Computer fan performance enhancement via acoustic perturbations

International Journal of Heat and Fluid Flow 34 (2012) 28–35

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Computer fan performance enhancement via acoustic perturbations David Greenblatt ⇑, Tzahi Avraham, Maayan Golan Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel

a r t i c l e

i n f o

Article history: Received 29 March 2011 Received in revised form 8 December 2011 Accepted 19 December 2011 Available online 20 January 2012 Keywords: Computer fan Separation control Cooling Periodic perturbations Acoustic perturbations Kelvin–Helmholtz instability

a b s t r a c t A novel technique for increasing computer fan effectiveness, based on introducing acoustic perturbations onto the fan blades to control boundary layer separation, was assessed. Experiments were conducted in a specially designed facility that simultaneously allowed characterization of fan performance and introduction of the perturbations. A parametric study was conducted to determine the optimum control parameters, namely those that deliver the largest increase in fan pressure for a given flowrate. The optimum reduced frequencies corresponded with those identified on stationary airfoils and it was thus concluded that the exploitation of Kelvin–Helmholtz instabilities, commonly observed on airfoils, was responsible for the fan blade performance improvements. The optimum control inputs, such as acoustic frequency and sound pressure level, showed some variation with different fan flowrates. With the near-optimum control conditions identified, the full operational envelope of the fan, when subjected to acoustic perturbations, was assessed. The peak pressure and peak flowrate were increased by up to 40% and 15% respectively. The peak fan efficiency increased with acoustic perturbations but the overall system efficiency was reduced when the speaker input power was accounted for. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Small axial fans are ubiquitous for the cooling of all modern personal computers. Moreover, the number of fans per computer has increased over time because increases in processor clock speed have resulted in greater power consumption. Hence all critical computer components need to be sufficiently cooled to avoid overheating that could lead to unstable performance, shortened lifespan, and ultimately component failure or damage (e.g. Mueller, 2005). Fans are mounted in a variety of configurations; they can be mounted in exhaust or intake configurations with the system load upstream or downstream of the fan respectively. Power supply exhaust configurations are common on PC power supply units. On the other hand, central processing unit (CPU) fans are mounted directly above a heat sink such that the heated surface area is in contact with high momentum air, which greatly improves the cooling effectiveness. In larger server farms, with thousands of processors, performance is limited by cooling the systems rather than by the power of the processors. As demand grows, power consumption is expected to become an increasing fraction of the total worldwide power consumption (e.g. Mills, 1999). Anticipating this demand, a number of new and innovative alternative concepts have been proposed (e.g. Tamburello and Amitay, 2008; Kimber and Garimella, 2009).

⇑ Corresponding author. E-mail address: [email protected] (D. Greenblatt). 0142-727X/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2011.12.003

Most computer fans are relatively small (<150 mm diameter) and rotate at relatively low speeds (several thousand rpm) and thus have correspondingly low blade Reynolds numbers, typically less than 50,000 and often as low as several thousand. The best performing blade profiles at these Reynolds numbers are thin, cambered plates which fix the separation point at the leading-edge (Mueller, 1999). The aerodynamic benefits of cambered plates, combined with their relatively low manufacturing costs, have dominated low Reynolds number fan blade profile design concepts for several decades. However, because boundary layer transition often does not occur at these low Reynolds numbers, the boundary layer separates from the blade leading-edges when the blades are moderately loaded. Boundary layer separation, also known as stall, results in significant performance losses exemplified by a lower pressure rise across the fan disk and a substantial increase in blade drag, noise and vibrations (Barber, 2004). To date, no effective method of blade separation control has been demonstrated, mainly due to the difficulty associated with attaching actuators to the fan blades and providing the means to operate them. Despite the lack of progress associated with fan blade separation control, it is well known that flow separation from solid surfaces can be controlled by the introduction of periodic perturbations. Initial demonstrations were made on airfoils by introducing acoustic perturbations into the test sections of wind tunnels. This was typically achieved using conventional acoustic loudspeakers or specialized acoustic drivers (e.g. Zaman et al., 1989). Typically, significant post-stall lift coefficient increases are observed on airfoils; as much as 50% of the post-stall lift coefficient. Two basic

D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

29

Nomenclature c ch ct Cl fe Fl F+ Fþ t pp p0 Q R Rh Rt Re SPL U U1

Vf Vrms If _a W _f W _s W

local fan blade or airfoil chord length blade hub chord length blade tip chord length airfoil lift coefficient: F l = 12 qU 21 c speaker excitation frequency lift force dimensionless frequency dimensionless frequency based on the blade tip speed plenum static pressure surrounding atmospheric pressure volumetric flow rate fan radius blade hub radius blade tip radius Reynolds number based on local chord length sound pressure level (dB) mean air velocity through the fan disk free-stream velocity

Z /

a c gs goverall l q x w ff fs

mechanisms were identified for lift enhancement: forcing of laminar–turbulent transition; and direct control of the separated shear layer (e.g. Greenblatt and Wygnanski, 2000). In recent years, investigators have dispensed with acoustic drivers and prefer to use actuators that are mounted on, or within, the airfoil or wing itself. This approach is far more effective and efficient because the perturbations can be applied only where they are needed and much larger hydrodynamic perturbations are possible with a much smaller power input. Common methods of actuation include surface mounted actuators and zero mass-flux blowing. An extensive review of modern techniques can be found in the review by Cattafesta and Sheplak (2009). The objective of this work was to assess the changes in effectiveness and efficiency of a computer fan subjected to acoustic perturbations. Acoustic perturbations were introduced as a means of controlling separation on the fan blades; the hypothesis was that acoustic perturbations, known to be effective on stationary wings, could also improve the performance of the fan blades. This objective was realized by designing a computer fan testing facility that allowed the introduction of acoustic perturbations. Using this facility, a parametric study was conducted and, after determining the optimum control conditions, the full operational envelope of the fan was assessed. Details of the experimental setup including the test setup, fan, acoustic speaker and all auxiliary signal generation and measurement techniques are described in Section 2. Parameters governing the fan performance are discussed in Section 3. Section 4 contains a summary of the parametric study, the fan performance characterization and a basic analysis of the data. Finally, the main conclusions are summarized in Section 5.

test fan

wire mesh

DC voltage supplied to the fan rms speaker voltage DC current drawn by the fan fan air power Dp  Q electrical input power Vf  If acoustic speaker power V 2rms =Z acoustic speaker resistance dimensionless fan flow rate angle of attack relative to the blade chord fan blade angle _ a =W _ f (%) fan static efficiency: W _ a =ðW _ f þW _ s Þ (%) overall system static efficiency: W air viscosity at 25 °C air density at 25 °C fan rotational speed dimensionless fan static pressure dimensionless fan power dimensionless speaker power

2. Experimental setup The experimental setup comprised a fan testing facility (Fig. 1a) that was connected to a flow meter and suction pump (Fig. 1b). The facility consisted of an acoustic speaker, test fan, several flanged cylinders all of diameter 90 mm (adapters and a plenum) and a flanged nozzle. The components were connected by their flanges and sealed to prevent leaks. The fan was connected to the upstream adapter, which in turn was connected to the plenum. A wire mesh was located between the adapter and plenum to equalize the plenum pressure. The overall length of the facility was 305 mm. Four circumferential pressure ports were deployed at the center of the plenum and these were connected to a Fuess 550c inclined alcohol (SG = 0.8) manometer that was used to measure the plenum static pressure relative to the atmospheric pressure (Dp  pp  p0). The manometer was adjustable for five ranges of operation, the lowest being 0–78 Pa (1:20, inclination angle) that was used for all experiments presented here. The resolution error at this inclination angle was ±0.2 Pa. Downstream of the nozzle a butterfly valve was connected which in turn was connected to the lower end of a rotameter flow meter (Dwyer 50 SCFM) via flexible tubing (see Fig. 1b). The upper side output from the rotameter was connected to a Russel-Hobbs Hepa Cyclonic 2200 suction pump. The fan used was a Zalman Model: ZM-F2 Plus. It has a 92 mm diameter with a maximum rated input voltage of 12 volts corresponding to a rated power of 3 W. It has seven blades with a hub radius Rh = 1.7 cm and a tip radius Rt = 4.4 cm. The chord lengths vary from ch = 1.5 cm at the hub to ct = 2.8 cm at the tip in a curved

plenum

circumferential pressure ports

to flow meter

speaker

perforated adapter

adapter

nozzle

Fig. 1a. Schematic showing the main elements of the fan testing facility.

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D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

flexible tubing suction pump

flow meter

valve fan testing facility Fig. 1b. Schematic showing the fan testing facility connections to the flow meter and suction pump.

Fig. 1e. Photograph of the Zalman Model: ZM-F2 Plus 3 W computer fan showing the upstream side of the blades and the fan housing.

70

ΔSPL (dB) 60 50 fe

40

120 Hz 140 Hz 180 Hz 220 Hz 240 Hz

30 20 0.01 Fig. 1c. Partial plan view schematic of the fan showing a single blade with its dimensions in millimeters; fan spins counterclockwise.

0.1

1

10

100

Ws (watts) Fig. 2. Measured change in sound pressure level on the fan blades as a function of speaker input power.

Table 1 List of instrumentation employed in the present experimental study.

Fig. 1d. Side view of the fan blade showing the blade angle, twist and camber.

fashion (Fig. 1c). The blade camber varies from 17% at the hub to 11% at the tip and the blade is twisted with an angle of c(Rh) = 45° at the hub and c(Rt) = 33° at the tip (Fig. 1d). A photograph showing the upstream side of the fan blades and the fan housing is shown in Fig. 1e. In order to facilitate the introduction of acoustic perturbations onto the fan blades, a perforated adapter (cylinder with four 25 mm diameter holes) was attached to the fan. The speaker (Pyle 400 acoustic speaker: rated at 180 W; impedance Z = 4 O) was attached to upstream end of the perforated adapter. With the speaker inactive, the fan was considered to be operating in its baseline (conventional) state. With the speaker active, nominally planar acoustic waves could be introduced onto the blades. The fan was driven by a DC Power Supply, where the supply voltage and current drawn were monitored. In addition, the fan rpm was measured using a LED reflector and a tachometer. For control cases, the speaker was driven by pure sine-wave excitation using a function generator in conjunction with an audio amplifier.

Instrument

Make and type

Tachometer Power supply Function generator Audio amplifier Multimeter

Lutron DT 2240D Long Wei DC TPR3005-2D Agilent 33210A Stage Line 200 W Fluke 115C

The AC voltage supplied to the speaker was monitored using a multimeter. The sound pressure level (SPL) resulting from the acoustic perturbations was measured using a calibrated microphone with the fan blade stationary. This was done by placing the microphone at the fan blade location, selecting a frequency and varying the _ s . The SPL measured was then subtracted speaker power input W from the background level: DSPL  SPLs  SPL0 . Typical results of this calibration are shown in Fig. 2 for various speaker excitation frequencies and show, as expected, a logarithmic increase in SPL as a function of speaker power. The measurement instrumentation mentioned above is summarized in Table 1.

3. Governing parameters When characterizing fan performance we are generally inter_ a ) or efficiency as ested in fan (plenum) pressure pp, air power (W

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D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

a function of the fan parameters and fluid properties. Taking pressure relative to the surroundings p0 as the dependent variable, for example, we can list the variables as:

_ f ; R; c; x; l; q; fe ; W _ sÞ Dp  pp  p0 ¼ f1 ðQ ; W

ð1Þ

w ¼ f2 ð/; ff ; F þ ; fs Þ

ð2Þ

where the dimensionless pressure and volumetric flow rate are respectively:

p  p0

ð3Þ

qðxRt Þ2

1 2

and

/¼

Q

ð4Þ

ðxRt ÞpðR2t  R2h Þ

Similarly, the dimensionless fan and speaker power parameters are:

ff ¼

_f W 1 2

ð5Þ

qðxRt Þ3 pðR2t  R2h Þ

and

fs ¼

_s W 1 2

qðxRt Þ pðR2t  R2h Þ

ð7Þ

where U 1 is the free-stream velocity. In the case of the rotating fan blades encountered in this work, the chord-length varies as a func-

2.0 watts

0.04

2.9 watts

0

0

0.1

0.15

0.2

Fig. 4. Dimensionless fan pressure as a function of dimensionless flowrate for three fan input power settings (0.43 6 ff 6 0.49).

tion of the radius c = c(R); moreover the characteristic velocity is a vector combination of the rotation speed xR and the mean velocity through the blades U ¼ Q =pðR2t  R2h Þ. In addition, there is a swirling velocity component that rotates with the blade and tends to reduce flow velocity relative to the blade. Hence the reduced frequency is not constant along the blade span; neither is it constant throughout the operational range of the fans. Extending the definition in Eq. (7) directly results in

fe  cðRÞ F þ  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxRÞ2 þ U 2

ð8Þ

Note that the swirling velocity component is not explicitly accounted for. Notwithstanding the difficulty of defining a unique reduced frequency, we define a dimensionless frequency based on the blade tip speed, namely

fe ct

ð9Þ

xRt

with the understanding that this represents the conditions at the blade tips at zero flow rate, where U = 0. A wide range of different investigations indicate that the reduced frequencies that produce the largest improvements in lift coefficient Cl are mainly in the approximate range 0:3 6 F þ 6 2 (Greenblatt and Wygnanski, 2000). Very few active separation control investigations have been conducted on thin cambered or flat plates at low Reynolds numbers with leading-edge separation due to practical difficulties associated with placing actuators on the airfoil or wing. One exception is the

2.5

12

Wf

Wf 1.2 watts

9

1.2 watts

2

2.0 watts

2.0 watts 2.9 watts

η s (%)

Δp (Pa)

0.05

φ

F þt 

fe  c U1

Wf 1.2 watts

ð6Þ

3

respectively. A similar expression to that shown in Eq. (2) can be _ a =W _ f as the dependent written for static efficiency gs  W parameter. The dimensionless frequency F þ encountered on the fan blades does not have a simple definition as for example its definition on stationary airfoil (2D wing) studies, which is:

Fþ 

0.08

ψ

where the first seven bracketed terms on the right hand side are the volumetric flow rate, fan electrical input power, representative rotor radius, representative rotor blade chord length, rotational speed, air viscosity and density. The last two terms are the speaker acoustic wave excitation frequency and power input respectively. Dimensional analysis leads to a maximum of seven independent dimensionless parameters. In this study, we maintain constant geometric ratios c=Rt and assume that Reynolds number does not play a significant role. Hence the remaining five dominant dimensionless parameters are written:

w¼

0.12

6

2.9 watts

1.5

1

3 0.5 0

0

2

4

6

8

10

12

Q (liters/s) Fig. 3. Fan pressure as a function of flowrate for three fan input power settings (0.43 6 ff 6 0.49). Error bars are based on resolution and statistical uncertainty.

0

0

0.05

0.1

0.15

0.2

φ Fig. 5. Fan static efficiency as a function of flowrate for three fan input power settings (0.43 6 ff 6 0.49).

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D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

0.6

0.16

0.5 Rh/Rt

0.12

0.08

F

ψ

+

0.4 0.3 0.2

U/ωRt=0, 2.9 watts U/ωRt=0.2, 2.9 watts U/ωRt=0, 1.2 watts U/ωRt=0.3, 1.2 watts

0.04

0

0

0.2

Φ=0

Φ=0.077

Φ=0.093

Φ=0.163

0.4

0.1 0

0.6

0

0.25

0.5

Ft+

0.75

1

R/R t

Fig. 6. Variation of plenum pressure as a function of dimensionless speaker _ s ¼ 11:4 W (fs = 1.9) for different fan flowrates. Fan input power frequency at W _ f ¼ 2:9 W (ff = 0.49). W

Fig. 7. Reduced frequency variation with blade span for the maximum and minimum power settings considered for an excitation frequency fe = 140 Hz (based on Eq. (8)).

use of surface-mounted dielectric barrier discharge actuators (Schüle et al., 2008; Greenblatt et al., 2008; Vey et al., 2010) discussed in Section 5 below.

values shown in Fig. 5 are typical of these fans due to their low pressures. 4.2. Fan blades subjected to acoustic perturbations

4.1. Baseline characteristics Initial experiments were performed without acoustic perturbations to characterize the basic fan performance and estimate the experimental errors. Experiments were performed by maintaining constant input power and then varying other parameters in a systematic fashion. The majority of experiments were conducted at _ f ¼ 2:9 W (the measured value Vf = 12 volts corresponding to W was slightly less than the manufacturer rating of 3 W). In order to check experimental consistency and vary the perturbation through a greater range of parameters (see next section), the baseline performance was assessed at three different fan input voltages _ f . The three power setVf, and hence three power input settings W tings selected were 2.9, 2.1 and 1.2 W and corresponded to rotational velocities of x = 2690, 2420 and 2100 rpm respectively. For each power setting the fan performance was characterized by varying the flowrate via the suction pump and recording corresponding pressures. These results are shown in Fig. 3. In addition to the manometer resolution uncertainty discussed in the previous section, the effect of statistical averages was quantified by conducting five experiments all under identical fan power settings and with identical flow rate increments. These results were averaged and compared with a separate experiment performed under identical fan power settings and initial conditions but with arbitrary flow rate increments. This comparison indicated that when conducting individual experiments the uncertainty in the dimensionless pressure data was always less than ±0.15 Pa. Combining the resolution and statistical errors resulted in an overall uncertainty of 0.25 Pa and this is indicated in Fig. 3. It is common, when characterizing fan performance, to present the data in dimensionless form as shown for dimensionless pressure and flowrate in Fig. 4 (see Eqs. (3) and (4)) and for static efficiency in Fig. 5. The collapse of the data for dimensionless pressure versus flowrate is excellent. The assumption of the previous section, namely that Reynolds number is not an important parameter, is confirmed here. Despite the relatively large change in fan input power investigated (from 2.9 W to 1.2 W), x only varies from 2690 to 2100 and this translates to a relatively small reduction of Reynolds number of approximately 20%. The low peak efficiency

A common technique for determining the optimum control parameters on stationary airfoils and wings is to select a constant control input amplitude and then systematically vary the control frequency (e.g. Greenblatt et al., 2008). For the present investigation, a similar technique was employed for the fan driven at its de_ s ¼ 11:4 W (fs = 1.9). sign power input with the speaker power at W The main difference was that here the frequencies were varied for different volumetric flowrates. Specifically, these included zero flowrate (fully stalled blades), intermediate flowrates near the maximum efficiency and a flowrate close to /max (Fig. 6). The data show a strong dependence on frequency, but this dependency is not uniform for the different flowrates. For the fully stalled flow (/ = 0), excitation always results in beneficial effects, namely an increase in the plenum pressure. Here there is an almost uniform increase in pressure for the reduced frequency range 0:1 6 F þ t 6 0:45. This is consistent with separation control on thin cambered stationary airfoils with leading-edge perturbations that show an approximate optimum frequency range 0:2 6 F þ 6 0:6 (Schüle et al., 2008). In contrast to this, at intermediate flowrates in the vicinity of maximum efficiency (/ = 0.077 and 0.093), the perturbation

0.16

0.12

ψ

4. Discussion of results

0.08

0.04

0 0.01

Φ=0 Φ=0.077 Φ=0.124

Φ=0.046 Φ=0.093 Φ=0.155

0.1

1

10

ζs Fig. 8. Variation of plenum pressure as a function of dimensionless speaker power _ at F þ t ¼ 0:33 for different fan flowrates. Fan input power W f ¼ 2:9 W (ff = 0.49).

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D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

Wf 2.9 watts, baseline 2.9 watts, control 2.0 watts, baseline 2.0 watts control 1.2 watts, baseline 1.2 watts, control

Δp (Pa)

12

8

4

0 0

2

4

6

8

10

12

Q (liters/s) Fig. 9. Overall fan performance map for different fan power setting: baseline and _ s ¼ 11:4 W and 0:33 6 F þ 6 0:42. control. Control cases are W t

for different flowrates. This reduced frequency was selected because it produced an increase in fan pressure at all flowrates considered previously (see Fig. 6). Note that the data are shown here on a logarithmic speaker power scale, but this could be replaced with a linear scale if plotted in terms of the SPL (see Fig. 2). With the fan fully stalled (/ = 0), the absolute increase in plenum pressure increases continuously with speaker power. This observation is qualitatively consistent with separation control data on thin airfoils (with leading-edge separation) that are set at angles far greater than the corresponding static stall angles (deep stall). In these instances the lift coefficient of the airfoil increase continuously with increasing perturbation amplitude (Greenblatt and Wygnanski, 2000). As the flowrate increases and the separation on the blades is reduced, so the effectiveness of control decreases. It is assumed that separation on the blades is negligible here, much like the flow over airfoils and wings at low angles of attack. At flowrates greater than those corresponding to the maximum efficiency there is a curious situation, where the plenum pressure increases initially at low power, but then decreases as the amplitude is increased. This observation is not consistent with the expectation that increases in power generally result in performance increases. This effect becomes more pronounced as the flowrate is increased. By comparing Fig. 8 with Fig. 6 it can be seen that a lower power would have produced a higher pressure near /max. It is also speculated that the pressure drop observed at F þ t  0:2 in Fig. 6 could have been eliminated, or at least ameliorated, by using a lower speaker power, but this was not investigated further.

Wf

0.16

2.9 watts, baseline 2.0 watts, baseline 1.2 watts, baseline 2.9 watts, control 2.0 watts, control 1.2 watts, control

0.12

ψ

produces a small pressure drop in the vicinity of F þ t ¼ 0:2, while for Fþ t > 0:25 the effect is positive. The small reduction in pressure for / > 0 in the region of F þ t ¼ 0:2 may be due to forced separation of the flow from the blades. Particularly, the large amplitude perturbation may be forcing separation from the lower part of the blades (see below). Another possibility is that the relatively low frequency forcing is causing dynamic separation and reattachment (e.g. Carr, 1988; Greenblatt and Wygnanski, 2009). With increasing flowrate close to Qmax, these effects are more pronounced; the pressure drops to half of its baseline value at F þ t  0:2 while it more than doubles at F þ  0:47. t In all experiments, the excitation frequency was chosen such that the acoustic wavelength was significantly larger than the largest dimension of the fan testing facility, namely that a=fe  305 mm, where a is the isentropic speed of sound. The highest frequency considered here was 260 Hz resulting in a wavelength of 0.94 m. Moreover, the effect of acoustic perturbations with the fan stationary and with the fan removed from the facility was considered. This was achieved by varying the speaker throughout all frequencies considered at the full range of speaker input power. Furthermore, these tests were conducted with the butterfly valve closed and open for Q = 0 as well as at varying flowrates. In all instances the changes to the plenum pressure were negligible. These measurements were important because they eliminated the suspicion that an acoustic effect, such as standing waves, caused the observed pressure increases shown in Fig. 6. The reduced frequency F þ t used for presenting the data here should be considered only as an indication of the range of reduced frequencies experienced along each blade span. This can be better understood by quantifying the variation of F þ along the span of the blade for a constant frequency. Consider the example shown for fe = 140 Hz in Fig. 7, based on the definition of Eq. (8). For fully stalled fan blades (U = 0) at the fan design power (2.9 W), F+ varies from 0.48 at the hub to 0.33 at the tip. At conditions of maximum flowrate, corresponding to U/xRt = 0.2, the variation of F+ along the span is smaller due to the relatively large effect of U near the hub. A similar variation of F+ can be seen at the lowest power setting. The design of the fan blades, with an increasing chord-length in the radial direction (Fig. 1c), compensates partially for the increasing rotational velocity xR and hence the variation of F+ is typically less than 0.1 from the hub to the span. The similarity of the reduced frequencies that produce enhanced lift on cambered plate airfoils and those that increase the pressure on the fan blades lead us to speculate that similar mechanisms are present in both cases. The reason for the increase in fan pressure at the range of frequencies shown in Fig. 6 can be better understood by considering investigations, where dielectric barrier discharge actuators were used at the leading-edges of flat and cambered plate airfoils at 3000 6 Re 6 20,000 – virtually identical to the range considered here (Schüle et al., 2008; Schneider et al., 2008). They observed that increases in lift were brought about by a rollup of Kelvin– Helmholtz instability waves (Drazin and Reid, 2004) into leadingedge vortices. The generation, amplification and advection of these leading-edge vortices is regulated by the periodic perturbations. They further observed that the largest increases in lift do not occur at a single frequency or over a narrow frequency band, but rather over a range of reduced frequencies varying from approximately 0.2 to 0.6. Notwithstanding the small variation along the blade span here, the correspondence of the F+ of Schüle et al. (2008) with that observed here, lends credence to the hypothesis that the Kelvin–Helmholtz mechanism is also active here. In this investigation, however, no flow field measurements were made and this hypothesis could not be verified directly. The variation of plenum pressure as a function of speaker power is shown in Fig. 8, for a constant frequency (fe = 140 Hz) corresponding to F þ t ¼ 0:33, where once again the data are presented

0.08

0.04

0

0

0.05

0.1

0.15

0.2

0.25

φ Fig. 10. Dimensionless pressure versus dimensionless flowrate for different fan power settings: baseline and control. Control cases are at 0:33 6 F þ t 6 0:42.

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D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

It was assumed here that the boundary layer separating at the blade leading-edge is laminar due to the low Reynolds numbers encountered on the blades. This can be shown by calculating the range of Reynolds numbers encountered according to

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Re ¼ qV rel cðRÞ=l ¼ q ðxRÞ2 þ U 2 cðRÞ=l

ð10Þ

that varies between approximately 5000 and 21,500 from the hub to the tip. On airfoils at these Reynolds numbers the boundary layer is completely laminar and passive tripping does not force transition to turbulence (Carmichael, 1981). Furthermore, separated boundary layers do not reattach downstream as is common at Reynolds numbers an order of magnitude higher (Carmichael, 1981). 4.3. Overall fan performance benefit On the basis of the parametric study described in the previous section, a full fan characterization, together with acoustic perturbations, was conducted in the same manner as that described in Section 4.1 for the baseline case. Here the speaker was driven at a constant frequency and power (140 Hz and 11.4 W) that were observed to produce an increase in pressure at the different flowrates considered in Section 4.2. This resulted in the reduced frequency range 0:33 6 F þ t 6 0:42 for the three different fan power settings described in Section 4.1. It is evident from Fig. 6 that the introduction of acoustic waves at this range of reduced frequencies results in an increase in plenum pressure regardless of the flowrate. Although these control conditions are not necessarily optimal for all flowrates, as shown in Fig. 7, they suffice to provide a first order estimation of the effect of periodic perturbations on fan performance improvements. The results of the characterization are shown in Fig. 9 together with the baseline cases described in Section 4.1. It is evident that the performance of the fan is increased over its entire operational envelope. As expected, the largest effects are seen at low flowrates Q, where the fan blades are fully stalled, and at large Q, where the blades produce low pressures. In the intermediate Q range the improvements are modest due to limited flow separation in the baseline cases. This leads to a qualitatively different fan characteristic for the controlled cases. The absolute improvement in pressure at Q = 0 and Dp = 0 are approximately the same for all cases. It can be seen from Fig. 9 that running the fan at low rotational speeds combined with acoustic control can achieve the same peak pressure and flowrate as at higher rotational speeds. For example, compare the 2.0 W control case (x2.0W = 2420 rpm) with the 2.9 W baseline case (x2.9W = 2690 rpm). This result also indicates that the

2.5

ηs (%)

2

1.5

Wf 1 2.9 watts, baseline 2.0 watts, baseline 1.2 watts, baseline 2.9 watts, control 2.0 watts, control 1.2 watt, control

0.5

0

0

0.05

0.1

0.15

0.2

0.25

φ Fig. 11. Static efficiency as a function of dimensionless flowrate for baseline and controlled fan cases at three fan power settings. Control cases are at 0:33 6 F þ t 6 0:42.

introduction of perturbations may be viable to reduce fan noise because the sound power generated is observed to vary with the 6th power of the blade tip speed (Wang et al., 2005). This noise is generally broadband and results from turbulence and vortex generation, together with superimposed pure tone components related to geometry and fan speed (Barber, 2004). Based on this, we can estimate the change in SPL only as a result of the perturbations from the relationship:

DSPL  SPL2:9W  SPL2:0W ¼ 60 logðx2:9W =x2:0W Þ ¼ 3 dB

ð11Þ

Given that this reduction is modest (only 3 dB) and the acoustic perturbations have not been accounted for it is unlikely that the present method could result in a meaningful noise reduction. Consideration of the data in dimensionless form (Fig. 10) emphasizes the difference in the qualitative trends of the baseline and controlled fan characteristics. Here the peak dimensionless pressure increase is between 30% and 40% while the peak flow rate is increased by approximately 15%. It is also evident that the relative performance increases at the lower fan power settings. This can be clearly seen by considering the dimensionless pressure axis under zero flowrate. The most probable reason for this is the larger relative SPL impinging on the blades. This can be understood by considering the ratio of the pressure fluctuations as a result of acoustic perturbations relative to the dynamic pressure experienced by the rotating blade. Reducing the rotational speed from x2.9W = 2690 rpm to x1.2W = 2100 rpm results in an increase in the relative SPL on the blades of (x2.9W/x1.2W)2 = 1.61 or a 61% increase. These results are also reflected in the efficiency considerations shown in Fig. 11. It should be noted here that the overall system static efficiency described in this paper, taking into account the speaker power, namely:

_ W

goverall ¼ _ a _ Wf þ Ws

ð12Þ

is in general lower than the baseline efficiency. This is because relatively large speaker power is required to bring about an increase in fan pressure, particularly at low Q. Clearly the method is effective for increasing fan pressures. However, the specific configuration and setup described here does not, in general, appear to be efficient when speaker power is accounted for. For an energy efficient design, larger acoustic perturbations would need to be realized but with substantially lower electrical power to the speaker. One way in which this can be achieved is to use the speaker in conjunction with a Helmholtz oscillator as a means of increasing the perturbation amplitude while minimizing the electrical power to the speaker. Alternatively, perturbations could be introduced externally by means of vibrating piezoelectric elements (e.g. Kimber and Garimella, 2009) or zero mass-flux devices, also known as synthetic jets (e.g. Tamburello and Amitay, 2008). This investigation was carried out with the objective of controlling separation primarily in the flow regime corresponding to large angles of attack. This was expected to occur at low flowrates Q and indeed this is what was observed. However, the increased performance near the maximum flowrates was not expected. It was hypothesized that at low angles of attack corresponding to high Q the flow separated from the lower surface of the blade. The range of angles-of-attack experienced by the blade is a combination of the blade chord geometry cðRÞ and the vector combination of the blade rotational speed and the flow though the blade U ¼ Q =pðR2t  R2h Þ. Here we ignore the swirling flow component generated by the fan blades. Hence, the angle of attack of the flow relative to the blade (Vrel) was calculated by

aðRÞ ¼ cðRÞ  tan1 ðU=xRÞ

ð13Þ

D. Greenblatt et al. / International Journal of Heat and Fluid Flow 34 (2012) 28–35

where c(R) is the blade angle that varies with radius R. Based on the data acquired the angle of attack varies by approximately 27°. Due to the fact that the blades are cambered, the condition of maximum flowrate, where there is no pressure difference across the fan disk, will occur when the blades are at a negative anglesof-attack relative to the flow. At negative angles, with large camber, flow separation from the lower surface will certainly be present (e.g. Mueller, 1999). Hence we speculate that the increases in pressure observed under these conditions are caused by amelioration of the separated flow on the lower surfaces of the blades. 5. Considerations for up-scaling Axial-flow computer fans in general have similar geometry and it is possible to predict performance benefits that can be expected on larger fans using standard fan laws. However, for much larger fans, particularly large industrial machines with disk diameters from approximately 1 m (kilowatts) to several meters (hundreds of kilowatts) the option of an acoustic perturbation source is impractical. Effective and efficient control of separation on these fans is no less important, considering that their energy consumption accounts for a large fraction of the industrial total (Elliott and Nadel, 2003; Cory, 2004). On large fans, blade stall has always been accepted as a physical limitation that has never seriously been challenged from a control perspective; only managed by means of detection and avoidance. The principal reason is that it is difficult deploy and operate effective flow control devices on the blade surfaces. Indeed, the primary difficulty does not necessary lie in controlling separation, but rather finding a technologically appropriate tool to do so. Another important aspect of up-scaling is the large increase in Reynolds number associated with the larger blades and higher relative velocities. Empirical results show that the fluidic forces produced by the actuator scale with dynamic pressure encountered by the blade (e.g. Greenblatt and Wygnanski, 2000). One example of how larger actuator forces could be achieved is by means of pulsed dielectric barrier discharge (DBD) plasma actuators (Corke et al., 2007). These actuators are an attractive option because they convert electrical energy directly into a body force without intermediate mechanical elements. Pulsation frequencies can be arbitrarily selected and hence can be employed to excite the Kelvin–Helmholtz instabilities associated with separation. Moreover, they can be operated at low power, by lowering their pulsation duty cycles, at a given pulsation frequency (Greenblatt et al., 2008). For applications to rotating systems, DBD plasma actuators were recently applied to the blades of a small wind turbine. When operating the actuators during blade stall, turbine power increased significantly, by nearly 40% (Greenblatt et al., 2012), comparable to the gains observed in this work. A parametric study showed that the actuator duty cycle independence observed on airfoils was also observed on the turbine. A future research opportunity in the context of axial fans is to evaluate DBD plasma actuators mounted on the blade surfaces. 6. Concluding remarks Experiments conducted on a small computer fan showed that its performance can be significantly improved via the introduction of acoustic perturbations. The maximum pressure increases measured were between 30% and 40%. Despite some variation of the local chord length and blade relative velocity, the results showed that the reduced frequencies that are known to be effective on stationary cambered-plate airfoils are also effective on rotating fan blades. It was thus concluded that the Kelvin–Helmholtz instability mechanism present in separated flows, and commonly exploited

35

for separation control, can be exploited on rotating fan blades. In addition to pressure increases resulting from perturbations at low flowrates, where the blades are stalled, the maximum flowrate was also increased by approximately 15%. It was hypothesized that this increase resulted from the control of flow separation from the lower surface. The experiment as described here was not efficient when the speaker power was factored into the calculation. It is suggested to design a system using a Helmholtz resonator to increase the acoustic sound pressure level while minimizing speaker power. Alternatively, an energy efficient piezoelectric device or zero mass-flux devices could be employed instead of the speaker. For application to significantly larger fans, blade surface-mounted dielectric barrier discharge actuators may prove to be an effective method for perturbing the flow. References Barber, A., 2004. Handbook of Noise and Vibration Control. Elsevier (Section 7). Carmichael, B.H., 1981. Low Reynolds Number Airfoil Survey. (vol. I), NASA Contractor Report 165803. Carr, L.W., 1988. Progress in the analysis and prediction of dynamic stall. AIAA Journal of Aircraft (1), 6–17. Cattafesta, L., Sheplak, M., 2009. Actuators and sensors. In: Joslin, R.D., Miller, D. (Eds.), Fundamentals and Applications of Modern Flow Control. Progress in Astronautics and Aeronautics Series, 231, Published by AIAA, 2009, ISBN-10: 156347-983-4, ISBN-13: 978-1-56347-983-0, 149-157. (Chapter 6). Corke, T.C., Post, M.L., Orlov, D.M., 2007. ‘‘SDBD plasma enhanced aerodynamics: concepts. Progress in Aerospace Sciences 43, 193–217. Cory, W.T.W., 2004. Fans – just how mature are they. In: C631/100/2004 IMechE International Conference on Fans, One Birdcage Walk, London, UK, pp. 9–10, ISBN:978-1-86058-475-6. Drazin, P.G., Reid, W.H., 2004. Hydrodynamic Stability. Cambridge University Press. Elliott, R.N., Nadel, S., 2003. Realizing Energy Efficiency Opportunities in Industrial Fan and Pump Systems. American Council for an Energy-Efficient Economy. (accessed February, 2008). Greenblatt, D., Wygnanski, I., 2000. The control of separation by periodic excitation. Progress in Aerospace Sciences 36 (7), 487–545. Greenblatt, D., Wygnanski, I., 2009. Physical concepts underlying the development and application of active flow control. In: Joslin, R.D., Miller, D. (Eds.), Fundamentals and Applications of Modern Flow Control. Progress in Astronautics and Aeronautics Series, 231, Published by AIAA, 2009, ISBN-10: 1-56347-983-4, (Chapter 1, ISBN-13: 978-1-56347-983-0, 21-57). Greenblatt, D., Göksel, B., Rechenberg, I., Schüle, C., Romann, D., Paschereit, C.O., 2008. Dielectric barrier discharge flow control at very low flight Reynolds numbers. AIAA Journal 46 (6), 1528–1541. Greenblatt, D., Schulman, M., Ben Harav, A., 2012. Vertical axis wind turbine performance enhancement using plasma actuators. Renewable Energy 37, 345– 354. Kimber, M.L., Garimella, S.V., 2009. Measurement and prediction of the cooling characteristics of a generalized vibrating piezoelectric fan. International Journal of Heat and Mass Transfer 52, 4470–4478. Mills, M.P., 1999. The Internet Begins with Coal. Green Earth Society, USA. Mueller T.J., 1999. Aerodynamic Measurements at Low Reynolds Numbers for Fixed Wing Micro-Air Vehicles. Presented at the RTO AVT/VKI Special Course on Development and Operation of UAVs for Military and Civil Applications, VKI, Belgium, September 13–17. Mueller, S., 2005. ‘‘Upgrading and Repairing PCs, fifth ed. Que Publishing, pp. 1274– 1280. Schneider, T. Schüle, C.Y. Greenblatt, D. Nayeri, C.N., Paschereit, C.O., 2008. Experimental and computational investigation of active flow control with DBD plasma actuators at low Reynolds numbers. In: 2nd International Conference on Jets, Wakes and Separated Flows, Technical University Berlin, September 16–19, Berlin, Germany. Schüle, C.Y., Greenblatt, D., Paschereit, C.O., 2008. Combined plasma and gurney flap flow control at very low flight reynolds numbers. In: 2nd International Conference on Jets, Wakes and Separated Flows, September 16–19, Technical University of Berlin, Berlin, Germany. Tamburello, D., Amitay, M., 2008. Manipulation of an axisymmetric jet by a single synthetic jet actuator. International Journal of Heat and Fluid Flow 29 (4), 967– 984. Vey, S., Nayeri, C.N., Paschereit, C.O., Greenblatt, D., 2010. Plasma flow control on low aspect ratio wings at low Reynolds numbers. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, January 4–7, AIAA paper 2010-1222. Wang, J., Huang, L., Cheng, L., 2005. A study of active tonal noise control for a small axial flow fan. Journal of the Acoustical Society of America 117 (2), 734–743. Zaman, K.B.M.Q., McKinzie, D.J., Rumsey, C.L., 1989. A natural low-frequency oscillation of flow over an airfoil near stalling conditions. Journal of Fluid Mechanics 202, 403–442.