ASEN 2002Wind Tunnel Calibration

Experimental LabGroup # 8 - November 17, 2017

Jarrod Puseman ∗ , Matthew Maddux-Lehmann † , Matthew McCallum ‡ , Kyle Ivy §

University of Colorado - Boulder

The purpose of this report is to discuss the nature of airflow through the test sectionof a wind tunnel, while comparing the effectiveness of pressure transducers and watermanometers in determining the airflow’s velocity. In this lab, there are two methodsemployed for measuring the pressures required to find this velocity. The first utilizes aPitot-Static Probe that is introduced to the test section while the tunnel operates, and thesecond incorporates a Venturi tube setup that compares the static pressures at the reservoirof the wind tunnel and the entrance of the test section. The analysis then uses Bernoulli’sequation for incompressible flow to solve for the test section velocity according to theconditions of each method. The accuracy of the transducer and water manometer thendepend on the method incorporating them which changes from group to group. Followingthe analysis, it is clear that the static ring and pitot-static tube setups are comparable inaccurately measuring the required differential pressures. However, the U-tube manometeris ultimately the more reliable tool for accurate velocity calculations.

Nomenclature

∆P = Differential Pressureδlaminar = Laminar Boundary Layer Height[mm]δturbulent = Turbulent Boundary Layer Height[mm]

ν = Kinematic Viscosity [m2

s ]patm = Atmospheric Pressure[Pa]Rex = Reynold’s NumberV = Velocity [ms ]v∞ = Velocity Upstream [ms ]

psid = Pounds per Square Inch, Differential [ lbsin2 ]

∗104003252†105071187‡106279461§107043894

ASEN 2002 Section 014 1 of 16 Fall 2017

Contents

I Introduction 3

II Experimental Setup and Measurement Techniques 3

III Airspeed Calculation and Airspeed Model 4

IV Airspeed Measurement Uncertainty 5

V Boundary Layer Influence 8

VI Conclusions 9

2

I. Introduction

Figure 1: CU Wind Tunnel Components of the ITLL wind tunnel

The ITLL wind tunnel will be a fun-damental portion of the CU Aerospaceengineering curriculum. Therefore, es-tablishing a firm understanding of howit works will be a valuable asset for eachengineering student.

The tunnel consists of an inlet, flowconditioners, a settling chamber that con-tracts into the test section, the actual testsection, and a diffuser that opens to thetunnel’s motor and fan. The system’smotor and fan are located downstreamfrom the test section and work to pull airfrom the ambient environment into thetunnel. This acceleration can be creditedto the decrease in area from the inlet tothe nozzle by a factor of 9.5 which alleviates pressure from the test section causing the flow velocity toincrease. The final increase in area from the test section to the diffuser then slows the air once again as itexits the tunnel (limiting the differential pressure across the body). The remaining components then serveto ensure that the flow is steady throughout its journey from the inlet to the exit. But the function of thesecomponents is the topic of this lab.

Now, measuring the airspeed within the tunnel’s test section by direct temperature and pressure mea-surements is not this report’s only purpose. The analysis also compares the effectiveness of manometers andpressure transducers in measuring differential pressures, while examining the formation of viscous boundarylayers during operation of the wind tunnel. The end goal of the overall analysis is to determine whether ornot the boundary layer produced by the test section influences centerline flow, and to provide students witha foundational understanding of how the wind tunnel operates for use in future courses.

II. Experimental Setup and Measurement Techniques

Group 8 was tasked with measuring the test section airspeed at 2, 4, 6, 8, and 10 volts while using amanometer for the pitot-static probe measurements and a pressure transducer for the static ring measure-ments. Each of the setups is presented below, but note that the manometer in Fig. 2b is replaced by apressure transducer for this analysis.

(a) Pitot-Static/Manometer Setup A Pitot-static tube isattached to the wind tunnel manometer for differential pres-sure measurement.

(b) Venturi Tube/Pressure Transducer Setup Appli-cation of static rings where the illustrated manometer is re-placed by an airspeed pressure transducer.

Figure 2: Velocity Voltage Test Setups

The measurements from the pressure transducer were simply recorded by the given LabVIEW VI, butthe water manometer measurements were taken by measuring the change in height between the two columnsof liquid. One member from the group recorded these measurements in a lab notebook. The setups depictedabove varied for each team as groups 1, 5, 9, and 13 connected their pitot-static probe to a pressure transducer

ASEN 2002 Section 014 3 of 16 Fall 2017

and their Venturi tube setup to a manometer; while groups 3, 7, 11, and 15 followed the setup utilized forthis analysis.

III. Airspeed Calculation and Airspeed Model

The two equations for calculating airspeed can be seen below (equation (3) and equation (4)). Theseequations were derived from Bernoulli’s Equation (1) and the continuity equation (2). Equation (3) is usedto calculate the airspeed using a Pitot-Static Probe, and equation (4) is for the static rings. The airspeedwas calculated by taking the mean of the 500 ∆p samples measured and using this ∆p in the appropriateequation.

p0 +1

2ρV 2

0 = ps +1

2ρV 2

s (1)

A1V1 = A2V2 (2)

V =

√2 ∆p

(R Tatmpatm

)(3)

V =

√√√√√ 2 ∆p R Tatm

patm

(1−

(A2

A1

)2) (4)

Figure 5 and Figure 6 show the data for the Pitot-Static Probe and the Static Rings respectively. Both setsof data are very similar, which shows that they are both equally good measures of airspeed velocity. This is tobe expected as the calculated velocity for both readings is based on the same equation (Bernoulli’s Equation).The U-Tube manometer/Pitot-static probe data, shown in Figure 3, shows slightly higher velocities thaneither of the measurements made using the pressure transducer (Figures 5 and 6). Fig. 4 also comparesthe water manometer to the transducer over an identical set-up (where the measured voltages are the sameand the differential pressure is from the pitot-static probe). The error in the velocity of the manometer isvisually much smaller.

Figure 3: Velocity by Voltage for Water Manometer. This plot shows the calculated velocity for each voltagewith data from the water manometer as well as the line of best fit modelling this data.

ASEN 2002 Section 014 4 of 16 Fall 2017

This could be due to the lower error in the U-Tube measurement or due to some bias from the peoplereading the manometer. (The errors in the U-Tube and pressure transducer is discussed more in section 4.)A mathematical model relating input voltage to airspeed can be generated by calculating a line of best fitfor the data relating voltage to airspeed. Each data set generates its own line of best fit, so to calculate amore general equation the coefficients of the equations are averaged and those averaged values are used tocreate a final equation relating voltage to airspeed. Performing this operation yields the following equationthat relates input voltage to the airspeed within the test section of the wind tunnel.

V elocity = 5.8211 ∗ V oltage− 2.3449 (5)

Figure 4: Comparison of Water Manometer to Air Pressure Transducer This plot shows the calculatedvelocity for each of the specific voltages assigned to this configuration. The left plot uses a differential pressuremeasured with the manometer while the right differential pressure was measured with the air pressure transducer.

IV. Airspeed Measurement Uncertainty

To calculate the airspeed uncertainty, it is important to first consider the two equations used to calculateairspeed in this analysis (equations (3) and (4)).

From these equations it is clear that the test-section velocity depends on three variables that can begathered from the Excel data. These are: airspeed differential pressure, atmospheric temperature, andatmospheric pressure. The uncertainty in each of these variables is required before finding the airspeeduncertainty. Each one depends on the error associated with random fluctuations of measurement, errorsassociated with measurement hardware, and errors provided by the sensor manufacturer relating to thesensor calibration and performance. In this lab, only manufacturer quoted errors and random error in themeasurements will be considered. The reported systematic errors are as follows: the Freescale SemiconductorMPX4250A Absolute Pressure Sensor, used to measure ambient or atmospheric pressure in the ITLL, hasan accuracy of ±1.5% of the full scale span of 20 kPa to 250 kPa, which is 3.45 kPa. The LM35 PrecisionCentigrade Temperature Sensor, used to measure ambient or atmospheric temperature, has an accuracy of±0.25◦C. For the manometer utilized for this analysis, an uncertainty of ±0.05in of water (or 12.442 Pa)isassumed since the column heights were measured by approximately 0.1 inch intervals. Finally, the airspeeddifferential pressure is taken using two separate Honeywell SCX01DN differential pressure sensors, whichhave an accuracy of ±1% of the full scale span, 0 psid to 1 psid, which is .01 psid or 68.94757 Pa. Usingthis information, calculating the uncertainty in each of these variables is nothing more than simple errorpropagation.

ASEN 2002 Section 014 5 of 16 Fall 2017

With regards to the uncertainties and their trend versus speed, Figures 5 and 6implies uncertainty inairspeed decreases as airspeed itself increases. This happens because at larger differential pressures, the errorbecomes less significant.

Figure 5: Velocity by Voltage for Pitot-Static Probe. This plot shows the calculated velocity and error foreach voltage with data from the pitot-static probe as well as the line of best fit modelling these data.

The largest source of uncertainty in this analysis comes from the atmospheric pressure measurementstaken by the Freescale Semiconductor MPX4250A Absolute Pressure Sensor. Its determined uncertaintywas 3450 Pa, which is relatively large when compared to the other uncertainties in this report. Perhaps theerror could be improved by using a device with more accuracy, the U-tube manometer for example. Themanometer’s uncertainty was much smaller and that should lead to a more accurate measurement of airspeedvelocity.

Moreover, this smaller uncertainty-even though measurements from the manometer were taken manually-then suggests that it provides a more accurate measurement of the wind tunnel’s velocity. Perhaps astronger focus on accuracy on the manufacturers part could close the gap between the reliability of pressuretransducers and manometers for accurate differential pressure readings.

ASEN 2002 Section 014 6 of 16 Fall 2017

Figure 6: Velocity by Voltage for Static Rings. This plot shows the calculated velocity and error for eachvoltage with data from the static rings as well as the line of best fit modelling these data.

Figure 7: Velocity as Measured with the Water Manometer. This plot shows the calculated velocity anderror for each voltage with data from the water manometer measuring the pitot probe as well as the line of best fitmodelling these data.

ASEN 2002 Section 014 7 of 16 Fall 2017

V. Boundary Layer Influence

To measure the boundary layer height at port 8 (the port assigned to this group), all the standard infor-mation recorded by the LabVIEW VI was taken. These measurements include the atmospheric pressure, theatmospheric temperature, an unused airspeed differential pressure (from either a pitot probe or a set of staticrings), an auxiliary differential pressure (measured by a pitot probe above port 8), probe translation, probeheight, and voltage. The data used to study the boundary layer are the atmospheric pressure, atmospherictemperature, auxiliary pressure differential, and the ELD probe height.

To actually calculate the boundary layer information, a for-loop reads in each set of boundary layer data.csv files collected during section 14 of ASEN 2002 Lab. For each set of data, a nested loop checks fordata measurements at each possible height data could have been recorded. For all rows in the data with aheight within .1 mm of this target height, the script calculates the average atmospheric pressure, averageatmospheric temperature, and average differential pressure. Using these, the velocity can be calculatedusing equation (3) and stored in a matrix of velocities sorted by port and height. Once all the velocitiesare calculated, the boundary layer height is found by modelling the velocities with a square root functionat each port and then solving for the height at a where the calculated velocity is greater than .95 times thefree stream velocity calculated with the velocity-voltage model developed above.

Predicting the height of the boundary layer is done with the equations provided in Lecture 6.5 Slides [1].These predicted values are reported in Table 1.

δturbulent =.37x

Re0.2x

= .37x0.8(ν

v∞

)0.2

(6)

δlaminar =5.2x√Rex

= 5.2

√νx

v∞(7)

One level of complication to these equations, however, is that the turbulent delta assumes the boundarylayer from the very front of the plate is turbulent where in reality, the boundary layer starts laminar andtransitions to a turbulent boundary layer at some critical distance. Luckily, this distance can be calculatedand an appropriate shift added to the turbulent depth predictions to accommodate the turbulent sectionstarting not at the beginning of the plate. See the code in Appendix B for the calculations.

The velocity profiles at each port are shown in figure 8. The arrow length is only a qualitative represen-tation of the calculated velocity at each height for each port. The data group 8 specifically measured are thearrows at every non-integer height at port 8 (15.91 in). These measurements appear to fit well with otherteam’ measurements since the velocity trend over height at each port appears similar. We see that at everyport, velocity close to the wall is smaller than the velocity away from the wall. These velocities also appearto increase at a decreasing rate (in other words, the velocity change from height to height is greater closerto the wall).

Getting the boundary layer thickness is simple: find the height where the velocity is 95% of the freestream velocity. The free stream velocity is found using the model developed from section ??. For us, thefree stream velocity was calculated to be 26.94 m/s for 5 volts. A for-loop simply calculates the a squareroot model of the velocities at each port . Results are displayed in Table 1.

Table 1: Boundary Layer Height by Distance from Front of Test Section

Port 714.93 in

Port 815.91 in

Port 916.89 in

Port 1017.87 in

Height [mm] 6.1 6.4 6.6 6.8

Expected Turbulent Height [mm] 4.7 5.2 5.8 6.4

Expected Laminar Height [mm] 2.4 2.5 2.6 2.6

As evident in Table 1, the predicted heights of the boundary layers for laminar and turbulent flow arenot quite the same as the calculated heights, but the turbulent heights are closer.

Based on these predictions, the boundary layer at port 8 (the measurement location assigned to thisgroup) appears to be turbulent. The port itself is located behind the critical transition point, indicatingturbulence in the boundary layer. Also, the calculated heights match closer to the predicted heights of theturbulent layer. On top of this, the actual boundary layer starts before the front of the test section. In

ASEN 2002 Section 014 8 of 16 Fall 2017

Figure 8: Boundary Layer Velocity Profiles by Distance This plot is the compilation of all data from section14. The arrow length is proportional to velocities measured at that height and distance from the front of the testsection.

fact, it develops along the entire inside of the nozzle. As a result, the transition region begins even beforethe calculated critical point, so this puts port 8 further into the expected turbulent regime of the boundarylayer.

Finally, the velocity of the air in the center of the tunnel appears not to speed up appreciably, despitethe theory explaining it should. See Table 2. This could be due to error in the measurement equipmentsimply being not sensitive enough to detect this velocity change. The velocity change was expected to befairly small, and the random error in the measurements and calculations may simply overpower the changein velocity. There is one indicator of an accelerated air velocity, however. The calculated free stream velocityis still less than the calculated velocities in the center of the tunnel above these ports, which may indicatethe air does speed up from its velocity at the front of the test section.

Table 2: Boundary Layer Height by Distance from Front of Test Section

Port 714.93 in

Port 815.91 in

Port 916.89 in

Port 1017.87 in

Velocity [m/s] 27.3 27.2 27.3 27.3

VI. Conclusions

To some surprise, the preceding analysis suggests that the U-tube manometer is a better option foraccurately measuring differential pressures within a wind tunnel. Considering that the pressure readingsfrom the manometer were recorded from student approximations of the difference in column height of themanometer (meaning the initial uncertainty was simply based on the smallest unit of measurement onthe provided tool), it seems like these values would be subject to greater uncertainty than the pressuretransducer readings. After all, with student judgment, the most accurate predictions wouldn’t expand

ASEN 2002 Section 014 9 of 16 Fall 2017

beyond one or two decimal places. However, correct error propagation supports the manometer’s superioraccuracy. Furthermore, the analysis implies that there is no significant difference in the uncertainties of theVenturi Tube style set up (static pressure rings) and the pitot-static probe setup. Therefore, when it comesto deciding on configurations for measuring airspeed in the ITLL wind tunnel, this group would prefer thata manometer is used for differential pressures regardless of the choice of a pitot-static probe or Venturi tubesetup. This decision resides on the fact that the uncertainties in the velocity measurements were far lowerwhen the manometer was used as compared to the pressure transducer.

According to the boundary layer velocity profiles in Fig. 8, the boundary layer created by the test sectionwalls did not have a significant impact on the centerline airspeed. Although, had this not been the case,perhaps the test velocities could be held at higher values in the future to ensure the height of the boundarylayer doesn’t reach the centerline. After all, since the boundary layer eventually becomes turbulent acrossthe test section, lower airspeeds will almost maximize the height of the boundary layer as air elements tryto separate from the flow. So maximizing test velocities when possible is certainly one way to mitigate theinfluence of viscous flow in future experiments.

References

1Farnsworth, John. ASEN 2002 Lecture 6.5 Slides. CU, 2017. PDF.

Appendix A

Contributions

Matthew Maddux-Lehmann - Airspeed Calculations, Report WritingKyle Ivy - Airspeed UncertaintyMatthew McCallum - Airspeed Relations, Water Manometer AnalysisJarrod Puseman - Boundary Layer Velocities, Thickness

ASEN 2002 Section 014 10 of 16 Fall 2017

Appendix B: MATLAB Code

1 %S c r i p t f o r ASEN 2002 Aero Lab 12 %Written by Matthew Lehmann , Matthew McCallum , Kyle Ivy , Jarrod Puseman3 %Created 25 October 20174 %Last Modif ied 16 Nov 20175 %P r o f e s s o r Farnsworth678 %This s c r i p t ana lyze s data gathered from the ITLL wind tunne l to meet the9 %requirements f o r the f i r s t aerodynamics lab o f ASEN 2002 at the Un ive r s i ty

10 %of Colorado Boulder .1112 %F i r s t get c l ean13 c l e a r ; c l c ; c l o s e a l l ;1415 nameID = { ' 01 ' , ' 03 ' , ' 05 ' , ' 07 ' , ' 09 ' , ' 11 ' , ' 13 ' , ' 15 ' } ;16 v o l t a g e s =[ .5 , 1 , 1 . 5 , 2 , 2 . 5 , 3 , 3 . 5 , 4 . 0 , 4 . 5 , 5 . 0 , 5 . 5 , 6 . 0 , 6 . 5 , 7 . 0 , 7 . 5 ,

8 . 0 , 8 . 5 , 9 . 0 , 9 . 5 , 1 0 . 0 ] ;17 R = 287 ; %[ J /( kg∗K) ]181920 %% Airspeed Analysis and Uncertainty21 %Store s v e l o c i t y from p i t o t and unce r ta in ty22 Ve loVo l t sP i tot =ze ro s (3 , 20 ) ;23 Ve loVo l t sP i tot ( 1 , : )=v o l t a g e s ;2425 %Store s v e l o c i t y and unce r ta in ty measured in s t a t i c r i n g s26 VeloVoltsRing =ze ro s (3 , 20 ) ;27 VeloVoltsRing ( 1 , : )=v o l t a g e s ;2829 %Loop over a l l the data30 f o r i =1:831 name=[ ' Veloc i tyVoltage S014 G ' nameID{ i } ' . csv ' ] ;32 data=x l s r e a d (name) ;3334 f o r j =1:5 %Each team takes exac t l y f i v e measurements35 idx=f i n d ( v o l t a g e s==data (1 , 7 ) ) ;36 indexData=f i n d ( data ( : , 7 )==data (1 , 7 ) ) ;37 l en=length ( indexData ) ;38 P=mean( data ( indexData , 1 ) ) ;39 T=mean( data ( indexData , 2 ) ) ;40 deltaP=mean( data ( indexData , 3 ) ) ;4142 sigmaP=s q r t ( ( . 015∗230000)ˆ2+std ( data ( indexData , 1 ) ) / s q r t ( l ength (

indexData ) ) ˆ2) ; %Root mean square e r r o r o f sy s t emat i c e r r o r andrandom e r r o r

43 sigmaT=s q r t ( ( . 2 5 ) ˆ2+std ( data ( indexData , 2 ) ) / s q r t ( l ength ( indexData ) ) ˆ2) ;44 sigmaDeltaP=s q r t ( ( . 0 1∗6 8 9 4 . 7 6 ) ˆ2+std ( data ( indexData , 3 ) ) / s q r t ( l ength (

indexData ) ) ˆ2) ;4546 data ( indexData , : ) = [ ] ;4748 i f mod( s t r2doub l e (nameID{ i }) , 4 )==1 %Transducer was on p i to t−s t a t i c

probe

ASEN 2002 Section 014 11 of 16 Fall 2017

49 Ve loVo l t sP i tot (2 , idx ) = s q r t (2∗ deltaP ∗(R∗T/P) ) ;5051 %Uncerta inty52 p a r t i a l d e l t a P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗T/P) ;53 p a r t i a l T = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗ deltaP /P) ;54 p a r t i a l P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2)∗ (−1∗(2∗ deltaP ∗R∗T∗P

ˆ(−2) ) ) ;55 Ve loVo l t sP i tot (3 , idx ) = s q r t ( ( p a r t i a l d e l t a P ∗ sigmaDeltaP ) ˆ2 + (

p a r t i a l T ∗sigmaT ) ˆ2 + ( p a r t i a l P ∗sigmaP ) ˆ2) ;565758 e l s e %Transducer was on the s t a t i c r i n g s59 VeloVoltsRing (2 , idx ) = s q r t ( (2∗ deltaP ∗R∗T) /(P∗(1−(1/9.5) ˆ2) ) ) ;6061 %Uncerta inty62 p a r t i a l d e l t a P =1/2∗((2∗ deltaP ∗R∗T) /(P∗(1−(1/9.5) ˆ2) ) ) ˆ(−1/2) ∗ ( (2∗R

∗T) /(P∗(1−(1/9.5) ˆ2) ) ) ;63 p a r t i a l T = 1/2∗((2∗ deltaP ∗R∗T) /(P∗(1−(1/9.5) ˆ2) ) ) ˆ(−1/2) ∗ ( (2∗R∗

deltaP ) /(P∗(1−(1/9.5) ˆ2) ) ) ;64 p a r t i a l P =1/2∗((2∗ deltaP ∗R∗T) /(P∗(1−(1/9.5) ˆ2) ) ) ˆ(−1/2) ∗ (−1∗(2∗

deltaP ∗R∗T) /(1−(1/9.5) ˆ2) ∗Pˆ(−2) ) ;65 VeloVoltsRing (3 , idx ) = s q r t ( ( p a r t i a l d e l t a P ∗ sigmaDeltaP ) ˆ2 + (

p a r t i a l T ∗sigmaT ) ˆ2 + ( p a r t i a l P ∗sigmaP ) ˆ2) ;66 end67 end68 end69707172 %% Airspeed Velocity Relation73 % Charac te r i z e the Airspeed Ve loc i ty r e l a t i o n74 %subplot ( 2 , 2 , 1 ) ;75 f i g u r e76 hold on ;77 PolyPitot = p o l y f i t ( Ve loVo l t sP i to t ( 1 , : ) , Ve loVo l t sP i tot ( 2 , : ) , 1 ) ;78 x = VeloVo l t sP i to t ( 1 , : ) ;79 %p lo t (x , Ve loVo l t sP i tot ( 2 , : ) )80 p l o t (x , po lyva l ( PolyPitot , x ) )81 e r r o rba r (x , Ve loVo l t sP i tot ( 2 , : ) , Ve loVo l t sP i tot ( 3 , : ) )82 t i t l e ( ' Ve loc i ty from Pitot−S t a t i c Probe ' ) ;83 legend ( ' Data ' , ' Best Fit ' ) ;84 x l a b e l ( ' Voltage ' )85 y l a b e l ( ' Ve loc i ty ' )86 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )87 p r i n t ( ' VeloPitot ' , '−dpng ' ) %Save8889 % subplot ( 2 , 2 , 2 ) ;90 f i g u r e91 hold on ;92 PolyRing = p o l y f i t ( VeloVoltsRing ( 1 , : ) , VeloVoltsRing ( 2 , : ) , 1 ) ;93 x = VeloVoltsRing ( 1 , : ) ;94 p l o t (x , VeloVoltsRing ( 2 , : ) )95 p l o t (x , po lyva l ( PolyRing , x ) )96 e r r o rba r (x , VeloVoltsRing ( 2 , : ) , VeloVoltsRing ( 3 , : ) )97 t i t l e ( ' Ve loc i ty from S t a t i c Rings ' ) ;

ASEN 2002 Section 014 12 of 16 Fall 2017

98 legend ( ' Data ' , ' Best Fit ' ) ;99 x l a b e l ( ' Voltage [V] ' )

100 y l a b e l ( ' Ve loc i ty [m/ s ] ' )101 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )102 p r i n t ( ' VeloRings ' , '−dpng ' ) %Save103104105 PolyAvg = [ mean ( [ PolyPitot (1 ) PolyRing (1 ) ] ) ,mean ( [ PolyPitot (2 ) PolyRing (2 ) ] ) ] ;106107108109110 %% Water Manometer111 % Read in the Water Manometer data112 T = 3 0 0 . 5 ; % K ( Approximated from data )113 P = 82575; % Pa ( Approximated from data )114 rhoW = 1000 ; % Kg/mˆ3115 Mono = csvread ( 'WaterManometer . csv ' ) ;116 Mono ( : , 2 )=Mono ( : , 2 ) ∗ . 0 2 5 4 ;117 VeloMono = [ 2 4 6 8 10 ;0 0 0 0 0 ;0 0 0 0 0 ] ;118 VeloCompliment=VeloMono ;119 f o r i =1:5120 deltaP = rhoW ∗ 9 .81 ∗ Mono( i , 2 ) ; % deltaP = pm g h121 VeloMono (2 , i ) = s q r t (2∗ deltaP ∗(R∗T/P) ) ;122123 %Get e r r o r124 sigmaP = .015∗230000 ;125 sigmaT = . 2 5 ;126 sigmaDeltaP = 1 2 . 4 4 2 ; %[ Pa ]127128 p a r t i a l d e l t a P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗T/P) ;129 p a r t i a l T = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗ deltaP /P) ;130 p a r t i a l P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2)∗ (−1∗(2∗ deltaP ∗R∗T∗Pˆ(−2) ) ) ;131 VeloMono (3 , i ) = s q r t ( ( p a r t i a l d e l t a P ∗ sigmaDeltaP ) ˆ2 + ( p a r t i a l T ∗sigmaT ) ˆ2

+ ( p a r t i a l P ∗sigmaP ) ˆ2) ;132 end133134 %Plot I t135 f i g u r e136 hold on ;137 x = 2 : 2 : 1 0 ;138 PolyMono = p o l y f i t (x , VeloMono ( 2 , : ) , 1 ) ;139 e r r o rba r (x , VeloMono ( 2 , : ) , VeloMono ( 3 , : ) )140 p l o t (x , po lyva l ( PolyMono , x ) )141 t i t l e ( 'Manometer ' ) ;142 x l a b e l ( ' Voltage (V) ' )143 y l a b e l ( ' Ve loc i ty (m/ s ) ' ) ;144 legend ( ' Data ' , ' Best Fit ' , ' Locat ion ' , ' southeas t ' ) ;145 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )146 p r i n t ( ' ManometerError ' , '−dpng ' )147148 %Plot I t149 f i g u r e150 hold on ;151 p l o t (x , VeloMono ( 2 , : ) )

ASEN 2002 Section 014 13 of 16 Fall 2017

152 p l o t (x , po lyva l ( PolyMono , x ) )153 t i t l e ( 'Manometer ' ) ;154 x l a b e l ( ' Voltage (V) ' )155 y l a b e l ( ' Ve loc i ty (m/ s ) ' ) ;156 legend ( ' Data ' , ' Best Fit ' , ' Locat ion ' , ' southeas t ' ) ;157 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )158 p r i n t ( 'Manometer ' , '−dpng ' )159160161 %Compare D i r e c t l y to the A i rp r e s su r e Transducer162 data = x l s r ea d ( ' Veloc i tyVoltage S014 G05 . csv ' ) ;%This data ' s t ransducer

measured the same setup as our manometer163164 f o r j =1:5 %Each team takes exac t l y f i v e measurements165 indexData=f i n d ( data ( : , 7 )==data (1 , 7 ) ) ;166 l en=length ( indexData ) ;167 P=mean( data ( indexData , 1 ) ) ;168 T=mean( data ( indexData , 2 ) ) ;169 deltaP=mean( data ( indexData , 3 ) ) ;170171 sigmaP=s q r t ( ( . 015∗230000)ˆ2+std ( data ( indexData , 1 ) ) / s q r t ( l ength (

indexData ) ) ˆ2) ; %Root mean square e r r o r o f sy s t emat i c e r r o r andrandom e r r o r

172 sigmaT=s q r t ( ( . 2 5 ) ˆ2+std ( data ( indexData , 2 ) ) / s q r t ( l ength ( indexData ) ) ˆ2) ;173 sigmaDeltaP=s q r t ( ( . 0 1∗6 8 9 4 . 7 6 ) ˆ2+std ( data ( indexData , 3 ) ) / s q r t ( l ength (

indexData ) ) ˆ2) ;174175 data ( indexData , : ) = [ ] ;176177 VeloCompliment (2 , j ) = s q r t (2∗ deltaP ∗(R∗T/P) ) ;178179 %Uncerta inty180 p a r t i a l d e l t a P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗T/P) ;181 p a r t i a l T = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2) ∗2∗(R∗ deltaP /P) ;182 p a r t i a l P = 1/2∗(2∗ deltaP ∗(R∗T/P) ) ˆ(−1/2)∗ (−1∗(2∗ deltaP ∗R∗T∗Pˆ(−2) ) ) ;183 VeloCompliment (3 , j ) = s q r t ( ( p a r t i a l d e l t a P ∗ sigmaDeltaP ) ˆ2 + ( p a r t i a l T

∗sigmaT ) ˆ2 + ( p a r t i a l P ∗sigmaP ) ˆ2) ;184185 end186187 subplot ( 1 , 2 , 1 )188 hold on ;189 e r r o rba r (x , VeloMono ( 2 , : ) , VeloMono ( 3 , : ) )190 p l o t (x , po lyva l ( PolyMono , x ) )191 t i t l e ( 'Manometer ' ) ;192 x l a b e l ( ' Voltage (V) ' )193 y l a b e l ( ' Ve loc i ty (m/ s ) ' ) ;194 legend ( ' Data ' , ' Best Fit ' , ' Locat ion ' , ' southeas t ' ) ;195196 subplot ( 1 , 2 , 2 )197 hold on198 e r r o rba r (x , VeloCompliment ( 2 , : ) , VeloCompliment ( 3 , : ) )199 PolyComp = p o l y f i t (x , VeloCompliment ( 2 , : ) , 1 ) ;200 p l o t (x , po lyva l (PolyComp , x ) )201 t i t l e ( ' Air Pressure Transducer ' )

ASEN 2002 Section 014 14 of 16 Fall 2017

202 x l a b e l ( ' Voltage ' )203 y l a b e l ( ' Ve loc i ty [m/ s ] ' )204 legend ( ' Data ' , ' Best Fit ' , ' Locat ion ' , ' southeas t ' ) ;205 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )206 p r i n t ( ' ManoComparison ' , '−dpng ' )207208209210 %% Boundary Layer Height211 %Now do the boundary l a y e r c a l c u l a t i o n s212 he i gh t s = [ 0 : . 5 : 1 0 1 5 2 . 4 ] ;213 v e l o c i t i e s B L=NaN(4 ,22 ) ;214 f o r i =1:8215 name=[ ' BoundaryLayer S014 G ' nameID{ i } ' . csv ' ] ;216 data=x l s r ea d (name) ;217218 f o r j =1:21 %Just gonna check each he ight219 %NOTE: Taking the average o f a l l measures and c a l c u l a t i n g v e l o c i t y220 %once y i e l d s the same answers as c a l c u l a t i n g the v e l o c i t y f o r each221 %entry and f i n d i n g the average o f the se i n d i v i d u a l v e l o c i t i e s222 inds = not ( abs ( s i gn ( s i gn ( he i gh t s ( j )−.1 − data ( : , 6 ) ) + s i gn ( he i gh t s ( j )

+.1 − data ( : , 6 ) ) ) ) ) ;223 P = mean( data ( inds , 1 ) ) ;224 T = mean( data ( inds , 2 ) ) ;225 deltaP = mean( data ( inds , 4 ) ) ;226 V=s q r t (2∗ deltaP ∗(R∗T/P) ) ;227 i f ˜ i snan (V) %teams did not take measurements at some he i gh t s228 v e l o c i t i e s B L ( f l o o r ( ( i +1)/2) , j ) = nanmean ( [ v e l o c i t i e s B L ( f l o o r ( ( i +1)

/2) , j ) V] ) ;229 end230 data ( inds , : ) = [ ] ;231 end232 %Need to somehow account f o r mid−l i n e measurements a l l that i s l e f t i s233 %the mid l ine at t h i s po int because we have been d e l e t i n g rows234 %The reason we cannot j u s t do t h i s in the o r g i n a l f o r loop i s because235 %SOME teams ( cough cough ) didn ' t read the v e l o c i t i y in the very cente r236 %of the tunne l − they were o f f by a l i t t l e b i t ( cough )237 P = mean( data ( : , 1 ) ) ;238 T = mean( data ( : , 2 ) ) ;239 deltaP = mean( data ( : , 4 ) ) ;240 V=s q r t (2∗ deltaP ∗(R∗T/P) ) ;241242 v e l o c i t i e s B L ( f l o o r ( ( i +1)/2) , end ) = nanmean ( [ v e l o c i t i e s B L ( f l o o r ( ( i +1)/2) ,

end ) V] ) ;%Averge o f whatever was the re be f o r e and the new measurement−> t h i s i s okay because each spot w i l l have AT MOST two measurements ,so none w i l l get an unequal weight

243 end244245 %subplot ( 2 , 2 , 4 )246 f i g u r e247 hold on ;248 x =[14.93 15 .91 16 .89 1 7 . 8 7 ] ; %[ in ]249 qu iver (x , he i gh t s ( 1 : end−1) , v e l o c i t i e s B L ( : , 1 : 2 1 ) ' , z e r o s (21 ,4 ) ) ;250 t i t l e ( ' Ve loc i ty P r o f i l e s at Each Port ' )251 x l a b e l ( ' Distance from Star t o f Test Sec t i on [ in ] ' )

ASEN 2002 Section 014 15 of 16 Fall 2017

252 y l a b e l ( ' Height [mm] ' )253 s e t ( gcf , ' Pos i t i on ' , [ 1 00 100 1100 70 0 ] )254 p r i n t ( ' BLVeloProf i l e ' , '−dpng ' ) %Save255256257258 %% Boundary Layer Thickness259 %Now l e t ' s study the t h i c k n e s s o f the boundary l a y e r260 V in f = po lyva l ( PolyAvg , 5 ) ; %EQUATION RELATING VOLTAGE TO AIRSPEED261 A = [ ( he i gh t s ( 1 : 2 1 ) ) . ˆ ( 1 / 2 ) ' ones (21 ,1 ) ] ; %Use l e a s t−squares est imat ion ,

assumed base equat ion y = a∗ s q r t ( x )+b262263 boundHeights=ze ro s (1 , 4 ) ;264 f o r i =1:4265 d = v e l o c i t i e s B L ( i , 1 : 2 1 ) ' ;266 Pls = (A' ∗A)ˆ−1∗A' ∗ d ; %Pls w i l l be the c o e f f i c i e n t o f the root func t i on we

used to model the se267 boundHeights ( i ) = ( ( ( . 9 5 ∗ V inf )−Pls (2 ) ) / Pls (1 ) ) ˆ2 ;268 end269270271272 %Expected t h i c k n e s s − r e c a l l i n compre s s i b l e f low273 nu = 1.516 e−5; %From t a b l e in back o f Thermodynamics textbook274 x c r = 5e5∗nu/ V in f ;275276 ExpectedLaminar = 5.2∗ s q r t ( ( nu∗x ∗ . 0254) / V in f ) ; %[m]277278 %Expected Turbulent he ight279 laminarHeight = 5.2∗ s q r t ( ( nu∗ x c r ) / V in f ) ;280 TurbuX = ( laminarHeight / . 37/ ( nu/ V in f ) ˆ . 2 ) ˆ ( 1 / . 8 ) ;281 s h i f t=x cr−TurbuX ;282283 ExpectedTurbulent = . 3 7∗ ( ( x ∗ . 0254)− s h i f t ) . ˆ 0 . 8 ∗ ( nu/ V in f ) ˆ . 2 ; %[m]284285 %% Make Nice for Other People286 f p r i n t f ( 'The vol tage−v e l o c i t y r e l a t i o n s h i p i s g iven by :\n Ve loc i ty = %f ∗

vo l tage + %f \n\n ' , PolyAvg (1) , PolyAvg (2 ) )287 f p r i n t f ( [ 'The c a l c u l a t e d boundary l a y e r he i gh t s are [mm] : \ n ' ...288 ' Port 7 Port 8 Port 9 Port 10\n%.1 f %10.1 f %10.1 f %10.1 f \n\n ' ] ,

boundHeights (1 ) , boundHeights (2 ) , boundHeights (3 ) , boundHeights (4 ) )289 f p r i n t f ( [ 'The expected laminar he i gh t s are [mm] : \ n ' ...290 ' Port 7 Port 8 Port 9 Port 10\n%.1 f %10.1 f %10.1 f %10.1 f \n\n ' ] ,

ExpectedLaminar (1 ) ∗1000 , ExpectedLaminar (2 ) ∗1000 , ExpectedLaminar (3 )∗1000 , ExpectedLaminar (4 ) ∗1000)

291 f p r i n t f ( [ 'The expected turbu l ent he i gh t s are [mm] : \ n ' ...292 ' Port 7 Port 8 Port 9 Port 10\n%.1 f %10.1 f %10.1 f %10.1 f \n\n ' ] ,

ExpectedTurbulent (1 ) ∗1000 , ExpectedTurbulent (2 ) ∗1000 , ExpectedTurbulent(3 ) ∗1000 , ExpectedTurbulent (4 ) ∗1000)

ASEN 2002 Section 014 16 of 16 Fall 2017