Aerodynamic noise prediction of a centrifugal fan considering the volute effect using IBEM

Applied Acoustics 132 (2018) 182–190

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Aerodynamic noise prediction of a centrifugal fan considering the volute effect using IBEM

T

⁎

Chen Jiana, He Yuanb, Gui Lib, Wang Canxingb, , Chen Liua, Li Yuanruib a b

School of Energy and Power Engineering, University of Shanghai for Science and Technology, 200093 Shanghai, China Institute of Fluid Engineering, Zhejiang University, 310027 Hangzhou, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Centrifugal fan Noise Dipole source LES Indirect boundary element method Volute

Customer demands for quieter centrifugal fans in the industry have brought their noise to the forefront. It is found that dipole sources on the surfaces of the rotating impeller and volute are the main acoustic noise sources. The volute effect is seen to have a significant influence on the radiation characters of the fan, although this is frequently ignored by previous studies. Hence, the indirect boundary element method (IBEM) is employed to study the noise of an industrial forward-curved centrifugal fan and to take the effect of volute reflection and scattering of the sound wave into consideration. A large eddy simulation (LES) is used to gain reliable pressure fluctuations on the surfaces of volute and rotating blades. Then the FW-H equation and Lowson equation are applied to calculate the dipole sources on the surfaces of the volute and the blades respectively. The predicted aerodynamic noise of the fan with and without the volute is compared to experiment. The results indicate that the pressure fluctuations on the volute surfaces, especially on the tongue surface, are the main dipole source. It is also found that the application of IBEM can improve the prediction accuracy greatly, especially for the blade passing frequency and its higher harmonics.

1. Introduction The centrifugal fan is widely used both in industries and civil engineering as a ventilation, dust removing, and cooling device. A lot of attention has been paid to the fan noise problem due to the growing demand for reducing noise levels and rigorous noise regulations [1]. Hence, there is a rich history of research involved in the study of centrifugal fan noise. Compared to the experimental method, computational aero-acoustic (CAA) is becoming more and more popular in engineering applications due to the rapid development of the computer science [2]. Generally, the acoustic calculation methods can be categorized into three types, exclusively numerical approaches, exclusively analytical approaches, and hybrid methods [3]. Exclusively numerical approaches solve full nonlinear Navier-Stokes equations to compute the hydrodynamic sources as well as to predict the propagation of acoustic fluctuations to the observer. Those exclusively numerical approaches usually require tremendous computer resources to capture small acoustic fluctuations in large computational domain [4]. The second way to study the acoustic problems is the exclusively analytical approaches, especially the acoustic analogy which separates the propagation of the acoustic disturbances from the sources of these

⁎

Corresponding author. E-mail address: [email protected] (C. Wang).

https://doi.org/10.1016/j.apacoust.2017.10.015 Received 22 July 2016; Received in revised form 9 October 2017; Accepted 10 October 2017 0003-682X/ © 2017 Published by Elsevier Ltd.

disturbances. The first acoustic analogy is proposed by Lighthill [5] in 1954, which rearranged the Navier-Stokes equations into a linear wave equation including the non-isentropic and viscous effects in the source terms. Many Lighthill’s analogy studies [6,7] ignored the viscous effect and isentropic behavior to simplify the stress tensor. There are also some of the extensions or reformations of Lighthill’s analogy, such as Curle’s analogy [8], Ffowcs-Williams and Hawking’s analogy [9], Goldstein’s analogy [10] and Howe’s vortex sound formulation [11]. It is difficult to find analytical expressions without introduction of simplifying assumptions for the realistic applications, especially for the applications whose source includes turbulence [3]. Thus, hybrid methods combine the strengths of the numerical and analytical approaches [12] are the most popular way to handle the realistic engineering problems. In general, the computational domain is split into two zones, one zone is in the near-field describing the source of the aerodynamic noise, another zone is the acoustic far-field describing the propagation of sound. Therefore, this method has two steps. In the first step, the CFD technology [13,14] is usually used to gain the unsteady near-field flow of the centrifugal fan. Most of the previous researches adopted the Reynolds-averaged Navier–Stokes (RANS) equations to simulate the unsteady flow field of fans and gain the sound generation in the near-field [15–19]. However, the RANS

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method has inherent limitations in predicting the unsteady nature of a flow field [20]. More recently, researchers have employed the LES [21–24] to get the relatively accurate pressure fluctuation because the LES can gained the large-scale separation much more accurately than RANS-based computation [25]. In the second step (far-field), the analogy theory is adopted to predict the aerodynamic noise based on the noise source extracted from the unsteady flow field [26,27]. Many research groups used the free-space Green’s function to predict the aerodynamic noise in free space. This function neglects the reflection and scattering effect of solid boundaries on the sound propagation. For centrifugal fan problems in particular, the reflection and scattering effect of the volute and blades should not be neglected. Therefore, the finite element method (FEM) and boundary element method (BEM) are introduced to consider this effect of the volute. The use of the finite element method for acoustics was initiated by Gladwell [28] and it has been applied in many engineering fields from the seventies [29,30]. It can easily deal with inhomogeneous domains. Generally, a large number of elements are needed to represent the oscillatory wave as the polynomial function can only represent a restricted spatial variation. According to a general rule of thumb, at least 10 elements per acoustic wavelength are required [31]. Hence, the application of the FEM for practical industry problems commonly involves large sizes of model and expensive computational efforts. Compared with the FEM, the size of matrices of BEM is substantially smaller than that of FEM due to the reduction in dimensionality of BEM. This reduction makes BEM a more practical numerical tool for the acoustic problem [32,33]. Many researchers have used the BEM to compute the noise of a centrifugal fan. Jeon et al. [26] simplify the structure of a centrifugal fan to one impeller and volute tongue without the volute casing. The Kirchhoff–Helmholtz BEM is used to simulate the noise reflection and scattering by the tongue and impeller. Langthjem and Olhoff [34] adopted the conventional BEM to analyze the sound radiation and scattering of a two-dimensional centrifugal pump. Polacsek et al. [16] used the BEM to simulate the interaction noise of a fan. All BEMs mentioned above are direct BEM which can only handle an interior or exterior acoustic problem with a closed boundary surface or thin-body separately. That is the reason why a lot of previous research was conducted without the consideration of the effect of volute reflection and scattering to the sound wave. Hence, some researchers proposed the imaginary surface [35] to construct a closed surface or a thin-body BEM [36] and take the scattering effect of the volute into consideration. Harwood and Dupere [31] used Dirichlet-to-Neumann (DtN) mapping operator to evaluate geometrically complex regions. Mao and Qi [37] employed the thin BEM to compute the rotating blade noise of a centrifugal fan scattered by volute. However, errors related to BEM were found. Those errors included the computing the influence coefficients, evaluation of the internal points near the boundary and the discretization. And the inclusion of the DtN added a new source of error into the BEM [3]. Different from the direct BEM, the IBEM can not only handle the combined interior/exterior problems but also deal with acoustic problems with an open boundary surface. Zhang et al. [38] employed the IBEM to compute the transfer considering the presence of openings and radiation from both sides of the piston type sources. The IBEM was also implemented to study the vibro-acoustics of an exhaust manifold acoustic radiation [39]. Another major advantage of the IBEM is that it can model the acoustic domains on both sides of a thin structure [40]. The computational domain of a centrifugal fan is a domain with opening and thin surfaces. Therefore, IBEM seems a very promising method to predict the aerodynamic noise of a centrifugal fan. In this paper, we adopted the LES turbulence model to gain the unsteady flow field of an industrial centrifugal fan with forward swept blades. Moreover, the FW-H equation and Lowson equation are employed to calculate the far-field noise by solving the free space Green’s function, and the IBEM is employed to study the noise radiation

Fig. 1. A 3D model of the fan.

considering the effect of the volute. 2. Description of the fan and numerical noise prediction model 2.1. Description of the centrifugal fan The industrial centrifugal fan studied in this paper consists of an impeller, a vaneless diffuser and a volute. In order to get a reliable flow field, the internal leakage between the impeller front shroud and volute is taken into account. Fig. 1 and Table 1 present the 3D model and detailed dimensions of this fan. The computational domain is separated into four parts, the inlet domain, the impeller domain, the volute domain and the outlet domain. Designed rotating speed is 2900 rpm and the design volumetric flow is 0.35 m3/s for this fan. According to the number of blades and rotating speed, the blade passing frequency (BPF) of the fan is 580 Hz. 2.2. Noise prediction procedure The inflow which generates the aerodynamic noise of the centrifugal fan is very complex. The noise source can be divided to monopole, dipole and quadrupole. The dipole caused by the pressure fluctuations on the blades and volute surface is the main source in a low Mach number fan [32]. The noise prediction procedure in this paper is shown in Fig. 2. This prediction procedure has two steps, the simulation of the flow field and the calculation of the noise and the detailed procedure will be discussed in the following paragraphs. 2.2.1. Simulation strategies of flow field 3D modeling, mesh generation, steady simulation and unsteady simulation are included in this part. 3D modeling was constructed with the parameters presented in Table 1. The model meshing is dominantly influenced by the turbulence model. A steady simulation was conducted firstly to reduce the computational cost and it offers a relatively reasonable initial flow field for the unsteady simulation. The RNG k-ε model is applied in this steady simulation to consider the effects of curvature, swirl and rotation [37]. A standard logarithmic wall function Table 1 Dimensions of the fan. Vaneless diffuser outlet diameter Impeller blade outlet diameter Impeller blade inlet diameter Impeller inlet diameter Impeller outlet width Impeller inlet width Blade thickness Blade number Blade inlet angle Blade outlet angle Volute width Distance between impeller and tongue Gap between impeller front shroud and volute

183

460 mm 400 mm 164 mm 155 mm 36 mm 70 mm 2.5 mm 12 38° 126° 64 mm 40 mm 2.7 mm

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Fig. 2. The noise prediction procedure.

simulated values is negligible. All of the simulated values are close to the testing value. Hence, the 4-million mesh number is used in the following case to capture more acoustic information. Fig. 4(a) presents the global view of the computational domain which contains totally 4110324 hexahedral elements. Fig. 4(b) gives a cut-plane view which is perpendicular to the fan rotating axial. The areas close to blade trailing edges and volute tongue are refined as well as some of small areas, such as the gap between impeller front shroud and gap between the impeller front shroud and inlet shown in Fig. 4(c) and (d), respectively. The boundary layer mesh was grown on the blade surfaces and showed in Fig. 4(c) to resolve the turbulent boundary layer properly. Table 2 summarizes the CFD strategies applied to the simulation of the steady and unsteady flow field in this paper. The boundary conditions of the steady and unsteady simulation are the same. The inlet velocity is uniformly distributed on the inlet surface, and the direction is perpendicular to the inlet surface, and the inlet turbulence intensity is 5 percent. The outlet boundary condition is set as static pressure outlet boundary condition which is the atmosphere pressure. And all the wall boundary conditions are regarded as no-slip conditions. The definition of the time step of the unsteady simulation is based on the consideration of convergence and the greatest noise frequency concerned. The rotation speed of the impeller is 2900 rpm and the constant time step is set to 4.04095e-5s. The number of iterations between two time steps is adjusted to achieve an acceptable residual value. The number of turns usually needs more than 10 to reach the stable periodic variation of performance parameters. The moving mesh is suitable for unsteady flow and convenient to transfer data between the interfaces of the rotating and stationary field. So, the moving mesh is used when the unsteady calculation is performed [35]. It is pointed out by Liu et al. [23] that the value of static pressure fluctuation rate can indicate the intensity of dipole aeroacoustics source. In order to investigate the sound dipole source of the impeller and volute, several groups of monitoring points are set up on the inner surfaces of the volute, volute tongue, blade pressure side and blade suction side, as showed in Fig. 5. Monitoring points V1, V2, V3, V4 and V5 are located on volute tongue surface; points s1, s2, s3 and p1, p2, p3 are located on the suction and pressure surface of blades, respectively.

is used. The turbulence model for the unsteady simulation is crucial to get a reliable flow field and the noise source, it is shown that the LES can be applied to obtain the surface pressure fluctuations accurately [37,41], and has a great promise for acoustic computations such as understanding of the noise generation and improvement of noise prediction model. Hence, the LES is used to simulate the unsteady flow. The time and space integration scheme is the second-order scheme. The dynamic Smagorinsky model (DSM) is applied as a sub-grid scale (SGS) model [37] to avoid the shortcoming of the standard Smagorinsky model. More details of the model implementation and its validation can be found in [42]. The scheme used to achieve a LES is FVM. The LES model has a very high requirement for grid quality, and there are some issues when employing unstructured grids, such as the effects of different grid topologies, and rapidly changing volumes [41]. Hence, the whole computational domain is discretized by the structured hexahedral elements. Mesh density on the blade surface is higher than the area far from blades. The mesh independent studies were also carried out using the unsteady solve for a case with six different total mesh numbers (about 1, 1.5, 1.7, 2, 3, and 4 million) at flow rate 21 m3/min. The simulation results are presented in Fig. 3 as well as the comparison with the experimental results. The difference between six

Fig. 3. Mesh-independence study.

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Fig. 4. Detailed mesh of fan: (a) Sketch of the fan structured mesh. (b) Mesh distribution at the middle span of impeller. (c) Mesh of gap between the volute tongue and impeller. (d) Mesh at the gap between the impeller front shroud and inlet.

Table 2 CFD strategies. Conditions

Steady method

Unsteady method

Turbulence model Rotation model Solving algorithm Discretization schemes Inlet condition Outlet condition Wall condition

RNG k-ε MRF SIMPLEC Second order upwind Velocity-inlet Pressure-outlet No slip condition

LES Sliding mesh

2.2.2. Numerical calculation theory for fan noise The FW-H equation and Lowson equation are employed to calculate the far-field noise by solving the free space Green’s function. And, the IBEM is adopted to calculate the sound pressure considering reflection and scattering of the volute.

Fig. 5. Monitoring points on volute tongue and impeller at the central cross section of the fan.

2.2.2.1. The acoustic analogy. The FW-H equation can be expressed as a type of inhomogeneous Helmholtz equation as follows [43]

∂2Tij 1 ∂ 2p ∂ 2p ∂⎛ ∂ − 2 = (pij nj δ (f ) ⎟⎞ + ⎜ρvj nj δ (f )− 2 2 ∂t ⎝ ∂x i ∂x i ∂x j ∂x i c0 ∂t ⎠

The free field sound pressure can be calculated by using free-space Green’s function to solve the Eq. (1)

(1)

p (x i,t ) =

where c0 is the sound velocity, p is far field sound pressure fluctuation, ρ is the density, δ (f ) is the Dirac δ function, where nj is the normal vector of the body surface, pij nj represents the normal force per unit area acting on the fluid. Tij is the Lighthill stress tensor.

(

(x i−yi )

(

(x − y ) 4πr 2c0 1− i r i

vi co

)

(x − yi ) vi co

⎡ ∂ 1− i r Fi ⎢ ∂Fi + 2 (x − y ) v ⎢ ∂t ∂t 1− i r i c i o ⎣

) ⎤⎥ ⎥ ⎦

Lighthill equation is extended to obtain Lowson equation [44] 185

(2)

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Fig. 6. Modeling of noise generated by one point force on blade. Fig. 7. Acoustic grid.

p (x i,t ) = Mi =

(xi − yi )

∂F ⎡ i 4πr 2c0 (1 − Mr )2 ⎣ ∂t

ui ,Mr c0

=

(xi − yi ) M |xi − yi | i

=

F ∂M + (1 − iM ) ∂t r ⎤ r ⎦τ (xi − yi ) M i r

(3)

Mi is the Mach number, Mr is the component of Mi in noise propagation direction. The Lowson formula, representing the dipole source on the impeller in frequency domain, can be obtained x inB2ω inωB → c0 p′inc (→ x ,nB ) = e 4πc0→ x

∞

π

ei (nB − m) (φ − 2 )·

∫∫ ∑ S

Fig. 8. Pressure transfer between CFD surfaces mesh and acoustic mesh.

m →−∞

⎧ ′ − m (kn→ i sin θJnB y sin θ) Fr (m) ⎨ ⎩ nB−m ⎫ → ⎤ +⎡ ⎢cos θFa (m)− nBM→ Ft (m) ⎥ JnB − m (kn y sin θ) ⎬ dS y ⎣ ⎦ ⎭

(4)

ω nc , 0

Fr (m) , Ft (m) and Fa (m) are where, B is the number of blades, kn ≡ components of Fourier coefficient in radial, axial and tangential direction, respectively, which can be obtained by Fourier series expansion →ω as shown in Fig. 6, M→ y = y c is the Mach number of rotating sound 0 source. When n = 1, it is corresponding to the fundamental frequency. 2.2.2.2. The acoustic boundary element mesh and receiving points. In order to decrease the noise simulation time, the pressure fluctuations on the inner side of the structured volute mesh is transformed to the acoustic boundary element mesh, see Fig. 7. There should be at least ten boundary elements per wave number, and the detailed discussion can be found in [45]. The Eq. (5) shows the interpolation method, and Fig. 8 shows the reference element used.

PA =

P1 (1/d1) + P2 (1/d2) + P3 (1/ d3) + P4 (1/ d4 ) (1/ d1) + (1/ d2) + (1/ d3) + (1/ d4 )

Fig. 9. Receiving points of noise directivity pattern.

(5) second order inhomogeneous Helmholtz equation is

As showed in [45], the analytical point of the sound spectrum is selected according to the Chinese national standard of noise measurement GBT2888-2008 (The noise measurement of the fan and roots Blower) [46]. The length between the analytical point and the central point of the fan outlet surface is 1 meter, and angle between the axis and the normal vector of the outlet surface is 45 degrees. In order to investigate the dipole sound pressure level (SPL) verse radiation angle, the noise receiving points are specified as shown in Fig. 9.

∇2 p + k 2p = −jρ0 ωq

(6)

where p is the far-field acoustic pressure, the ρ0 denotes the mean 2πf

ω

density, k = c = c is the acoustic wave number, c0 is the sound speed 0 0 in the medium and q is the dipole source which is expressed in the Eq. (1). The sound pressure contributed by the dipole source on either the volute or the rotating blade surface can be calculated by applying the Eq. (2), but the effect of scattering and the reflection by the volute are not considered. As we know, for the inhomogeneous acoustic problems, the total

2.2.2.3. The calculation model of volute acoustic radiation (IBEM). In recent years, the boundary element method has become a valuable modeling alternative for the acoustic pressure field calculation. The 186

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sound pressure p is the superposition of an inhomogeneous sound pressure pa and a homogeneous sound pressure pb

p = pa + pb

σ (rb) = 0,

(7)

σ (rb) = −jkβμ (rb),

pa is the sound pressure which satisfies the free-field inhomogeneous Helmholtz equation and the Summerfield radiation boundary condition ∂G (r ,ra) lim r − ra →∞ r −ra ⎛ + jkG (r ,ra)⎞ = 0 ⎝ ∂ r −ra ⎠ ⎜

⎟

e−jk r − ra 4π r −ra

(8)

p (r ) = −

(9)

(10)

By using the Green’s second identity and the Green’s kernel function, the homogeneous Helmholtz/Kirchhoff integral equation can be deduced as

∫Ω

b

⎡G (r ,rb) ∂p (rb) −p (rb) ∂G (r ,rb) ⎤ dΩb ∂n ∂n ⎦ ⎣

(11)

where Ωb is the surface of the acoustic domain, n is the unit normal at the position vector rb . By defining the direction, normal to the closed boundary surface Ωb , with a positive orientation into the unbounded domain, the direct boundary integral formulation for exterior problems is obtained. This equation is the so- called direct integral equation. The term “direct” indicates that the variables, which are necessary to evaluate the sound field pb , on the boundary surface have a direct physical meaning, i.e. the surface pressure and normal velocity. Since the direct boundary integral formulation requires that the boundary surface Ωb is closed, it can only represent either an interior or an exterior pressure field, but not a combined interior/exterior field. At the same time, for combined interior and exterior acoustic problems with a bounded boundary or exterior acoustic problems with an open boundary surface, there is equation called indirect boundary element integral equation which can be derived by applying the direct boundary element integral equation to the acoustic domains. After some manipulation, the indirect element integral equation can be expressed as follows [1]

pb =

∫Ω

b

⎡μ (rb) ∂G (r ,rb) −σ (rb) G (r ,rb) ⎤ dΩb ∂n ⎦ ⎣

(13)

μ (rb) =

p+ (r

(14)

v

μ (rb)

∂G (r ,rb) dΩ v (rb) ∂n (rb)

∂G (r ,rb) μ (rb) ⎡ + jkβ (rb) G (r ,rb) ⎤ dΩz (rb) ⎢ ⎥ ⎣ ∂n (rb) ⎦

(18)

σ (rb) = ΣNσi (rb) σi, rb ∈ Ωσ

(19)

μ (rb) = ΣNμi (rb) μi ,rb ∈ Ωμ

(20)

(21)

The system of equations on the whole surface are then transformed to discretize systems for each of the sub-surface (boundary element) with equations of the form as below

Aσi = − Aμi =

∫Ω

p

∫Ω +

v

Nσi (rb) G (r ,rb) dΩp (rb)

Nvi (rb)

∫Ω

z

(22)

∂G (r ,rb) dΩ v (rb) ∂n (rb)

∂G (r ,rb) Nvi (rb) ⎡ + jkβ (rb) G (r ,rb) ⎤ dΩz (rb) ⎢ ⎥ ⎣ ∂n (rb) ⎦

(23)

When the IBEM is used, the boundary conditions of pressure, velocity, acoustic impedance on inner and outer walls in the normal direction, as well as the acoustic boundary conditions at infinity are required to be satisfied.

In this section, validation of the simulation results through the comparison between the simulated and tested performances of fan, such as the total pressure and internal efficiency, will be tested firstly. Then, the main source of the centrifugal fan will be identified and the comparison of the sound radiation directivity without and with volute will be done. Finally, a discussion on three calculated SPLs and one measured SPLs will be progressed.

The superscript “+” and “−” indicate the positive and negative side of the normal direction n at the boundary surface position and outward direction is regarded as positive. The single layer potential is the difference of the normal pressure gradient between two sides of the boundary surface Ωb and related to the velocity jumps across surface. The double layer potential is the difference of pressure on both sides of the boundary surface Ωb . Once the single and double potential layers are known, an acoustic pressure pa which uniquely satisfies the Eq. (11) and the summerfield radiation boundary condition can be evaluated. Assuming the boundary surface is a thin surface, pressure, velocity and impedance boundary conditions are as below

μ (rb) = 0, p (rb) = p , rb ∈ Ωp

z

∫Ω

3. Result and discussion

∂p+ (r b) ∂p− (rb) − ∂n ∂n b)

∫Ω

σ (ra) G (r ,rb) dΩp (rb) +

p (r ) = [Aσi ]T {σi} + [Aμi ]{μi }

(12)

σ (rb) =

b

(17)

where Nσi , Nui are global shape weighting functions, σi , μi are the single and double potential layer of each node on the surface. The determination of variables distribution on the whole surface is transformed to determination of variables within the subsurface which is the discretization elements on the surface. And algebraic equation is:

In the equation we term μ (r b) and σ (r b) as double and single layer potential respectively and their expressions are

)−p− (r

∂p (rb) = −jkβp (rb), rb ∈ Ωz ∂n

Obviously, it is almost impossible to get the analytical solution of Eq. (17) with a complex boundary surface. So, the boundary element method is adopted to transform the integral Eq. (17) to a numerically solvable algebraic equation. Based on the indirect element integral equation, the boundary element method transforms the boundary problem into a vibration formulation and uses the shapes functions on each sub-surface (boundary surface) to approximate the boundary variables.

And pb satisfies the homogeneous Helmholtz equation and the boundary conditions associated with the scattering surfaces

pb =

∫Ω

p

+

∇2 pb + k 2 • pb = 0

(16)

where Ωp is the sound pressure boundary surface, Ω v is the velocity boundary surface and Ωz is the impedance boundary surface. Applying these relations, the indirect boundary integral Eq. (11) can be reformulated as

where r and ra is the position vector of recovery point and sound source point respectively, Gr,ra is the Green’s kernel function

G (r ,ra) =

∂p (rb) = −jρ0 ωvn rb, rb ∈ Ω v ∂n

3.1. Validation of the total pressure and internal efficiency The most important performance parameters of the centrifugal fan are the total pressure and the internal efficiency.

η=

(15)

QPt 2πnT

(24)

where η , n, T, Q and Pt are the internal efficiency, rotating speed, 187

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Fig. 12. The average static pressure fluctuation rate.

Fig. 10. Comparison between the numerical and experimental total pressure.

average static pressure fluctuation rate on volute tongue is higher than that of the blade suction surface and pressure surface. It means that the outflow from the impeller channels impacts the volute tongue surface, which causes high pressure fluctuation. This strong interaction between impeller and volute tongue causes the higher amplification of noise in the centrifugal fan [47]. Liu et al. [23] have calculated the dipole acoustic source of the volute and impeller respectively, and it also indicated that the dipole source on the blade surface is much smaller than that on the volute tongue surface.

torque, volumetric flow rate and total pressure. In order to validate the simulation results, we compared our simulation results with the experimental results of [14]. The total pressure comparison between numerical results using the RNG k-ε turbulence model and experimental results is presented in Fig. 10. Generally, the simulated total pressure at different flow rates fit well with that of experiment, the difference is less than 5%. It is also found that the numerical results of internal efficiency are in good agreement with the experiment throughout the entire range of flow rates, the difference is less than 3%, see Fig. 11. The results indicate that the grid system and the CFD strategies are reliable and appropriate to calculate the performance of the centrifugal fan. The surface dipole intensity can be approximated by the root mean square value of the time-derivative of the static pressure shown in Eq. (24).

3.2. Noise prediction results

where Psound is the average pressure fluctuation rate, N is the number of samples. The Psound result is shown in Fig. 12, it is obvious that the difference between the static pressure fluctuation rate on the suction surface and that on the pressure surface is tiny. The possible reason for this small difference is that the flow in impeller channels produces lower pressure fluctuation at such high efficiency condition. It is found that the

The free space sound pressure fluctuation generated by the volute and blades surfaces at the measuring point is presented in Fig. 13. It illustrates the sound pressure generated by the volute surface is greater than the sound pressure generated by the blades surface. The sound pressure produced by blades surface fluctuates close to zero. Hence, the volute surface is the main noise source of the centrifugal fan. The directionality of the radiation without and with volute in the free space is presented in Fig. 14. The figure (a) is the simulated results without volute. It is found that the maximum sound pressure level is distributed at the oblique top of volute outlet and its opposite direction. It has two humps for the entire range of radiation angle, this radiation character is a classic dipole radiation [23]. The figure (b) is the sound radiation pattern with the consideration of volute’s reflection and scattering. Different from the figure (a), the shape of dipole

Fig. 11. Efficiency comparison between the numerical and experimental results.

Fig. 13. Variations of calculated sound pressures.

Psound =

1 N

N

∑ 1

2

⎛ ∂p ⎞ ⎝ ∂t ⎠

(25)

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Fig. 14. Comparison between sound radiation directivity without and with volute.

demonstrates a ‘quadrupole’ due to the reflection, scattering and complex shape of the volute. It is noticed that the overall sound pressure level with the volute is less than that without the volute, the possible reason for this reduction is that the volute is treated as a rigid and no transmission surface in the IBEM calculation, thus, the sound wave is reflected and scattered by the inner surface of the volute, and can just radiate from the inlet and the outlet of the volute. Fig. 15 depicts the comparison of the predicted and measured the sound pressure level at the measuring point. The red curve is the simulated case from [14] without volute, the blue and megenta curves are our predicted cases without and with volute, and the black curve is experimental case, the overall trend of three simulated cases and the experimental one agrees. Our simulated tend without volute is also comparable to that of [14], both are Two peaks located at blade passing frequency and its second harmonic in the SPL spectrum, but the amplitude of BPF is remarkably larger than other frequencies, this phenomenon is caused by the impact of air flow on the volute tongue when blades pass through, and this impact is responsible for the characteristic dipole source. Deviations are found in the lower and higher frequency ranges between the two simulated cases without volute and

experimental case, the following reasons may be responsible for those deviations. Firstly, although the LES method and relatively fine grids are used to discrete the fluid domain, but the internal flow of a centrifugal fan is considerably complicated, it is still a challenge to capture the high-frequency pressure fluctuation induced by small-scale eddies. Second, the model is neglected the noise generated by the blades, quadrupole source and the vibration noise source, these simplifications cause the deviation in the low-frequency range [48]. It is also found that predicted SPLs without volute are higher than the tested SPLs, Paramasivam et al. have come up with similar predictions [49]. The reason is that the solution of inhomogeneous sound problem is solved through free space Green function without consideration the volute’s radiation directivity. By using the IBEM method, the deviation between the simulated and tested results in the lower and higher range of frequency is reduced. It is also noted that the sound pressure levels calculated by the IBEM is much closer to the tested ones than the free space radiation values calculated by the free space Green function, especially at the BPF locations circled in Fig. 15, because the SPLs is the superposition of an inhomogeneous sound pressure and a homogeneous sound pressure. In other word, the application of IBEM can improve the prediction accuracy significantly. 4. Conclusion In this paper, an improved aeroacoustics prediction model with a hybrid acoustic computational method for a centrifugal fan is developed and investigated to predict the aeroacoustics noise of an industrial centrifugal fan. Unsteady flow field is calculated to obtain the pressure fluctuations on the surfaces of rotating impeller and volute, then the Lowson equation and FW-H analogy are applied to get information of the noise source. Finally, IBEM is adopted to calculate the far-field sound pressure considering reflection and scattering of the volute. The calculation results show that this method is capable of more accurate prediction when compared to experimental measurements. The investigation is summarized as follows. 1. The average static pressure fluctuation rate on the volute tongue is higher than that of the blade channel. It means that the outflow from the impeller channels impacts strongly on the volute tongue surface, which causes high pressure fluctuation.

Fig. 15. Comparison of calculated SPLs and measured SPLs.

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2. The noise directivity pattern is dipole shape without considering volute. While the shape is changed to that of a quadrupole with IBEM calculating the reflection and scattering of the volute, thus, it is important to consider the volute’s effect conducting the noise prediction. 3. The predicted results using the IBEM considering the volute effect are more accurate than that without the volute effect. The SPLs using IBEM are closer to the measured values especially at the BPF and its harmonics.

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