Fan Noise Control by Enclosure Modification Moohyung Lee a, J. Stuart Bolton b, Taewook Yoo c, Hiroto Ido d, Kenichi Seki e a,b,c Ray W. Herrick Laboratories, Purdue University 14 South Intramural Drive, West Lafayette IN, 4797-231, USA d,e SONY Corporation, 7-35 Kitashinagawa 6-chome, Shinagawa-ku, Tokyo, 141-1, Japan a leemoohy@ecn.purdue.edu; b bolton@ecn.purdue.edu; c tyoo@purdue.edu; d Hiroto.Ido@jp.sony.com; e Kenichi.Seki@jp.sony.com Abstract In the present study, a structural modification approach to reducing the sound power radiated by an axial fan mounted to an enclosure is described. An axial fan operating in free-space exhibits a dipole-like radiation pattern at sufficiently low frequencies that the source is compact. When a fan is mounted to an enclosure, however, the sound radiation pattern becomes monopole-like since only one side of the fan is exposed to the exterior space; thus it radiates more efficiently than the same fan operating in free-space. Also, it is possible for the source level to be amplified by coupling with the interior resonances of the enclosure. The radiation enhancement can be suppressed by introducing a second path that allows the sound fields on both sides of the fan to interact with each other while also providing damping for the acoustical cavity, thus reducing the radiation efficiency of a fan towards its free-space value. Experimental results are presented here to demonstrate this effect. The sound fields radiated by two fans mounted to a consumer electronics enclosure were visualized by using near-field acoustical holography, and the baseline results were compared with those for various enclosure modifications. First, the top of the enclosure was replaced by an acoustically-transparent mylar sheet. Then two types of acoustical openings, i.e., a grilled port and a perforated panel, were introduced on the top of the original enclosure close to fan locations. A significant reduction of sound power resulted from the enclosure modifications, in particular at the fundamental and twice the blade passing frequencies, and a clearer conversion from a monopole to a dipole-like radiation pattern was observed when the size of the opening was made larger. 1. INTRODUCTION Axial fans are widely used for electronic cooling, but their use often results in a noise nuisance. To find efficient noise control solutions for these cases, it is important to
understand the noise generation mechanisms of a fan. Among the various source mechanisms that contribute to the overall noise emission, the most dominant source type, especially in the case of the low-speed fans that are considered in the present study, is known to be the dipole-like source that is generated by the fluctuating pressure distribution on the surface of the blades [1]. Thus, an axial fan in free-space can be modeled as a point dipole whose source strength is proportional to the magnitude of a fluctuating point force so long as the compact source assumption holds true (i.e., when the dimensions of the fan are much smaller than an acoustic wavelength). It is also known that the source strength of an aerodynamically-induced dipole source of the latter kind is proportional to the sixth power of the flow speed [1]. Therefore, the simplest remedy for fan noise problems is to decrease the rotational speed of a fan while maintaining the volume flow rate by increasing the size of a fan in order to achieve the same cooling performance; the application of the latter approach is often restricted, however, either by the design layout or cost issues. Instead, a careful optimization of the blade shape can help reduce the aerodynamic noise generation. But, in addition to reducing noise at the source, some consideration should be given to practical issues that would help ensure low noise emission: e.g., the fan location must be chosen so that it does not entrain disturbed aerodynamic inflow since a disturbed inflow condition resulting from obstructions that are located close to the fan inlet results in an increase in noise. Since noise caused by structural vibrations is also of concern, a fan should be well-balanced so that it does not cause significant vibration, and a fan should be well-isolated from the structure to which it is mounted. In addition, when a fan is mounted to an enclosure, the sound radiation pattern becomes monopole-like rather than dipole-like since the interaction between the sound fields on the two sides of the fan is prevented by the enclosure. Since a lower-order source radiates sound more efficiently than higher-order sources, a fan mounted to an enclosure results in a higher radiated sound power level than the same fan operating in free-space. Also, the sound level can be amplified by the effect of the enclosure s interior acoustical resonances. The structural modification scheme described in the present study is based on a physical understanding of the latter aspects of acoustical sources. The main idea is to introduce an acoustical path between the sound fields on the two sides of the fan so that cancellation can occur, thus reducing the overall sound radiation, while at the same time weakening the effect of the interior acoustical resonances. In the present study, the proposed scheme was applied to a consumer electronics enclosure, which was equipped with two cooling fans. Some examples of enclosure modification are presented, and their noise reduction effect was verified experimentally by using near-field acoustical holography. 2. NEAR-FIELD ACOUSTICAL HOLOGRAPHY Near-field acoustical holography (NAH) [2] is an array-based measurement technique that allows various acoustical properties (e.g., the sound pressure, the particle velocity, and the acoustic intensity) to be reconstructed in three-dimensional space based on the use of the sound pressure measured on a two-dimensional surface (i.e., the hologram surface). In DFTbased NAH, the projection of the sound field onto a surface of interest is performed in the wave number domain. That is, in planar NAH of the type which was implemented in the present study, the wave number spectrum of the acoustical property to be reconstructed, a ( kx, ky, z), is obtained by multiplying the wave number spectrum of the measured pressure on the hologram surface, p ( k, k, z ), by appropriate propagator functions: i.e., x y h
a( k, k, z) = F α ( k, k ) G( k, k, z z ) p ( k, k, z ), (1) x y x y x y h x y h where z and z h are the vertical locations of the reconstruction surface and the hologram surface, respectively, G ( k, k, z z ) is a diagonal matrix whose elements are given by x y h = e G ( k, k, z z ) k = e ρck ikz( z zh) i x y h z ikz( z zh), for the sound pressure, for the normal particle velocity (2) α F ( kx, ky ) is a diagonal matrix that implements wave number filtering, and k is the wave number that satisfies the relation k 2 = k 2 2 2 x + ky + kz. The filtering procedure is necessary especially when back-projecting towards a source since the reconstruction results can be degraded by the amplification of measurement noise associated with evanescent wave componenets that cannot be accurately estimated during a measurement owing to their rapid α decay. Various regularization methods [3] can be used to construct F ( kx, ky ), and, in the present study, modified Tikhonov regularization was implemented in conjunction with the Mozorov discrepancy principle. Once a ( kx, ky, z) is obtained by using Eq. (1), the spatial distribution, a( x, yz, ), can be obtained by taking the two-dimensional inverse Fourier transform of a ( kx, ky, z). In practical holography measurements of a source comprising a number of uncorrelated sub-sources [4], as in the present case, a cross-spectral procedure based on the use of a set of fixed references must be used to identify the phase distribution of each partial field; it is recommended that a larger number of references than the actual number of sub-sources be used to minimize the effect of measurement noise [4]. The composite sound field measured in the latter approach needs to be decomposed into spatially coherent partial fields in order to enable the holographic projection described earlier, and the total sound field is then obtained by adding the projected significant partial fields together on an energy basis. The number of significant partial fields can be identified as the number of fields that causes the sum of the virtual coherence functions to have a unity value over the entire hologram surface [4]. 3. EXPERIMENTAL SETUP In Fig. 1, the research prototype of consumer electronics enclosure used in the present study and the NAH measurement setup are shown. The consumer electronics enclosure had a dimension of 42 cm x 34 cm x 7.5 cm (L x W x H), and two 6 cm diameter fans were installed on both sides of the unit: an intake fan was mounted on the left side (at x = cm and y = -21 cm), and an exhaust fan was mounted on the right side (at x = cm and y = 21 cm); the blue arrows in Fig. 1 show the direction of air flow through the two fans. During measurements, the unit was placed on a rigid surface, and seven reference microphones were distributed around it. Two references were placed near each fan and three references were placed over the top of enclosure. The sound field on the planar hologram surface located 2 cm above the top of the enclosure was measured at 11-by-16 points: i.e., a linear array comprising eleven, equally-spaced (8 cm) field microphones was traversed in the y-direction in 16 steps with an increment of 8 cm. The measurement bandwidth was 2.5 khz, and the frequency resolution was 2 Hz.
Scanning array (11 mics.) x y Figure 1: The consumer electronics enclosure and the NAH measurement setup (red and blue arrows represent reference microphones and the direction of air flow, respectively). The enclosure was modified in three ways: first, the whole top of the enclosure was replaced by an acoustically-transparent mylar sheet, thus allowing the sound fields on both sides of fans to interact with each other freely while the air flow was maintained within the enclosure (see Fig. 2(a)). The next two modifications were chosen considering their applicability to real products. A grilled port and a perforated panel were added to the top of the enclosure near the fan locations as shown in Figs. 2(b) and (c). In both cases, a mylar sheet was also applied to the openings to prevent air from flowing out through them. In all cases, the same current was provided to the two fans so that they operated at the same nominal rotational speed. Nonetheless, a small difference in the two fans speed in each case was observed presumably due to slight changes of the flow conditions experienced by the fans. 8 cm 26.5 cm 5 cm 7 cm (a) mylar top (b)grilled port and mylar (c) perforated panel and mylar Figure 2: Modifications of the enclosure. 4. RESULTS In Fig. 3, the singular values of the reference cross-spectral matrix are presented, and the green line represents the sum of the singular values (i.e., the total autospectral amplitude of the reference signals). In the original enclosure case (see Fig. 3(a)), it was observed that the first two blade passing tones dominated the frequency spectrum, and that the overall level of the sum of the singular values in the ~ 2 khz band was 71.3 db. In comparison, it was observed that the levels of the two dominant blade passing tones were reduced by the enclosure modifications; however, the higher harmonics of the blade passing tones were increased slightly in some cases (see Figs. 3(b), (c), and (d)). The overall level of the
summed singular values was reduced to 7.9 db in the mylar top case, 71.1 db in the grilled port case, and 7.8 db in the perforated panel case. Note that the overall level change does not accurately reflect the noise reduction effect at the blade passing tones since blade passing tones are usually narrow-band, the overall level usually being dominated by broadband noise. Also, the reference signals measured at a small number of points in a source s nearfield may not be correlated with the farfield sound power when the effects of either nearfield or farfield radiation directivity are significant. 8 6 8 6 Singular Values [db] 6 4 2 4 2-2 Sum of Singular Values [db] Singular Values [db] 6 4 2 4 2-2 Sum of Singular Values [db] -2 5 1 15 2 Frequency [Hz] (a) original enclosure case -2 5 1 15 2 Frequency [Hz] (b) mylar top case 8 6 8 6 Singular Values [db] 6 4 2 4 2-2 Sum of Singular Values [db] Singular Values [db] 6 4 2 4 2-2 Sum of Singular Values [db] -2 5 1 15 2 Frequency [Hz] -2 5 1 15 2 Frequency [Hz] (c) grilled port and mylar case (d) perforated panel and mylar case Figure 3: The singular values of the reference cross-spectral matrix (the green line represents the sum of the singular values). In Fig. 4, an example of the use of the virtual coherence function is shown. It can be seen that the sum of the virtual coherence functions calculated by using the first two partial fields at 328 Hz in the original enclosure case was close to unity over the entire hologram surface; the latter observation led to a conclusion that the first two partial fields were required to construct the total sound field. The same result was found in the other cases considered. 1.5 1.5 1 15 1 8 1 8 6 6 x 4 5 y x 4 5 2 2 1 y 15 (a) when the first partial field was used (b) when the first two partial fields were use Figure 4: The sum of the virtual coherence functions in the original enclosure case at 328 Hz.
In Figs. 5 and 6, the first and second partial fields are plotted at the fundamental blade passing frequency to show how the sound field was changed by the enclosure modifications; real parts of the partial fields are plotted, and the vertical and horizontal planes represent the plane containing the two fans, and the source surface (i.e., the top of the enclosure), respectively. When the original enclosure was used, it can be seen that the sound fields generated by both fans exhibited a monopole-like radiation pattern (see Figs. 5(a) and 6(a)). In contrast, when the top of the enclosure was either replaced by a mylar sheet or when a perforated panel was added, the sound field was converted into a dipole-like field (i.e., the sound field on both sides of each fan were out-of-phase, and a pressure null was observed in the direction perpendicular to the fan axis) and the sound levels were reduced. When a grilled port was introduced, the sound fields remained monopole-like; however, the sound level was reduced although the latter reduction was smaller than in the other two cases. From the latter results, it can be concluded that the degree of source-type conversion depends on the size of the additional acoustical path. In addition, it was judged that the opening had an influence on the behavior of the acoustic cavity: the latter effect presumably played, at least, a partial role in reducing the sound level at the sources. When the opening was large (i.e., the mylar top and perforated panel cases), the sound fields radiated from the two fans were wellseparated (i.e., the first and second partial field consisted essentially of the sound fields radiated by the intake and exhaust fan, respectively). In the other two cases, however, the partial fields comprised the sound fields radiated from both fans, which might be evidence of the role of the acoustic cavity (i.e., the sound field was amplified within the acoustic cavity and was radiated from the location of the other fan as well). By a comparison of the amplitudes of the sound fields at the location of both fans, it can be observed that the level of the sound field radiated by the fan on the left side (i.e., the intake fan) was larger than that radiated by the fan on the right side (i.e., the exhaust fan). The latter result could be anticipated since the air flow flowing into the intake fan was disturbed due to the grill located in front of the fan inlet. (a) original enclosure case (at 328 Hz) (b) mylar top case (at 328 Hz) (c) grilled port and mylar case (at 326 Hz) (d) perforated panel and mylar case (at 324 Hz) Figure 5: The first partial field at the fundamental blade passing frequency (real parts are plotted).
(a) original enclosure case (at 328 Hz) (b) mylar top case (at 328 Hz) (c) grilled port and mylar case (at 326 Hz) (d) perforated panel and mylar case (at 324 Hz) Figure 6: The second partial field at the fundamental blade passing frequency (real parts are plotted). In Fig. 7, the acoustic intensities at the fundamental blade passing frequency are shown along with the amplitudes of the total sound pressure fields on the plane defined by x =. The difference between the sound fields can be seen more clearly in this figure: i.e., a larger opening resulted in a clearer conversion to dipole-like radiation and a greater nearfield effect. Although the overall radiation pattern remained monopole-like in the grilled port case, a significant change in the radiation pattern was nonetheless obvious. (a) original enclosure case (at 328 Hz) (b) mylar top case (at 328 Hz) (c) grilled port and mylar case (at 326 Hz) (d) perforated panel and mylar case (at 324 Hz) Figure 7: The acoustic intensity and the total sound pressure field at the fundamental blade passing frequency on the plane defined by x =.
In Fig. 8, the sound powers at the fundamental blade passing frequency and its harmonics are compared to quantify the effect of the enclosure modifications. The sound power was calculated by using the first and second partial fields in the frequency band between the half-power points of the blade passing tones. At the first two blade passing tones, it can be seen that a larger opening resulted in a greater reduction of the sound power while at the same time causing a slight increase in the sound power of the higher harmonics of the blade passing tones. The latter increase, however, was smaller than the increase observed in the level of the summed singular values due to the source-type conversion to a dipole: i.e., an increase in the sound pressure level resulting from the openings was local and directional. The resulting total sound power of the blade passing tones was reduced from 34.5 db to 24 db in the mylar top case, to 3.3 db in the grilled port case, and to 25.7 db in the perforated panel case. Figure 8: A comparison of the sound power at the blade passing frequencies. In summary, the effect of an enclosure is expected to appear in various ways depending on the precise details of each situation. At low frequencies, when the fan s sound field is best described by a point dipole, an enclosure renders the radiation pattern monopole-like by preventing the interaction between the sound fields on both sides of a fan, thus enhancing radiation efficiency, and, in addition, the sound level at the source is likely to be amplified by being coupled with the enclosure s interior acoustical resonances. At high frequencies, in contrast, the amplification of the sound power caused by the effect of an enclosure is not likely to be significant, not only since the source-type conversion is not clear compared to that at low frequencies, but also since, except for very small devices, the lowest interior resonance frequency typically appears below 1 khz. In the latter case, the sound muffling effect of an enclosure may be larger than the amplification, so that the opening causes an increase in the sound power. As a result, the modification scheme described in the present study may sometimes not be suitable. Therefore, in a practical implementation, the characteristics of noise radiated from a fan should be identified first, and the size and location of the enclosure openings should then be chosen carefully depending on the situation to achieve an optimal result. In many practical cases, however, simply using a large acoustical
path is expected to provide good results. Also, using other types of material (e.g., porous material) rather than a mylar sheet may help suppress the radiation of the high frequency noise through an opening while still preventing significant air flow through it. 5. CONCLUSIONS In the present study, it was shown that a fan mounted to an enclosure radiates sound more efficiently than a fan operating in free space, and that the latter enhancement of radiation efficiency can be reduced by introducing an acoustical path that both allows the sound fields on two sides of the fan to interact, and that reduces the effect of the interior acoustical resonances. Near-field acoustical holography measurements were performed to visualize the sound fields corresponding to various enclosure modifications and to quantify the effect of enclosure modifications. The results showed that the proposed scheme helps reduce the radiated sound power when a fan generates a larger sound field owing to the effect of an enclosure than it does in free-space. ACKNOWLEDGEMENTS This research was supported by SONY Corporation, Japan. REFERENCES [1] M. J. Lighthill, On Sound Generated Aerodynamically. Part I. General Theory, Proceedings of the Royal Society of London A211, 564-587, 1952 [2] E. G. Williams, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, Academic Press, New York, 1999 [3] E. G. Williams, Regularization Methods for Near-Field Acoustical Holography, Journal of the Acoustical Society of America 11(4), 1976-1988, 21 [4] M. Lee and J. S. Bolton, Scan-Based Near-Field Acoustical Holography and Partial Field Decomposition in the Presence of Noise and Source Nonstationarity, submitted for publication to Journal of the Acoustical Society of America