aeroacoustics of a low-speed free tip fan with a complex

Aeroacoustics of a Low-Speed Free Tip Fan With a Complex Clearance GeometryAEROACOUSTICS OF A LOW-SPEED FREE TIP FAN WITH A COMPLEX CLEARANCE GEOMETRY
Dominic Lallier-Daniels Department of Mechanical Engineering
Université de Sherbrooke Sherbrooke, Québec, Canada
Email: [email protected]
Sherbrooke, Québec, Canada Email: [email protected] Email: [email protected]
ABSTRACT The influence of tip leakage flow on the performance of tur-
bomachinery, both from an aerodynamic and acoustic point of view, has been demonstrated by several authors. However, most studies present in the literature are focused on the effects of tip leakage from an aerodynamic point of view and often forgo the mechanisms associated with the acoustics effect. The effect of different tip geometries is also still ill understood.
The current advancement of a numerical study delving into tip leakage flow noise in low-speed turbomachinery applications is presented in this paper. The study as a whole aims to investigate the mechanisms associated with tip leakage flow noise on different axial fans with varying tip configurations. The study is carried out using lattice-Boltzmann simulations that allow to obtain the aerodynamic and aeroacoustic field simultaneously.
As a first step in this investigation of tip flow noise, this paper focuses on a free-tip axial flow fan with a complex tip geometry. The global aerodynamic and acoustic performance of the fan is evaluated numerically and compared to available experimental results. An investigation of the simulated flowfield with regards to the observed acoustics is then carried out.
NOMENCLATURE Fi External forces (N) Q Flowrate (m3/s) S Strain tensor
−→c Particle velocity (m/s) f Frequency (Hz) f = f (−→x ,−→c , t) Particle distribution function f eq Maxwell-Boltzmann distribution m Molecular weight (g/mol) p Pressure (Pa) p Differential pressure rise (Pa) r Radius (m) t Time (s) −→u Macroscopic fluid velocity (m/s) −→x Spatial coordinates Vorticity tensor λi ith eigenvalue of the pressure Hessian ρ Macroscopic fluid density (kg/m3) τ Relaxation time
INTRODUCTION Understanding and controlling the performance of turboma-
chinery systems is a very complex problematic even in ideal configurations, with many phenomena degrading both aerodynamic and aeroacoustic performance. One such phenomenon, tip leakage flow, is unavoidable in turbomachine applications and can potentially lead to drastic performances losses and increased noise.
Experimental studies have shown the effect of tip leakage flow on overall noise in axial fans [1–7] to different degrees, with
Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014
November 14-20, 2014, Montreal, Quebec, Canada
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1 Copyright © 2014 by ASME
leakage flow generating an inherently unsteady flow in the tip region of the blades and affecting broadband as well as tonal noise levels. A detailed experimental study on a stationary airfoil performed by Grilliat [8] also showed that the noise sources due to tip leakage flow can be related to the diffraction of turbulent eddies formed by the tip leakage jet-like structures. More recently, simulations on a ring-shrouded fan geometry used in automotive cooling were carried out using several unsteady methods by Magne et al. [9–12], including URANS and the lattice- Boltzmann method (LBM); analysis showed that sub-harmonic humps observed in the acoustic spectra were caused by large coherent structures forming in the tip gap and that the frequencies above 1 kHz were dominated by tip noise. More recently, a numerical study by Zhu et al. [13] studied the contribution of tip leakage flow in a free-tip tube-axial fan using the lattice- Boltzmann method and showed it had an important influence on overall noise levels.
Several authors have also explored methods to try and control tip leakage flow. Three dimensional blade design (skew, sweep) was shown to have an effect on the performance of turbomachines with regards to stall and efficiency by reducing the spanwise flows and tip leakage flowrate [14, 15]. Others [1, 16] also studied the effect of adding a ring-shroud at the tip of axial fan blades to eliminate leakage flow over the blade tip surface, which was shown to increase the efficiency and stall characteristics of the fan as well as leading to lowered noise levels. This, however, does not eliminate the tip leakage flow com- pletely and leads to a fairly complex flow topology in the tip region [17]. Several casing modifications aiming to control this tip flow can be identified in industrial patents on low speed axial fans [18–21]. However, the tip leakage control methods cited here mostly focus on increasing the aerodynamic characteristics (pressure rise, efficiency, stall) of the studied fans, with little em- phasis on the mechanisms responsible for the lowered aeroacoustic noise and no analysis on the effect of the tip geometry.
The current study presents the current advancement of a numerical investigation into the aerodynamic and aeroacoustic performance of low-speed axial fans aimed at studying the contribution of tip leakage flow to overall fan noise. The research seeks to bridge the gap seen in literature by analyzing and quantifying the contribution of tip flow noise for different tip configurations using numerical simulation, which would allow for an extensive investigation of the flowfield. In order to perform this analysis, a lattice-Boltzmann method flow solver is being used, allowing for direct acoustic simulation taking into account the aerodynamic phenomena and the environmental geometry for the propagation of sound.
This is opposed to the more widely used indirect acoustic evaluation methods using for example the Ffowcs Williams Hawkings (FWH) analogy [22], where a solid or porous surface on which the unsteady flowfield is recorded is used to calculate and propagate the resulting acoustic field in a simplified environ-
ment, coupled with unsteady flow solvers to circumvent the use of large meshes and unreasonable computing times. Examples of FWH usage to evaluate turbomachinery noise can be found in [9, 11, 23, 24]. It is to be noted that the FWH analogy can still be used in LBM calculations, as is shown in the paper.
The simulation subject presented in this paper is an axial automotive cooling fan with a free-tip configuration, highly swept blades and a converging static shroud geometry. The fan has been subjected to experimentation campaigns to quantify its aerodynamic and aeroacoustic performance. Thus, comparison of the aerodynamic performance of the fan predicted by the simulations is first presented. The acoustic performance of the fan is then also compared with the available experimental results and an analysis of the noise sources in the flow are investigated. This is the first step in a larger frame of study of tip noise, which has elected to study three fans with different tip configurations; the second fan that will be studied is a ring-shrouded fan for which LBM calculations have already been carried out [9, 12, 25] as well as a tube-axial free-tip fan [26, 27]. Research is ongoing and this paper presents the current advancement of the numerical investigation campaign using LBM aiming at taking advantage of the method’s ability to resolve the aerodynamic and aeroacoustic fields concurrently for low-speed fan applications.
LATTICE-BOLTZMANN METHOD The lattice-Boltzmann method has been used in this paper
to carry out the flow simulations using the CFD software Pow- erFlow 4.4. The method is based on the kinetic theory devel- oped by Boltzmann in 1872 and thus is based on a mesoscopic approach to calculate the flowfield and derive the macroscopic quantities. The continuous Boltzmann equation can be written as in Eq. 1
∂ f ∂ t
) coll
(1)
with f = f (−→x ,−→c , t) the particle distribution function at spatial coordinates−→x and time t possessing a speed−→c while Fi corresponds to external forces and m is the molecular weight of the gas considered. The term
( ∂ f ∂ t
) coll
is dubbed the collision term and regulates the interaction of the particles with each other. The collision operator currently used in PowerFlow is the Bhatnagar- Gross-Krook operator, or BGK [28], which is of the form seen in Eq. 2.
( ∂ f ∂ t
with f eq the thermodynamic equilibrium function also called the Maxwell-Boltzmann distribution and τ is the relaxation time. Using this collision operator and a Chapman-Enskog development [], Eq.1 recoups the Navier-Stokes equations.
Resolution of the continuous Boltzmann equation, however, is no easier than direct resolution of the Navier-Stokes equations. Thus the equation is further discretized by constraining the num- ber of velocities that a given particle can possess, thus yielding a discretized velocity form of the Boltzmann equation (DVBE). The adoption of the discrete velocity model limits the validity of the LBM to relatively low Mach numbers (Mach 0.4-0.5 is cited as the maximum in literature) but makes it suitable for low-speed applications.
For applications with moving parts, specifically turbomachine applications, a local reference frame approach is imple- mented to the LBM calculations [29, 30].
A modified relaxation time τ → τturb derived from a renor- malization group k− ε transport equations [31, 32] is also used to model the unresolved small scale flow features.
The LBM possesses some key advantages over traditional CFD methods. First off, the LBM is inherently an unsteady and compressible method. This is of importance when trying to study fundamentally transient phenomena such as turbomachinery applications. Also, while the LBM is of global 2nd order, it shows acoustic dissipation properties equivalent to 6th order centered Navier-Stokes schemes and dispersion equivalent 2nd or 3rd order Navier-Stokes schemes [33–35]. This is of prime importance as it potentially allows for direct acoustic simulation.
The LBM equation is also explicit in nature, with the calculation of a step being split into a collision and convection process, allowing for massive parallelization of the algorithm and the pos- sibility to perform simulations of complex/large geometries with a reasonable return time in exchange for the use of massively parallel computer resources.
LBM Case Studies In recent years, a series of studies using the LBM have been
published, of which we present here a sample. Brès et al. [36] performed calculations on a tandem cylinder
configuration used as a benchmark for the evaluation of land- ing gear noise which were compared to experimental data gathered by NASA. Comparison of streamlines, velocity field and turbulent kinetic energy contours is favorable and the fluctuat- ing pressure spectra at the surface of the cylinders is accurately reproduced by the LBM.
Sanjosé et al. [37] also used LBM simulations to study the self-noise of a Controlled Diffusion (CD) airfoil for which there exists an extensive collection of experimental data. The study shows a good agreement with the experiments with regards to the mean flow characteristics on the airfoil (pressure coefficient and boundary layer profile) as well as the unsteady pressure fluc-
(a) (b)
FIGURE 1. ILLUSTRATION OF THE GEOMETRY OF THE AU- TOMOTIVE COOLING FAN (A) FAN ROTOR, (B) AXIS CUT OF THE SHROUD.
tuations and radiated noise levels in the farfield. The LBM was also shown to be able to accurately reproduce
the behavior of complex low-speed fan geometries. Pérot et al. and Magne et al. [9, 25] simulated a low-speed
ring-shrouded axial fan intended for automotive engine cooling applications and showed that the simulation was able to reproduce the global aerodynamic performance of the fan as predicted by experimental data. Recent work by Magne et al. [12] also showed what the far-field acoustics of the fan could be very accurately reproduced by LBM simulations given a proper repre- sentation of the installation.
Other work by Pérot et al. on an axial free-tip tube-axial test fan [26] showed similar results with regards to the capture of the aerodynamic performance of the fan.
TESTED FAN AND EXPERIMENTAL DATA Tested Fan Geometry
The fan studied in the current paper is designed for the pur- pose of automotive engine cooling. The fan itself is an axial 5- bladed fan with an outer radius of 16 cm and a 6 cm radius hub. The fan blades are highly skewed and have a variable profile and angle of attack along the span of the blades.
The tip of the blades is free, as opposed to often seen ring- shroud configurations in similar fans, and is shown to have a variable radius along the chord in conjunction with a convergent static shroud. The tip clearance is constant at 3 mm along the chord normal to the blade tip surface. The fan and shroud geometries are illustrated in Fig. 1.
During normal operation, the fan rotates at 2630 RPM and its design flowrate is 0.43 m3/s.
Available Data Experimental data was made available for this fan and in-
cluded both aerodynamic and aeroacoustic data. However, aero-
FIGURE 2. SCHEMATIC OF THE AMCA TEST CHAMBER
dynamic and aeroacoustic data were collected on separate test rigs.
Aerodynamic Setup The first rig was used to collect aerodynamic performance data conforming with the ANSI/AMCA 230-12 standards. A schematic of the AMCA flow chamber is presented in Fig. 2. In the setup, the fan/shroud assembly was inserted into a 700 mm diameter duct with an intake bellmouth and terminated by a perforated plate with a 20 cm (8 in) diameter circular aperture.
The performance curve of the fan (pressure rise as a function of flowrate) was measured on this setup through the use of two series of 4 static pressure wall taps located at 90o from each other located respectively 25 mm upstream and 35 mm downstream of the fan to measure the pressure differential across the fan plane. The pressure difference was measured using a Baratron 220CD differential capacitance manometer with a 0.15% accuracy. The torque applied to the fan was also measured using a Himmelstein & co. MCRT 3-08TLS torquemeter with a 0.01356 Nm accuracy. Additionally, a 5-hole probe was used to measure the spanwise time-averaged velocity profiles 30 mm behind the trailing edge of the fan blades for the 0.53 m3/s flowrate case.
Acoustic Setup A second experiment was setup to evaluate the acoustic performance of the fan in an anechoic environment. An assembly composed of a duct containing the fan/shroud similar to the AMCA setup was suspended and centered in an anechoic room with a length of 4.8 m, a width of 3.5 m and a height of 2.6 m to the end of the acoustic lining of the chamber. The flowrate through the fan was controlled through the use of a damper plate . A schematic of the test rig is presented in Fig. 3.
In the experiment, acoustic pressure was recorded at 81 locations located upstream of the fan, as illustrated in Fig 4. The data was recorded using a sampling rate of 24 kHz over 20 s for the 0.53 m3/s flowrate. The microphones used were BSWA Tech model MPA201 1/2 inch microphones.
Differences in Experimental Setups The main differences in the described experimental setups mainly pertains to
FIGURE 3. SCHEMATIC OF THE ANECHOIC TEST CHAMBER
FIGURE 4. MICROPHONE ARRAY FOR ACOUSTIC MEASURE- MENTS
the acoustic properties of the test environment. The AMCA experimental setup was used as a means to investigate the aerodynamic performance of the fan and was thus not placed in anechoic conditions, whereas the anechoic chamber setup was concerned with obtaining the acoustic pressure upstream of the fan using an array of microphones, as illustrated in Fig. 4.
However, there are some geometric differences in the two setups. First of all, the test duct termination was different between the two cases; the AMCA experiment used a simple perforated plate, as the flowrate through the fan was driven through the use
TABLE 1. DIMENSIONS OF THE TEST DUCT ASSEMBLY IN THE EXPERIMENTAL SETUPS
Case D1 D2 L1 L2 L3
(mm) (mm) (mm) (mm) (mm)
AMCA 1167 700 560 870 1050
Anechoic 1167 700 560 650 1050
of an auxiliary fan whereas in the acoustic setup, flowrate had to be controlled through a sliding plate used to set the system resistance.
The length of the test ducts were also a little different between the two cases, as highlighted in Tab. 1; the dimensions to those present in Figs. 2 and 3.
SIMULATION SETUP In order to try and reproduce the experimental conditions
used for both the aerodynamic and acoustic data measurement campaigns as faithfully as possible, simulations were run on two different cases.
Aerodynamic Setup For the AMCA case, the scope of the simulations was restrained to the bellmouth/duct geometry, and did not include the fairly complex flow chamber topology, including the diverse flow straighteners. Thus, the fan rig was placed inside a large prismatic domain (33 m across) reminiscent of a semi-anechoic chamber, with solid wall boundary conditions being imposed on all but two of the surfaces. On these last two surfaces atmospheric pressure is imposed. The flowrate through the fan is varied in the simulations through the modification of the radius of the hole in the diaphragm downstream of the fan and is not imposed artificially through boundary conditions, but rather resolved given the physics of the flow.
In the simulation, two circular arrays of 24 measurement points located 25 mm upstream and 35 mm downstream of the fan on the duct wall are used to mimic the pressure taps used in the experiment to evaluate the pressure rise across the fan. A series of spanwise probes was also used to measure the velocity profiles 30 mm behind the fan trailing edge to compare with the experimental 5-hole probe data gathered on the 0.53 m3/s flowrate case.
The simulations were achieved with a maximum resolution of 0.5 mm in close proximity to the fan, with the resolution in the outer layers of the simulation decreasing to 1024 mm. This resulted in 25M voxels and 37M surfels total for the simulation mesh. The timestep was 1.914*10−6 s to achieve unity CFL. A
series of coarser simulations with a resolution of 1 mm were also run, and we will hereafter refer to these simulations as ’Aero Coarse/Fine’. The resolutions used here are similar to those used in previous axial fan studies using PowerFLOW [25–27].
Acoustic Setup In the case of the simulations reproduc- ing the anechoic chamber setup, the simulation was made to include the complete geometry of the fan test rig (duct with bellmouth and damper plate assembly). The rig was then placed in a simulation volume with dimensions coinciding with those of the anechoic chamber used for gathering the experimental data to the inside of the acoustic lining of the chamber walls. A porous medium that was used to mimic the effect of the acousticly ab- sorbant liner used in the experiment. Solid walls boundary conditions are imposed on the outer limits of the simulation volume.
Besides the probes described for the AMCA simulation, additional probes were used to collect acoustic pressure upstream of the duct bellmouth according to the microphone locations used in the experimental anechoic setup. The probes resolve the pressure fluctuations up to 2080 Hz.
As with the AMCA configuration, a maximum resolution of 0.5 mm was used in proximity to the fan with the resolution in the outer layers of the simulation decreasing to 128 mm. This resulted in a mesh with 24 M voxels and 36 M surfels in total. The timestep was the same as the AMCA case. Similarly, a series of simulations with a coarser 1 mm resolution were run, and we will hereby refer to the acoustic numerical cases as ’Acoustic Coarse/Fine’.
As a visual aid, the mesh in close proximity to the duct of the anechoic simulation setup is shown in Fig. 5. The voxel regions (VRs) are identified along with the voxel size associated. It is to be noted that the grid in close proximity to the fan, VR 11 (0.5 mm elements), is set in a volume created from the offset of the fan surfaces and is difficult to vizualise in a plane.
RESULTS Aerodynamic Results
As a first step of the investigation into the performance of the simulations, the aerodynamic properties of the fan obtained numerically were compared with the available experimental data collected on the AMCA setup, namely the Q-P performance curve as well as spanwise velocity profiles behind the fan.
The data presented here is based on the simulations realized with the model mimicking the AMCA rig unless otherwise mentioned.
Global Fan Performance With regards to global fan performance, available data included the pressure rise as well as the torque applied to the fan for a series of flowrates. The characteristic performance curve of the fan can be observed in Fig. 6.
(a)
(b)
(c)
FIGURE 5. ILLUSTRATION OF THE MESH AROUND THE FINE ANECHOIC SIMULATION SETUP (A) VIEW OF THE GRID AROUND THE DUCT (B) VIEW OF THE GRID AROUND THE FAN (C) VIEW OF THE GRID NEAR THE TIP OF THE FAN.
FIGURE 6. PRESSURE CHARACTERISTIC OF THE TESTED FAN.
Present on Fig. 6 are the predictions for the pressure rise across the fan as predicted by the AMCA and anechoic simulations for the coarse and fine resolutions. Overall, it can be seen that the simulations underpredict the experimental levels by a maximum of 20 %. However, from the series of coarse simulations on both setups, it appears that the slope of the fan characteristic is reproduced by the simulations, level discrepancies not withstanding.
As was mentioned before, since the flowrate was not imposed through the use of boundary conditions, the main aim of the coarse simulations was to be able to adjust the simulations to obtain the nominal 0.53 m3/s flowrate for the fine simulations for both the AMCA and anechoic cases. However, there is a small discrepancy of approximately 3% in the flowrates, with the fine simulations exhibiting a lower flowrate than the expected 0.53 m3/s.
The torque applied to the fan is also presented in Fig. 7. A trend similar to the pressure characteristic can be observed for the torque curve, where the simulation underpredicts the experimental values by approximately 20% but seems to be able to evaluate the experimental slope as a function of flowrate.
From these results, it would appear that additional mesh con- vergence is required in order to correctly simulate the characteristics of the tested fan, as it seems to be a configuration that is very sensitive to the quality of the grid, especially when consid- ering the acoustics that are presented in a subsequent section.
Spanwise Velocity Profiles As mentioned before, time-averaged spanwise velocity profiles were also measured ex- perimentally via the use of a 5-hole probe located 3 cm behind the trailing edge of the fan on the AMCA experimental setup. This included the measurement of axial, tangential and radial ve-
FIGURE 7. TORQUE APPLIED TO THE FAN AS A FUNCTION OF FLOWRATE.
FIGURE 8. COMPARISON OF TIME-AVERAGED AXIAL VE- LOCITY 3 CM BEHIND THE TRAILING EDGE OF THE TESTED FAN ON THE AMCA SETUP
locity. The axial velocity profile is presented in Fig. 8 and com-
pared to the aforementioned 5-hole probe data.There is a good correlation between the experiment and simulation, with a small discrepancy in the flowrate (approximately 3-4 %) probably ex- plaining most of the differences seen for the fine case whereas the coarse case was very close to the 0.53 m3/s nominal flowrate. This also confirms the proper prediction of the flowrate.
Similarly, the spanwise azimuthal velocity profile is shown in Fig. 9. Overall, the shape and velocity levels from the experi-
FIGURE 9. COMPARISON OF TIME-AVERAGED AZIMUTHAL VELOCITY 3 CM BEHIND THE TRAILING EDGE OF THE TESTED FAN ON THE AMCA SETUP
ment are correctly reproduced in the simulation. However, there are still some important discrepancies. First off, the experimental data shows the appearance of a large spike in azimuthal velocity at r
rtip,T E = 0.4, which corresponds to the hub radius. There is
however a smaller amplitude spike in the numerical results. The experimental value here seems rather high for that particular po- sition as it exceeds by 66 % the value near the tip of the blade
r rtip,T E
= 1.
Near the tip of the blade, the velocity distribution is also a bit different between the simulation and the experiment, with the experimental curve showing a sharp drop in azimuthal velocity over a r
rtip,T E value of 1 whilst the simulation shows a kind of
forked profile in the tip region; the velocity levels are however very similar in that area for the fine case and the experiment. It can be seen that the velocity values near the tip were overestimated by the coarse case, with the finer mesh allowing for a better resolution of the tip flow.
In the mid-span region, a similar shape in the azimuthal velocity profile is predicted by both the simulation and experiment, with a 0.5 to 1 m/s difference being observable however between the two.
Except for the tip region, the differences in the azimuthal velocity profile predicted by the coarse and fine simulations are virtually identical.
Radial velocity profiles are not presented here, as the level of uncertainty in the experimental data was high regarding the levels of velocity due to the unsteady nature of the flow.
FIGURE 10. PSD MEASURED ON THE MICROPHONE LO- CATED ON THE ENTRANCE PLANE OF THE BELLMOUTH ON THE ROTATION AXIS OF THE FAN
Aeroacoustic Results With the aerodynamic results having proven relatively sat-
isfactory, the current study then shifted towards the main point, which is concerned with the acoustics of the fan and the related mechanisms. As previously stated, the available acoustic data consists of acoustic pressure measurements collected on an array of 81 microphones upstream of the fan for the 0.53 m3/s flowrate.
Microphone Array As a first step, the acoustic pressure predicted by the simulations was compared with the experimental data made available on the aforementioned microphone array. Figure 10 shows the power spectral density (PSD) predicted by the simulation for the coarse and fine meshes at the microphone located on the fan axis in the bellmouth plane and the corresponding experimental data. The blade passing frequency (BPF) harmonics are highlighted up to 4th.
On the graph, the spectral resolution of all presented spectra was set up to be 4 Hz. The rather coarse resolution is due to the fact that there was only 0.5 s of converged time usable in the fine simulation to evaluate the aeroacoustics; additional calculation time is being put into the simulation in order to alleviate this problem.
However, from the preliminary results, several observations can be made. First off, it can be see that the fine simulation seems to be able to capture peaks associated with the first, second and third harmonics of the BPF while they are not clearly captured on the coarse mesh. The levels, however, are not yet in accordance with the experimental results, as the simulation underestimates the first and third BPF by 8 and 15 dB respectively whereas the second BPF is overestimated by 15 dB. This suggests that noise
FIGURE 11. ACOUSTIC PRESSURE STILL SHOWING THE AP- PEARANCE OF A ROTATING (2,0) MODE IN THE 243-275 HZ BAND IN THE DOWNSTREAM CHAMBER OF THE ANECHOIC SIMULATION
predictions for this particular fan geometry are very sensible to the mesh resolution near the fan. More refined models of the setup will be run incessantly to try and reach grid independance.
The fine simulation also predicts the appearance of strong peaks in the frequency range between the BPF harmonics that, while coinciding with minor peaks in the experimental spectrum, seem exacerbated. These particular frequency bands were analyzed in more depth and are presented in the next section.
Acoustic Pressure in the Test Duct The acoustic pressure field was analyzed on an axial cut of the duct for the inter-BPF high-level frequency bands identified on the spectra in Fig. 10. The occurrence of strong rotating duct modes was observed in the downstream portion of the duct.
For example, the 243-275 Hz band thus shows the appearance of a standing rotating (2,0) duct mode, as illustrated in Fig. 11. The acoustic field in the downstream portion then drives the acoustic waves propagation along the duct wall in the upstream portion as a (2,0) mode. Figure 11 shows a longitudinal cut of the duct in the upper left corner, while the other parts of the image show crosscuts of the duct whose locations are marked on the longitudinal cut.
In a similar visualization, a (3,0) rotating duct mode is seen to appear in the downstream chamber in the 279-303 Hz band, as illustrated in Fig. 12.
At higher frequencies, strong resonance is still observed in the downstream chamber, but the modes are not clearly identi- fiable using qualitative vizualisations of the acoustic pressure,
FIGURE 12. ACOUSTIC PRESSURE STILL SHOWING THE AP- PEARANCE OF A ROTATING (3,0) MODE IN THE 279-303 HZ BAND IN THE DOWNSTREAM CHAMBER OF THE ANECHOIC SIMULATION
whereas propagation upstream forms higher radial modes. These preliminary results show that the damper plate ter-
mination seems to facilitate the appearance of standing rotating modes in the simulation by creating an almost closed cav- ity. However, with the available data it is undetermined if these modes are as dominant in the experiment as they appear to be in the simulations.
Ffowcs-Williams and Hawkings analysis Using the fan surface as a source, the Ffowcs-Williams Hawkings (FWH) analogy with free-field propagation was also employed to compare with the direct acoustic results of the simulation. The result is shown in Fig. 13. The reader should keep in mind that that some of the differences in level between the FWH and the direct acoustic evaluation are attributable to the directivity effects of the duct and the absence of some sources in the FWH evaluation.
However, from the comparison of the direct acoustics and the FWH analogy, it can be observed that both the BPF harmonics and the inter-BPF peaks at 175 Hz, in the 332-405 Hz band and at 565 Hz that are present in the direct acoustic evaluation are also represented in the FWH spectra, which identifies the fan as the source of these frequency peaks. These inter-BPF peaks do coincide with peaks in the experimental spectra, albeit with exacerbated levels in the simulation.
It is however seen that the 243-275 Hz and 279-303 Hz peaks are absent in the FWH spectra, encouraging the interpreta- tion of these specific frequency peaks as being due to installation effects (strong duct modes).
FIGURE 13. PSD AT THE MICROPHONE LOCATION LOCATED ON THE ENTRANCE PLANE OF THE BELLMOUTH ON THE RO- TATION AXIS OF THE FAN AS MEASURED DIRECTLY IN THE SIMULATION AND THROUGH A FWH FREE-FIELD PROPAGA- TION USING THE FAN AS A SOURCE.
Surface PSD The pressure fluctuations on the fan blades corresponding to the different frequency bands where high-level peaks were present also analyzed.
Figures 14 to 17 present the PSD levels of the filtered pressure fluctuations on the surface of the fan, with the suction side shown in the left part and the pressure side shown on the right and a view of the tip surface in the middle for four different frequency bands, namely the 165-185 Hz, 210-230 Hz (1st BPF), 325-405 Hz and 485-605 Hz bands.
For the 165-185 Hz band in Fig. 14, it is possible to see that the pressure side presents the most elevated PSD levels, with a concentation being apparent in the tip region of the blade along the leading edge. There is also a high PSD level on the suction side along the leading edge in the tip region and along the tip edge.
Figure 15 presents the PSD levels of the filtered pressure fluctuations around 1st BPF, with the suction side shown on the left, the pressure side on the right and a view of the tip surface in the middle. From the suction side view, it can be seen that there is a high level of pressure fluctuations near the leading edge in the tip region of the blade. The same occurrence can be observed on the pressure side, but the elevated PSD region covers approximately a third of the blade chord instead of only the leading edge area. A similar pattern can be observed in the 325-405 Hz band in Fig. 16.
For the higher 485-605 Hz in Fig. 17 band, it can be seen that the tip region is the main zone of high levels of pressure fluctuations., with hotspots once again apparent near the leading
FIGURE 14. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN BLADES FOR THE 165-185 HZ FREQUENCY BAND.
FIGURE 15. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN BLADES FOR THE 210-230 HZ FREQUENCY BAND (1ST BPF).
edge of the blade and along the tip edge on the pressure side. These vizualisations highlights that the tip region of the
blade seems be subjected to intense pressure fluctuations. This is thought to be due to the influence of the vortices coming from the preceding blades’ tip gap flow.
Vortices can be identified using the λ2 criterion proposed by Jeong and Hussain [38]. The criterion is based on taking the gradient of the steady, incompressible and inviscid Navier-Stokes equations, which yields
S2 + 2 =− 1
ρ ∇(∇p) (3)
where S and are the symmetric and antisymmetric parts of ∇u and represent the strain and vorticity tensors, or
Si j = 1 2
∂xi
) (5)
and ∇(∇p) is the pressure Hessian. The criterion is made to take the eigenvalues λ1 ≥ λ2 ≥ λ3 of the matrix S2+
2 to deter- mine the existence of a local minima in the pressure distribution due to vortical motion when S2 +
2 has two negative eigenvalues, which ensures an ’excess’ of vorticity when compared to the strain in an eigenplane, thus defining a vortex core.
Using this criterion, a large vortex structure is seen forming in Fig. 18 on the suction side edge of the tip surface and is con- vected towards the following blade’s pressure surface, passing near the leading edge. These vortical structures are inherently unsteady and would produce high pressure fluctuations as they pass near the blade surface, impacting both the aerodynamic and acoustic performance of the fan. They could also be construed to be the main reason behind the appearance of BPF tones as they created distortions in what would otherwise be a clean inflow where the BPF tones would not be able to appear.
The tip surface is also presented in the middle of Figs. 15 to 17; it can be seen that there are important pressure fluctuations on the tip surface as well, which can be attributed to the high-speed jet-like flows associated with tip leakage flow [8, 39].
FIGURE 18. ISOSURFACES OF λ2 OF VALUE -0.5 SHOWING THE DEVELOPMENT OF VORTICAL STRUCTURES IN THE TIP GAP OF THE TESTED FAN
CONCLUSION In this paper, preliminary simulation results covering both
the aerodynamics and aeroacoustics of a low speed axial fan were presented.
It was shown from a comparison of the global performance characteristics of the fan that the simulations tended to underesti- mate the fan pressure rise. However the pressure characteristic’s slope was well represented. A similar trend is observed for the torque characteristic. This was surprising as good results were achieved on a ring-shrouded fan also used in automotive cooling applications in previous studies [12,25] with similar mesh resolutions. Further investigation is underway to verify that the current numerical setup correctly reflects the experimental conditions.
A good agreement was found between simulation and experiment for the axial velocity profiles behind the fan. Looking at the azimuthal velocity however, while the overall level and shape of the profiles were well reproduced by the fine simulation, discrepancies still exist near the hub and tip of the blade between the numerical results the experiment. An improvement in the prediction of the azimuthal velocity levels in the tip region with the refinement of the mesh was however observed.
Regarding the acoustics of the fan, it was first seen that the coarse anechoic simulation did not allow to properly capture the BPF harmonics seen in the experiment, whereas the fine case captured the three first harmonics, albeit with differences in the levels observed. The fine acoustic simulation also produced high peaks in the inter-BPF frequency bands that, while coinciding with minor peaks in the experimental spectra, seem exacerbated in level. These seem to be due to strong resonance effects in the downstream chamber and the formation of duct modes. However, a free-field FWH analysis using the fan surface as a source also highlighted the fact that some of the inter-BPF bands, namely the 175 Hz, 330-400 Hz and 565 Hz peaks, can be related to surface pressure fluctuations on the blades.
An analysis of the filtered pressure fluctuations on the fan blades also highlighted the presence of high levels of fluctuations associated with the tip region in the frequency bands associated with peaks in the numerical spectra. Elevated levels of pressure fluctuations near the leading edge on the suction side as well as hotspots present on the pressure side of the blades near the tip are throught to be due to the influence of vortical structures generated by tip leakage flow from the preceeding blades. Impor- tant fluctuations were also observed on the tip surface of the fan blades, which could be attributed to the jet-like flows associated with tip leakage. This tends to point to tip leakage flow as a potentially important contributor to the fan noise and provides a possible explanation of the strong BPF tones observed in this fan configuration. This could also explain the acoustic sensitivity of the configuration to the resolution of the mesh in the tip gap, as the fine mesh appears to resolve the tip flow better according to the spanwise velocity profiles.
However, the model still needs refinement, as it was observed that the acoustics of the fan in particular were very sensitive to grid refinement and that in this respect grid independance was almost surely not reached so far. Further simulations on this impeller are being run in order to ascertain these claims.
ACKNOWLEDGMENT This research was financed in part thanks to a scholarship
from NSERC-CREATE. A sincere thanks to Robert Bosch LLC for their financial and
technical support. Computations using PowerFLOW were made possible due
to an academic license agreement and technical support from the EXA Corporation and were performed on the supercomputer Mammouth-MP2 from Université de Sherbrooke, managed by Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innova- tion (CFI), NanoQuébec, RMGA and the Fonds de recherche du Québec - Nature et technologies (FRQ-NT).
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aeroacoustics of a low-speed free tip fan with a complex

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