European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 10-14, 2012
ZONAL LARGE EDDY SIMULATION FOR THE NUMERICAL PREDICTION OF THE ACOUSTIC PERFORMANCE OF AN AXIAL FAN M. De Gennaro1, A. Zanon1, H. Kuehnelt1, and P. Giannattasio2 1
AIT, Austrian Institute of Technology GmbH Giefinggasse 2, 1210, Vienna, Austria {michele.degennaro.fl, alessandro.zanon, helmut.kuehnelt}@ait.ac.at 2
Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, University of Udine Via delle Scienze 208, 33100, Udine, Italy
[email protected]
Keywords: CFD, Aeroacoustics, Zonal LES, Axial Fan, Numerical Simulation. Abstract. Advanced aerodynamic and aeroacoustic simulation methodologies are becoming a major topic in the modern vehicle industry and even more in the design of Heating, Ventilation and Air-Conditioning (HVAC) systems. The computation of airborne noise requires highly accurate numerical approaches to deal with the complexity of phenomena involved, such as turbulence, transition to turbulence and laminar instabilities. Moreover the requirements in terms of time and space resolution for the aeroacoustics as well as the identification and calculation of aeroacoustic sources make the computation of aerodynamic generated noise often extremely time demanding and thus not suitable for implementation within design and optimization loops. The objective of the present paper is to perform the aeroacoustic simulation of an axial fan by using an innovative LES technique, the Zonal LES. The proposed approach consists of a fully resolved LES in the acoustic generation region (embedded into the LES sub-domain) merged with a RANS solution in the outer flow region. In this way, the impact of the LES computational burden is significantly reduced and complex geometries can be simulated within reasonable computational time. The acoustic propagation is performed by using the Ffowcs Williams-Hawkings (FWH) acoustic analogy. The test-case chosen for this study is based on the geometry of a 5-bladed axial fan with an outer diameter of 350 mm, blade Reynolds number of 0.06 M at the root and 0.16 M at the tip and tested in free field condition. The aeroacoustic and aerodynamic predictions of the numerical model are compared with the experimental data collected by the authors.
M. De Gennaro, A. Zanon, H. Kuehnelt, and P. Giannattasio
1
INTRODUCTION
Aerodynamics and aeroacoustic design and optimization of ventilation systems pose a challenge for vehicle industry since passenger comfort and energy efficiency are becoming even more important objective in the design phase of HVAC components. If the aerodynamic performance is nowadays predicted quite easily by means of commercial CFD tools, the noise generated by aerodynamic sources is still far away to be assessed. This is due to the high complexity of the physical phenomena involved in noise generation mechanisms such as turbulence, transition to turbulence and laminar instabilities, together with the problems related to the numerical identification and simulation of acoustic sources generated in the flow field. In this direction many attempts to assess aeroacoustic sources identification are found in the literature as well as a number of practical applications involving trailing edge noise [1, 2, 3], axial fan noise [4, 5, 6, 7], propeller noise [8, 9, 10], acoustic duct response [11, 12, 13, 14], and slat noise [15, 16, 17] by means of Boundary Element (BE), Finite Element (FE) and Acoustic Analogy approaches. Despite of all those efforts an approach capable of dealing with aeroacoustic problems for general cases is not yet available today, even though excellent results have been reached in particular cases. Moreover the strict dependency of aeroacoustic predictions on the accuracy of flow data imposes highly CPU-demanding approaches such as Detached Eddy Simulation (DES) and Large Eddy Simulation (LES) which are sometimes not able to provide good results. Furthermore for a large number of problems the involved scales require very fine computational meshes, transient simulations and very small time step size, often resulting in a prohibitive computational cost for 3D complex configurations. The target of this paper is to evaluate the capability of an innovative Large Eddy Simulation technique (Embedded LES) coupled with the Ffowcs Williams and Hawkings [18] (FWH) acoustic analogy in simulating the noise generated by a 5-bladed axial fan. The added interest in this innovative numerical approach is its ability to provide accurate aeroacoustic results with affordable computational cost. The accuracy will be proved by comparing the numerical predictions with experimental data collected by the authors. 2
NUMERICAL MODEL
2.1 Aerodynamic modeling The turbomachinery problem can be approached by means of Computational Fluid Dynamics (CFD) via the solution of the Navier-Stokes (N-S) equations. The direct numerical resolution of these equations is hardly performed since the strong non-linearity and the spatial and temporal resolution required to properly describe the turbulent scales result in such an immense computational cost that it is never affordable for complex 3D industrial geometries. Therefore the solution of the N-S equations is usually approached by means of two techniques: the averaging of the equations (leading to the RANS model) and the filtering of the equations (leading to the LES model). In short, the RANS technique averages the equations over a sufficiently long time period in order to eliminate the turbulent fluctuations keeping the time dependence of the averaged quantities. This averaging process introduces the problem of the mathematical closure of the averaged equations, which results in the introduction of a turbulence model. On the other hand the LES technique filters the equations using the computational grid size as limit for either directly resolving the turbulent scales of large eddies or modeling the subgrid scales in a RANS-like manner with a subgrid turbulence model. The LES imposes severe requirements at the wall boundaries making this approach more accurate than RANS but also much more computationally demanding, resulting in a limited impact on industrial CFD simulations and suitable mainly for very low Reynolds number and un-
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bounded flow applications. In order to allow the resolution of large turbulent structures in industrial flow simulations, hybrid models such as Scale-Adaptive Simulation (SAS) or Detached Eddy Simulation (DES) have been developed. The first one tries to resolve the turbulence in unstable flow conditions based on large scale unsteadiness produced by RANS, which the SAS model adjusts in a dynamic way allowing the development of a turbulent spectrum in the detached regions. The SAS concept is based on the introduction of the von Karman length-scale dealing with the Rotta equation for the transport of turbulent kinetic energy scales. Therefore Rotta’s equation allows a term-by-term modeling of turbulent scales enabling the SAS model to provide a LES-like solution for detached unsteady flows and a RANS-like solution for steady flows. Details of the SAS model can be found in literature [19, 20, 21, 22]. As the DES approach is concerned the unsteady RANS model is applied in the boundary layer region while the LES treatment is applied to the separated region, where a turbulent core flow is detected and unsteady turbulent scales play a dominant role. The DES has been specifically designed to address high Reynolds number wall bounded flows, where the computational cost of a near wall LES would be prohibitive. However, even if the SAS and DES models provide huge potentialities in the frame of turbulent scales resolution, they still do not allow a full control of the solution since they require a global flow instability that is strong enough to switch on the generation of turbulent structures. In such situation zonal models are suitable, where a clear distinction between RANS and LES regions is made and the turbulence is converted from RANS to LES and vice versa at the interface. This approach is implemented in the Embedded LES (ELES) which consists of a fully resolved LES in a sub-domain region interfaced with a RANS solution in the outer domain. At the interfaces the turbulent kinetic energy of the RANS model has to be converted in resolved energy (RANS-LES boundary) and reverted back (LES-RANS boundary). These interfaces can be treated by means of Vortex Method or Spectral Synthesizer [22]. In the frame of turbomachinery problems the effect of the rotation can be introduced by two different techniques: the Sliding Mesh approach (SLM), where the entire computational grid is moved, and the Multiple Reference Frame (MRF), where the rotation is considered by transforming the equations in a moving reference frame. Usually, the SLM approach is considered more computationally expensive since it requires transient simulation and grid handling capabilities, while the MRF is less computationally demanding and also allows performing steady simulations which can be accurate enough for a wide number of practical applications. In this paper we use both ELES approaches, together with the MRF technique, for aerodynamic modeling of an axial fan. The computational domain is composed of a large RANS region for the farfield flow simulation plus a LES box which embeds the blade. The LES subdomain is affected by the near-wall turbulence on the blade which is responsible for the noise production. Further details concerning the solution domain and the computational mesh are provided in next paragraphs. The simulations were performed by using the commercial software ANSYS-Fluent, release 13. 2.2 Aeroacustic modeling Lighthill’s equation (1), proposed by James Lighthill in the 1950s and targeted to the prediction of noise associated to free jets, represents a milestone in the frame of the aeroacoustics and forms the basis for the most widely used numerical approaches for airborne noise computations [23, 24]. Formally it is a rearrangement of the Navier-Stokes equations to an inhomogeneous wave equation, thereby providing a connection between fluid mechanics and acoustics. The acoustic pressure p’, defined as difference of local hydrodynamic pressure and asymptotic pressure, is modeled by a non-stationary wave equation plus a source term, right3
M. De Gennaro, A. Zanon, H. Kuehnelt, and P. Giannattasio
hand side of equation (1), which includes the so called Lighthill turbulence stress tensor Ti,j equation (2). This tensor plays a key-role since it contains all the noise generation mechanisms which can occur for unbounded flows (quadrupoles): unsteady flow convection (Reynold’s stress), shear stress and non-linear pressure generated noise. ∂ 2Ti , j 1 ∂2 p ' 2 − ∇ p ' = ao 2 ∂t 2 ∂xi ∂x j
(1)
Tij = ρ vi v j − τ ij + ( p '− a 2 ρ ')δ ij
(2)
In order to introduce the effect of solid and permeable boundaries the Lighthill analogy was extended first by Curle and later by Ffowcs Williams and Hawkings, resulting in equation (3) [18, 22]. Therefore, the FWH acoustic analogy is a reformulation of the Lighthill equation enhanced by two additional sources (monopoles and dipoles) F and Q and multiplied by the Heaviside function H(f). This function works as a switch to identify emitting surfaces in the domain (physical or virtual) as a function of the position of their nodes in space and time f(x,t). Even moving surfaces can be taken into account [25], making this approach the most suitable for turbomachinery applications. ∂F δ '( f ) ∂Qδ '( f ) 1 ∂2 H ( f ) p ' ∂2 2 [ H ( f ) p '] [Ti , j H ( f )] + i − ∇ = + 2 2 ∂xi ∂x j ∂xi ∂t a ∂t
(3)
FWH equation is solved by means of the free-space Green function G, equation (4), which is the solution of the elementary wave propagation equation forced by time and space impulses, equation (5). G ( x, t ) =
1 r δ ' t −τ − 2 a 4π a r
(4)
∂ 2G − a 2 ∇ 2 G = δ '(t − τ ) ⋅ δ '( x − y ) 2 ∂t
(5)
The solution is given in equation (6) as the sum of the acoustic pressures arising from the different sources, monopoles, dipoles and quadrupoles, related to body thickness, flow interaction with moving bodies and unsteady stresses, respectively. It is important to notice that monopole and dipole contributions can be reformulated as surface integrals while quadrupoles are volume sources. For low Mach number flows the quadrupole contribution is small compared to mono- and dipoles. For computational reasons it is therefore not considered in the performed calculations [22]. p '( x, t ) = p 'T ( x, t ) + p 'F ( x, t ) + p 'Q ( x, t ) = =
1 ∂ 4π ∂xi ∂x j 2
∫
Ω1
Tij H ( f ) x −ξ 1− Mr
dΩ −
1 ∂ 4π ∂xi
∫
Γ
S
Fiδ '( f ) 1 ∂ dΓ + x − ξ 1− Mr 4π ∂t
∫
Γ
S
Qiδ '( f ) dΓ x −ξ 1− Mr
(6)
The FWH has the main advantage to be not computationally demanding and easily coupled with CFD results. Since the main problem of volumetric aeroacoustic solvers (e.g. Finite Elements) is to store the aerodynamic field data in the sampling period up to the microphone location, the FWH only needs data on the emitting boundary surfaces to compute the mono-
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Figure 1: CAD model of the tested axial fan (left), computational grid details at the leading edge and on the suction side of the blade (right)
pole and dipole sources. Therefore, the acoustic pressure can be computed in every receiver location. This is a great advantage, especially for far-field noise computations. 2.3 Test-Case Geometry The fan geometry tested in the present work was designed for industrial HVAC applications at the University of Udine, Italy, in 2010. The rotor has five blades based on a F-Series aerofoil with chord length ranging from 85 to 95 mm. The blade tip and root diameters are 350 mm and 102 mm, respectively. The Reynolds number experienced by the blade, at the nominal working condition of 1400 rpm, ranges approximately from 0.06 M at the root to 0.16 M at the tip. 2.4 Computational details The CAD model of the blade used for the rapid prototyping of the fan is imported in ANSYS-Gambit where it is mounted on the cylindrical hub. A triangular surface mesh is generated which is then handed over to ANSYS-TGrid where a hybrid (prisms/tetrahedra) volume mesh is generated with periodic boundary conditions on the side walls (only 1 blade is simulated). The mesh is then converted to polyhedra in ANSYS-Fluent before performing the computation. The conversion allows saving approximately 60% of the cells without losing the resolution quality of the boundary layer. Three different computational meshes were generated for this geometry (coarse – mid – fine mesh). The coarse mesh was only used to test the scripting of the CFD simulations, therefore only the results obtained with the mid- and finemesh will be presented. The mid mesh consists of a one-blade periodic hybrid mesh with 2.5M cells in the 1-blade domain, 20 layers of extruded prisms in the boundary layer region over the blade surface and polyhedral cells filling the rest of the domain. It has been designed to have an acceptable number of cells in the physical boundary layer (~15) and LES driven values of y+ (~1), x+ and z+ on the blade surface for the operating condition considered (1400 rpm). The fine mesh is comparable with the mid one for its overall structure but it has a higher surface cells density on the blade, resulting in a total cells number of 5.2M and more stringent grid wall properties. A picture of the CAD model and the mesh details at the blade leading edge and suction side are given in Figure 1. 5
M. De Gennaro, A. Zanon, H. Kuehnelt, and P. Giannattasio
The CFD approach used for the aeroacoustic simulation was the innovative Zonal LES technique for the computation of the aerodynamic flow field, namely, the Embedded LES (ELES) coupled with a Multiple Reference Frame (MRF) to take into account the rotation. A steady RANS simulation with the k-ω SST turbulence model was performed on the LES grid and used to initialize the LES simulation. This RANS solution was also used to compare the flow field with the time-averaged PIV measurements (see section 4.1, where only the results for the 2.5M mesh are reported). Further details will be given later. The ELES approach was applied in two different formulations: the Wall Modeled LES (WM-LES) and the Wall Adapting Local Eddy-viscosity (WALE) LES. The WM-LES model is a hybrid approach classified in the frame of Improved Delayed DES (IDDES) which is able to provide a more flexible and convenient scale-resolving simulation model for high Reynolds number flows. This model is able to provide additional properties to the standard DES model such as the possibility to provide shielding against the grid induced separations (similar to the Delayed DES). Furthermore it allows running the LES simulation resolving the wall boundary layer in the case of unsteady inlet conditions (e.g., RANS-LES interface treated by means of Vortex Method or Spectral Synthesizer) and modeling the IDDES length scale in the turbulent kinetic energy equation by means of both RANS turbulent length scale and LES grid scale, making this approach a DES-LES hybrid one. On the other hand the WALE-LES model is a full-LES approach with a subgrid turbulence model alternative to the classical Smagorinsky-Lilly and dynamic Smagorinsky-Lilly models. From a practical side the WALE model introduces a different equation for the subgrid turbulent viscosity modeling, which is designed to give the correct asymptotic behavior of the turbulent wall shear stress for bounded turbulent flows and zero turbulent viscosity for laminar shear flows. For this reason it represents an improvement with respect to the Smagorinsky-Lilly model and it is preferable for wall bounded LES calculations. It is important to highlight that the grid requirements of WM-LES and WALE-LES are quite different. The WALE-LES has the typical LES requirements (∆x+~ ∆z+ ~ 20) while the WMLES has less stringent grid requirements (∆x+~ ∆z+~ 0.05/0.1 δ, where δ is the boundary layer thickness). In the present case both computational meshes satisfies the WMLES requirements, whereas they might be a bit coarse for the WALE requirements. Nevertheless the numerical solution performed on the two meshes provides a solution trend which does not show a dramatic dependence of the quality of the numerical results on the mesh. The ELES simulations were performed with these two approaches because they represent the most advanced DES-LES and full-LES methods available in the commercial framework of Zonal LES. Moreover, a comparative analysis of these approaches is a key issue for industrial aeroacoustic applications. All the ELES simulations were initialized from the converged steady RANS solution, switching to the unsteady model enabling the LES sub-domain and the RANS-LES interfaces. The transient simulations were performed with a time-step of 2.8571e5 seconds, corresponding to 1500 time steps per revolution (300 time steps per blade passage) and to a sampling frequency of 35 kHz for the acoustic signal. After one complete revolution of the fan performed to initialize the unsteady flow field, the sampling period was carried out over 2 complete revolutions (10 blade passages) for a total simulation time equal to 0.085 seconds, corresponding to a spectral frequency resolution of about 10 Hz. The simulation time was approximately 100 hours for the mid mesh and 200 hours for the fine mesh including the RANS and LES initialization part as well as the LES transient simulation and acoustic sampling. The runs were carried out on a cluster equipped with the CPU Intel Xeon E3120 3.16 GHz using 8 cores. The acoustic propagation is performed by using the Ffowcs WilliamsHawkings analogy (FWH) presented in sec. 2.2. Simulations were performed by using commercial software ANSYS-Fluent, release 13 [22].
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(a) Measurement plane
(b) Measurement windows
Figure 2: Particle Image Velocimetry measurement location.
3
EXPERIMENTAL TECHNIQUES
The aerodynamics and the aeroacoustics of the fan were investigated by means of 2D Particle Image Velocimetry and acoustic measurements in an anechoic chamber, respectively. The fan rotor, realized by means of the rapid prototyping technique, was mounted on the shaft of a controlled DC brushless motor, which was connected to a structure made of aluminum profiles and placed in the center of a closed room of dimensions: 5 m × 3.2 m × 3 m for the PIV measurements and 6 m × 3.6 m × 3 m for the acoustic measurements. In the following sections a brief description of the experimental approaches is given, while the reader is referred to [26] for an extensive description. 3.1 Particle Image Velocimetry The rotor aerodynamics was investigated in the laboratories of the Austrian Institute of Technology by using a planar Particle Image Velocimetry technique (2D-PIV). The seeding particles injected into the airflow were 1 µm oil-based fog droplets. The particles have been illuminated by a Dantec DualPower Nd:YAG laser with 532 nm wavelength, nominal pulse duration of 4 ns and pulse energy of 200 mJ at 15 Hz. The laser sheet thickness was about 1.5 mm and the separation time was set in order to guarantee a suitable displacement of the tracer particles (≈10 pixels) and to limit their out-of-plane displacement. A Dantec C9300-501 digital camera with a resolution of 2048 × 2048 pixels, a lens of 60 mm focal length and f-stop 4 was used. The nominal magnification was 14 pixels/mm and the resulting Field of View (FoV) was 146 mm. The flow field was investigated in a plane containing the fan rotation axis (see Figure 2(a)) divided in 4 measurement windows (RZ1 to RZ4 in Figure 2(b), where R = r/RTIP, Z = z/ RTIP and RTIP is the radius of the blade tip) which were acquired separately in order to guarantee a high spatial resolution. The data acquisition and processing were performed by using the commercial software tools Dantec Dynamic Studio and PivView. The images were cross-correlated by means of a window displacement-distortion multi-grid algorithm with interrogation window size from 64x64 to 32x32 pixels and window overlap of 50%. The outcome of the post processing was a field of 127 × 127 displacement vectors in each measurement area with a spatial resolution of 1.14 mm.
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3.2 Acoustic measurements The acoustic measurements on the axial fan in free field conditions have been performed in the anechoic chamber of the University of Music and Performing Arts of Vienna. The testsetup was placed at the centre of the room to ensure a suitable distance from the bounding walls (> 5 diameters). The acoustic data have been acquired by 13 measurement microphones (Roga MI 171/4" IEPE, sensitivity of 50 mV/Pa) placed every 9 degrees along a semicircle of 1m radius centered in the fan rotor – coordinates (0,0) in Figure 2(b) – and having an edge on the rotation axis. The signals have been acquired by the National Instruments PXIe-4496 system with a sampling rate of 40 kHz. The number of samples for each fan working condition was 4M (corresponding to an acquisition time of 100 seconds). 4
RESULTS
In order to validate the numerical approaches presented above, in the following sections the predicted fan aerodynamic and aeroacoustic performances are compared with the experimental data collected by the authors. Subsequently, by using the added information available from numerical simulation, the correlation between the noise emitted from the fan and the pressure fluctuations on the blade surface are analyzed. 4.1 Validation of the aerodynamic and aeroacoustic numerical models The first step in the validation process is to assess the capability of the numerical models in predicting the main features of the fan aerodynamics. Table 1 shows the percentage error, / 100, on the time averaged volume flow rate computed through a circular surface of radius RTIP located at 2 cm from the blade leading edge. is the value predicted by the different numerical models and meshes and is the value obtained from the PIV experimental velocity map. The error is acceptable and tends to decrease by moving from the steady RANS (2.5M mesh) to the unsteady LES simulations and by increasing the mesh resolution, providing a consistent simulation results trend. 2.5M RANS 9.4 %
2.5M LES-WALE 7.5 %
2.5M WM-LES 7%
5.2M LES-WALE 6%
5.2M WM-LES 4.6 %
Table 1: Percentage error in the prediction of the time averaged volume flow rate through the fan.
Figure 3: Time variation of the error in the prediction of the volume flow rate for the different numerical models and meshes
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Figure 4: Contour plot of dimensionless axial velocity Ua=U/(ωRTIP) and streamlines at 1400 rpm. PIV measurements
Figure 5: Contour plot of dimensionless axial velocity Ua and streamlines at 1400 rpm. RANS simulation
However, it has to be mentioned that the mean value computed from the transient solutions is based on two rotor revolutions. The foreseen development of this work will involve simulations with more rotor revolutions, in order to improve the aerodynamic results as well as the frequency resolution of the noise spectra. Figure 3 shows the percentage errors on the instantaneous volume flow rates predicted by the different numerical models and meshes. For
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the RANS steady simulation (2.5M mesh) a constant value is depicted as a reference. The error trend suggests an unsteady non periodic behavior of the flow. Hence a longer simulation time is desirable in future investigations. The volume flow rate is an integral quantity and can mask cancellation errors. A deeper evaluation of the numerical model accuracy is reported in Figure 4 and Figure 5 where the dimensionless axial velocity map (Ua = U/ωRTIP, where U is the axial velocity [m/s] and ω is the rotational speed [rad/s]) and the streamlines are represented as predicted by the RANS simulation and measured by the PIV technique. An excellent agreement can be observed in both the streamline orientation and the axial velocity contours. Deviations are present in the rear part of the domain (due to a mismatch of the cylindrical hub shape between the physical and the numerical model) and at the tip of the blade where the predicted recirculation region is smaller than in the experimental data. At the fan inlet the magnitude of the axial velocity is slightly overpredicted resulting in the above mentioned overestimation of the volume flow rate of 9.4 %. Figure 6 compares the power spectral density level of the sound pressure (PSDLp) at microphone 1 (reference pressure po = 2 · 10-5 and frequency f0 = 1 Hz) measured in the anechoic chamber with the numerical predictions of the WALE and WM LES models for the two considered meshes. Since the numerical models are unable to predict the Blade Passing Frequency (BPF) peaks (due to some physical features that are not included in the numerical simulation [27], e.g. the asymmetric inflow due to the experimental room, the not fully balanced impeller, the stability of the rotor speed) they are depicted with a dashed line.
Figure 6: Comparison of experimental and numerical power spectral density level of the sound pressure at microphone 1 (on the fan rotation axis). (a) 2.5M WALE-LES, (b) 2.5M WM-LES, (c) 5.2M WALE-LES and (d) 5.2M WM-LES simulation
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The predicted PSDLp for the 2.5M mesh (Figures 6(a) and 6(b)) are in excellent agreement with the experimental data for both LES approaches, especially at higher frequencies (1 kHz 7 kHz). Only a slight underestimation is found in the WM simulation in the frequency range 1 kHz and 1.5 kHz. The WM model captures better the second bump (≈ 4 kHz) while the third bump is not predicted by both numerical models. This could be due to limitations of the numerical approach, e.g., underresolving small turbulent scales and high frequency limitations of the FWH analogy. At lower frequencies (100 Hz - 800 Hz) the PSDLp is overpredicted and some peaks could be singled out. Some of them match well the experimental BPF peaks (especially the one at the 5th BPF, predicted by both models). However further investigations with a higher number of samples are desirable to improve the quality of the signal especially at the lower frequencies. Moreover in Figures 6(c) and 6(d) is reported the solutions of the WALE and WM LES models computed with the finer mesh (5.2M cells). At lower frequencies the main trend is comparable with the 2.5M mesh (the peak at the 5th BPF disappears) as well as at the higher frequencies. It has to be noticed that two minor differences can be singled out. The PSDLp between 1 kHz and 2 kHz is slightly underestimated in the solutions obtained with the finer mesh and the bump observed in the experimental data at 4 kHz is not caught as well as in the 2.5M mesh solutions. Possible reasons of these small differences are analyzed in the next section where the relations between the noise emitted from the fan and the pressure fluctuations on the blade surface are investigated. 4.2 Surface pressure fluctuations on the fan blade In this section the surface pressure fluctuations on the fan blade predicted by the WALE model for the two meshes (2.5M and 5.2M) are reported in order to detect the physical phenomena involved in the noise emission. Figure 7 shows the predicted 1/3 octave band power spectral density level of the surface pressure fluctuations (PSDLs) on the blade suction side for the 2.5M mesh, in different radial planes for probes placed between 10% and 90% of the aerofoil chord from the leading to the trailing edge. In Figure 7(a) the levels decrease logarithmically with increasing the frequency for all the probes on the blade section. Only a small peak is observed at 30% chord, probably due to shedding of weak vortical structures. By moving towards the blade tip, see Figure 7(b), the spectra change; up to 10% chord the boundary layer is laminar and the pressure fluctuations levels have a logarithmic decrease, as observed in Figure 7(a). At 20% chord the laminar boundary layer starts to become unstable and shedding of vortical structures occurs (boundary layer transition). As a consequence, a strong narrow peak (f ≈ 1.6 kHz) and its second harmonic (f ≈ 3.2 kHz) appear in the spectrum at 30% chord. By moving downstream, along the blade chord, due to the increase of the boundary layer thickness, the pressure fluctuation levels at lower frequencies increase (in agreement with [28]) till the tonal peak is not longer identifiable (see the probe signal at 60% chord). The same behavior is observed in Figures 7(c) and (d) with an increase in both intensity and frequency of the first narrow peak. The second peak is not clearly identifiable in Figure 7(c) and three harmonics appear at 20% chord in Figure 7(d). The above analysis of the pressure fluctuations spectra allows the suction side of the blade surface to be split in three main regions. The first region is close to the leading edge, where the boundary layer is laminar and the pressure fluctuations contribute substantially only at low frequencies. The second region is located in the rear part of the blade (close to the trailing edge) where pressure fluctuations are high and broad in a large portion of the spectra. Finally, the third one is the mid-region, characterized by strong narrowband pressure fluctuations. An exception has to be made for the blade surface close to the rotor root where only the first re11
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Figure 7: Power spectral density level of the blade surface pressure (PSDLs) predicted by LES-WALE for the 2.5M mesh at different iso-radial blade chord positions. PSDLs at 32% (a), 48% (b), 65% (c) and 89% (d) of the blade
gion can be singled out (see Figure 7(a)). To visualize these three regions, Figure 8 shows the contour plots of the 1/3 octave band PSDLs on the suction side of the blade for three selected 1/3 octave band center frequencies: 800, 1600 and 2000 Hz. For each frequency the solutions obtained by using the 2.5M and the 5.2M mesh are depicted on the left and right column, respectively. For this frequency range, as expected, the PSDLs is low in the region close to the leading edge and in the inner part of the blade. At 800 Hz the noise sources are spread over a large part of the blade, namely, in the turbulent boundary layer and especially at the trailing edge. At 1600Hz the main contribution for noise emission is detected in the third region (boundary layer transition region) where the maximum of PDSLs is reached in the inner part of the blade (35% < R < 50% of the blade), see also Figure 7(b). Finally, the contour plot for 2000 Hz shows a large spatial extension of the region where the peak in the PSDLs was observed at this frequency (in Figures 7(c) and (d)). In the trailing edge region the PDSLs is relevant mainly at low to mid frequencies but, especially close to the blade tip, they are not negligible also at higher frequencies. At the tip section of the blade we find only relevant contributions to the PDSLs at the trailing edge. This is most probably due to the presence of the tip vortex. The different contributions of the three blade regions to noise emission can be observed by referring to the PSDLp graph in Figure 6(a). The low frequency broadband noise (from 100 to
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Figure 8: Contour plot of the 1/3 Octave Band PSDLs on the suction side of the blade as seen from the fan intake at three selected center frequencies: 800, 1600 and 2000 Hz. In the left column the solution of 2.5M WALE simulation and in the right the 5.2M WALE simulation
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M. De Gennaro, A. Zanon, H. Kuehnelt, and P. Giannattasio
1000 Hz) is mainly due to the region close to the trailing edge, whereas the hump at 2 kHz and its harmonic at 4 kHz are due to the narrow peaks observed in the pressure fluctuation spectra located in the mid region of the blade. The low level bump at 8 kHz is identifiable only in the experimental data. In the previous section some differences were observed in the PSDLp predicted by the WALE model using the 2.5M and the 5.2M meshes, mainly between 1 and 2 kHz. From the analysis reported above we concluded that the PSDLp in this frequency range is correlated to the presence of a narrow peak in the PSDLs due to the shedding of vortical structures in the boundary layer transition region. Therefore it is expected that the differences in the PSDLp predicted with the 2.5M and the 5.2M meshes can be justified with a small deviation of the physical phenomena involved in noise emission in this frequency range. Comparing the left and the right columns of Figure 8 (2.5M and 5.2M mesh results, respectively) the underestimation of the noise in the 5.2M mesh solution could be ascribed to the smaller extension of the region with high PSDLs at 1600 and 2000 Hz. This could be caused by a faster decay of the vortical structures released from the laminar boundary layer related to the development of hairpin structures (see the streaked region with high PSDLs at 2 kHz for the 5.2M mesh). Such flow structures are not fully captured in the 2.5M mesh solution due to the coarser spatial resolution. The PSDLs peaks localized on a line close and parallel to the leading edge in the blade tip region (Figure 8, 5.2M mesh at 1.6 and 2 kHz) are due to a jump in the mesh size caused by polyhedral mesh conversion, which will be improved in further work. However, with both meshes the same physical phenomena are captured and the predictions are in excellent quantitative agreement. Therefore the solution dependence on the mesh resolution is negligible and the use of the 2.5M mesh is sufficient to properly predict the acoustic and aerodynamic fan performance. It should be mentioned that the small deviations observed in the two numerical simulations can be also due to the limited number of pressure samples used; therefore the future developments will involve also longer simulations with higher number of samples. 5
CONCLUSION
The aeroacoustic simulations of an axial fan for industrial applications performed by means of an innovative LES technique, the Zonal LES, coupled with the Ffowcs WilliamsHawkings (FWH) acoustic analogy have been presented. The aerodynamic predictions, computed by means of the RANS model, turned out to agree well with the experimental PIV velocity maps collected by the authors. Only a slight overestimation of the time averaged volume flow rate was observed. The predicted acoustic power spectral density of the axial fan, computed by means of the Zonal LES in the WALE and WM formulations, was also in excellent agreement with the experimental acoustic data. By using the numerical results the main sources of the noise generated by the fan were singled out, namely a combined effect of the pressure fluctuations on the blade surface due to laminar to turbulent boundary layer transition and the turbulent boundary layer. The added information available from the numerical simulation allowed also the location of the noise sources on the blade surface to be identified. Due to the complexity of the fan aerodynamics and aeroacoustics, a suitable mesh convergence test was carried out. The comparison of the PSDLp and the PSDLs showed that the solution dependence on the mesh resolution is negligible.
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ACKNOWLEDGEMENTS The authors are grateful to the EC for supporting the present work, performed within the EU FP7 Marie Curie ITN project VECOM (Grant Agreement 213543). The authors wish to thank the company OESSE srl, Porcia (PN), Italy, which supported the design of the axial flow fan and provided the rotor prototype tested in the present work. Furthermore the authors are grateful for the support received from Dr. Domenico Caridi, ANSYS S.r.l. Italia. REFERENCES [1] R. Ewert, W.Schroeder: On the simulation of trailing edge noise with hybrid LES/APE method. Journal of Sound and Vibration, 207, 509-524, (2004). [2] M.Herr: Design Criteria for Low-Noise Trailing-Edges. in AIAA 2007-3470, 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, May 21-23, (2007). [3] Bertanoglio: Trailing Edge Noise Model Applied to Wind Turbine AirfoilsRisø-R1633(EN), (2008). [4] T. Carolus, M. Schneider, H. Reese: Axial flow fan broad-band noise and prediction. Journal of Sound and Vibration, 300, 50-70, (2007). [5] T. Carolus, M. Stremel: Blade surface pressure fluctuations and acoustic radiation from an axial fan rotor due to turbulent inflow. Acta Acustica united with Acustica, 88, 472-482, (2002). [6] S. Moreau, M. Henner, D. Casalino, J. Gullbrand, G. Iaccarino, M. Wang: Toward the prediction of low-speed fan noise. in Proceedings of the Summer Program, Center for Turbulence Research, Stanford Univ./NASA Ames, (2006). [7] Y.Rozemberg, M.Roger, S.Moureau: Fan Blade Trailing Edge Noise Prediction Using RANS Simulation. in Proceedings of the Euronoise Conference, Paris, France, June 29 - July 4, (2008). [8] M. De Gennaro, D.Caridi, C.de Nicola: Noise Prediction of NASA SR2 Propeller in Transonic Condition. AIP Conference Series Journal, 1281, 167-170, (2010). [9] M. De Gennaro, H. Kuehnelt: Broadband Noise Modelling and Prediction for Axial Fans. in Proceedings of the Internataional Conference Fan Noise, Technology and Numerical Methods, (2012). [10] M. De Gennaro, D. Caridi, M. Pourkashanian: Ffowcs Williams-Hawkings Acoustic Analogy for Simulation of NASA SR2 Propeller Noise in Transonic Condition. in Proceedings of ECCOMAS CFD 2010 Conference, (2010). [11] W. Polifke, A. Poncet, C.O. Paschereit, D. Doebbling: Reconstruction of Acoustic Transfer Matrices by Instationary Computational Fluid Dynamics. Journal of Sound and Vibration, 245, no. 3, 483-510, (2001). [12] P. Martinez-Lera, C. Schram: Acoustic Source Identification in a T-Joint at Low Mach Numbers. in 16th International Congress on Sound and Vibration, Krakow, Poland, July 5-9, (2009). [13] M. De Gennaro, H. Kuehnelt: Wiener-Hopf Technicque for Acoustic Characterization of Duct Elements. in Proceedings of the Forum Acusticum Conference, Aalborg, Denmark, (2011). [14] H. Kuehnelt, T. Täuml, A. Haumer: SoundDuctFlow: A Modelica Library for Modeling Acoustics and Flow in Duct Networks. in Proceedings of the 7th Modelica Conference, (2009). 15
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