Kailash Wt Perf Analysis

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Wind Tunnel Performance Analysis(Measuring Power Requirement)

Practical Training Report Submitted by

Kailash Kotwani

Under guidance of

Professor S K Sane and Dr. Hemendra Arya

Center for Aerospace System and Design EngineeringDepartment of Aerospace Engineering

Indian Institute of Technology, BombayAugust, 2003


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Abstract

An experiment analyzing performance of wind tunnel and co-relating theoretical

analysis is presented. Various losses at different sections in tunnel have been calculated

and total pressure drop across the wind tunnel has been estimated using them.Accordingly, total power required or total power invested to run a open circuit wind

tunnel is calculated at different flow velocities. An experiment is conducted to measurethe electrical power consumed by wind tunnel fans at different velocities. Calculated

power required and measured power input will give the efficiency of system.Second task was to determine the input power required at flow velocities beyond

the maximum achievable flow velocity in tunnel. That is the present tunnel system

provides maximum velocity of 10 m/s and estimation has been conducted to calculatepower required at 25 m/s. For the same purpose trend of results of experiment was

extrapolated and again efficiencies were obtained at velocities beyond 10 m/s.

Nomenclature

= Density (kg/m3)a = Air density (kg/m

3)

R = Universal gas constant (J/kg.K)T = Temperature (K)

p = Pressure drop (Pa)Dp = Dynamic pressure head (Pa)

P = Pressure (Pa)

w = Density of water (kg/m3)

V = Flow Velocity (m/s)g = Acceleration due to gravity (m/s2)

h = Manometeric height (mm of H2O)Pt = Total pressure (Pa)Q = Volume flow rate (m3/s)

Contents

AbstractNomenclature

1. Introduction

2. Calculating theoretical power required at different flow speeds2.1 Theory

2.2 Calculation of all Kis

2.3 Calculations and results3. Experiment to measure power consumed by fans at different flow velocities

3.1 Apparatus3.2 Theory

3.3 Description3.4 Precautions3.5 Observations

3.6 Calculations and Results4. Extrapolation to determine the power consumption at higher velocities

5. Co-relating theoretical and experimental results


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6. ConclusionsReferences

AppendixA) Wattmeter Multiplier chart

B) Matlab Code

C) Charts for lossesAcknowledgement

1. Introduction

In most basic sense, wind tunnels are ground-based experimental facilitiesdesigned to produce flows of air (or sometimes other gases), which simulate natural flows

occurring outside the laboratory. For most aerospace engineering applications, windtunnels are designed to simulate flows encountered in the flight of airplanes, missiles or

space vehicles. Since last 150 years, man has always constantly endeavored in thedirection of improving performance and efficiencies of tunnel system i.e. gettingmaximum velocity at minimum input power. This exercise proceeds in the same

direction.An open wind tunnel was fabricated at IIT Bombay (Image 1) during the 2002-

summer for the purpose of designing and developing an MAV (Mini Aerial Vehicle). Thesize of test section is 1m X 1m X 1.25m as shown in Fig. 1 and one can use it for therange of velocities from 0 m/s to 10 m/s. Air inside the tunnel is circulated using six

single-phase motor-driven fans and voltage is controlled by 230 V range Auto-Transformer. In near future the fans of this wind tunnel will be upgraded to provide

velocities in the range of 20 m/s. The sole purpose this exercise is to predictapproximately electrical power requirement and efficiency at that speed.

Image 1: Wind tunnel set up2


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When air flows through a channel of varying cross-section then it undergoes thechange in velocity as per the continuity principle. If there is rise in static pressure then the

dynamic pressure will drop down and vice versa. Therefore, it appears that the totalpressure, which is the sum of static pressure and dynamic pressure, remains constant.However, in practice these velocity changes are not loss free. Some energy will be lost

(or rather turned into heat which is not significant when the fluid is incompressible). Theloss in each element of the system (bend, duct length, branches, and obstructions) is

dependent on average velocity through it. Here it was assumed that flow is uniform andvelocity is constant throughout the crossection. All these losses are measured in terms ofpressure drop ultimately which provides power required. On other hand an experiment is

conducted to measure the power supplied to fans at different flow velocities. Assumingthe fact, power is proportional to cube of flow velocities the results obtained are

extrapolated to obtain power consumption at higher velocities. Then theoretical andexperimental results at measured range and at extrapolated range are co-related to analyzethe general trend of power consumption and efficiency of system.

Number over text as superscript denotes the number of reference given at the end of report.

Figure 1 : Wind Tunnel Details


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2. Theoretically Calculating Power required at different flow speeds

Final output power produced by fans in an open circuit wind tunnel is invested inovercoming various losses and ultimately flow possessing kinetic energy (Rate of energy

is power) is thrown into the ambient atmosphere. This total output power is power

required to run the wind tunnel. Here in this section this power will be calculatedtheoretically at different speeds.

2.1 Theory

Ifp is total pressure drop in (Pa) and Q is Volume flow rate (m3/s) then power requiredin (W) is given as

Preq = p*Q (1)The total pressure drop between point 1 and point 2 due to losses is given as-

ct lengthsion in due to frictdrop duVKt

Pt

P +=2

121

5.0

In other way, 21 ppp += (2)Where the value of constant K is sum of all Kis calculated for each different type

of loss.The different losses are -

1. Losses at entry to the system from atmosphere.2. Losses at changes of duct area or shape.3. Losses at bend and changes of direction.

4. Losses at division of flow into branches.5. Losses caused by obstructions, grills and louvers.

6. Losses at discharge from system to atmosphere

2.2 Calculation of all Kis

1) Loss at inlet

Radius of inlet (curved part) r =0.125m,Equivalent diameter d=1.1m

r/d = 0.1136 (r is the radius at inlet and d is the mean diameter)From image 2, Appendix C, K1 = 0.06 for r/d =0.125

2) Loss at obstructions,

Aerofoil dimension is 0.5*0.01Area blocked due to obstruction = 0.5 * 0.01 = 0.005 m2

Total wind tunnel cross section area = 1m2

Blocked area / total area = 0.005From image 3, appendix C, for streamlined strut K2= 0.01Blocked area due to tube= length of tube*diameter of tube.

= 0.5*0.01

= 0.005From image 3, appendix C, for round tube K3 = 0.01


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3) Pressure drop in duct diffuser,

A2 =1.6*2.4 =3.84 m2,A1 = 1m

2A2 / A1 = 3.84 (A1, A2 are the inlet and outlet areas of the duct)

Calculating average height (a) and width (b) for tunnel

a = 1.3 m, b = 1.7Calculating De from eqn 4,

De = 1.6 mL = Length of diffuser = 3.75

L/ De =2.343 K4= 0.45 (From Image 4, appendix C)

4) Loss at outlet,

For losses at outlet,Ko = 1 (From Image 5, appendix C)

But at outlet, velocity is different from that of the test section. For incompressible flowcontinuity eqn is given as

A1.V1 = A2.V2 (3)Where A1, V1 and A2, V2 are area of crossection and velocity at test-section and outletrespectively.

V2 = (A1/A2).V1 = 0.2604.V1Pressure lose at outlet = .Ko..(V2)

2 = . (0.0678).. (V1)2

Resultant K for losses at outlet = K5 = 0.0678

5) Loss due to the duct friction,

This loss depends on equivalent diameter and the flow velocity. Equivalent diameter isgiven as1

(4)

Where a and b are dimensions of rectangular duct.

Equivalent diameter for straight channel = 1.1 mAnd Equivalent diameter for diffuser section = 1.51 m.

Using these values, the loss is calculated for different velocities with the he lp of

graph in image 6, appendix C. While calculating the duct friction loss, additionalfactor of 1.25 was assumed to take into account bolts within the ducts. Loss iscalculated as shown in calculations.

Area of crossection of test section = 1 m2

Flow velocity = Volume flow rate

2.0

6.06.0

)(265.1

ba

baD

e

+=


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2.3 Calculations and results:

1) Total pressure drop calculation due to all KiThe value of resultant K is obtained by summing all values of Kis.

6028.00678.045.001.001.0065.05

1

54321=++++=++++==

=

=

i

i

iKKKKKKK

(4)

Then, P1 = pressure drop = K * 0.5 *a * (V1)2 (4A)

Where, a =1.225 kg/m3.

This pressure loss is calculated at different test-section velocities (Table 1) and then the

graph is plotted.

2) Calculating pressure drop due to duct friction loss

Total duct friction loss = friction loss in test section + friction loss in diffuser

Duct Skin friction losses are calculated in the following way:

For the straight channel, .1.1,1,1 mDba e === (from eqn 3)For a given flow, say Q= sec,/10 3m and ,1.1 mDe =

F1= Pressure drop = 0.9 Pa/m (Image 6, Appendix C)

So for the 3.25 m length of the straight channel (inlet + test),

Pressure drop = 0.9*3.25= 2.925 Pa.

For the diffuser section average a= 1.7 m, b= 1.3m,

Correspondingly, 6.1=eD m (from eqn 3)

For Q= 10 m3/s & 6.1=eD m,

F2 = Press drop = 0.14 Pa/m (Image 6, appendix C)

For the 3.75 m length of the diffuser, pressure drop = 0.14*3.75= 0.49 Pa.

While calculating the duct friction loss, a factor of 1.25 was assumed to take intoaccount bolts within the ducts

Complete formula for duct friction loss can be written as

2P = ( ) 25.1*75.325.3 21 FF+ (4B)

Using eqn 2, 3, 4, 4A and 4B to calculate total pressure drop (given in table 1) at

different flow velocities and plotting them (graph 1)


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Table 1: Calculation of Total Pressure drop at different flow velocities

Flow

Velocity(m/s)

Pressure loss due

to K factors (Pa)

P1

Pressure loss due to duct

friction (Pa)

P2=(3.25 F1 + 3.75 F2)*1.25

Total pressure

drop (Pa)

P=P1+P2

2 1.48 0.41 1.886864 5.91 0.58 6.48744

6 13.29 1.32 14.61174

8 23.63 2.44 26.06976

10 36.92 4.31 41.2315

15 83.07 9.53 92.603375

20 147.67 16.56 164.246

25 230.76 28.13 258.889375

30 332.29 37.38 369.6735

y = 0.4115x2

+ 0.0066x

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35Flow Velocity (m/s)

Totalpressuredrop

(Pa

Graph 1: Total pressure Drop at different Flow Velocity


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3. Experiment to measure power consumed by fans at different flow velocities

3.1 Apparatus1) 3 Wattmeters (Single element electrodynamic portable wattmeter)

2) Micro-manometer (Max p 199.9 mm H2O)

3) Pitot static tube (mounted in tunnel)

3.2 TheoryTo measure the density of air, the ideal gas equation is given as

P = RT (5)Where P and T are measured laboratory pressure and Temperature.

The relationship between dynamic pressure head and velocity is given as

p = *aV2 (6)

Where Micro-manometer measures pressure in mm of H2O

p = wgh (7)Solving 2 and 3 to obtain,

V =

a

ghw

2(8)

3.3 DescriptionOpen channel wind tunnel is mounted with six fans for producing flow of desired

velocity. Six fans run on single-phase supply. Each two fans receive supply from single

line. Hence there are total three supply lines. Each connected to one wattmeter formeasurement using three wattmeter method. Chart for selecting voltage and current range

is given in Table 5, appendix A. A pitot static tube mounted at the center of crossectionand at the distance of 78 cm from entry is connected to Micro-manometer for measuring

dynamic pressure head.After considering voltage and current ratings of fans, the following range was

selected on wattmeter

Voltage range: 220 VCurrent range: 5 AmpMultiplier = 8 (from table in Appendix A)

3.4 Precautions

1) Ensure that pitot static tube is normal to the plane of crossection of wind tunnel2) Close all the slits and holes of wind tunnel using insulating tape before starting the

experiment

3) After increasing dimmer stat voltage, fan speed increases very slowly so givesufficient time to stabilize micro-manometer readings.

3.5 Observations Date: 30th July 2003

Experiment begins at: 3:07 pm Ends at: 4:05 pmTemp at start and end: 29/29 deg C

Pressure at start and end: 1003/1003 mbarHumidity at start and end: 77/77 %


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Table 2: Measurement of dynamic pressure and power consumption

Obs

no.

Dimmer stat

Voltage (V)

Dynamic Pressure

(mm of H2O)

Wattmeter 1

(W1)

Wattmeter 2

(W2)

Wattmeter 3

(W3)

1 65 0.14 11 8.5 8.5

2 80 0.27 19 15.5 16

3 95 0.58 26 24 254 110 1.05 35 33 33

5 125 1.77 45.5 43 43

6 140 2.75 54 53 50.5

7 155 3.74 58.5 59 53

8 170 4.42 61.5 61 55

9 185 4.85 62.5 62 56

10 200 5.10 64.5 64 58.5

11 215 5.35 66.5 66 61

12 230 5.60 69 68 63

13 245 5.70 73 71 67

During the experiment Micro-manometer was fluctuating over a larger range so it wasdecided to repeat the experiment to reduce the measurement error induced due to Micro-

manometer.Date: 30th July, 2003Experiment starts at: 4:21 pm Ends at: 5:05 pm

Temp at start/ End: 29/29 deg CPressure at start/ End: 1003/1003 mbar

Humidity at start/End: 76/78 %

Table 3: Measurement of dynamic pressure and power consumption

Obsno.

Dimmer statVoltage (V)

Dynamic Pressure(mm of H2O)

Wattmeter 1W1

Wattmeter 2W2

Wattmeter 3W3

1 65 0.1 10 8 10.5

2 80 0.3 17 15 15

3 95 0.6 26 24 25

4 110 1.0 35 32 32

5 125 1.7 45 42 42

6 140 2.5 52 52 47

7 155 3.8 56 57 50

8 170 4.6 59 59 53

9 185 4.9 60 61 5410 200 5.2 63 62 57

11 215 5.4 65 64 59

12 230 5.7 67 67 62

13 245 5.7 71 70 65

3.6 Calculations and Results

P = 1.003*103 Pa; T = 273 + 29 = 302 KR = 287 J/Kg K


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= P/RT = 1.1572 Kg/m3

Flow velocity is calculated using eqn no. 8

V =

a

ghw

2

Multiplier for wattmeters for selected range of voltage and current is 8, Power consumption = 8*(W1+W2+W3)

Using these equations, wind tunnel power consumption has been calculated atdifferent flow velocities in Table 4. Results for both data sets have been plotted in Graph

2. A curve fitting line has been obtained for both the data sets altogether in Graph 3.

Table 4: Calculating flow velocity and power consumption by the fans of tunnel

Velocity of

flow (m/s)

Power consumption (Watt)Dimmer stat

Voltage (V)

Dynamic

Pressure (mm

of H2O) 8*(W1+W2+W3)

65 0.14 1.54 224

80 0.27 2.14 404

95 0.58 3.13 600

110 1.05 4.22 808

125 1.77 5.48 1052

140 2.75 6.82 1260

155 3.74 7.96 1364

170 4.42 8.65 1420

185 4.85 9.06 1444

200 5.10 9.29 1496

215 5.35 9.52 1548

230 5.60 9.74 1600

245 5.70 9.83 1688

65 0.10 1.30 228

80 0.30 2.25 376

95 0.60 3.19 600

110 1.00 4.12 792

125 1.70 5.37 1032

140 2.50 6.51 1208155 3.80 8.02 1304

170 4.60 8.83 1368

185 4.90 9.11 1400

200 5.20 9.38 1456

215 5.40 9.56 1504

230 5.70 9.83 1568

245 5.70 9.83 1648


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0

200

400

600

800

1000

12001400

1600

1800

0 5 10 15Flow Velocity (m/s)

Powerconsumption(W

att)

Set 1 Data

Set 2 Data

Graph 2: Tunnel power consumption at different flow velocities

Passing a curve fitting line through these data points and we will obtain the following

curve.

0

200

400

600

800

1000

1200

1400

1600

1800

0 2 4 6 8 10 12Flow Velocity (m/s)

PowerConsumption(Watt)

Graph 3: Approximate curve-fitting line of power consumption vs flow Velocity forboth data sets.


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4. Extrapolation to determine the power consumption at higher velocities

Analyzing Graph 3 carefully, one can say that curve is linear for low flowvelocities on other hand for higher flow velocities power consumption start increasing

exponentially. In general, we know that power is proportional to the cube of velocity.

P V3

So ideally if there would have been no losses in the motors of fans and across itsblades we should have obtained cubic relationship between power and flow velocity. Ourobjective is to determine approximately correct relationship between power consumption

and flow velocity so that we should be able to extrapolate it to find power consumption at25 m/s.

While conducting experiment one fact was realized for low velocities below 4 m/s(that is in the voltage range of 65 to 100), output of Micro manometer was fluctuatingover the larger ranges hence reliability of these readings is low. Secondly, the fans inside

the tunnel are designed for voltage rating of 220 V. It is not correct to run these fans onsuch low voltage ranges. These are the factors, which have brought error in our analysis,

and we can see the curve for lower range of velocities is almost linear. So for purpose ofextrapolation we will not consider first three measurements (65 V to 110 V).After analyzing readings above 220 V we can say that there is not substantial

increase in flow velocity whereas there is sufficient increase in power consumption.Though we cannot conclude the exact reason behind it but some of the possible reasons

may be--1) Stalling of fan blades due to high RPM and forward velocities.2) Above power rating limit of fans, no appreciable increase in flow velocity resulting in

poor performance.3) Selected maximum voltage range on wattmeter is 220, so it may be providing

erroneous results beyond voltage limit of 220 V.

Hence we will not consider two set of observations noted above 220 V.Finally analyzing remaining selective reading and plotting them on graph.

0

200

400

600

800

1000

1200

1400

1600

1800

0 2 4 6 8 10 12

Flow velocity (m/s)

Power

Consumption(Watt)

Set 1 Data Set 2 Data

Graph 4: Power consumption for selected flow velocities


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A Matlab code (appendix B) was written for analysis purpose considering onlythe readings plotted in Graph 4. This code used polyfit and polyval functions and

generated following set of data and equation.

Y=1.0e+003 *(0.0054*X3 - 0.1222*X2+1.0097*X - 1.6801) (9)

(This equation is valid for flow velocities greater than or equal to 5 m/s)

Where Y= Power consumption (Watt), X = Flow Velocity (m/s)Using eqn 9, calculating power consumption at higher velocities in table 5 and

comparing them with measured values to check the validity of eqn 9. Calculated power(using eqn 9) is plotted against velocity in Graph 5.

Table 5: Determining power consumption at higher velocities and comparison withmeasured values

Flow Velocity

(m/s)

Calculated Power

Using eqn 9 (Watt)

Measured Power

(Watt)

% Error

5 987 960 2.817.5 1290 1320 -2.27

10 1579 1632.5 -3.27

12.5 2358 NA NA

15 4132 NA NA

17.5 7405 NA NA

20 12680 NA NA

22.5 20464 NA NA

25 31259 NA NA

0

5000

10000

15000

20000

25000

30000

35000

0 10 20 30

Flow Velocity (m/s)

Powe

rConsumption(Watt)

Graph 5: Relationship between Estimated power consumption and flow velocity


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5. Co-relating theoritical and experimental results

Power consumption calculated using eqn 9 gave a very small error withexperimentally measured values under velocity 10 m/s which proves the validity of

estimated eqn 9. Table 6, gives power consumption using eqn 9 (extrapolation), Output

power calculated theoretically through losses and efficiency of the system at differentvelocities and efficiency of the system then efficiency is plotted in Graph 6.

Table 6: Estimating efficiency of system from theoretical and extrapolated results

Flow Velocity(m/s)

Powerconsumption

(Watt)

Calculatedtheoretical Power

(Watt)

Efficiency ofsystem (%)

5 987 51.60 5.23

7.5 1290 173.97 13.49

10 1579 412.16 26.10

12.5 2358804.74 34.13

15 4132 1390.30 33.65

17.5 7405 2207.40 29.81

20 12680 3294.64 25.98

22.5 20464 4690.58 22.92

25 31259 6433.81 20.58

0

5

10

15

20

25

30

35

40

0 10 20 30

Flow velocity (m/s)

Efficiency%

Graph 6: Efficiency Vs flow velocity


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6.Conclusions

1) The present set of fans inside the tunnel provides maximum velocity up to10 m/s. If we upgrade tunnel using same set of fans to get higher velocities

they will give maximum efficiency in 12.5 m/s velocity range beyond that

efficiency will go down gradually. So it would be best to use same kind offans only up to 12.5 m/s.

2) Though efficiency of present system goes down in the range of 25 m/s butthis analysis give rough estimate of amount of input power which will be

required to achieve velocities around 25 m/s and this knowledge will helpin decision process of upgrading the present tunnel system.

3) Suppose we target to achieve a wind tunnel system which will be able to

provide maximum velocity of 25 m/s with an efficiency of around 50% soone can predict the minimum power required from above analysis and that

will be close to 13 k Watt. With an added factor of safety of 2 k Watt onecan say with confidence that at 15 k Watt this system will provide velocityin the range of 25 m/s and two huge motors of 7.5 k Watt may suit our

requirements.References

1) B. B. DALY, Woods Practical Guide to Fan Engineering, Woods ofColchester Limited publisher,1979

2) http://www.casde.iitb.ac.in/IMSL/index.html

Appendix A) Wattmeter Multiplier chart

Voltage range (V) Current range (A) Multiplier

55 2.5 1

55 5 2110 2.5 2

110 5 4

220 2.5 4

220 5 8

Appendix B) Matlab Code

X1 = [4.217144407 5.475331979 6.82480379 7.959020518 8.65236751 9.0634739849.294133605 9.519205758];

Y1 = [808 1052 1260 1364 1420 1444 1496 1548];X2 = [4.115511534 5.365970539 6.507195092 8.02260891 8.826788876 9.110073129

9.384810226 9.56358458];Y2 = [792 1032 1208 1304 1368 1400 1456 1504];Q=[5 7.5 10 12.5 15 17.5 20 22.5 25];

X3=[X1 X2];Y3=[Y1 Y2];P3 = polyfit(X3,Y3,3);

Z3=polyval(P3,Q);plot(Q,Z3)

xlabel('flow velocity (m/s)');ylabel('Power consumption (Watt)');


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Appendix C) Charts for losses

Image 2: losses at inlet1

Image 3: Losses at obstructions 1


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Image 4: Losses in duct diffuser1

Image 5: Losses at the outlet1


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Image 6: Losses due to duct friction1


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Acknowledgement

I take this opportunity to express our sincerest gratitude to Prof. S.K. Sane, forshowing us the way and being there by our side at all the crucial moments throughout

project work.

I would like to thank Dr. Hemendra Arya and Dr. K Sudhakar for their kind co-operation and guidance in this project.

I am thankful of Propulsion Laboratory Incharge, Mr Deshpande for his help inproject. We are thankful of Mr. Tagare, Mr. Nimkar, Mr. Gade, Mr. Mungekar and Mr.

Badekar who helped us with deep gratitude in this project.

-Kailash

Kailash Wt Perf Analysis

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