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Tonal noise prediction in a small high speed centrifugal fan and experimental validation
Applied Acoustics 125 (2017) 59–70
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Tonal noise prediction in a small high speed centrifugal fan and experimental validation Kishokanna Paramasivam a, Srithar Rajoo b, Alessandro Romagnoli c,⇑, Wira Jazair Yahya a a
Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia UTM Centre for Low Carbon Transport in Cooperation with Imperial College London, Universiti Teknologi Malaysia, Johor, Malaysia c Nanyang Technological University, School of Mechanical & Aerospace Engineering, 50 Nanyang Drive, Singapore b
a r t i c l e
i n f o
Article history: Received 13 July 2016 Received in revised form 2 April 2017 Accepted 11 April 2017
Keywords: Centrifugal fan Aeroacoustics Tonal noise Jet-wake flow Aerodynamic noise prediction
a b s t r a c t This paper presents the work done to establish a methodology that is capable of predicting tonal noise generation in high speed centrifugal fans. The deliverables from this work emphasize on identifying and characterizing the source of tonal noise in the centrifugal fan. Computational fluid dynamics (CFD) modeling was performed using 3-D Detached Eddy Simulation (DES) to compute the unsteady flow field in the fan. The calculated time history of surface data from the CFD is then used in Ffowcs WilliamsHawkings (FW-H) solver to predict the far field noise levels. The predicted aerodynamics and aeroacoustics results are in good agreement with the experimental data acquired from the flow testing facility and the anechoic chamber. The study conducted on the centrifugal fan shows that the aerodynamic interaction between the non-uniform impeller outflow and the leading edge of the diffuser vane is the source of tonal noise generation. The impingement of the jet-wake flow structure from the impeller outflow causes periodical pressure fluctuation on the leading edge of the diffuser vanes which leads to the tonal noise generation at the blade passing frequency (BPF). Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The wide range application of turbomachines has led to intensive research and development towards improving its efficiency in designing highly efficient turbomachines. Most of the turbomachines operate at high rotational speed in order to fulfil the power output requirement for its given size. It is well established through many previous studies that the flow field in turbomachines are highly unsteady [1]. Hence, increase in rotational speed causes more turbulence, large scale of velocity and pressure fluctuation which in turn generates higher noise level. The flow induced noise from turbomachines is generally characterized by broadband noise with prevailing discrete frequency tones. Among these two, the discrete frequency tones or also known as tonal noise is the most noticeable in sound spectrum compared to the broadband noise [2–8]. According to Raitor and Neise [9], the aerodynamic power output of a turbomachine is proportional to the cube of its rotational speed where else the aeroacoustics noise level rises in the fifth to sixth order. This relationship raises concern among researchers that it is necessary to consider aeroacoustics noise control measures during the design stage of ⇑ Corresponding author. E-mail address: [email protected] (A. Romagnoli). http://dx.doi.org/10.1016/j.apacoust.2017.04.009 0003-682X/Ó 2017 Elsevier Ltd. All rights reserved.
turbomachines. Furthermore, it is also important that noise sources in the turbomachines are identified and characterized in order to implement suitable noise control techniques. As stated by Lee et al. [10], the best solution in reducing noise generation is to identify the noise source and completely understand its mechanism. Earlier works in predicting flow induced noise in turbomachines were more focused on theoretical and experimental studies. One of the earliest theoretical formulations established in predicting noise from rotating machinery was the FW-H equation by Ffowcs Williams and Hawkings in 1969 [11]. The FW-H equation is an extension of the acoustic analogy developed by Sir James Lighthill which focuses on prediction of noise generated by the jet of an aircraft turbojet engine [12,13]. This extension to the acoustic analogy includes the dipole and monopole source distributions. In term of experiments, studies were conducted by making geometrical changes to the turbomachines and determining its effect on the noise generation. A very comprehensive review summarising all the research work done from 1960 to 1975 in the effort to reduce tonal noise from centrifugal fan was presented by Neise [3]. Neise and Koopmann [14,15] then experimentally studied a noise reduction method for centrifugal fan using acoustics resonator. Dong et al. [16] used particle image velocimetry (PIV), surface pressure and noise measurement to study the effects of modifying the
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Nomenclature b2 c0 d2 Fi H n p0 P Q r t T ij U u2 xi xj Z
Pt;t
R
dðf Þ
blade width at discharge (m) speed of sound ðm s1 Þ blade diameter (m) force acting on fluid (N) Heaviside function impeller rotational speed (rpm) sound pressure (Pa) pressure (Pa) volume flow rate ðm3 s1 Þ radius (m) time (s) Lighthill’s tensor flow velocity impeller peripheral speed ðm s1 ) cartesian coordinates of the observer (m) cartesian coordinates of the source (m) number of blade total to total pressure ratio relative error Dirac-delta distribution
cut-off tongue and impeller geometries on the flow structure, local pressure fluctuation and noise. Nonetheless, with the advancement in computational technology, numerical simulations such as computational fluid dynamics (CFD) and computational aeroacoustics (CAA) enable noise prediction in turbomachinery to be more feasible. Thus through the combination of experimental work and numerical simulation, deeper understanding on the unsteady flow field and the aerodynamic noise generation mechanism in turbomachinery can be achieved [17]. Jeon et al. [5] introduced an incompressible two dimensional discrete vortex method (DVM) to analyse the unsteady flow field of centrifugal fan. Then, using the calculated unsteady force data in the fan flow region, the noise radiations are predicted through FW-H equation. A two-part paper was then published by Langthjem and Olhoff [18,19] to study the flow induced noise phenomenon in a two-dimensional centrifugal pump where they adopted the DVM to estimate the strength of the dipole sources due to the unsteady surface force. In order to predict the noise generation within the volute of the centrifugal pump, they employed the newly developed boundary element method (BEM). In order to further improve understanding of the noise generation in an unsteady flow field, Liu et al. [20], Ballesteros-Tajadura et al. [6], Khelladi et al. [21], and Mao et al. [22] performed three-dimensional numerical calculations on centrifugal fan. They employed Reynolds Averaged Navier-Stokes (RANS) calculation to solve the unsteady flow of the centrifugal fan and the aeroacoustics modelling was performed using the FW-H equation. The results from their investigations provide better qualitative predictions compared to the twodimensional results presented by previous researchers. Despite the knowledge accumulated over the past few decades on the noise generation mechanism in centrifugal turbomachines, the prediction of noise generation in such complex flow is still difficult especially in high speed turbomachinery and requires much deeper understanding. In this paper, a methodology that is capable of identifying and characterising the tonal noise source in a high speed centrifugal fan is presented. This paper is an advancement of the previously published papers by Paramasivam et al. [23,24] which focuses on the reduction of tonal noise through the application of guide vane and tapered guide vane.
q u
air density flow coefficient total pressure coefficient generic variables viscosity
w
u l
Subscripts t total Abbreviations BEP best efficiency point BPF blade passing frequency CFD computational fluid dynamics CAA computational aeroacoustics dB decibel dB(A) A-weighting decibel SPL sound pressure level
The centrifugal fan adopted for this study mainly consists of an impeller with 11 blades, diffuser vanes, a circular casing and a universal motor as shown in Fig. 1. The aerodynamic and the geometrical characteristics of the centrifugal fan are presented in Tables 1 and 2. 2. Experimental methodology 2.1. Aerodynamic performance measurement In order to obtain the aerodynamic performance of the centrifugal fan, a flow bench as shown in Fig. 2 was setup. A straight PVC pipe was fitted at the inlet of the centrifugal fan and an orifice plate which was designed in accordance to ISO 5167-1 and ISO 5167-2 [25,26] was installed at the mid-point. The flow rate of the centrifugal fan was obtained based on the static pressure difference across the orifice plate using U-tube manometer. Pressure transducers are flushed mounted at the inlet of centrifugal fan, exit of the impeller and the exit of diffuser – to measure static pressures across the centrifugal fan. Fig. 3 shows the location of pressure transducers on the centrifugal fan. In addition to the pressure measurement, the temperature of the air flow was also measured simultaneously. Furthermore, an inductive proximity sensor was used to measure the impeller rotational speed which corresponds to the universal motor speed. The following uncertainties were established for the measured and calculated magnitudes: I. II. III. IV.
U-Tube Manometer: ±19.6 Pa Pressure Transducer: ±1.7 kPa Inductive Proximity Sensor: ±5% K-type Thermocouple: ±2.2 °C
Since the centrifugal fan constantly operates at its best efficiency point (BEP), only one operating speed was considered in this work. The measured rotational speed was 34,560 RPM and since the number of blade is 11, thus the blade passing frequency (BPF) of the centrifugal fan would be 6336 Hz. The BPF can be determined using Eq. (1):
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Fig. 1. Exploded view of the centrifugal fan.
BPF ¼ Table 1 Aerodynamic performance characteristics of the centrifugal fan. Descriptions
Value
Rotational speed Flow rate
34,560 (rev= min) 0.0479 (m3 =s)
Table 2 Geometrical characteristics of the centrifugal fan. Descriptions Radius of blade inlet (mm) Angle of blade inlet (°) Radius of blade exit (mm) Angle of blade exit (°) Number of blades
Shroud Hub
Impeller
Diffuser Vane
18 18 9.2 51.5 32.18 11
53 53 2.8 62.5 19.8 15
nrpm Z blade 60
ð1Þ
2.2. Acoustics measurement In this research work, the sound pressure level of the centrifugal fan was determined based on the guideline provided in ISO-3745, (2012). The acoustics measurement was conducted in a full anechoic chamber located at Nanyang Technological University, Singapore (NTU). The dimension of the anechoic chamber is 4:0 m 5:0 m 3:0 m and the cut-off frequency is 230 Hz. The sound pressure level (SPL) of the centrifugal fan is measured by using GRAS 46AE Free-Field ½ Preamplifier microphone which has frequency range of 3.15 Hz to 20 kHz. The uncertainty of the microphone is ±1dB (5 Hz – 10 kHz) and ±2 dB (3.15 Hz – 20 kHz). The microphone was calibrated using Larson Davis CAL200 acoustics calibrator which has an uncertainty of ±0.2 dB. Before performing an acoustics measurement, it is important to determine the position of the microphone. If an acoustics measure-
Fig. 2. Schematic diagram of centrifugal fan flow bench.
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Fig. 3. Location of pressure transducers on centrifugal fan.
ment is conducted in the region closer to the source, the accuracy of the measurement will be low. This is because in near field, the sound pressure and acoustics particle velocity will not be in phase, thus the propagation of the sound wave will be unstable. The position of the microphone is dependent on the radius of the measurement surface. Measurement surface is a hypothetical surface of area on which the microphone is located and enveloping the noise source under test. For the current study, hemispherical measurement surface was opted since the centrifugal fan was placed on the floor of the anechoic chamber. ISO-3745 [27] recommends that the radius of the measurement surface should be either 1 m or twice the largest dimension of the source under test. For the current acoustics measurement, the radius of the measurement surface was decided to be 1 m as shown in Fig. 4. 3. Numerical modeling 3.1. Computational fluid dynamics (CFD) modelling This section presents the overview of the computational fluid dynamic (CFD) modeling using ANSYS FLUENT. The fundamental of CFD is that it solves the partial differential flow equations mainly the conservation of mass and conservation of momentum. Conservation of mass is shown in Eq. (2) and Eq. (3) defines the conservation of momentum.
@q þ r ðqUÞ ¼ 0 @t
q
DU ¼ rp þ lr2 U Dt
ð2Þ ð3Þ
Fig. 4. Sound pressure level measurement of centrifugal fan at NTU anechoic chamber.
The computation domain for CFD consists of 5 fluid domains: the upstream inlet, the gap between the casing and impeller, the impeller, the volute and the downstream outlet. Some of the geometries are simplified in the fluid domain in order to improve the mesh quality and reduce the computing time. Furthermore, the inlet and outlet domains are extended in order to allow the flow to be fully developed. The entire 5 fluid domains are attached through non-conformal interfaces. Hybrid meshing technique is adopted: tetrahedral for the impeller and the diffuser channels volumes, hexahedral for the upstream and downstream fluid volumes. Similar meshing technique was employed by Khelladi et al. [28] in their study. The total number of mesh elements of the centrifugal fan model is 4:6 106 . Fig. 5 shows the representation of the 3D model, fluid domain and the meshed fluid domain. The turbulence model employed for the CFD was SST k x variant of the Detached Eddy Simulation (DES) due to its capabilities in resolving eddies for noise prediction. DES approach combines the advantages of RANS and LES, in which the model is not as demanding as LES formulation, thus reducing the computational time [29– 31]. According to Travin et al. [32], DES functions as a subgrid-scale model in regions where the grid density is fine enough for LES and as a RANS model in regions where it is not. Moreover, DES models have been specifically designed to address high Reynolds number wall bounded flows [33]. It is also important to state that the SST model interchanges between k e variant in the core flow region and the k x variant near the walls [34]. Borges et al. [35] stated that the SST model provides good prediction for experimental validations. In terms of boundary conditions, the inlet is defined as ‘‘total pressure inlet” and at the downstream outlet is specified as ‘‘static pressure outlet”. The value for the inlet is defined based on the experimental results conducted on the centrifugal fan. As for the outlet, since the air flow from the centrifugal fan is discharged to the ambient it is assigned as atmospheric pressure. The impeller fluid domain is defined as ‘‘moving mesh” and the rotational speed is set as 34,560 rpm as per the experiment. For the surfaces that rotate, ‘‘moving wall” is assigned. This technique is known as sliding mesh method (SLM). The SLM introduces rotation by assigning the rotational component of velocity to all the nodes in the domain. Gennaro [36] stated that in order to perform timedependent simulation involving turbomachinery application, the SLM technique is the most suitable and accurate. The SLM is based on relative motion of two domains/cell zones where these domains are bounded by at least one ‘‘interface” boundary condition. The interface is a surface where the fluid variables are transported from one zone to the other. The RANS equation is solved in each cell zone and fluxes are computed at each time step [33,36]. As the rotating domain changes positions at each time step, the previ-
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Fig. 5. Representation of 3-D model, fluid domain and meshed fluid domain.
ously calculated fluxes are recomputed. Every time step is set to represent 1° rotation of the impeller. Hence, it will take 360 time steps to complete one revolution. 3.2. Computational aeroacoustics modeling The noise prediction in the centrifugal fan was carried out using hybrid CAA which is based on the Ffowcs-Williams and Hawkings (FW-H) formulation. The use of the FW–H equation allows the noise sources to be separated into monopole, dipole, and quadrupole [37]. The FW-H equation is written as in Eq. (4).
"
# 1 @ 2 p0 @ 2 p0 @ @ @2 2 ¼ ½Qdðf Þ ½F i dðf Þ þ ½T ij Hðf Þ @t @xi @xi @xj @xi c20 @t 2
ð4Þ
The three terms on the right side of Eq. (4) are known as monopole source, dipole source and quadrupole source respectively. The monopole sound source is associated with the fluid volume displacement due to the surface motions. The dipole source represents the sound generated due to the unsteady forces exerted by the moving surfaces where else the quadrupole source represents the sound generation by the volume distribution outside of the surfaces [11,20,21,37]. The solution at a far-field receiver location can be computed using the generalised function theory and the free-space Green’s function. The sound pressure at a far-field receiver location is given by Eq. (5). Detailed derivations of Eq. (5) can be found in work presented by Farassat [38]. The solution consists of surface and volume integrals. The surface integrals represents the contributions from the monopole and dipole sources, where else the volume integral represents the quadrupole source.
Z Q ðy; t jxyjÞ Z F i y; t jxyj c0 1 @ 1 @ c0 dS p0 ¼ dS jx yj jx yj 4pc20 @t S 4pc20 @xi S Z T ij y; t jxyj c0 1 @2 dV ð5Þ þ jx yj 4pc20 @xi @xj V with t jxyj = retardation time c0 jx yj = distance between source point and observer point
The sound pressure data at far-field receiver location are then obtained by post processing the output of Eq. (5) with Fast Fourier Transform (FFT) algorithm. The Sound Pressure level (SPL) is obtained with respect to the reference sound pressure as given by Eq. (6).
SPL ¼ 20log10
" # p0rms pref
ð6Þ
where pref ¼ 2 105 Pa The adopted method is integrated under the assumption of freespace and the absence of obstacles between the sound source and the receiver. Thus, the effects of scattering, diffractions, as well as the reflections of casing and blades are not considered [20,21,33]. The acoustics wave is also assumed to exert no forces on the fluid flow [39]. 4. Validation exercise Since most of the discussion is based on the CFD results, its validation with experiments is necessary in order to gain confidence on the accuracy of the simulation model. The performance parameters of the centrifugal fan obtained from the aerodynamic experiment are directly compared with the CFD results. The parameters used for validations are the flow coefficient u, total pressure coefficient w, and the total-to-total pressure ratio Pt;t as presented in Eqs. (7) – (9).
u¼ w¼
Q
ð7Þ
pb2 d2 u2 DP t 0:5qu22
ð8Þ
Pt;out P t;in
ð9Þ
Pt;t ¼
Comparisons between the measured experimental and CFD predicted results are presented in Table 3, in which the relative error, for the generic variables, is defined as in Eq. (10).
eR ð%Þ ¼
juCFD uEXP j
uEXP
100
ð10Þ
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Table 3 Comparison between experiment and CFD results for validation.
EXP CFD eR ð%Þ
u
w
Pt;t
0.136 0.129 4.86
0.604 0.594 1.67
1.129 1.125 0.35
Fig. 6. Comparison of tonal noise SPL between predicted and experiment for centrifugal fan.
Based on Table 3, it can be seen that the CFD model underpredicts the unsteady performance of the centrifugal fan. These deviations are probably due to the simplified geometry used to represent the universal motor in the 3-D modelling. In the experiment, the universal motor commutator rotates which provides momentum to the air flow. However, in the simulation the universal motor is defined as stationary in order to reduce the computing time. This causes the CFD to under predict the volume flow rate. Nonetheless, the small deviation (max <5%) between the prediction and experiment values indicates the CFD model can be utilized for further evaluation. Besides CFD model validation, the CAA model is also validated against the acoustics experiment. The comparison between the predicted tonal noise SPL and the results from the acoustics experiment is shown in Fig. 6. Based on the SPL, the predicted values show similar pattern and consistent deviation in terms of magnitude with the acoustics experiment. These deviations in the magnitude are due to limitations of the CAA model in ANSYS FLUENT as stated in the Section 3.2.
Nevertheless, focusing on the prediction patent, it can be stated that the CAA model can be accepted and suitable for further analysis. 5. Flow field analysis of centrifugal fan with diffuser vanes This section presents the results and discussion on the flow field behaviour within the centrifugal fan with diffuser vanes. Based on the validated CFD model, Fig. 7 presents radial velocity contour of outflow from the impeller. It can be observed that the outflow from the impeller consists of low velocity and high velocity zones. The low velocity zone occurs at the shroud-suction side of the impeller blade. Meanwhile, the high velocity zone occurs at the hubpressure side of the impeller blade. This distorted flow patterns of high and low energy leads to non-uniform flow at the impeller outflow. These non-uniform outflows are also known as jet-wake phenomenon. Due to the centrifugal forces, low momentum fluid accumulates in the shroud-suction side. This causes the impeller outflow to develop a low velocity zone (wake) at the suction side and high velocity zone (jet) at the pressure side [40,41]. Fig. 8 presents the velocity profile of the impeller outflow with increasing radial distance from the impeller outlet. By referring to Fig. 8, high velocity occurs at the hub side of the impeller and reduces as it reaches the shroud side of the impeller. The velocity is lower near the hub and the shroud surfaces of the impeller due to the effect of fluid viscosity which resists the fluid motion. Furthermore, it is important to realise that as the radial distance from the impeller outlet (51.5 mm) increases, the velocity profile becomes much more uniform. The velocity profile does not exhibit much change from 54.5 mm onwards. Fig. 9 presents the contour of static pressure at the hub and shroud side of the diffuser vane leading edge. It is clear that high strength interaction occurs at the hub side of the diffuser vane compared to the shroud side. The uneven interaction strength is due to the non-uniform outflow from the impeller where the hub side encounters stronger impingement from the high velocity outflow meanwhile the shroud side only encounters impingement from the low velocity outflow. These interactions cause unsteady pressure fluctuation at the leading edge of the diffuser vane. Fig. 10 shows the averaged pressure fluctuation on the leading edge of diffuser vane for one revolution. Based on Fig. 10, it can be observed that the unsteady pressure fluctuation generated at the leading edge is periodic over time and one can also notice that there are 11 peaks for one period of rotation, 0.00174 s. These 11 peaks represent the number of blade impellers and each of the pressure fluctuation periods corre-
Fig. 7. Radial velocity contour at impeller outlet.
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sponds to the BPF. This is because as the impeller blade approaches the leading edge of the diffuser vane, the amplitude of pressure increases and as the blade moves away from the diffuser vane lead-
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ing edge, the amplitude of pressure decreases. The rise and drop in the pressure amplitude at the leading edge of diffuser vane is shown as sequence in Fig. 11.
Fig. 8. Velocity profile of the impeller outflow with increasing radial distance from impeller outlet.
Fig. 9. Static pressure contour at the leading edge of diffuser vane(a) Hub side (b) Shroud side.
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Fig. 10. Pressure fluctuation at the leading edge of diffuser vane for one period of rotation from CFD.
Position 1
Position 2 Fig. 11. Static pressure contour as the impeller blade approaches leading edge of diffuser vane.
These periodic fluctuations of pressure will lead to the generation of tonal noise at BPF. Since dipole noise source is associated with the fluctuation of forces generated by the time varying pressure distributions, the tonal noise source identified is a dipole type noise source. 6. Case study The presented methodology on tonal noise prediction was then adopted to study the effect of replacing the diffuser vane with guide vane and tapered guide vane as part of tonal noise reduction
strategy. The geometrical schematic and characteristics of the vanes are shown in Fig. 12 and Table 4, respectively. The guide vane was designed by taking into account the slip factor which reflects the actual absolute velocity angle of the impeller outflow. This leads to the leading edge angle of the guide vane to be 14.14° compared to 2.8° of the diffuser vane. The guide vane was further reshaped by tapering its leading edge with inclining angle from the shroud to hub. Detailed information on design methodology of the guide vane and the tapered guide vane are presented in Paramasivam et al. [23,24].
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Fig. 12. Geometrical schematic of (a) Guide vane (b) Tapered guide vane (c) Diffuser vane.
Table 4 Geometrical characteristics of the guide vane, tapered guide vane and diffuser vane. Descriptions Radius of blade inlet (mm)
Shroud Hub
Angle of blade inlet (°) Radius of blade exit (mm) Angle of blade exit (°) Number of blade
Guide vane
Tapered guide vane
Diffuser vane
53 53 14.14 62.5 13.8 15
53 54.5 14.14 62.5 13.8 15
53 53 2.8 62.5 19.8 15
Table 5 Predicted aerodynamic performance of the investigated prototypes.
u w
Pt;t
Diffuser vane
Guide vane
Tapered guide vane
0.129 0.594 1.125
0.128 0.598 1.128
0.130 0.580 1.125
Fig. 13. Comparisons of the predicted tonal noise SPL for the investigated vanes.
6.1. Numerical prediction results for guide vane and tapered guide vane By employing the validated numerical model, the predicted aerodynamic and acoustics of both the guide vane and tapered guide vane are evaluated against the diffuser vane. Table 5 presents the predicted aerodynamic performance comparison, where
it can be established that both the guide vanes have similar performance with the diffuser vane. In term of acoustics, the predicted tonal noise SPL for both the guide vane and tapered guide vane are evaluated against the diffuser vane, as shown in Fig. 13. It can be seen that the guide vane design exhibits SPL reduction at 1st and 3rd BPF. Meanwhile, tapered guide vane shows SPL reductions in all 1st, 2nd and 3rd BPF. These reductions in the tonal noise are related to the reduction in the pressure fluctuations at the leading edge of the vanes as shown in Fig. 14. Referring to Fig. 14, pressure fluctuations at both the guide vane and tapered guide vane are lower compared to the diffuser vane. Lowest pressure fluctuations are generated at the leading edge of the tapered guide vane. Fig. 15 presents the comparisons of static pressure contour on the leading edge of the investigated vanes. It can be observed that the static pressure distribution on the leading edge of diffuser vane has a comparable profile as the radial velocity profile presented in Fig. 8. The static pressure distribution on the leading edge of guide vane is lower compared to the leading edge of diffuser vane. The reason being is by taking account the slip factor; the incidence angle of the flow at guide vane leading edge is coherence with the outflow from impeller. The flow pressure distribution is more even at this incidence angle as shown in Fig. 15. This indicates that by designing vane leading edge corresponding to the actual absolute flow angle leads to reduction in the impingement of the outflow. By further referring to Fig. 15, the tapered guide vane exhibits low and uniform static pressure distribution on its leading edge. This is because since the leading edge of the tapered guide vane is inclined from shroud to hub, the radial distance at the hub from the impeller trailing edge is larger. Thus, the impingement strength of the high velocity outflow onto the leading edge of the tapered guide vane at the hub side is lower. This leads to a more uniform impingement. Based on these numerical results, reduction in tonal noise at fundamental BPF and its harmonics are expected for both
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Fig. 14. Averaged pressure fluctuation at the vane’s leading edge for one period of rotation.
Fig. 15. Static pressure contour on the leading edge (a) diffuser vane, (b) guide vane and (c) tapered guide vane.
Fig. 16. Geometrical comparison of fabricated (a) tapered guide vane and (b) diffuser vane.
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phenomenon inside the impeller. The interaction leads to unsteady pressure fluctuation which is periodic over time. The periodic pressure fluctuation corresponds to the BPF of the impeller which then generates tonal noise.
Acknowledgement This work was supported by Universiti Teknologi Malaysia through Grant VOT 4L174 and the acoustic experiment in anechoic chamber facility was conducted through the support of Energy Research Institute (ERI@N), Nanyang Technological University, Singapore.
References Fig. 17. Tonal noise SPL of diffuser vane and tapered guide vane from acoustics experiment.
Table 6 Comparison of aerodynamic performance between diffuser vane and tapered guide vane.
Diffuser vane Tapered guide vane Difference (%)
u
w
Pt;t
0.136 0.135 0.7
0.604 0.612 1.3
1.129 1.131 0.2
the guide vane and tapered guide vane. Since the tapered guide vane exhibits the highest reduction in tonal noise, it is chosen to be fabricated and experiment was conducted to validate the predictions. Fig. 16 shows the image of the fabricated tapered guide vane in comparison to the diffuser vane. 6.2. Experimental results of tapered guide vane The acoustics and aerodynamic experimental results for the tapered guide vane are presented in this section. The tonal noise SPL of the tapered guide vane in comparison with the diffuser vane is shown in Fig. 17. It can be seen that the tapered guide vane exhibits reduction in the tonal noise at the BPF and its harmonics as predicted by the numerical modelling. Tonal noise is reduced by 6.8 dB at the fundamental BPF, where else reduction of 4.1 dB and 17.5 dB for its 2nd and 3rd harmonics is achieved respectively. In terms of the centrifugal fan with tapered guide vane, it only exhibits maximum difference of 1.3% compared to the centrifugal fan with diffuser vane as illustrated in Table 6. This indicates that the aerodynamic performance of the centrifugal fan is not affected by adopting the tapered guide vane. 7. Conclusion In this work, a methodology has been established to reduce the air flow induced noise generation in high speed centrifugal fan. The focus was given on the tonal noise generated in the centrifugal fan. 3-D computational fluid dynamics (CFD) models were used to provide details on the flow field behaviour within the centrifugal fan and also to identify the tonal noise sources. Aerodynamic and acoustics experimental work was conducted to validate the information obtained from the numerical models. The analysis on the flow field characteristics with the validated CFD model shows that the tonal noise generation is due to the interaction of the nonuniform outflow from the impeller with the leading edge of the diffuser vane. The non-uniform outflow occurs due to the jet-wake
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[24] Paramasivam K, Rajoo S, Romagnoli A. Suppression of tonal noise in a centrifugal fan using guide vanes. J Sound Vib 2015;357. http://dx.doi.org/ 10.1016/j.jsv.2015.07.003. [25] ISO 5167-1. Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full—Part 1: general principles and requirements. Int Stand Organ 2003:24. http://dx.doi.org/ 10.1016/S0378-7753(02)00712-7. [26] ISO 5167-2. Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full – Part 2: orifice plates. Int Stand Organ 2003:24. [27] ISO-3745, Acoustics—determination of sound power levels and sound energy levels of noise sources using sound pressure—precision methods for anechoic rooms and hemi-anechoic rooms using sound pressure—precision methods for reverberation test rooms, ISO, Int. Stand. Organ; 2012. [28] Khelladi S, Kouidri S, Bakir F, Rey R. Flow study in the impeller-diffuser interface of a vaned centrifugal fan. J Fluids Eng 2005;127:495. http://dx.doi. org/10.1115/1.1900138. [29] Xu C, Chen L, Lu X. Large-Eddy and Detached-Eddy simulations of the separated flow around a circular cylinder. J Hydrodyn Ser B 2007;19:559–63. http://dx.doi.org/10.1016/S1001-6058(07)60153-X. [30] Spalart PR. Detached-Eddy simulation. Annu Rev Fluid Mech 2009;41:181–202. http://dx.doi.org/10.1146/annurev.fluid.010908.165130. [31] Spalart PR, Jou WH, Strelets M, Allmaras SR. Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. In: Adv. DNS/LES; 1997. p. 4–8.
[32] Travin A, Shur M, Strelets M, Spalart P. Detached-Eddy simulations past a circular cylinder. Flow Turbul Combust 2000;63:293–313. http://dx.doi.org/ 10.1023/A:1009901401183. [33] Ansys, ANSYS FLUENT Theory Guide; 2011. [34] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 1994;32:1598–605. http://dx.doi.org/10.2514/3.12149. [35] Borges SS, Zdanski PSB, Barbieri R. A hybrid analytical/experimental model for evaluation of the aerodynamic noise in fans. Appl Acoust 2015;90:81–7. http://dx.doi.org/10.1016/j.apacoust.2014.11.007. [36] De Gennaro M. Computational fluid dynamics and computational aeroacoustics for turbomachinery applications with emphasis on high speed propellers and vertical axis wind. Università Degli Studi Di Napoli Federico II; 2010. ,
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Tonal noise prediction in a small high speed centrifugal fan and experimental validation Kishokanna Paramasivam a, Srithar Rajoo b, Alessandro Romagnoli c,⇑, Wira Jazair Yahya a a
Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia UTM Centre for Low Carbon Transport in Cooperation with Imperial College London, Universiti Teknologi Malaysia, Johor, Malaysia c Nanyang Technological University, School of Mechanical & Aerospace Engineering, 50 Nanyang Drive, Singapore b
a r t i c l e
i n f o
Article history: Received 13 July 2016 Received in revised form 2 April 2017 Accepted 11 April 2017
Keywords: Centrifugal fan Aeroacoustics Tonal noise Jet-wake flow Aerodynamic noise prediction
a b s t r a c t This paper presents the work done to establish a methodology that is capable of predicting tonal noise generation in high speed centrifugal fans. The deliverables from this work emphasize on identifying and characterizing the source of tonal noise in the centrifugal fan. Computational fluid dynamics (CFD) modeling was performed using 3-D Detached Eddy Simulation (DES) to compute the unsteady flow field in the fan. The calculated time history of surface data from the CFD is then used in Ffowcs WilliamsHawkings (FW-H) solver to predict the far field noise levels. The predicted aerodynamics and aeroacoustics results are in good agreement with the experimental data acquired from the flow testing facility and the anechoic chamber. The study conducted on the centrifugal fan shows that the aerodynamic interaction between the non-uniform impeller outflow and the leading edge of the diffuser vane is the source of tonal noise generation. The impingement of the jet-wake flow structure from the impeller outflow causes periodical pressure fluctuation on the leading edge of the diffuser vanes which leads to the tonal noise generation at the blade passing frequency (BPF). Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The wide range application of turbomachines has led to intensive research and development towards improving its efficiency in designing highly efficient turbomachines. Most of the turbomachines operate at high rotational speed in order to fulfil the power output requirement for its given size. It is well established through many previous studies that the flow field in turbomachines are highly unsteady [1]. Hence, increase in rotational speed causes more turbulence, large scale of velocity and pressure fluctuation which in turn generates higher noise level. The flow induced noise from turbomachines is generally characterized by broadband noise with prevailing discrete frequency tones. Among these two, the discrete frequency tones or also known as tonal noise is the most noticeable in sound spectrum compared to the broadband noise [2–8]. According to Raitor and Neise [9], the aerodynamic power output of a turbomachine is proportional to the cube of its rotational speed where else the aeroacoustics noise level rises in the fifth to sixth order. This relationship raises concern among researchers that it is necessary to consider aeroacoustics noise control measures during the design stage of ⇑ Corresponding author. E-mail address: [email protected] (A. Romagnoli). http://dx.doi.org/10.1016/j.apacoust.2017.04.009 0003-682X/Ó 2017 Elsevier Ltd. All rights reserved.
turbomachines. Furthermore, it is also important that noise sources in the turbomachines are identified and characterized in order to implement suitable noise control techniques. As stated by Lee et al. [10], the best solution in reducing noise generation is to identify the noise source and completely understand its mechanism. Earlier works in predicting flow induced noise in turbomachines were more focused on theoretical and experimental studies. One of the earliest theoretical formulations established in predicting noise from rotating machinery was the FW-H equation by Ffowcs Williams and Hawkings in 1969 [11]. The FW-H equation is an extension of the acoustic analogy developed by Sir James Lighthill which focuses on prediction of noise generated by the jet of an aircraft turbojet engine [12,13]. This extension to the acoustic analogy includes the dipole and monopole source distributions. In term of experiments, studies were conducted by making geometrical changes to the turbomachines and determining its effect on the noise generation. A very comprehensive review summarising all the research work done from 1960 to 1975 in the effort to reduce tonal noise from centrifugal fan was presented by Neise [3]. Neise and Koopmann [14,15] then experimentally studied a noise reduction method for centrifugal fan using acoustics resonator. Dong et al. [16] used particle image velocimetry (PIV), surface pressure and noise measurement to study the effects of modifying the
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Nomenclature b2 c0 d2 Fi H n p0 P Q r t T ij U u2 xi xj Z
Pt;t
R
dðf Þ
blade width at discharge (m) speed of sound ðm s1 Þ blade diameter (m) force acting on fluid (N) Heaviside function impeller rotational speed (rpm) sound pressure (Pa) pressure (Pa) volume flow rate ðm3 s1 Þ radius (m) time (s) Lighthill’s tensor flow velocity impeller peripheral speed ðm s1 ) cartesian coordinates of the observer (m) cartesian coordinates of the source (m) number of blade total to total pressure ratio relative error Dirac-delta distribution
cut-off tongue and impeller geometries on the flow structure, local pressure fluctuation and noise. Nonetheless, with the advancement in computational technology, numerical simulations such as computational fluid dynamics (CFD) and computational aeroacoustics (CAA) enable noise prediction in turbomachinery to be more feasible. Thus through the combination of experimental work and numerical simulation, deeper understanding on the unsteady flow field and the aerodynamic noise generation mechanism in turbomachinery can be achieved [17]. Jeon et al. [5] introduced an incompressible two dimensional discrete vortex method (DVM) to analyse the unsteady flow field of centrifugal fan. Then, using the calculated unsteady force data in the fan flow region, the noise radiations are predicted through FW-H equation. A two-part paper was then published by Langthjem and Olhoff [18,19] to study the flow induced noise phenomenon in a two-dimensional centrifugal pump where they adopted the DVM to estimate the strength of the dipole sources due to the unsteady surface force. In order to predict the noise generation within the volute of the centrifugal pump, they employed the newly developed boundary element method (BEM). In order to further improve understanding of the noise generation in an unsteady flow field, Liu et al. [20], Ballesteros-Tajadura et al. [6], Khelladi et al. [21], and Mao et al. [22] performed three-dimensional numerical calculations on centrifugal fan. They employed Reynolds Averaged Navier-Stokes (RANS) calculation to solve the unsteady flow of the centrifugal fan and the aeroacoustics modelling was performed using the FW-H equation. The results from their investigations provide better qualitative predictions compared to the twodimensional results presented by previous researchers. Despite the knowledge accumulated over the past few decades on the noise generation mechanism in centrifugal turbomachines, the prediction of noise generation in such complex flow is still difficult especially in high speed turbomachinery and requires much deeper understanding. In this paper, a methodology that is capable of identifying and characterising the tonal noise source in a high speed centrifugal fan is presented. This paper is an advancement of the previously published papers by Paramasivam et al. [23,24] which focuses on the reduction of tonal noise through the application of guide vane and tapered guide vane.
q u
air density flow coefficient total pressure coefficient generic variables viscosity
w
u l
Subscripts t total Abbreviations BEP best efficiency point BPF blade passing frequency CFD computational fluid dynamics CAA computational aeroacoustics dB decibel dB(A) A-weighting decibel SPL sound pressure level
The centrifugal fan adopted for this study mainly consists of an impeller with 11 blades, diffuser vanes, a circular casing and a universal motor as shown in Fig. 1. The aerodynamic and the geometrical characteristics of the centrifugal fan are presented in Tables 1 and 2. 2. Experimental methodology 2.1. Aerodynamic performance measurement In order to obtain the aerodynamic performance of the centrifugal fan, a flow bench as shown in Fig. 2 was setup. A straight PVC pipe was fitted at the inlet of the centrifugal fan and an orifice plate which was designed in accordance to ISO 5167-1 and ISO 5167-2 [25,26] was installed at the mid-point. The flow rate of the centrifugal fan was obtained based on the static pressure difference across the orifice plate using U-tube manometer. Pressure transducers are flushed mounted at the inlet of centrifugal fan, exit of the impeller and the exit of diffuser – to measure static pressures across the centrifugal fan. Fig. 3 shows the location of pressure transducers on the centrifugal fan. In addition to the pressure measurement, the temperature of the air flow was also measured simultaneously. Furthermore, an inductive proximity sensor was used to measure the impeller rotational speed which corresponds to the universal motor speed. The following uncertainties were established for the measured and calculated magnitudes: I. II. III. IV.
U-Tube Manometer: ±19.6 Pa Pressure Transducer: ±1.7 kPa Inductive Proximity Sensor: ±5% K-type Thermocouple: ±2.2 °C
Since the centrifugal fan constantly operates at its best efficiency point (BEP), only one operating speed was considered in this work. The measured rotational speed was 34,560 RPM and since the number of blade is 11, thus the blade passing frequency (BPF) of the centrifugal fan would be 6336 Hz. The BPF can be determined using Eq. (1):
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Fig. 1. Exploded view of the centrifugal fan.
BPF ¼ Table 1 Aerodynamic performance characteristics of the centrifugal fan. Descriptions
Value
Rotational speed Flow rate
34,560 (rev= min) 0.0479 (m3 =s)
Table 2 Geometrical characteristics of the centrifugal fan. Descriptions Radius of blade inlet (mm) Angle of blade inlet (°) Radius of blade exit (mm) Angle of blade exit (°) Number of blades
Shroud Hub
Impeller
Diffuser Vane
18 18 9.2 51.5 32.18 11
53 53 2.8 62.5 19.8 15
nrpm Z blade 60
ð1Þ
2.2. Acoustics measurement In this research work, the sound pressure level of the centrifugal fan was determined based on the guideline provided in ISO-3745, (2012). The acoustics measurement was conducted in a full anechoic chamber located at Nanyang Technological University, Singapore (NTU). The dimension of the anechoic chamber is 4:0 m 5:0 m 3:0 m and the cut-off frequency is 230 Hz. The sound pressure level (SPL) of the centrifugal fan is measured by using GRAS 46AE Free-Field ½ Preamplifier microphone which has frequency range of 3.15 Hz to 20 kHz. The uncertainty of the microphone is ±1dB (5 Hz – 10 kHz) and ±2 dB (3.15 Hz – 20 kHz). The microphone was calibrated using Larson Davis CAL200 acoustics calibrator which has an uncertainty of ±0.2 dB. Before performing an acoustics measurement, it is important to determine the position of the microphone. If an acoustics measure-
Fig. 2. Schematic diagram of centrifugal fan flow bench.
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Fig. 3. Location of pressure transducers on centrifugal fan.
ment is conducted in the region closer to the source, the accuracy of the measurement will be low. This is because in near field, the sound pressure and acoustics particle velocity will not be in phase, thus the propagation of the sound wave will be unstable. The position of the microphone is dependent on the radius of the measurement surface. Measurement surface is a hypothetical surface of area on which the microphone is located and enveloping the noise source under test. For the current study, hemispherical measurement surface was opted since the centrifugal fan was placed on the floor of the anechoic chamber. ISO-3745 [27] recommends that the radius of the measurement surface should be either 1 m or twice the largest dimension of the source under test. For the current acoustics measurement, the radius of the measurement surface was decided to be 1 m as shown in Fig. 4. 3. Numerical modeling 3.1. Computational fluid dynamics (CFD) modelling This section presents the overview of the computational fluid dynamic (CFD) modeling using ANSYS FLUENT. The fundamental of CFD is that it solves the partial differential flow equations mainly the conservation of mass and conservation of momentum. Conservation of mass is shown in Eq. (2) and Eq. (3) defines the conservation of momentum.
@q þ r ðqUÞ ¼ 0 @t
q
DU ¼ rp þ lr2 U Dt
ð2Þ ð3Þ
Fig. 4. Sound pressure level measurement of centrifugal fan at NTU anechoic chamber.
The computation domain for CFD consists of 5 fluid domains: the upstream inlet, the gap between the casing and impeller, the impeller, the volute and the downstream outlet. Some of the geometries are simplified in the fluid domain in order to improve the mesh quality and reduce the computing time. Furthermore, the inlet and outlet domains are extended in order to allow the flow to be fully developed. The entire 5 fluid domains are attached through non-conformal interfaces. Hybrid meshing technique is adopted: tetrahedral for the impeller and the diffuser channels volumes, hexahedral for the upstream and downstream fluid volumes. Similar meshing technique was employed by Khelladi et al. [28] in their study. The total number of mesh elements of the centrifugal fan model is 4:6 106 . Fig. 5 shows the representation of the 3D model, fluid domain and the meshed fluid domain. The turbulence model employed for the CFD was SST k x variant of the Detached Eddy Simulation (DES) due to its capabilities in resolving eddies for noise prediction. DES approach combines the advantages of RANS and LES, in which the model is not as demanding as LES formulation, thus reducing the computational time [29– 31]. According to Travin et al. [32], DES functions as a subgrid-scale model in regions where the grid density is fine enough for LES and as a RANS model in regions where it is not. Moreover, DES models have been specifically designed to address high Reynolds number wall bounded flows [33]. It is also important to state that the SST model interchanges between k e variant in the core flow region and the k x variant near the walls [34]. Borges et al. [35] stated that the SST model provides good prediction for experimental validations. In terms of boundary conditions, the inlet is defined as ‘‘total pressure inlet” and at the downstream outlet is specified as ‘‘static pressure outlet”. The value for the inlet is defined based on the experimental results conducted on the centrifugal fan. As for the outlet, since the air flow from the centrifugal fan is discharged to the ambient it is assigned as atmospheric pressure. The impeller fluid domain is defined as ‘‘moving mesh” and the rotational speed is set as 34,560 rpm as per the experiment. For the surfaces that rotate, ‘‘moving wall” is assigned. This technique is known as sliding mesh method (SLM). The SLM introduces rotation by assigning the rotational component of velocity to all the nodes in the domain. Gennaro [36] stated that in order to perform timedependent simulation involving turbomachinery application, the SLM technique is the most suitable and accurate. The SLM is based on relative motion of two domains/cell zones where these domains are bounded by at least one ‘‘interface” boundary condition. The interface is a surface where the fluid variables are transported from one zone to the other. The RANS equation is solved in each cell zone and fluxes are computed at each time step [33,36]. As the rotating domain changes positions at each time step, the previ-
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Fig. 5. Representation of 3-D model, fluid domain and meshed fluid domain.
ously calculated fluxes are recomputed. Every time step is set to represent 1° rotation of the impeller. Hence, it will take 360 time steps to complete one revolution. 3.2. Computational aeroacoustics modeling The noise prediction in the centrifugal fan was carried out using hybrid CAA which is based on the Ffowcs-Williams and Hawkings (FW-H) formulation. The use of the FW–H equation allows the noise sources to be separated into monopole, dipole, and quadrupole [37]. The FW-H equation is written as in Eq. (4).
"
# 1 @ 2 p0 @ 2 p0 @ @ @2 2 ¼ ½Qdðf Þ ½F i dðf Þ þ ½T ij Hðf Þ @t @xi @xi @xj @xi c20 @t 2
ð4Þ
The three terms on the right side of Eq. (4) are known as monopole source, dipole source and quadrupole source respectively. The monopole sound source is associated with the fluid volume displacement due to the surface motions. The dipole source represents the sound generated due to the unsteady forces exerted by the moving surfaces where else the quadrupole source represents the sound generation by the volume distribution outside of the surfaces [11,20,21,37]. The solution at a far-field receiver location can be computed using the generalised function theory and the free-space Green’s function. The sound pressure at a far-field receiver location is given by Eq. (5). Detailed derivations of Eq. (5) can be found in work presented by Farassat [38]. The solution consists of surface and volume integrals. The surface integrals represents the contributions from the monopole and dipole sources, where else the volume integral represents the quadrupole source.
Z Q ðy; t jxyjÞ Z F i y; t jxyj c0 1 @ 1 @ c0 dS p0 ¼ dS jx yj jx yj 4pc20 @t S 4pc20 @xi S Z T ij y; t jxyj c0 1 @2 dV ð5Þ þ jx yj 4pc20 @xi @xj V with t jxyj = retardation time c0 jx yj = distance between source point and observer point
The sound pressure data at far-field receiver location are then obtained by post processing the output of Eq. (5) with Fast Fourier Transform (FFT) algorithm. The Sound Pressure level (SPL) is obtained with respect to the reference sound pressure as given by Eq. (6).
SPL ¼ 20log10
" # p0rms pref
ð6Þ
where pref ¼ 2 105 Pa The adopted method is integrated under the assumption of freespace and the absence of obstacles between the sound source and the receiver. Thus, the effects of scattering, diffractions, as well as the reflections of casing and blades are not considered [20,21,33]. The acoustics wave is also assumed to exert no forces on the fluid flow [39]. 4. Validation exercise Since most of the discussion is based on the CFD results, its validation with experiments is necessary in order to gain confidence on the accuracy of the simulation model. The performance parameters of the centrifugal fan obtained from the aerodynamic experiment are directly compared with the CFD results. The parameters used for validations are the flow coefficient u, total pressure coefficient w, and the total-to-total pressure ratio Pt;t as presented in Eqs. (7) – (9).
u¼ w¼
Q
ð7Þ
pb2 d2 u2 DP t 0:5qu22
ð8Þ
Pt;out P t;in
ð9Þ
Pt;t ¼
Comparisons between the measured experimental and CFD predicted results are presented in Table 3, in which the relative error, for the generic variables, is defined as in Eq. (10).
eR ð%Þ ¼
juCFD uEXP j
uEXP
100
ð10Þ
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Table 3 Comparison between experiment and CFD results for validation.
EXP CFD eR ð%Þ
u
w
Pt;t
0.136 0.129 4.86
0.604 0.594 1.67
1.129 1.125 0.35
Fig. 6. Comparison of tonal noise SPL between predicted and experiment for centrifugal fan.
Based on Table 3, it can be seen that the CFD model underpredicts the unsteady performance of the centrifugal fan. These deviations are probably due to the simplified geometry used to represent the universal motor in the 3-D modelling. In the experiment, the universal motor commutator rotates which provides momentum to the air flow. However, in the simulation the universal motor is defined as stationary in order to reduce the computing time. This causes the CFD to under predict the volume flow rate. Nonetheless, the small deviation (max <5%) between the prediction and experiment values indicates the CFD model can be utilized for further evaluation. Besides CFD model validation, the CAA model is also validated against the acoustics experiment. The comparison between the predicted tonal noise SPL and the results from the acoustics experiment is shown in Fig. 6. Based on the SPL, the predicted values show similar pattern and consistent deviation in terms of magnitude with the acoustics experiment. These deviations in the magnitude are due to limitations of the CAA model in ANSYS FLUENT as stated in the Section 3.2.
Nevertheless, focusing on the prediction patent, it can be stated that the CAA model can be accepted and suitable for further analysis. 5. Flow field analysis of centrifugal fan with diffuser vanes This section presents the results and discussion on the flow field behaviour within the centrifugal fan with diffuser vanes. Based on the validated CFD model, Fig. 7 presents radial velocity contour of outflow from the impeller. It can be observed that the outflow from the impeller consists of low velocity and high velocity zones. The low velocity zone occurs at the shroud-suction side of the impeller blade. Meanwhile, the high velocity zone occurs at the hubpressure side of the impeller blade. This distorted flow patterns of high and low energy leads to non-uniform flow at the impeller outflow. These non-uniform outflows are also known as jet-wake phenomenon. Due to the centrifugal forces, low momentum fluid accumulates in the shroud-suction side. This causes the impeller outflow to develop a low velocity zone (wake) at the suction side and high velocity zone (jet) at the pressure side [40,41]. Fig. 8 presents the velocity profile of the impeller outflow with increasing radial distance from the impeller outlet. By referring to Fig. 8, high velocity occurs at the hub side of the impeller and reduces as it reaches the shroud side of the impeller. The velocity is lower near the hub and the shroud surfaces of the impeller due to the effect of fluid viscosity which resists the fluid motion. Furthermore, it is important to realise that as the radial distance from the impeller outlet (51.5 mm) increases, the velocity profile becomes much more uniform. The velocity profile does not exhibit much change from 54.5 mm onwards. Fig. 9 presents the contour of static pressure at the hub and shroud side of the diffuser vane leading edge. It is clear that high strength interaction occurs at the hub side of the diffuser vane compared to the shroud side. The uneven interaction strength is due to the non-uniform outflow from the impeller where the hub side encounters stronger impingement from the high velocity outflow meanwhile the shroud side only encounters impingement from the low velocity outflow. These interactions cause unsteady pressure fluctuation at the leading edge of the diffuser vane. Fig. 10 shows the averaged pressure fluctuation on the leading edge of diffuser vane for one revolution. Based on Fig. 10, it can be observed that the unsteady pressure fluctuation generated at the leading edge is periodic over time and one can also notice that there are 11 peaks for one period of rotation, 0.00174 s. These 11 peaks represent the number of blade impellers and each of the pressure fluctuation periods corre-
Fig. 7. Radial velocity contour at impeller outlet.
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sponds to the BPF. This is because as the impeller blade approaches the leading edge of the diffuser vane, the amplitude of pressure increases and as the blade moves away from the diffuser vane lead-
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ing edge, the amplitude of pressure decreases. The rise and drop in the pressure amplitude at the leading edge of diffuser vane is shown as sequence in Fig. 11.
Fig. 8. Velocity profile of the impeller outflow with increasing radial distance from impeller outlet.
Fig. 9. Static pressure contour at the leading edge of diffuser vane(a) Hub side (b) Shroud side.
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Fig. 10. Pressure fluctuation at the leading edge of diffuser vane for one period of rotation from CFD.
Position 1
Position 2 Fig. 11. Static pressure contour as the impeller blade approaches leading edge of diffuser vane.
These periodic fluctuations of pressure will lead to the generation of tonal noise at BPF. Since dipole noise source is associated with the fluctuation of forces generated by the time varying pressure distributions, the tonal noise source identified is a dipole type noise source. 6. Case study The presented methodology on tonal noise prediction was then adopted to study the effect of replacing the diffuser vane with guide vane and tapered guide vane as part of tonal noise reduction
strategy. The geometrical schematic and characteristics of the vanes are shown in Fig. 12 and Table 4, respectively. The guide vane was designed by taking into account the slip factor which reflects the actual absolute velocity angle of the impeller outflow. This leads to the leading edge angle of the guide vane to be 14.14° compared to 2.8° of the diffuser vane. The guide vane was further reshaped by tapering its leading edge with inclining angle from the shroud to hub. Detailed information on design methodology of the guide vane and the tapered guide vane are presented in Paramasivam et al. [23,24].
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Fig. 12. Geometrical schematic of (a) Guide vane (b) Tapered guide vane (c) Diffuser vane.
Table 4 Geometrical characteristics of the guide vane, tapered guide vane and diffuser vane. Descriptions Radius of blade inlet (mm)
Shroud Hub
Angle of blade inlet (°) Radius of blade exit (mm) Angle of blade exit (°) Number of blade
Guide vane
Tapered guide vane
Diffuser vane
53 53 14.14 62.5 13.8 15
53 54.5 14.14 62.5 13.8 15
53 53 2.8 62.5 19.8 15
Table 5 Predicted aerodynamic performance of the investigated prototypes.
u w
Pt;t
Diffuser vane
Guide vane
Tapered guide vane
0.129 0.594 1.125
0.128 0.598 1.128
0.130 0.580 1.125
Fig. 13. Comparisons of the predicted tonal noise SPL for the investigated vanes.
6.1. Numerical prediction results for guide vane and tapered guide vane By employing the validated numerical model, the predicted aerodynamic and acoustics of both the guide vane and tapered guide vane are evaluated against the diffuser vane. Table 5 presents the predicted aerodynamic performance comparison, where
it can be established that both the guide vanes have similar performance with the diffuser vane. In term of acoustics, the predicted tonal noise SPL for both the guide vane and tapered guide vane are evaluated against the diffuser vane, as shown in Fig. 13. It can be seen that the guide vane design exhibits SPL reduction at 1st and 3rd BPF. Meanwhile, tapered guide vane shows SPL reductions in all 1st, 2nd and 3rd BPF. These reductions in the tonal noise are related to the reduction in the pressure fluctuations at the leading edge of the vanes as shown in Fig. 14. Referring to Fig. 14, pressure fluctuations at both the guide vane and tapered guide vane are lower compared to the diffuser vane. Lowest pressure fluctuations are generated at the leading edge of the tapered guide vane. Fig. 15 presents the comparisons of static pressure contour on the leading edge of the investigated vanes. It can be observed that the static pressure distribution on the leading edge of diffuser vane has a comparable profile as the radial velocity profile presented in Fig. 8. The static pressure distribution on the leading edge of guide vane is lower compared to the leading edge of diffuser vane. The reason being is by taking account the slip factor; the incidence angle of the flow at guide vane leading edge is coherence with the outflow from impeller. The flow pressure distribution is more even at this incidence angle as shown in Fig. 15. This indicates that by designing vane leading edge corresponding to the actual absolute flow angle leads to reduction in the impingement of the outflow. By further referring to Fig. 15, the tapered guide vane exhibits low and uniform static pressure distribution on its leading edge. This is because since the leading edge of the tapered guide vane is inclined from shroud to hub, the radial distance at the hub from the impeller trailing edge is larger. Thus, the impingement strength of the high velocity outflow onto the leading edge of the tapered guide vane at the hub side is lower. This leads to a more uniform impingement. Based on these numerical results, reduction in tonal noise at fundamental BPF and its harmonics are expected for both
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Fig. 14. Averaged pressure fluctuation at the vane’s leading edge for one period of rotation.
Fig. 15. Static pressure contour on the leading edge (a) diffuser vane, (b) guide vane and (c) tapered guide vane.
Fig. 16. Geometrical comparison of fabricated (a) tapered guide vane and (b) diffuser vane.
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phenomenon inside the impeller. The interaction leads to unsteady pressure fluctuation which is periodic over time. The periodic pressure fluctuation corresponds to the BPF of the impeller which then generates tonal noise.
Acknowledgement This work was supported by Universiti Teknologi Malaysia through Grant VOT 4L174 and the acoustic experiment in anechoic chamber facility was conducted through the support of Energy Research Institute (ERI@N), Nanyang Technological University, Singapore.
References Fig. 17. Tonal noise SPL of diffuser vane and tapered guide vane from acoustics experiment.
Table 6 Comparison of aerodynamic performance between diffuser vane and tapered guide vane.
Diffuser vane Tapered guide vane Difference (%)
u
w
Pt;t
0.136 0.135 0.7
0.604 0.612 1.3
1.129 1.131 0.2
the guide vane and tapered guide vane. Since the tapered guide vane exhibits the highest reduction in tonal noise, it is chosen to be fabricated and experiment was conducted to validate the predictions. Fig. 16 shows the image of the fabricated tapered guide vane in comparison to the diffuser vane. 6.2. Experimental results of tapered guide vane The acoustics and aerodynamic experimental results for the tapered guide vane are presented in this section. The tonal noise SPL of the tapered guide vane in comparison with the diffuser vane is shown in Fig. 17. It can be seen that the tapered guide vane exhibits reduction in the tonal noise at the BPF and its harmonics as predicted by the numerical modelling. Tonal noise is reduced by 6.8 dB at the fundamental BPF, where else reduction of 4.1 dB and 17.5 dB for its 2nd and 3rd harmonics is achieved respectively. In terms of the centrifugal fan with tapered guide vane, it only exhibits maximum difference of 1.3% compared to the centrifugal fan with diffuser vane as illustrated in Table 6. This indicates that the aerodynamic performance of the centrifugal fan is not affected by adopting the tapered guide vane. 7. Conclusion In this work, a methodology has been established to reduce the air flow induced noise generation in high speed centrifugal fan. The focus was given on the tonal noise generated in the centrifugal fan. 3-D computational fluid dynamics (CFD) models were used to provide details on the flow field behaviour within the centrifugal fan and also to identify the tonal noise sources. Aerodynamic and acoustics experimental work was conducted to validate the information obtained from the numerical models. The analysis on the flow field characteristics with the validated CFD model shows that the tonal noise generation is due to the interaction of the nonuniform outflow from the impeller with the leading edge of the diffuser vane. The non-uniform outflow occurs due to the jet-wake
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