FEDSM AERODYNAMIC NOISE SIMULATION OF PROPELLER FAN BY LARGE EDDY SIMULATION

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1 Proceedings of FEDSM27 5th Joint ASME/JSME Fluids Engineering Conference July 3-August 2, 27 San Diego, California USA FEDSM AERODYNAMIC NOISE SIMULATION OF PROPELLER FAN BY LARGE EDDY SIMULATION Shingo Hamada ADVANCED TECHNOLOGY R&D CENTER MITSUBISHI ELECTRIC Corp , Tsukaguchi-honmachi, Amagasaki, Hyogo, , Japan Chisachi Kato Institute of Industrial Science, The University of Tokyo Komaba, Meguro-ku, Tokyo, , Japan Seiji Nakashima ADVANCED TECHNOLOGY R&D CENTER MITSUBISHI ELECTRIC Corp , Tsukaguchi-honmachi, Amagasaki, Hyogo, , Japan Yoshinobu Yamade Institute of Industrial Science, The University of Tokyo Komaba, Meguro-ku, Tokyo, , Japan ABSTRACT In this paper, unsteady flow and aerodynamic noise are numerically investigated for a half-open type propeller fan used for outdoor air conditioner components. The flow field is calculated by Front Flow/Blue, which is based on Large Eddy Simulation (). The Standard Smagorinsky Model (SSM) and Dynamic Smagorinsky Model (DSM) were used as sub-grid scale models. Aerodynamic noise was calculated by Curle's equation based on the pressure fluctuation on the blade surface computed by. The computed static pressure rise of the fan showed reasonable agreement with the measured equivalent. The time-averaged distributions of the three velocity components downstream of the blades were also compared with those measured by hotwire anemometry, which showed satisfactory agreement between the computed and measured velocity profiles. But the tip vortex passage which was detached from the blade surface predicted by was not stable as measured by the experiment. Finally, the predicted far-field sound spectrum agrees reasonably well with measurements in a frequency range of 1 to 1 Hz although the sound pressure level was underpredicted in the lower frequency range. Keywords: Aerodynamic Sound, Propeller Fan, Prediction, Validation Decoupling Method, Curle's Equation, Large Eddy Simulation, Tip Vortex 1. INTRODUCTION The aerodynamic noise of a propeller fan is a major noise source of air conditioners and ventilating systems. Such noise rapidly increases with the rotational speed of the fan, which cannot be avoided by product restrictions. In fact, the aerodynamic noise of a propeller fan increases with the 5 th to 6 th power of the rotational speed of the blades. Therefore, further reduction in aerodynamic noise is crucial to the design of a new fan shape. Figure 1 shows a picture of our company's products in which a propeller fan is assembled. A half-open type propeller fan, for which the blade tip greatly protrudes outside the bellmouth, as shown on the right in Fig. 1, is designed to produce a relatively small pressure head and is used in the outdoor component of air conditioners or ventilating systems. 1 Copyright 27 by ASME

2 propeller fan achieved. Also, the noise generation mechanism of propeller fans has not yet been clarified. In this study, we conduct numerical calculation for a half-open type propeller fan, predict aerodynamic noise, and discuss the three-dimensional flow structures that primarily influence aerodynamic noise generation. air conditioner ventilating fan Figure 1. Industrial products using propeller fans At present, the basic parameters of a half-open type propeller fan are investigated in the prototyping of a product, and noise reduction of the products is accomplished by choosing the most suitable design parameters available within our company. However, further noise reduction seems to be difficult with this conventional approach based on "rules of thumb" and, we believe it cannot be achieved without clarifying the noise source and understanding the mechanism of noise generation from such a fan. There have been many studies on the internal flow of axialflow fans based on Reynolds Averaged Navier-Stokes Simulation (RANS) (Gerhard et al., 21; Nallasamy et al., 22). Since RANS is based on time-averaged calculation, its ability to explain the phenomena in an unsteady flow is limited. On the other hand, recently numerical calculation has often been used for understanding unsteady phenomena for which RANS is not suitable. Jang et al. (21) and Furukawa et al. (23) conducted numerical calculation for a half-open type propeller fan and found that the flow field around the blade has three-dimensional complex vortical structures. They also found that low-energy fluid accumulated between the tip vortex and the pressure side of the neighborhood blade because the blade leakage flow and wake from the leading edge of the blade was rolled into the strong rotating and swirling flow of the tip vortex. On the other hand, based on, developed a flow analysis code called "Front Flow/Blue" and showed various applications to the internal flow of turbo-machinery and aerodynamic noise prediction (Kato, C. and Ikegawa, M., 1991; C. Kato, et al., 23, 27). Miyazawa (25) conducted numerical calculation that resolved the turbulent boundary layer on an isolated airfoil (NACA12) by the above code and showed that aerodynamic noise from the airfoil can be accurately predicted. Yamade et al. (25, 26) conducted numerical calculations for a ducted axial-flow fan with six blades by using a numerical grid with approximately same resolution as Miyazawa used for his computation. They concluded that the characteristics of the turbulent boundary layer on the blades were qualitatively caught by the longitudinal vortex structures. However, none of the above computations discuss the validation of their computation in terms of the frequency spectra of the far-field sound of a propeller fan, and quantitative prediction of the sound pressure spectra has not yet been 2. NOMENCLATURE C m axial velocity component of absolute flow C r radial velocity component of absolute flow C u rotational velocity component of absolute flow D diameter of blade tip = 4 [mm] f frequency [Hz] R radius [mm] U t tip rotational speed = P pressure [Pa] Greek smbols density of fluid =1.25 [kg/m 3 ] 3. TEST PROPELLER FAN The half-open type propeller fan we considered in this study is shown in Fig. 2. Detailed specifications are shown in Table 1. The downstream (lower) part of the bellmouth is aligned with the meridional shape of the blades in the axial direction. hub 6 flow direction blade 2 Figure 2. Propeller fan model bellmouth 15 R15 tip clearance 6 2 Copyright 27 by ASME

3 Table 1. Specifications of propeller fan diameter of blade tip 4 [mm] hub diameter 12 [mm] hub ratio.3 [-] number of blades 3 [-] designed flow rate 3 [m 3 /min] density of air flow 1.25 [kg/m 3 ] number of revolutions 8 [r/m] tip speed tip clearance 6 [mm] blade pitch became a power of 2 (=2 9 ) to precisely output the frequency spectra. The upstream stationary grid was composed of 229,376 elements, the rotating fan's grid of 1,742,28 elements, and the downstream stationary grid of 229,376 elements. The rotating grid was overset to the stationary grid to maintain continuity between the rotating and stationary grids as already mentioned. The surface grid of the fan, shown in Fig. 4. was created from an H-shaped mesh between the neighbouring two blades, and the entire model was created by copying it three times. The inner area of the hub was based on a square mesh topology to avoid undesired grid concentration there. The maximum skewness of the grid was 62.8º, the minimum inner angle was 1.9º, and the minimum cell size was 5.67 * 1-4 normalized by the diameter of the blade tip D. 4D inlet boundary 4. CALCULATION METHOD In this research, we used a finite element method-based code that has second-order accuracy in time and space. Standard and dynamic Smagorinsky models were used as sub-grid scale models. The momentum equations were implicitly integrated with respect to time, and the fractional-step method was used for pressure calculations. Aerodynamic noise was calculated based on the pressure fluctuations that resulted from the unsteady flow field. The sound source was assumed to be compact, and Curle's equation was used. The computational grid used in this study is shown in Fig. 3. It is composed of hexahedral elements. The grid around the propeller fan has been removed for visibility. The total grid consisted of three parts: upstream, fan neighborhood and downstream and each part is overset with its upstream and downstream part with an approximate overlap margin where values of instantaneous velocity and pressure are interpolated from its neighbouring part. The streamwise length of the upstream and downstream parts are respectively 2D and 3D, and their diameter is 4D where D denotes the diameter of the blade tip. The uniform inlet boundary condition was set to the upstream grid, the pressure boundary condition was set to the downstream grid, and the non-slip boundary condition was set to the stationary walls. The upstream inlet boundary and the downstream pressure boundary used a non-reflective boundary condition (NRBC) to prevent unphysical pressure fluctuations. The low-mach-number assumption was used for stable computation of low-speed flow. The Mach-number (M) was set to.1 and.2. The reverse rotating condition was put on the bellmouth wall in the rotating grid because the wall was stationary from the absolute frame of reference. Starting from zero initial flow field for velocity and pressure, the computed flow field reached a satisfactory stable state after fifteen revolutions of the impeller. We conducted computation during additional ten revolutions of the impeller and obtained statistical averages of the flow field. The time steps for one impeller revolution were set to 1536, which resulted in 4.88 * 1-5 seconds in real time. It was set up so that the time steps for one 2D 3D non-slip wall propeller fan pressure boundary Figure 3. Computational grid 3 Copyright 27 by ASME

4 square mesh topology Fully Anechoic Room Microphone 1 Microphone 2 45º.7 m.7 m Flow Figure 4. Surface grid of propeller fan Chamber Room Rotating Shaft 5. EXPERIMENTAL METHOD Pressure rise characteristics and aerodynamic sound were measured to verify the validity of the numerical calculation. The experimental apparatus is shown in Fig. 5. The fan was rotated by connecting it to the rotating shaft in the chamber room, and exit flow from the fan was exhausted from the anechoic room to the chamber room. The background noise of the anechoic room was 12 [dba]. A microphone was set at.7 m upstream in the axial direction from the hub surface to measure the aerodynamic noise power spectrum. The maximum frequency was set to 5 khz, and the FFT line was set to 248, so the frequency resolution f corresponded to 6.25 Hz. The averaging number was set to 64, and data during 8192 fan rotations were sampled. For performing FFT, a Hanning window function was applied to each sampled data set. The spectrum level was corrected inside the measurement equipment to compensate for the effect of the window function. An antialiasing filter was used to remove unphysical high frequency components. The three-dimensional flow vectors of the wake of the fan were also measured in a plane at the lower edge of the hub using measurement technology developed by Kuroumaru et al. (1982), who used a hotwire probe that inclines at 45º to the main flow direction. Correlation between the degree of probe and output voltage of the hotwire sensor was changed to approximate function by a least-squares approach, and the flow magnitude and direction were calculated by solving simultaneous equations. The sampling frequency was selected as 8.5 khz, which corresponded to 638 points in one revolution. Ensemble-averaged flow field was obtained to calculate the time-averaged field. The measurement system is shown in Fig. 6. Capitalize Motor for Consistency Figure 5. Aerodynamic noise measurement Propeller Fan Traverse Rail Hotwire Probe Figure 6. Wake flow measurement Trigger Sensor 6. RESULTS 6.1 STATIC PRESSURE RISE A comparison of the static pressure rise is shown in Fig. 7. At 3 m 3 /min, which is the designed flow rate of the test fan, predicted static pressure rise is 21.9 Pa while the measured one is 25.9 Pa, which shows 15% underprediction in. The discrepancy may be attributed to the overprediction of the wall friction that results from insufficient grid resolution for resolving the turbulent boundary layer on the blades. Underprediction of the Euler's head may also be the reason for the discrepancy. 4 Copyright 27 by ASME

5 8 StaticPressureRise[Pa] FlowRate[m 3 /min] Figure 7. Static pressure rise computed by 6.2 WAKE FLOW Figure 8 shows a comparison of the predicted and measured distributions of the time-averaged velocity vectors in a cross section 1mm downstream of the bottom of the hub. Although the tip vortices are clearly seen in the measured distribution, they cannot be clearly seen in the, and their strength is much weaker than in the experiment. Comparisons of the magnitude and the three components of the time-averaged absolute velocity vectors behind the blades are shown in Fig. 9. The overall agreement between the predicted and measured distributions is satisfactory. In particular, the wake of the blades is quantitatively predicted by the present (Fig. 9-(c)). But the tip vortices are not clearly seen in, and their strength is much weaker compared to the measurement (Figs. 9-(b) and (c)), as mentioned already. This discrepancy may have resulted from the insufficient resolution of the computational grid around the tip leakage region. The predicted and measured velocity distributions behind the blades, which are averaged in terms of time and rotational direction, are compared in Fig. 1. The predicted magnitude of the velocity vector is smaller than the experiment, the predicted magnitude qualitatively agrees with the measured one. Both distributions have a peak at around R/D =.45 (Fig.1-(a)). The predicted radial velocity C r is larger than the experiment and has a peak near the tip leakage region (Fig. 1-(b), R=.45). But the experiment shows somewhat more uniform distribution except two slight peaks: R/D =.45 and R/D =.25. The predicted rotational velocity C u is larger than the experiment in the tip leakage region (Fig. 1-(c)). The tip vortex was seemed to be attached to the blade surface and rotated with it in the calculation; but in the experiment the tip vortex was seemed to be slightly detached from the blade surface, and the rotating speed of the tip vortex maybe deaccelerated. Regarding the axial velocity component, flow rate seems different. This is because the main flow direction which hits hotwire probe is shallow and includes errors. The predicted profile qualitatively agrees with the measured one and both profiles have a peak at around R/D =.4 (Fig.1-d)). (a) (b) Figure 8. Comparison of average flow field 5 Copyright 27 by ASME

6 R/D.3 13 (a) Magnitude of Velocity Vector C mag/u t (a) Magnitude R/D (b) Radial Component C r/u t (b) Radial component R/D (c) Tangential Component C u/u t (c) Tangential component R/D (d) Axial Component Figure 9. Comparison of magnitude and velocity components C m /U t (d) Axial component Figure 1. Comparison of the time and tangentially averaged distributions of absolute flow velocity downstream of blades 6 Copyright 27 by ASME

7 6.3 TIP VORTEX Instantaneous and ensemble-averaged velocity fields computed by which are in the section cut to pass through the center of the outer circular arc, are shown in Fig. 11. In the instantaneous velocity field, the tip vortex on the blade surface and the strong vortex from the upstream blade can be seen clearly. On the other hand, in the ensemble-averaged velocity field, the tip vortex on the blade surface can be seen clearly, but not the vortex from the upstream blade. This is probably because the tip vortex is likely to become unstable when it detaches from the blade surface due to the diffusion in the. To the contrary, the tip vortex stays stable even after it detaches from the blade surface in the experiment as clearly seen in Fig.8-(b). tip vortex strong vortex the broadband spectrum higher than this frequency is quantitatively predicted by the present. The predicted level by DSM is greater than that by SSM above the 3 rd harmonics (12 Hz). Regarding the Mach number, it doesn't shows no appreciable difference in the predicted sound pressure level except for high frequency which is effected by low-machnumber assumption. SoundPressureLevel[dB/HZ] Frequency[Hz] (a) Effects of SGS models,ssm,m=.2,nrbc,dsm,m=.2,nrbc control surface control surface (a) Instantaneous (b) Ensemble-averaged Figure 11. Velocity field computed by tip vortex weak vortex 6.4 AERODYNAMIC NOISE Finally, the aerodynamic sound predicted by was compared with the measurement, and the result is shown in Fig. 12. The blade passing frequency is 4 Hz. In the measurement, a peak is observed at the blade passing frequency (4 Hz) and its harmonics (8, 12 and 16 Hz). The peak levels predicted by at the blade passing frequency (4 Hz) and its second harmonics (8 Hz) are much lower than the measured values around 2 db. But, the level of the 3 rd harmonics (12 Hz) and SoundPressureLevel[dB/HZ] ,DSM,M=.1,NRBC,DSM,M=.2,NRBC Frequency[Hz] (b) Effects of Mach-Number, M Figure 12. Comparison of sound pressure levels 7. CONCLUSION In this study, numerical calculation was conducted for a half-open type propeller fan, and the computed pressure rise, wake flow behind the blades and aerodynamic noise were compared with experimental results. The flow field is calculated by Front Flow/Blue, which is based on Large Eddy Simulation. The Standard and Dynamic Smagorinsky Model were used as sub-grid scale models. Aerodynamic noise was calculated by Curle's equation based on the pressure fluctuation on the blade surface computed by. We obtained following results: calculation showed 15% smaller static pressure rise than measurement at the designed flow rate. 7 Copyright 27 by ASME

8 Flow field characteristics qualitatively agreed with the measurement in the wake. As for the swirling flow due to the tip vortex, calculation did not show it as clearly as in the measurements. The tip vortex was seemed to be attached to the blade surface and rotated with it in the calculation; but in the experiment the tip vortex was seemed to be slightly detached from the blade surface. The tip vortex generated on the blade surface is stable, but it can not seen clearly when it reached to the downstream blade in. The sound frequency of NZ, 2NZ, 3NZ, and 4NZ were quantitatively predicted. The 3NZ sound pressure level almost corresponded to the measured value. In the effects of Mach-number M, it doesn't shows no appreciable difference in the predicted sound pressure level except for high frequency. In the future, we will increase sampling times to clearly extract low frequency events. Grid resolution will also be fine for improving the accuracy of higher frequency. ACKNOWLEDGMENTS This research was done jointly between the Advanced Technology R&D Center at the Mitsubishi Electric Corporation and C. Kato Laboratory at The University of Tokyo. calculation software "Front Flow/Blue" developed at The University of Tokyo was used for the fluid analysis. This software was developed by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan under an IT research program called "Frontier Simulation Software for Industrial Science." The authors appreciated access to this software. Gerhard, A. et al., 21, "Numerical simulation of aeroacoustic sound generated by fans under installation conditions," AIAA Kato, C. and Ikegawa, M., 1991, "Large Eddy Simulation of Unsteady Turbulent Wake of a Circular Cylinder using the Finite Element Method," ASME FED-Vol. 117, pp Kuroumaru, M. et al., 1982, "Measurement of Three Dimensional Wake Flow from Impeller by Periodic Sampling," JSME, Japan Society of Mechanical Engineers, Series B (in Japanese), Vol. 48, No. 427, pp Miyazawa, M., 25, Doctoral thesis, The University of Tokyo (in Japanese). Nallasamy, M. et al., 22, "Fan Noise Source Diagnostic Test - Computation of Rotor Wake Turbulence Noise," AIAA Yamade, Y. et al., 25, "Large Eddy Simulation of Flow around Rotor Blades in an Axial-Flow fan," JSFM, Japan Society of Fluid Mechanics, E5-4. Yamade, Y. et al., 26, Large Eddy Simulation and Acoustical Analysis for Prediction of Aeroacoustics Noise Radiated From an Axial-Flow Fan., Proceeding of ASMEFEDSM, FEDSM REFERENCES C. Kato, et al., 23, An Overset Finite-Element Large- Eddy Simulation Method with Application to turbomachinery and Aeroacoustic, Transactions of the ASME, Journal of Applied Mechanics, vol.7, pp C. Kato, et al., 27, Numerical prediction of sound generated from flows with a low Mach number. Computers & Fluids, vol. 36, pp Furukawa, M., et al., 23, " Analysis of Separated Vortical Flow Field in a Propeller Fan," JSFM, Japan Society of Fluid Mechanics (in Japanese), A8-4. Jang, C-M, Furukawa, M. and Inoue, M., 21, Analysis of Vortical Flow Field in a Propeller Fan by LDV Measurements and : Part 1. Three-Dimensional Vortical Flow Structures, Transactions of the ASME, Journal of Fluids Engineering, Vol. 123, No. 4, pp Jang, C-M, Furukawa, M. and Inoue, M., 21, Analysis of Vortical Flow Field in a Propeller Fan by LDV Measurements and : Part 2. Unsteady Nature of Vortical Flow Structures due to Vortex Breakdown, Transactions of the ASME, Journal of Fluids Engineering, Vol. 123, No. 4, pp Copyright 27 by ASME