1% 7.4%

Table 4 Comparison of reverse airflow rates at the cut-off region for various operating points.

Original model Reduced cut-off clearance

Point A (cfm)

Point B (cfm)

Point C (cfm)

0.84 0.068

0.92 0.063

0.67 0.04

and numerical approach. The numerical visualization of flow-field characteristics provides significant information to improve the inner flow patterns for fan designers. According to the results of flow visualization, two modification alternatives are performed numerically to effectively reduce the reverse flow patterns and successfully enhance the fan performance. In addition, by the calculations of static efficiency and torque, the aerodynamic performance of fan is evaluated in details at each operating point. Also, the comparison of measured and calculated static efficiencies can be utilized to yield the motor loading characteristics, which is useful in choosing the fan motor. Moreover, the frequency spectra analysis of aerodynamic noise is conducted through both numerical simulation and experimental measurement. For demonstration purpose, an 80 mm-diameter BI centrifugal fan is chosen as the research subject. The result indicates that experimental P–Q curve and SPL spectrum agree to these of numerical simulations. The numerical deviations on maximum volumetric flow rate and static pressure are approximately 3% and 5%. As regards the acoustic characteristics, the overall SPLs for measured spectra and LES calculation are 31.2 dB and 29.2 dB, respectively.

Fig. 21. Performance and efficiency comparisons between the original model and the improving alternatives. (a) Performance curve and (b) static pressure efficiency.

Generally speaking, this integrated performance evaluation consists of aerodynamic performance analysis, efficiency estimation, motor characteristic identification, and noise prediction. Through this evaluation procedure, the fan designer can visualize the flow patterns and calculate the loading torque at various operating points. Additionally, the predicted fan noise qualitatively agrees well with experimental measurement at maximum volumetric flow rate. Thus fan designer can utilize the noise simulation as an analysis tool to obtain the noise fluctuation information and evaluate the fan acoustic behavior in a thorough manner. Furthermore, with the overall understanding of flow mechanism inside the centrifugal fan at various operating conditions, several modification alternatives are proposed in this comprehensive investigation to successfully enhance the fan performance. In summary, this study establishes an integrated aerodynamic, acoustic, and electro-mechanical evaluation approach that can be used as an important tool for fan designers. References [1] Lin SC, Chou CA. Blockage effect of axial-flow fans applied on heat sink assembly. Appl Therm Eng 2004;24:2375–89. [2] Lin SC, Chuang FS, Chou CA. Experimental study of the heat sink assembly with oblique straight fins. Exp Therm Fluid Sci 2005;29:591–600. [3] Raj D, Swim WB. Measurements of the mean flow velocity and velocity fluctuations at the exit of a F–C centrifugal rotor. J Eng Power 1981;103:393–9. [4] Lin SC, Huang CL. An integrated experimental and numerical study of forwardcurved centrifugal fan. Exp Therm Fluid Sci 2002;26:421–34. [5] Han SY, Maeng JS. Shape optimization of cut-off in a multi-blade fan/scroll system using neural network. Int J Heat Mass Transfer 2003;46:2833–9. [6] Liu Q, Qi D, Mao Y. Numerical calculation of centrifugal fan noise. Proc Mech Eng, Part C: J Mech Eng Sci 2006;220:1167–77. [7] Rafael BT, Sandra VS, Juan Pablo HC, Carlos SM. Numerical calculation of pressure fluctuations in the volute of a centrifugal fan. J Fluids Eng 2006;128:359–69. [8] Sandra VS, Rafael BT, Carlos SM, Bruno PG. Reduction of the aerodynamic tonal noise of a forward-curved centrifugal fan by modification of the volute tongue geometry. Appl Acoust 2008;69:225–32. [9] ANSI/AMCA Standard 210-99 (ANSI/ASHRAE 51-1999). Laboratory method of testing fans for aerodynamic performance rating. Air Movement and Control Association, Inc.; 1999. [10] CNS 8753. Determination of sound power level of noises for fan, blower, and compressors. Chinese National Standard; 1982. [11] Fluent 6.3 documentation. Fluent Inc.; 2006.

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[12] Bohanon HR. Laboratory fan test: error analysis. ASHRAE technical paper no. 2332; 1975. [13] Frank B. Fan handbook: selection, application, and design. McGraw-Hill Co.; 1998. [14] Leonard BP. The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput Methods Appl Mech Eng 1991;88:17–74. [15] Batchelor GK. An introduction to fluid dynamics. Cambridge, UK: Cambridge University Press; 1992 [Reprinted]. [16] Hinze JO. Turbulence. New York: McGraw-Hill Publishing Co.; 1975. [17] Launder BE, Spalding DB. Lectures in mathematical models of turbulence. London, England: Academic Press; 1972. [18] Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev 1963;91:99–164.

[19] Wang M, Freund JB, Lele SK. Computational prediction of flow-generated sound. Annu Rev Fluid Mech 2006;38:483–512. [20] Lighthill MJ. On sound generated aerodynamically I. General theory. Proc R Soc Lond 1952;211:564–87. [21] Ffowcs Williams JE, Hawkings DL. Sound generation by turbulence and surface in arbitrary motion. Philos Trans R Soc Lond 1969;264:321–42. [22] Escobar MSM. Finite element simulation of flow-induced noise using Lighthill’s acoustic analogy. Dissertation, Erlangen–Nurnberg Univ.; 2007. [23] Brandt T. A posteriori study on modeling and numerical error in LES applying the Smagorinsky model. Complex effects in large eddy simulation, Limassol; 2005. [24] Moser RD, Kim J, Mansour NN. Direct numerical simulation of turbulent channel flow up to Res = 590. Phys Fluid 1999;11:943–5.