Investigation and Recommendation of Placing Inlet Guide Vanes on the Z100 Server Room Ventilation...

8/9/2019 Investigation and Recommendation of Placing Inlet Guide Vanes on the Z100 Server Room Ventilation Fan to Decrease the Power Consumption

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Quido Server Solutions400 Falconer St.Pulaski, VA 24301

September 24, 2013

To: Tea Elisabeth, Engineer for Environmental Compliance

From: Ali Alhamaly

Subject: Inves tigation and Recommendation of Placing Inlet Guide Vanes on theZ100 Server Room Ventilation Fan to Decrease the Power Consumption

Summary and Introduction

As requested by the memo sent to us on A ugust 27, 2013, we performed severaltes ts to investigate the effectiveness of placing inlet guide vanes (IGV) on the ventilationfan to reduce the power consumption in order to satisfy the requirement of EnvironmentalImpact Reduction Association (EIRA). Based on our test results, placing IGV on the fan

is an effective way to reduce the fan power consumption and results in satisfying EIRAcertification levels. The experimental results indicate that setting the IGV at 35 degreesresults in power reduction of 21.6% from the current power consumption. The reductionof power necessitates a decrease in number of servers currently installed in the room by

two servers which makes the total number of servers that the fan can support aftermaking the recommend changes be 16 servers.

This report presents the detailed experimental approach that was used to analyze

the performance of the fan with IGV. The report s tarts by describing the experimentalsetup that was used to simulate the fan operation including the test apparatus and thegeneral tes t procedures. Next, the report discusses the data processing techniques thatwere used to calculate the flow rate from the direct measurements that were made at thetes t location. The next s ection presents a qualitative description of how the IGV change

the operating conditions of the fan. Next, the actual test results are presented in the formof performance curves of the fan. The results show quantitatively how the IGV changethe power level consumption and static pressure rise characteristic of the fan. Based onthe results shown in this section, the report presents our recommendations of the range of

IGVsett ings that yields the power reduction required by EIRA. As requested by thememo, the report discusses the repeatability of the measured values of the flow rate and

discusses the random uncertainty in the measurement. Finally the report concludes withsome suggestions to improve the quality of the flow rate measurements in the current test

setup.

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Experimental Setup

This section presents the experimental apparatus that was used to simulate the

server room vent ilation fan along with the test procedures.

Experiment Apparatus. The experiment investigate the relations between the fanpower consumption and the air flow rate through the fan duct and how these twoparameters vary as the IGV settings are changed. The experiment was done on test fan rigin which a centrifugal fan supply air through 18

circular duct that contains the meas uring

inst ruments and the flow control valve. The supplied air discharges to the outside

atmosphere at the end of the duct. The instruments in the fan duct includes radialtraversing Pitot static probe and static pressure tap both located at about four diametersdownstream of the fan(71inches to be exact). They are both connected through tubing toinclined water manometers that are set to measure the dynamic pressure for the case of

the Pitot probe and the gage static pressure for the case of the static pressure tap. At theend of the s traight portion of the duct a back pressure valve is located about eight

diameters downstream of the fan. A wattmeter is connected to the fan circuit to measurethe power consumption directly. The test room ambient pressure and temperature are

monitored by electronic barometer and temperature sensor respectively. The variableIGV are installed at the inlet of the centrifugal fan. The angle setting for the IGV iscont rolled by a manual handle located at the side of the fan. Figure 1a shows a photo ofthe actual test set-up showing the fan casing with instrumented circular duct. Figure 1b

shows a schematic diagram of the test setup with the main instruments indicated as well.

General Test Procedures. The main goal of the experiment is to assess theeffectiveness of the IGV in reducing the fan power consumption. In order to achieve thisgoal, the performance and the operating characteristics of the fan with different IGVsett ing are needed to be determined. This means that the dependence of the power

cons umption and the static pressure rise on the air flow rate through the fan need to beinves tigated for wide range of the IGV sett ing. From this rationale, the test procedure was

Static pressure tap

Figur e 1a.Photo of the test rig showing the fanand the downstream circular duct

Figure 1b.Schematic diagram of the test rigshowing the main instruments and their location

on the fan duct

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chosen to allow the investigation of the fan performance under wide range of air flowrate.

The test procedures for all the tests that we have conducted are very similar and

only vary in terms of specific settings that we impose to control the operation regime ofthe fan. The general idea of the test is to vary the air flow rate through the fan for each

IGV settings to investigate the change in operation and power consumption. The flowcontroller in our system is the back pressure valve and it was used to regulate the flow

rate through the duct. The test was carried out as follows:1. The IGV angle was set at the desired value for the test2. The back pressure valve was set at certain value and held fixed3. Using the Pitot static probe, the dynamic pressure was recorded for five

different radial plunge locations across the diameter of the duct. Exactlocations are (2,3,5,7,9) inches away from the duct wall

4. as the Pitot probe being traversed, the static pressure inside the duct wasrecorded once from the static pressure tap manometer

5. the fan power consumption was monitored throughout the traversing time and

average value of the power during that time was recorded6.

ambient pressure and temperature were recorded once during the traversingperiod of the Pitot probe

7. the test procedures 2-6 were repeated again but for different value of the backpressure valve settings

8. Once all the desired back pressure valve settings are obtained, the procedures1-7 were repeated for new IGV angle setting.

The eight steps mentioned above constitute the general procedure that wasfollowed in all the tests performed.

Test Matr ix . Following the general test procedures, we performed two main tests.

The initial testing was over wide range of IGV and back pressure valve (BPV) settings.Table 1 shows the test matrix for the initial testing with the specific setting values forboth IGV and BPV. Note that the BPV setting is given in percentage where 100% means

that the valve was fully open. The idea behind doing this initial testing with coarseincrements for the IGV and BPV settings was to establish the general trends in the fanoperation and to get an idea about the sensitivity of the IGV to both power consumptionand static pressure rise characteristic of the fan. In addition, the initial testing includes the

IGV of 90 degrees which corresponds to the fully open position. This setting replicatesthe current server room fan operation since the current fan doesnt have IGV installed onit. The 90 degrees IGV test is the most important test because it allows us to investigatethe current operating condition of the server room fan and hence enables us to determine

the current power consumption that need to be reduced.

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Table1.Initial test matrix IGV and BPV settings

IGV(degrees)

BPV (%)

90

o

25,50,75,10075o 25,50,75,100

60o 25,50,75,100

45o 25,50,75,100

30o 25,50,75,100

15o 25,50,75,100

After processing the initial test data, we have decided to conduct another test thatinvestigates the fan operation in narrow range of IGV setting. Table 2 shows the test

matrix for this test. The specific values for the IGV and BPV settings were chosen basedon the results we obtained from the initial test. We believed that the second test condition

will be helpful in finding the optimum IGV setting that will minimize the fan powerconsumption and still provide reasonable air flow rate. This observation will be revisited

in details in the results section of this report.We have made a third short test with the purpose of assessing the precision and

repeatability of our measurements. The test was at IGV of 90 degrees and BPV of: 30,35, 40 and 45 percent. The test was identically repeated for three times for the purpose of

finding the random uncertainty in the measured flow rate.Sample calculation of the flow rate is included in appendix A.All the measured

data from the three tests is included in appendix B in which it contains all the directmeasured quantities that were recorded.

Table2.Second test matrix IGV and BPV settings

IGV(degrees)

BPV (%)

55o

30,35,40,45

50o 30,35,40,45

40o 30,35,40,45

35o 30,35,40,45

Data Processing and Calculations

This section presents all the necessarily calculations to obtain the air flow ratefrom the direct measured quantity that were recorded during the tests. In addition, theassumptions that are made to use the specific equations and to perform the analysis are

highlighted.

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Calcu lation of Air Flow Rate. The air flow rate is one of the most importantparameters that we are concerned with in this investigation. The basic equation to find the

total air flow rate through the fan duct is given by:

=

Where is the volumetric flow rate,is the cross sectional area of the duct, is the airvelocity at the ithplunge location and is the associated weighting factor for the ithvelocity. From equation 1, it can be seen that the flow calculation requires knowing thevelocity distribution across the duct and hence the value of the air velocity is needed at

several location across the duct diameter. To calculate the air velocity from the measuredvalue in our experiment we need to use a basic fluid mechanics equation that relatesmomentum to fluid pressure, mainly the Bernoulli equation. The use of Bernoulliequation in our test condition is justified for two main reasons. First, the air velocity

inside the duct is very small compared to the local sonic velocity and hence Machnumber is extremely small which leads to the fact that we are dealing with

incompressible flow in our test condition. Second, our observations of the manometersthat are used to measure air pressure indicate that the flow was steady since the water

level in the manometer was not fluctuating with time at a given operating condition. Theabove justification shows the applicability of Bernoulli equation to our test condition, andfrom Bernoulli equation we can get that the air velocity is given by:

= 2 Where is the air dynamic pressure at the ithplunge location and is the air densityinside the duct. The dynamic pressure is measured directly in our experiment by using the

Pitot static probe, so what is left for the calculation of the air velocity is the determinationof the air density. The calculation of air density uses three main assumptions. First, the airis assumed to be an ideal gas and hence the ideal gas equation is used. Second, it isassumed that the variation of the static pressure of the air flowing through duct in theradial direction is negligible. This is important because we measured the static pressure ofthe air at one location only which was at the wall, so we assumed that the value of static

pressure at the wall resemble the whole value at the measuring plane. Lastly, we madethe assumption that the air temperature inside duct doesnt vary from the ambient airtemperature and hence we can use the ambient temperature sensor to obtain the airtemperature inside the duct. This assumption is reasonable since the fan power is

relatively low and hence the energy delivered to the air is low enough that the change in

its temperature is very negligible. Using the ideal gas equation with the assumption abovethe air density is given by:

= Where is the static pressure in the duct measured by the wall static tap, is the airambient temperature and is the air gas constant equals to 287. Note here that the

(1)

(2)

(3)

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static pressure tap manometer measures the gage pressure relative to ambient staticpressure, and hence the value of in equation is corrected by adding the ambientpressure to the measured pressure given by the static tap manometer. From equation 1, 2and 3 we can calculate the air flow rate using the measured quantity that we recorded inour tests. The last thing that we havent discussed yet is the weighting factor

in

equation 1. This factor is dependent on the number of measurement point that is madewith the Pitot probe and on the specific plunge location across the fan duct. For ourexperimental setup, we didnt use any standard plunge location and for this reason we

believe that the best representative value of the weighting factor that wont yield tobiased value of the flow rate is 1/n where n is the total number of plunge location. So, ourweighting factor reduces to 1/5.

Effects of IGV on the Fan Operation

This section presents main results of the investigation of the effects of the IGV onthe fan operation. The section starts with simple explanation of how IGV can alter the fanoperation and change the power and pressure rise characteristics. Additionally, theexperimental results of the effects of IGV on the fan performance are shown graphically.

The section concludes with a discussion on the possible operating conditions of the fan inthe server room after installing the IGV and the possible power reduction levels.

Qualit ative Descript ion of IGV Effects on th e Fan Performance. The

centrifugal fan has the ability to pull air from the ambient environment by creating apressure differential between the ambient air and the air close to the fan blades. In anyfan, the flow rate of the air is dependent upon the static pressure rise that the fan producesunder constant rotation speed. In a fan system (fan connected to a flow restriction) the air

static pressure rise created by the fan depends on the flow restriction pressure lossrequirements and hence the flow rate is ultimately determined by satisfying therequirement of the flow restriction device. The fan system resistance to air flow can berepresented analytically by the equation:

=2Where is the total static pressure drop throughout the fan system, is the air flow ratethrough the system and is a constant represent the impedance of the system to air flow.

for a given system need to be either measured or can be estimated based on the

knowledge of the system type.

IGV are mechanism that redirect the airflow through the fan and add a co-swirl(with the direction of fan rotation) velocity component to the incident air into the fan

blades. Changing the air incident angle on the fan blades will change the fan performanceregime by changing the dependency of the static pressure rise with the flow rate.Basically, the fan with IGV will operate at different rotation speed from the fan with noIGV and this change in the speed will change the performance of the fan and its power

(4)

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consumption. From this it follows that for each different setting of the IGV, the fan willoperate at different speed and hence at different operating conditions and this yields towide variations in the supplied airflow and in the power consumption of the fan. Its the

goal of this experimental investigation to quantitatively describe this variation in the fanperformance and assess the potential benefits from this variation in reducing the fan

power.

Experimental Results of Changing IGV Setti ngs on the Fan Operation.Theresults from the two main tests are presented here. The main results are the variation offan power and static pressure rise with air flow rate for several IGV settings. Figure 2shows a plot of the fan power versus flow rate for the initial test data. The figure shows

two main key points. The first is that the fan power increases with the flow rate for agiven IGV setting. This result is expected because the fan needs to do work on largeramount of air and hence the total power will increase. The second and the most importantkey is the variation of the fan power with different IGV settings. It can be seen looking at

figure 2 that the fan power consumption can be reduced with IGV settings. All the IGV

settings indicate lower fan power consumption compared to the case with no IGV(IGV=90) which indicates that placing IGV at the inlet of the fan is a successful approachto decrease the power consumption. Another aspect that figure 2 shows is the power

sensitivity with IGV settings. It can be seen that there is a large power reduction betweenIGV=90 and IGV= 75 and between IGV=60 and IGV=45. Between IGV=75 andIGV=60, the power stays relatively constant which indicates low sensitivity in the fanoperating conditions for this IGV range. In order to fully describe the change in the

performance of the fan with IGV settings, we need also to consider the static pressure risecharacteristic. Static pressure rise characteristic or fan pressure map for simplicity is auseful graphical representation of the fan-system possible operating conditions. The fanpressure map contains the fan pressure curves along with the fan system load line curve

or the fan system resistance curve. The possible steady state operating conditions for thewhole fan system occurs where the fan pressure curve intersects the load line curve.

Figure 2.Varation of the fan power versus flow rate with IGV settings for the initial test

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Figure 3 shows the fan pressure map for the initial test data. The load line in the figure isrepresented by equation 4 and it describes the actual server room flow resistance. Theconstant in equation 4 for the server room is found to be 8.23 105/2. Thevalue of the constant was obtained from the information provided to us in the request

memo.

Figure 3 shows the effects of the IGV on the pressure rise characteristic of the fan.Comparing Figures 2 and 3, it can be seen that the reduction in power comes as acompromise of the static pressure rise capability of the fan. This means that in order to

reduce the power consumption for a given flow restriction system (like the server roomload) the flow rate must be reduced as well. This can be seen from figure 3 in which theload line intersection points with the fan curves for all the IGV settings occurs at flowrate lower than that of the IGV=90 case.

From figure 3, we can get the server room operating flow rate and this is done byfinding the intersection point of the server room load curve with the fan curve at IGV=90. The intersection point occurs at flow rate of 2257 CFM. From the value of theoperating flow rate the power consumption of the server room fan can be obtained from

figure 2 by finding the power consumption at flow rate of 2257 CFM for the IGV=90case. From figure 2 we can see that this value is 355 W. the 355 W is the power level thatwe are trying to reduce by at least 15% in order to meet the EIRA requirement. 15%

power reduction from the current 355 W means that the fan power needs to be 302 W orlower. Examining figure 2 shows that IGV of 15, 30 and 45 satisfy this requirement andhence these settings are strong candidate solution.

Based on the initial data results, we have decided that the IGV between 35 and55 needs to be tested to seek more solutions. Figure 4 shows a plot similar to figure 2 of

the fan power map for the second test.

Figure 3.Fan pressure map with the server room load line for the initial test

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Figure 4 shows similar trends as figure 2. What is important here to notice is the powerlevel for each IGV. IGV settings of 55 and 50 have similar power levels and they exceedthe minimum power reduction. IGV settings of 35 and 40 both satisfy the minimum

power reduction level and can be added to the possible solutions. But to see whether thefan in the server room can operate with IGV settings of 35 and 40, we need to look again

at the pressure map plot. Figure 5 shows the pressure map for the second test with theserver room load curve. From figure 5 it can be seen that the fan pressure curves for IGV

of 35 and 40 do intersect the server room load curve and hence the fan can operate in theserver room with IGV settings of 35 and 40 and achieve the power reduction levelshowing in figure 4.

Figure 4.Varation of the fan power versus flow rate with IGV settings for the second test

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Recommendation of the IGV Settings to Reduce the Power Consumption

This section presents the possible IGV settings that will reduce the powerrequirement of the server room. The section also discusses the maximum possiblenumber of servers that can be installed in the server room after using the recommended

IGV settings.

Criteria for Choosing IGV Setti ngs. The main criteria for choosing an IGVsetting is the resulting power reduction from using that IGV compared with the case with

no IGV. From the previous section we saw that the fan currently consumes power at arate of 355 W and power consumption of 302 W or less is needed. Hence, the IGVsettings that yield to power consumption of less than 302 W are all possible solutions. Inorder to determine the number of servers that can be installed in the server room for each

IGV settings, the acceptable range of flow rate per server is needed. From the requestmemo that was sent to us, the rule of thumb for the acceptable range of flow rate is 110 140 CFM per server. Once the range of the IGV settings that reduce the powerconsumption is established, the intersection point of the server room load curve with the

particular IGV pressure curve will give the total flow rate that the fan will supply at thatspecific condition and from the total flow rate we can determine the number of serversbased on the rule of thumb mentioned above.

Recommended IGV Sett ings. Based on the criteria mentioned in the last section,the IGV settings that meet the power requirement are gathered in one plot. Figure 6shows a plot of the server room load curve with the intersection point of the fan curve ofthe IGV settings that satisfy the power requirement.

Figure 5.Fan pressure map with the server room load line for the second test

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Figure 6 shows all possible IGV settings that reduce the fan power by at least15% and the corresponding fan-system flow rate. These results are obtained by combingthe results in figures 3 and 5. Figure 6 shows also the current operating condition of the

fan with no IGV which is represented by IGV=90 in the figure. It can be seen that all thepossible solutions yields a reduction in the flow rate from the current existing conditions

in the server room.

Figure 7 shows a plot of the fan power for the IGV settings in the figure 6. Thefigure shows each IGV settings and its corresponding fan power consumption. Clearly allthese IGV settings achieve power reduction of more than the 15% requirement and hencethe choice of the specific IGV settings will be based on maximizing the total number of

servers that the fan can serve under the new conditions.From figure 7, we can see that IGV of 35 and 40 yields the highest flow rate among allother possible solutions. We can see also that the power consumption is lower for thecase of the IGV of 35. IGV of 35 has fan power of 278 W which corresponds to a 21.6%

power reduction from the base case (IGV=90) and operate at flow rate of 1794 CFM. Onthe other hand, IGV of 40 has fan power of 295 W which corresponds to a 16.9% powerreduction from the base case (IGV=90) and operate at flow rate of 1807 CFM.

Since the flow rate for the IGV 35 and 40 are very similar, both settings allows

the fan to support the same number of servers. However, the power reduction for the twocases is different and IGV of 35 achieve less power consumption. For this reason, webelieve that the IGV setting of 35 is the best possible solution and hence we recommendthe insulation of IGV at the inlet of the fan and set the angle at 35 degrees. The number of

Figure 6.Server room load curve with intersection locations of the fan curve for theIGV that satisfy the power reduction requirement

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servers that can be installed in the server room with this modification is 16 servers. Thiswas calculated based on 110 CFM per server given that the fan with IGV set at 35 willprovide a total of 1794 CFM.

Uncertainty Analysis

This section presents the results of the sensitivity study that was done to assess theprecision of the measurement of the air flow rate.

Random Uncertaint y of th e Measur ed Flow Rate. As mentioned in theexperimental setup section, a sensitivity test was performed to assess the precision of theflow rate measurement. The test was done at IGV of 90 and was repeated for three times.The results of the three trials are shown in figure 8 in which it shows the static pressure

rise versus the flow rate for each of the trials.

Figure 7.Fan power at the intersection locations of the server room load curve withthe fan curve

15% power

reduction

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Figure 8 indicates that in general the measured flow rate values for the three trials arevery close from each especially where load curve intersects the fan curves. The loadcurve intersects the three fan curves at 2220, 2236 and 2243 CFM respectively. So themaximum difference in the measured flow rate is about 23 CFM. This shows that the

precision in the flow rate measurements at the location of the intersection between theload curve and the fan curve is very high.

In order to assess the precision of the measured data more formally, the meanvalue of the measured flow rate at each trial should be compared with the standard

deviation of the mean from the three trials to find a confidence interval that the measuredflow rate lie in. the mean value of the measured flow rate will be given by:

= Where Q is the flow rate given within confidence interval, is the mean value of theflow rate for the three trials, t is the factor from the student t test table that is determined

by the desired confidence interval and the number of trials and is the standarddeviation of the mean calculated from the measured three trials of the flow rate. Thedesired confidence interval that we want to use is 90% two sided so this will give a t

value of 2.353. The random uncertainty in the measured flow rate will simply be ateach given mean flow rate. Figure 9 shows the random uncertainty in the measured flow

rate in percentage of the calculated mean value for each mean value of the flow rate. Thefigure shows that the uncertainty gets smaller for the higher value of the mean flow rates.This means that we have more confidence in knowing the high value of the flow ratesthan knowing it for the low value flow rates. What is important here is that the

uncertainty of the flow rate where the load and fan curves intersect (last point in the plot)is very low about 1.6% of the mean value which corresponds to 37 . Samplecalculation of the uncertainty is included in appendix A.

(5)

Figure 8.Static pressure rise versus flow rate at IGV=90

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Suggestions to Improve the Quality of the Measured Data

This section presents some suggestions that aim to increase the quality of themeasured flow rate.

Test Setup Improvements. The flow rate measurements in this test were madeby pressure measurements downstream of the fan. The flow profile downstream of acentrifugal fan tends to be non-uniform and possibly has a swirl component. The effect of

non-uniform swirling flow field on the flow rate measurements is to make it highlysensitive to the plunge locations of the Pitot probe. This means that more measuringpoints inside the fan duct are needed to capture the non-uniformity in the velocity profilein order to get an unbiased flux calculation of the flow rate. This being said, our choice of

the measurement locations inside the duct didnt take into account the need of finerspacing between plunge locations and hence the values of the flow rate we calculated willbe slightly overestimated or underestimated depending on the operating condition of thefan and the specific velocity profile at the measuring plane. In order to eliminate this

source of uncertainty, we suggest using a flow straightener downstream of the fan andupstream of the measuring location. The flow straightener will help establish a velocityprofile that resembles the fully develop turbulent velocity profile which is very uniformfor most part of the duct. In addition, the flow straightener will remove any residual swirl

component in the flow. Another way to achieve a steady uniform velocity profile for

Figure 9.Uncertainty of the measured flow rate at 90% confidence interval

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purpose of flow measurement by velocity traversing is to change the location of themeasuring station from downstream of the fan to upstream of the fan in suction duct,because the flow in the suction side of the fan is much uniform and more steady that the

flow downstream of fan.The last recommendation we have is motivated by the ASME Flow

Measurements Standard. The standard highly suggests that the flow measurement byvelocity traversing should be done across the whole diameter of the duct to assess the

symmetry of the velocity profile. In addition, the plunge locations of the Pitot probeshould be chosen to be at the center of equal area in order to weight the velocitycontribution to the total flow rate in an unbiased fashion. The current test setup that wehave does not allow us to apply this specific standard because the Pitot probe is short and

cannot traverse through the whole diameter. Also, due to the L-shaped geometry of theprobe, we were limited by a minimum distance of 2 inches from the duct wall and hencewe were not able measure centers of equal area.

Conclusions

The main focus of this experimental work was to investigate the effectiveness of

installing IGV on a ventilation server room fan for the purpose of reducing the powerconsumption. Several testing has been conducted to investigate the performancecharacteristics of the fan operation with wide range IGV settings. The relationshipsbetween the power and static pressure rise with fan flow rate have been investigated and

determined experimentally for each IGV settings.Based on the testing that has been conducted, its believed that the IGV is an

effective mechanism to reduce the power consumption of the fan to the limit that satisfiesthe EIRA requirement. Our testing shows that using IGV of 35 degrees yields a power

reduction of 21.6% from the current operating condition. Our testing shows also that atthis IGV setting the fan can support a total of 16 servers in the sever room. Thesensitivity study that we conducted shows that our measurements of the flow rate arerepeatable especially at the conditions that replicate the server room system. Our random

uncertainty in the measured flow rate at conditions very similar to the server roomoperating condition indicated a value of less than 2% from the mean value with aconfidence interval of 90%.

Attachments:

Appendix A: Sample calculations

Appendix B: Measured and Calculated Data

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Appendix A: Sample Calculations

This appendix presents sample calculations for the flow rate. The calculationsinclude all the necessarily steps to get the flow rate from the measured raw data. In

addition, the appendix presents a sample calculation for the uncertainty analysis.

A-1: Calculating the Flow Rate

The sample calculations presented here are taken from the conditions presented intable B-1 in appendix B for IGV of 90 and BPV of 100%. first, we need to calculate the

air density inside the fan duct, and to do that, we need the values of the static pressure inthe duct, the ambient temperature and the ambient atmospheric pressure. The density isgiven by equation 3 which is

=

The pressure is given by the sum of the ambient pressure and the gage static pressureform the wall static tap measurement

() =() +() = .94 (2) 249.176 ()1 (2) + 27.7912(.) 3386 ()1 () = 94335()

The temperature in the equation A-1 need to be given in absolute units. the conversion isgiven by

(

) = (

(

) + 459.67)

1()1

.

8(

)

= (74(

) + 459.67)

1()1

.

8(

)

= 296.48(

)

Given that air has gas constant of 287 (J/kg K) the density becomes form equation A-1

= 94355()287296.48() = 1.109()The air velocity in the fan duct is given by equation 2 which is = 2

1 = 2.

15 (

2

)

249.176 (

)

1(2)1.109() = 8.21( )

2 = 2.165 (2)249.176()1(2)1 .109( ) = 8.61( )

(A-1)

(A-2)

(A-3)

(A-4)

(A-5)

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3 = 2.16 (2)249.176 ()1 (2)1 .109() = 8.48( )

4 = 2.135 (2)249.176(

)

1(2)1.109() = 7.79( )

5 = 2.13 (2)249.176 ()1 (2)1 .109() = 7.64( )Form these veloctiy we can use equation 1 to calcualte the total flow rate.

=

= 4 18()

39.3701()1()

2 (8.21 + 8.61 + 8.48 + 7.79 + 7.64) 5

2118.9()1 (

3 ) = 2834 ()

A-2: Uncertainty Calculations

The sample calculations presented here are taken from the data in table B-11 and

B-12 of appendix B that corresponds to BPV of 40%. The random uncertainty is givenby equation

= Where the uncertainty is given by . t was chosen to be 2.353 which is the t studentvalue for three measurements with confidence interval of 90%.

= 1(1) ( )2 = (2188.9 + 2200.5 + 2050.1)()

3= 2146.5 ()

= 13 2 [(2188.9 2146.5)2 + (2200.5 2146.5)2 + (2050.1 2146.5)^2

(A-5)

(A-6)

(A-7)

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= 48.3 ()

= 2.353

48.3(

) = 113.6 (

)

Uncertainty is: 113.6 ()90% confidence interval

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Appendix B: Measured and Calculated Data

Table B-1.Initial test data (BPV =100%)

IGVAngle

(Deg.)

BPV (%)Fan

Power

(W)

Gage

Static

Pressure

(in H20)

Pitot TubePlunge

height (in.)

Dynamic

Pressure

(in.

H2O)

90 100 376 0.94

9 0.15

7 0.165

5 0.16

3 0.135

2 0.13

75 100 348 0.88

9 0.12

7 0.13

5 0.14

3 0.145

2 0.145

60 100 337 0.82

9 0.12

7 0.13

5 0.16

3 0.17

2 0.17

45 100 278 0.5

9 0.057

7 0.06

5 0.06

3 0.06

2 0.06

30 100 265 0.42

9 0.05

7 0.06

5 0.065

3 0.06

2 0.06

15 100 249 0.24

9 0.04

7 0.04

5 0.04

3 0.05

2 0.05

19


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IGV

Angle

(Deg.)

BPV (%)

Fan

Power

(W)

Gage

Static

Pressure(in H20)

Pitot Tube

Plunge height

(in.)

Dynamic Pressure

(in. H2O)

90 75 376 1.1

9 0.15

7 0.165

5 0.16

3 0.15

2 0.115

75 75 348 0.94

9 0.12

7 0.13

5 0.141

3 0.152 0.14

60 75 336 0.9

9 0.12

7 0.13

5 0.15

3 0.165

2 0.17

45 75 277 0.58

9 0.057

7 0.057

5 0.056

3 0.0562 0.055

30 75 262 0.42

9 0.05

7 0.05

5 0.06

3 0.06

2 0.06

15 75 248 0.28

9 0.04

7 0.04

5 0.04

3 0.0482 0.05

20


21/28


IGV

Angle

(Deg.)

BPV (%)

Fan

Power

(W)

Gage

Static

Pressure

(in H20)

Pitot Tube

Plunge height

(in.)

Dynamic

Pressure (in.

H2O)

90 50 367 1.6

9 0.08

7 0.095

5 0.12

3 0.14

2 0.16

75 50 340 1.33

9 0.1

7 0.105

5 0.12

3 0.132

2 0.149

60 50 329 1.32

9 0.085

7 0.1

5 0.12

3 0.13

2 0.14

45 50 276 0.86

9 0.05

7 0.06

5 0.06

3 0.06

2 0.06

30 50 263 0.52

9 0.05

7 0.05

5 0.05

3 0.055

2 0.055

15 50 244 0.4

9 0.04

7 0.04

5 0.04

3 0.04

2 0.05

21


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23/28


24/28

Table B-7.second test data (BPV =40%)

IGV

Angle

(Deg.)

BPV (%)Fan Power

(W)

Gage

Static

Pressure

(in H20)

Pitot Tube

Plunge

height (in.)

Dynamic

Pressure

(in. H2O)

55 40 320 1.42

9 0.07

7 0.07

5 0.075

3 0.09

2 0.09

50 40 315 1.4

9 0.06

7 0.07

5 0.07

3 0.075

2 0.075

40 40 287 1.24

9 0.05

7 0.05

5 0.05

3 0.05

2 0.04

35 40 282 1.16

9 0.04

7 0.05

5 0.05

3 0.05

2 0.05

24


25/28


IGV Angle

(Deg.)BPV (%)

Fan Power

(W)

Gage

Static

Pressure

(in H20)

Pitot

Tube

Plunge

height

(in.)

Dynamic

Pressure

(in. H2O)

55 35 317 1.48

9 0.06

7 0.07

5 0.07

3 0.07

2 0.07

50 35 314 1.46

9 0.06

7 0.06

5 0.06

3 0.06

2 0.06

40 35 287 1.36

9 0.04

7 0.045

5 0.05

3 0.05

2 0.05

35 35 280 1.32

9 0.04

7 0.04

5 0.05

3 0.052 0.05

25


26/28


IGV Angle

(Deg.)BPV (%)

Fan Power

(W)

Gage Static

Pressure (in

H20)

Pitot Tube

Plunge

height (in.)

Dynamic

Pressure

(in. H2O)

55 30 312 1.64

9 0.06

7 0.06

5 0.06

3 0.06

2 0.06

50 30 309 1.6

9 0.05

7 0.05

5 0.05

3 0.05

2 0.05

40 30 286 1.44

9 0.047 0.04

5 0.045

3 0.05

2 0.05

35 30 280 1.32

9 0.04

7 0.04

5 0.04

3 0.05

2 0.05

Table B-10.calculated flow rate values in CFM form second test

IGV

BPV(%)

15 30 60 75

30 1532.4 1549.9 1636.9 1793.1

35 1566.9 1584.6 1793.5 1908.4

40 1601.8 1601.6 1935.8 2054.745 1761.5 1730.1 2094.9 2212.6

26


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28/28

7 0.08

5 0.09

3 0.105

2 0.11

90 40 353 1.8

9 0.06

7 0.07

5 0.08

3 0.09

2 0.095

90 45 356 1.66

9 0.07

7 0.08

5 0.09

3 0.11

2 0.11

90 45 359 1.62

9 0.077 0.09

5 0.1

3 0.11

2 0.11

90 45 360 1.64

9 0.08

7 0.085

5 0.1

3 0.11

2 0.11

Table B-12.calculated flow rate values in CFM for the sensitivity test

Trial

BPV(%)

1 2 3

30 1463.4 1878.8 1960.9

35 1698.7 1926.1 1878.7

40 2188.9 2200.5 2050.1

45 2211.8 2260.8 2275.3

Date post:	01-Jun-2018
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