1

Experimental Investigation of the Discharge Coefficient and Impingement Heat Transfer Characteristics of a Single Jet in Cross Flow

A Thesis Presented

by

Brian Roberts

to

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Mechanical Engineering

in the field of

Thermofluids

Northeastern University

Boston, Massachusetts

May, 2012

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Abstract

This experimentation investigates the local heat transfer characteristics of an impinging

jet with the effects of cross flow. The jet is formed by a single round hole with a diameter of

0.25 inches, sharp edges and a length to diameter ratio of 4. For one combination of

impingement plate spacing and cross flow to jet flow mass velocity ratio, detailed photographs of

a sheet of liquid crystal were taken. These photographs were then used to create a Nusselt

number contour plot. Observations are made regarding the comparison of the Nusselt number

contour plots with and without cross flow. Comparisons are also made to data in open literature

citing the degradation of the average Nusselt number with cross flow to that without cross flow.

While the main focus of this study was the heat transfer of an impinging jet, a large

amount of discharge coefficient data was also gathered for a single, sharp edged, round hole in

the presence of cross flow. It compared very well to other investigator’s data and a correlation

relating the discharge coefficient to the mass velocity ratio is reported.

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Table of Contents

Abstract ........................................................................................................................................... 2

1 List of Figures ......................................................................................................................... 5

2 List of Tables .......................................................................................................................... 6

3 Preface & Acknowledgements ................................................................................................ 7

4 Nomenclature .......................................................................................................................... 8

5 Introduction ........................................................................................................................... 11

6 Test Apparatus ...................................................................................................................... 15

6.1 Jet Discharge Plate ........................................................................................................ 16

6.2 Jet Plenum ..................................................................................................................... 16

6.3 Cross Flow Plenum ....................................................................................................... 17

6.4 Cross Flow Circuit ........................................................................................................ 17

6.5 Impingement Plate ........................................................................................................ 17

6.6 Power Control ............................................................................................................... 17

6.7 Data Acquisition System............................................................................................... 18

6.8 Overall Test Setup & Limitations ................................................................................. 18

7 Discharge Coefficient Testing .............................................................................................. 19

7.1 Discharge Coefficient Test Procedure .......................................................................... 19

7.2 Discharge Coefficient Data Analysis ............................................................................ 20

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7.3 Discharge Coefficient Data Results .............................................................................. 21

7.4 Conclusions & Recommendations ................................................................................ 26

8 Jet Impingement Heat Transfer Testing ................................................................................ 27

8.1 Impingement Heat transfer Test Procedure .................................................................. 27

8.2 Liquid Crystal Calibration ............................................................................................ 27

8.3 Impingement Heat Transfer Data Analysis................................................................... 28

8.4 Impingement Heat Transfer Data Results with Copper Foil ........................................ 34

8.5 Impingement Heat Transfer Data Results without Copper Foil ................................... 37

8.6 Impingement Heat Transfer Uncertainty Analysis ....................................................... 43

8.7 Conclusions & Recommendations ................................................................................ 45

9 References ............................................................................................................................ 47

10 Appendix A – Data Reduction Program ............................................................................... 49

11 Appendix B – Labeling Routine: Nu Plot with Cross Flow ................................................. 60

12 Appendix C – Labeling Routine: Nu Plot without Cross Flow ............................................ 62

13 Appendix D – Discharge Coefficient Calculations ............................................................... 64

14 Appendix E – Discharge Coefficient Data............................................................................ 65

15 Appendix F – Jet Impingement Input for Data Reduction Program ..................................... 70

16 Appendix G – Jet Impingement Photographs ....................................................................... 73

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1 List of Figures

Figure 1: Heating Element Effect at High Power ......................................................................... 12

Figure 2: Impingement Plate Cross Section.................................................................................. 13

Figure 3: Jet Discharge and Impingement Plates .......................................................................... 16

Figure 4: Jet Impingement Test Setup .......................................................................................... 19

Figure 5: Discharge Coefficient for a Single, Sharp Edged, Round Hole with L/D = 4 .............. 22

Figure 6: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.3 .................................... 23

Figure 7: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.5 .................................... 23

Figure 8: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.8 .................................... 24

Figure 9: Round Hole Discharge Coefficients at Various Z/D and Mass Velocity Ratios........... 25

Figure 10: Liquid Crystal Calibration (Degrees Fahrenheit) ........................................................ 27

Figure 11: Nusselt Number Plot of Jet without Cross Flow (Rejet=15k, Z/D=0.5 & G=0.0) ....... 29

Figure 12: Thermal Resistance Representation of the Impingement Plate ................................... 30

Figure 13: Equivalent Thermal Representation of the Impingement Plate................................... 31

Figure 14: Impingement Plate with Copper Foil Layer ................................................................ 34

Figure 15: Liquid Crystal Photograph of Impingement Plate with Copper Foil .......................... 35

Figure 16: Nusselt Numbers with & without Copper Foil Rejet= 15k & Z/D=0.5 ....................... 35

Figure 17: ANSYS Analysis Showing Lateral Conduction Effect of Copper Foil Layer ............ 37

Figure 18: Nusselt Number versus R/D Ratio for Rejet= 15k & Z/D=0.5 .................................... 38

Figure 19: Nusselt Number versus R/D Ratio for Rejet=20k & Z/D=0.5 ..................................... 38

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Figure 20: Normalized Nusselt Number versus R/D Ratio .......................................................... 40

Figure 21: Nusselt Number Plot of Jet in Cross Flow (Rejet=15k, Z/D=0.5 & G=0.5) ................ 40

Figure 22: Calculated Average Nusselt Number with & without Cross Flow ............................. 42

Figure 23: Degradation of Average Nusselt Number Due to Cross Flow, Kercher [1] ................ 43

2 List of Tables

Table 1: Test Points ...................................................................................................................... 14

Table 2: Jet Discharge Coefficient Test Parameters ..................................................................... 15

Table 3: Impingement Plate Thermal Conductivities ................................................................... 30

Table 4: Variable Uncertainties .................................................................................................... 44

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3 Preface & Acknowledgements

Jet impingement heat transfer can be an effective way at controlling temperatures. The

understanding of its dependence on various aerodynamic and geometric parameters is vital for

proper implementation. In published literature, there is a lack of detailed, empirical, single jet

impingement heat transfer data with cross flow. Much of the literature focuses on the average

heat transfer of arrays of impingement holes. This research provides some initial data of a single

jet impinging on a flat plate in the presence of cross flow.

The completion of this work would not have been possible without the guidance and patience

of many people, most notably:

Professor Mohammad Taslim

My wife, Danielle, and daughter Abigail

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4 Nomenclature

Abbreviation Definition Units �� ����� Cross mass flow lb/s �� ��� Isentropic jet mass flow lb/s �� �� Jet mass flow lb/s Gr∗ Grashof Number HT���� Impingement plate heat transfer area in2

h���� Convective heat transfer coefficient on impingement

plate back side Btu/hr/ft2/R

L �� Jet hole length to diameter ratio Nu� Jet stagnation point Nusselt number Nu���� Nusselt number of impingement plate back side Q���� Heat flux through front half of impingement plate Btu/hr/ft2 R� Universal gas constant lbf ft /lbm R X �� Lateral jet hole spacing to diameter ratio X� Back side height of impingement plate in Y �� Longitudinal jet hole spacing to diameter ratio Z �� Plate spacing to jet diameter ratio "#$ Venturi throat area in2 "����� Physical cross sectional area of cross flow circuit in2 "�� Physical hole area of impingement jet in2 %& Jet discharge coefficient '(�)* Average impingement jet Nusselt number '(�� Impingement jet Nusselt number +�,� Ambient pressure psig +-.� Jet plenum pressure psig +)� Venturi pressure psig /$����� Heater heat generation Btu\hr\ft2 /���� Heat flux through back side of the impingement plate Btu\hr\ft2 /��& Radiation heat flux Btu\hr\ft2 0$����� Heater thermal resistance hr R \ btu 0�&$ Adhesive thermal resistance hr R \ btu 0�&$1 Adhesive thermal resistance hr R \ btu

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Abbreviation Definition Units 0��� Air thermal resistance hr R \ btu

0���� Equivalent thermal resistance from heater to

impingement plate back side hr R \ btu

0�� Black backer thermal resistance hr R \ btu

0��� Equivalent thermal resistance from liquid crystal to impingement plate front side

hr R \ btu

0��) Impingement plate back side convective resistance hr R \ btu 02�� Jet Reynolds Number

0���� Equivalent thermal resistance from heater to liquid crystal

hr R \ btu

0�� Jet convective thermal resistance hr R \ btu 0��- Kapton thermal resistance hr R \ btu 0.3 Liquid crystal thermal resistance hr R \ btu 0,4. Mylar thermal resistance hr R \ btu 0-.5 Plexiglas thermal resistance hr R \ btu 6$����� Heater temperature F 6��, Ambient air temperature F 6���� Impingement plate back side surface temperature F 6��., Back side of impingement plate film temperature F 6���� Impingement plate front surface temperature F 6�� Jet temperature F 6-.� Jet plenum temperature F 6.3 Liquid crystal temperature F 6)� Venturi temperature F 71��8 Watts to btu conversion btu/W 9� Gravitational constant

I Current though heating element Ampere k Air conductivity Btu/hr/ft/R Pr Air Prandtl number R Distance from jet stagnation point on impingement plate in V Voltage applied to heating element volt β Reciprocal of 6��., 1/F μ Air dynamic viscosity lbf s / ft2 ρ Air density lbm / ft3

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Abbreviation Definition Units � Discharge hole diameter in @ Mass velocity rate lbm/s/in2 @����� @A��B Cross flow to jet mass velocity ratio

C Discharge hole length in D Discharge to impingement plate spacing in E Specific heat ratio F Impingement plate front side emissivity G Stephan-Boltzman Constant Btu/hr/ft2/R4

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5 Introduction

The ability to control the cooling or heating of hardware is important in many engineering

applications. Particularly in gas turbine engines, active cooling schemes play important roles in

meeting many performance requirements, the most obvious being hardware life. Different

schemes, whether they are serpentine passages, turbulators, film cooling slots or impinging jets,

are used in various locations throughout the engine successfully. Having the ability to design

these cooling schemes, individually or in combination, requires an understanding of the effects

of different aerodynamic and geometric factors. Much of this understanding comes in the form

of empirical data that is reduced to relationships between non-dimensional parameters. This

provides the data to the designer in a concise format that is useful.

This research delves into the active cooling scheme of jet impingement heat transfer and is

built upon the research of Shapiro [1]. He investigated the local heat transfer effects of a single,

round jet impinging on a flate plate in the absence of cross flow at a variety of impingement plate

spacing to jet hole diameter ratios. Particular interest was paid to gathering data when this ratio

was less than 1. Comparisons of his empirical heat transfer data with open literature were good.

The approach taken to gather the data was unique. The process in much of the published

literature involves thermocouple temperature measurements at various distances from the jet

impingement point. Shapiro [1] embedded both a liquid crystal sheet and a heating element

within the impingement plate. For a given impingement jet Reynolds number, photographs of

the liquid crystal were taken for an array of heating element input power settings. This

methodology provids the unique ability to create a Nusselt number contour plot. For a single

impingement jet without cross flow this is trivial however as the Nusselt number has the same

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dependence on r/d in all directions eminating from the jet stagnation point on the impingement

plate. However, for a single impingement jet in the presence of cross flow it provides significant

insight at the local heat transfer effects. This research extends the work of Shapiro [1] with the

addition of cross flow. When Shaprio [1] constructed his test setup, a cross flow plenum and

circuit were included. This separate circuit provides the ability to vary the amount of flow

perpendiclur to the impinging jet.

During his research he encountered difficulty obtaining useful liquid crystal photographs at

r/d ratios of 1 and below as seen in Figure 1.

Figure 1: Heating Element Effect at High Power

This was due to the shape and size of the heating element as it serpentined up and down

across the impingement plate. Based upon this observation an attempt at sourcing a new heating

element with tigher spacing was made uncessfully. An alternative option, which was pursued,

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was to rebuild the impingement plate, adding a thin layer of copper foil inbetween the heating

element and the liquid crystal.

Figure 2: Impingement Plate Cross Section

The purpose of this foil layer was to smooth the temperature profile slightly in the lateral

direction so the heating element itslef would not be evident in the photographs. Unfortunately,

the addition of the foil layer provided far too much lateral conduction beyond the amount

deemed negligible. Some preliminary attempts were made at accounting for the lateral

conduction but they were abandoned because the added complexity and uncertainty in the final

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answer. A more appropriate solution was to rebuild the impingement plate, removing the foil

layer. After, the rebuilding process two test points were taken without cross flow that compared

well to Shapiro [1] and only one test point with cross flow was obtained. Table 1 summarizes

the test points for which the heat transfer data taken was reduced and will be presented herein.

Table 1: Test Points

Test Point Z/D Jet Reynolds Number Mass Velocity Ratio Copper Foil

1 0.5 15,000 0.0 No

2 0.5 20,000 0.0 No

3 0.5 15,000 0.5 No

4 0.5 15,000 0.5 Yes

As expected, there is good agreement between test points 1 and 2 from Table 2 and the work

of Shaprio [1]. An additional comparison was made with Chupp et al. [2] who provided some of

their emperical data as normalized Nusselt number versus r/d. for various z/d ratios. Although

not a direct comparison to the current work because of jet hole l/d and jet Reynolds differences

the data trends in a similar manor.

While the local Nusselt numbers of the impinging jet in cross flow were the main interest of

this research, there was also interest in the cross flow effect on the jet discharge coefficient. A

significant amount of jet discharge coefficient data was taken with and without cross flow at

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three impingement plate spacing to jet hole diameter ratios of less than 1. Table 2 provides the

range of test parameters for the jet discharge coefficient data gathered.

Table 2: Jet Discharge Coefficient Test Parameters

Z/D Jet Reynolds Number Mass Velocity Ratio

Infinity 10k to 55k NA

0.8 10k to 55k 0 to 1.5

0.5 10k to 55k 0 to 2.5

0.3 10k to 55k 0 to 4.0

The discharge coefficient without cross flow was in good agreement with other reported values

from Taslim & Ugarte [3] and Florschuetz & Isoda [4]. In the presence of cross flow, the data

was plotted against mass velocity ratio which was the approach of Florschuetz & Isoda [4]. This

methodology showed the discharge coefficient data with cross flow trended similarly to theirs,

Figure 9.

6 Test Apparatus

The experimental setup for both the jet discharge coefficient and impingement heat

transfer testing was identical. It was designed by Shapiro [1] with guidance from Professor M.

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Taslim, Northeastern University and constructed by United Industries, Inc. located in Everett,

Massachusetts.

6.1 Jet Discharge Plate

The jet discharge plate was manufactured from 1 inch thick Plexiglas. This plate was

attached to the jet plenum by eight, 1.5 inch long hex head screws along with a rubber gasket in

between to ensure a complete seal. All the data generated was with a single 0.25 inch diameter

hole. This single hole, shown in Figure 3, had a length to diameter ratio of 1 and sharp edges.

Figure 3: Jet Discharge and Impingement Plates

6.2 Jet Plenum

The jet plenum was constructed of 1 inch thick Plexiglas. The interior dimensions were 4

inches long by 4 inches wide by 4 inches tall. Pressurized air was delivered to the plenum

through a 1.5 inch diameter PVC adapter. Located in between the PVC adapter and the jet

discharge hole was a honeycomb flow straightener. Plenum air pressure was measured by a

single wall pressure tap placed between the honeycomb and jet discharge hole. Air temperature

was measured by one thermocouple inserted into the plenum between the honeycomb and jet

discharge hole also.

Jet Discharge Plate

Impingement Plate

Z

L

D

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6.3 Cross Flow Plenum

The cross flow plenum was made from 0.5 inch Plexiglas and was also fed pressurized air

through a 1.5 inch diameter PVC adapter. Originally there was no flow straightener within the

plenum. However, as a precaution, one was added consisting of a mesh screen placed around the

inlet to the cross flow circuit. Both plenum pressure and temperature were measured in a similar

manner to the jet plenum, with a single wall pressure tap and thermocouple located in between

the flow straightener and the cross flow circuit inlet.

6.4 Cross Flow Circuit

The cross flow circuit was 6 inches tall by 0.5 inches wide where it connected to the cross

flow plenum. It maintained this 0.5 inch width until approximately 3 inches upstream of the

edge of the impingement plate where it began to transition to the appropriate Z dimension for the

particular Z/D ratio that was being tested. This circuit was enclosed on four sides throughout its

complete length including as the flow passed perpendicularly to the impinging jet.

6.5 Impingement Plate

The impingement plate was 6 inches square. It consisted of a 0.5 inch thick piece of

Plexiglas, a thermographic liquid crystal sheet and five individual heating elements.

6.6 Power Control

The power the heating elements within the impingement plate generated was controlled

by modulating the applied voltage. This was done using an existing controller which used a 120

AC input. The controller provided the ability to individually set the voltage to each heating

element and also the ability to then scale them all up and down. This allowed the heat flux for

each heating element to consistently set and maintained.

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6.7 Data Acquisition System

For the thermocouple measurements, temperatures were read in real time on an Agilent

34970A Data Acquisition Unit. Both plenum pressure measurements were taken using

manometers. Relative to measuring the jet plenum pressure, if the jet Reynolds number was

30,000 or below an oil manometer was used which had a specific gravity of 0.826. For jet

Reynolds numbers above 30,000 a manometer with a specific gravity of 2.95 was used. In

general, the oil manometer with a 0.826 specific gravity was used to measure the cross flow

plenum pressure for the majority of the test points except some of the 0.3 Z/D points at high jet

Reynolds numbers and mass velocity ratios.

6.8 Overall Test Setup & Limitations

The test setup utilized pressurized air from the laboratory compressor. This air was held

within a tank before passing through a filter. There were two pressure regulators downstream of

the filter, one to feed the jet plenum and another for the cross flow plenum. In between the each

of the regulators and the plenums there was a critical flow venturi. These venturis were

manufactured by Fox Valve Development Corp. of Dover, New Jersey. The diameter of the

venturi upstream of the jet plenum was 0.08 inches. The venturi upstream of the cross flow

plenum had a diameter of 0.223 inches. Figure 4 is a top view of the test setup.

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Figure 4: Jet Impingement Test Setup

7 Discharge Coefficient Testing

7.1 Discharge Coefficient Test Procedure

The test procedure for gathering discharge coefficient data at various Z/D ratios began by

locating the impingement plate at the appropriate distance from the jet discharge hole in order to

set the Z/D ratio. It should be noted that for a Z/D ratio of infinity the impingement plate was

completely removed and that by doing this the cross flow circuit could not be utilized. The first

portion of data was gathered with no cross flow and the jet venturi pressure set to 5 psig. After a

stabilization period of 3 minutes the jet venturi pressure and temperature were recorded along

with the jet plenum pressure and temperature. Next, the jet venturi pressure was increased to 10

psig, followed again by a stabilization period and recording of the pressures and temperatures.

This process repeated in 10 psi increments up to a jet venturi pressure of 70 psig. Once

Jet Discharge Plate

Jet Plenum

Cross Flow

Plenum Cross Flow Circuit Impingement Plate

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completed, the venturi pressure for the cross flow circuit was set to 10 psig and the data was

again recorded for each jet venturi pressure increment. Also recorded now was the cross flow

venturi pressure and temperature as well as the cross flow plenum pressure and temperature.

This process was repeated in 10 psi cross flow venturi pressure increments up to 80 psig.

7.2 Discharge Coefficient Data Analysis

The data reduction was relatively straightforward for the discharge coefficient testing. Both

the mass flows for the jet and the cross flow circuit were determined by

Equation 1 which was provided by the venturi manufacturer.

�� H 0.5215"#$ O+)� P +�,�Q6)� P 460T

Equation 1

These mass flows were then used to calculate the cross flow to jet mass velocity ratio,

Equation 2, which is simply the ratio of cross flow mass flux to that of the jet.

@����� @��B H ,� UVWXX YUVWXX�,� Z[\ YZ[\B

Equation 2

The discharge coefficient for the jet is the ratio of the measured mass flow from Equation 1 to

the calculated mass flow assuming isentropic expansion from jet plenum pressure to ambient

pressure. For unchoked jet pressure ratios the isentropic jet mass flow is determined by Equation

3.

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�� ��� H +-.� O+�,�+-.�T]^_1] ` 29�EaE b 1c0�6-.� de+-.�+�,� f

]g_] b 1h_1 "��

Equation 3

The discharge coefficient is then Equation 4.

%i H e �� ���� ���f

Equation 4

7.3 Discharge Coefficient Data Results

The first set discharge coefficient data taken was at a Z/D ratio of infinity. The jet pressure

ratio ranged from 1.006 up to 1.136. This corresponded to jet Reynolds numbers from

approximately 11,000 to 55,000. Over this range the discharge coefficient was very consistent

and averaged 0.843 as seen in Figure 5. This compared well with Taslim & Ugarte [3] who

reported an average discharge coefficient of 0.855 for a sharp edged hole with an L/D ratio of 4.

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Figure 5: Discharge Coefficient for a Single, Sharp Edged, Round Hole with L/D = 4

The impingement plate was then installed for Z/D ratios of 0.3, 0.5 and 0.8. For each

installation the data collection process as described in Section 7.1 proceeded. Figure 6, Figure 7

and Figure 8 show the discharge coefficient data versus jet pressure ratio with lines of constant

cross flow venturi pressure.

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Figure 6: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.3

Figure 7: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.5

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Figure 8: Discharge Coefficient versus Jet Pressure Ratio for Z/D = 0.8

This was how the data was initially plotted however in order to show all the data on a single

figure the mass velocity ratio, Equation 2, was introduced. Figure 9 plots the jet discharge

coefficient versus mass velocity ratio. The colored symbols are the current data taken for Z/D

ratios of 0.3, 0.5 and 0.8. Also shown in Figure 9 are regression fits of data from Florschuetz &

Isoda [4] at Z/D ratios of 1, 2 and 3.

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Figure 9: Round Hole Discharge Coefficients at Various Z/D and Mass Velocity Ratios

The details of their experiment were slightly different than the current one. They tested a plate

with multiple holes at X/D and Y/D ratios of 5 and 4 respectively and at Z/D ratios of 1, 2 and 3.

Their L/D was 1 compared to 4 of the current testing and most of their data was generated at a jet

Reynolds number of 10,000. Despite these differences, the current data compares well with

Florschuetz & Isoda [4]. The current data trends similarly with mass velocity ratio and Z/D. A

regression of the data similar to Florschuetz & Isoda [4] was conducted using a iterative

technique to minimize the RMS of the error and is reported as

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%& H 0.85klm@ n 0.5opi D� q 1

%& H 8.586a@ P 3.006c_.stu klm@ v 0.5opi D� q 1

Equation 5

Worth noting is the rise in discharge coefficient data when the Z/D ratio is less than 1 and at

mass velocity ratios between 0 and 0.5. This phenomenon is also seen in the data of Taslim &

Ugarte [3] and Florschuetz & Isoda [4] but it is not discussed. The regression fits reported in

Florschuetz & Isoda [4] ignore this rise in discharge coefficient.

7.4 Conclusions & Recommendations

The average jet discharge coefficient at a Z/D of infinity and no cross flow agreed well with

other published values. No directly comparable published literature was available for jet

discharge coefficients with cross flow at the specific L/D, Z/D and jet Reynolds numbers tested

but the gathered data trended similarly to what was found.

Overall, based on the quality of the discharge data gathered, no modifications to the test

setup are proposed. It is recommended that the database of jet discharge coefficients be

expanded outside the Z/D ratios tested. Also, shaped holes (conical for example) or holes with

various inlet radii could also be tested.

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8 Jet Impingement Heat Transfer Testing

8.1 Impingement Heat transfer Test Procedure

The general test procedure for the jet impingement heat transfer testing was very similar to

the jet discharge coefficient testing outline in Section 7.1. The main difference was that for each

jet Reynolds number, Z/D and mass velocity ratio a number of photographs were taken at various

voltage levels applied to the heating elements within the impingement plate. A heat transfer

stabilization period of 5 minutes was used to ensure that the liquid crystal had reached thermal

equilibrium. As stated in Section 5, initially the impingement plate was rebuilt adding a thin

layer of copper foil. Later the impingement plate was again rebuilt restoring it to its original

state.

8.2 Liquid Crystal Calibration

A calibration of the liquid crystal was necessary before gathering the jet impingement heat

transfer data. The reason for the calibration was to determine the specific liquid crystal color and

temperature to use during the processing of the photographs. A sample piece of the liquid crystal

was placed within a bath of heated water. The bath was then allowed to cool and photographs

were taken every 0.1 of a degree Fahrenheit within the color change temperature range for the

liquid crystal. Figure 10 depicts the liquid crystal’s range of color change and the temperature

associated with the specific color.

Figure 10: Liquid Crystal Calibration (Degrees Fahrenheit)

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Based on the results from the liquid crystal calibration a temperature of 93.6 degrees Fahrenheit

and its associated color shown in Figure 10 were chosen for the photograph processing.

8.3 Impingement Heat Transfer Data Analysis

The heat transfer data analysis was more involved than that of the discharge coefficient data.

Each picture of the impingement plate taken had to be reduced to a single contour of temperature

at 93.6 degrees Fahrenheit based on the color from the liquid crystal calibration. For the cases

without cross flow this was straight forward because the contours were circles due to the

axisymmetric nature of the impinging jet. However when cross flow as added the contours took

on completely different shapes. Attempts were made at having Adobe Photoshop or Matlab

recognize the specific color of interest and create the desired contour automatically but they were

unsuccessful. A contour smooth enough to be useful could not be generated automatically.

Instead, contours were created manually by tracing the photographs along the color associated

with the chosen 93.6 degree Fahrenheit temperature. For the test points with no cross flow

where the contours were circular as in Figure 11, the radius of the contours were measured with

Matlab. The location of the jet stagnation point is represented by the black dot.

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Figure 11: Nusselt Number Plot of Jet without Cross Flow (Rejet=15k, Z/D=0.5 & G=0.0)

The Nusselt number for each contour at a given jet Reynolds number, Z/D ratio and mass

velocity ratio was then determined using a data reduction program [5]. The data reduction

program [5] solved the heat transfer through the thickness of the impingement plate using an

iterative technique. Figure 12 depicts the thermal circuit through the thickness of the

impingement plate and Table 3 contains the thermal conductivities for the individual layers

which were inputs into the program.

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Figure 12: Thermal Resistance Representation of the Impingement Plate

Table 3: Impingement Plate Thermal Conductivities

Material Label Thickness (inches)

Thermal Conductivity (btu/hr/ft/F)

Kapton Rkap 0.002 0.0942

Adhesive Radh 0.001 0.1272

Heating Element

Rheater 0.0015 9.0152

Adhesive Radh 0.001 0.1272

Kapton Rkap 0.002 0.0942

Adhesive Radh2 0.0015 0.1272

Black Backer

Rbb 0.003 0.1650

Liquid Crystal

Rlq 0.002 0.1650

Mylar Rmyl 0.005 0.0850

Air Gap Rair 0.001 0.0148

Plexiglas Rplx 0.500 0.1100

The thermal resistivities were then combined into three equivalent resistances and a guess for the

natural convective resistance on the backside of the impingement plate was made for the initial

iteration.

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Figure 13: Equivalent Thermal Representation of the Impingement Plate

With the temperature of the liquid crystal known by the calibration to be 93.6 degrees Fahrenheit

and the ambient temperature also known, the flux leaving through the backside of impingement

plate could be solved for by Equation 6.

/���� H a6.� b 6��,c0���� P 0��)

Equation 6

The backside impingement plate surface temperature was then solved for in order to improve the

initial guess of the natural convection coefficient with Equation 7.

6���� H 6.� b /����0����

Equation 7

Knowing the backside impingement plate surface temperature the new natural convection

coefficient was then calculated progressing from Equation 8 through Equation 13.

6��., H 6���� P 6��,2

Equation 8

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w H xyz{|}

Equation 9

@m∗ H 9�~/�������� ����1

Equation 10

'(���� H 0.6a@m∗+mc�.1

Equation 11

����� H '(�������

Equation 12

����� H x�����

Equation 13

Next the heating element temperature was solved for by

6$����� H /����0��� P 6.� Equation 14

where

/���� H /$����� b /����

Equation 15

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and

/$����� H ���6����71��8

Equation 16

Once the heating element temperature is known the front side impingement plate temperature is

solved for by Equation 17.

6���� H 6$����� b /����0���� Equation 17

Before the jet impingement convective heat transfer coefficient could be solved for the radiation

heat flux leaving the front side of the impingement plate was accounted for.

/��& H FG�6����� b 6��� � Equation 18

Finally, with the measured jet temperature the jet impingement convective heat transfer

coefficient is then,

��� H /$����� b/���� b /��&6���� b 6��

Equation 19

and the jet impingement Nusselt number is calculated by

'(�� H ���

Equation 20

34

This entire calculation process was then iterated on, improving the guess of the backside natural

convection coefficient each time until convergence was reached.

8.4 Impingement Heat Transfer Data Results with Copper Foil

As described in Section 5, initially jet impingement heat transfer data was taken with a layer

of copper foil added to the impingement plate as shown in Figure 14.

Figure 14: Impingement Plate with Copper Foil Layer

The copper foil was added to in order to reduce the appearance of the heating element in the

liquid photographs. It was successful at doing so however the amount of lateral conduction was

far too greater and because of this the foil negated the one dimensional assumption necessary to

calculate the local Nusselt number reliably. Figure 15 shows the effect the copper foil when

large voltages are applied to the heating element. In Figure 15 the liquid crystal colors transition

35

smoothly from one to another due to the lateral conduction of the copper foil as compared to

Figure 1 when no foil was present within the impingement plate. As a result of adding the

copper foil, the Nusselt numbers calculated with the data reduction program were far lower than

those calculated when the copper foil was removed as is shown in Figure 16.

Figure 15: Liquid Crystal Photograph of Impingement Plate with Copper Foil

Figure 16: Nusselt Numbers with & without Copper Foil Rejet= 15k & Z/D=0.5

36

In order to substantiate the lateral conduction effect of the copper foil a two dimensional

axisymmetric ANSYS thermal model was created. The boundary conditions applied to the

model consisted of the jet impingement temperature and convective coefficients based on the

Nusselt number profile from the data taken without the copper foil, a power input to the heating

element and the natural impingement plate backside convective coefficient along with the

ambient temperature. Figure 17 shows the ANSYS predicted temperature profile of the liquid

crystal versus R/D ratio with and without the lateral conduction effect of the copper foil. The

prediction substantiates the smoothing of the liquid crystal temperatures and therefore color

transitions seen in Figure 15. Due to this the ANSYS analysis also supported the fact that by

adding the copper foil the one dimensional heat transfer assumption required by the data

reduction program to calculate the jet impingement Nusselt number was no longer valid. This

ultimately forced the removal of the copper foil layer from the impingement plate.

37

Figure 17: ANSYS Analysis Showing Lateral Conduction Effect of Copper Foil Layer

8.5 Impingement Heat Transfer Data Results without Copper Foil

The iterative process to calculate the jet impingement Nusselt number was completed for all

test points listed in Table 1. Test points 1 and 2 were repeats of Shapiro [1] without cross flow.

For these cases the radius of each photograph’s contour was normalized by the jet hole diameter

and plotted against the Nusselt number from the data reduction program. Figure 18 and Figure

19 show the comparison between the data taken during this study and the work of Shapiro [1].

38

Figure 18: Nusselt Number versus R/D Ratio for Rejet= 15k & Z/D=0.5

Figure 19: Nusselt Number versus R/D Ratio for Rejet=20k & Z/D=0.5

Both figures show good agreement between the reported data as expected. Some variation in

Nusselt number is evident at low R/D ratios. This is most likely attributed to the interputation of

39

the Nusselt number due to the heating elements geometry when high voltages are applied as seen

in Figure 1.

Although the test data does not extend to the minimum R/D ratio of zero which would be

the jet stagnation point, the predicted values based on a correlation from empirical data generated

by Chamberlain [6] is very reasonable. For Z/D ratios of less than 7 he reported Equation 21 as

the correlation for stagnation point Nusselt number.

'(� H 1.1602���.���+m�.uuuklmD/� n 7

Equation 21

Using this correlation would predict the stagnation point Nusselt number to be 76 for the test

point shown in Figure 18 and 87 for that shown in Figure 19. Purely analytic attempts by other

authors as reported in Livingood & Hrycak [7] based on free jet potential theory combined with

laminar boundary layer techniques always under predict measured values, sometimes by

significant amounts.

Another comparison of the data without cross flow was made to Chupp et al. [2]. This

author’s test setup simulated the internal geometry of a turbine airfoil with a leading edge that

was impingement cooled. He reported local Nusselt numbers normalized by the stagnation point

Nusselt number versus the distance from the stagnation point normalized by the jet hole

diameter. Figure 20 show a comparison between his data and the data generated by this author.

The trends in the data shown appear to agree well and the variation most likely attributed to

differences in impingement plate curvature as well as L/D ratio.

40

Figure 20: Normalized Nusselt Number versus R/D Ratio

For test point 3 in Table 1 the contour plot of Nusselt number is shown in Figure 21. The

difference between Figure 21 and Figure 11 is the mass velocity ratio (0.5 & 0.0 respectively).

Figure 21: Nusselt Number Plot of Jet in Cross Flow (Rejet=15k, Z/D=0.5 & G=0.5)

41

In Figure 21 the cross flow was from left to right and this shifted the point where the maximum

Nusselt number occurred to the right 1 jet hole diameter as compared to the its location in Figure

11. This is explained by the cross flows influence on the impinging jets potential core. Another

observation of Figure 21 is the symmetry between the upper and lower halves of the contour plot

indicating no significant cross flow asymmetry. In order to make additional meaningful

observations and to compare the data to Kercher [8] an attempt was made to calculate the

average Nusselt number for the test points shown in Figure 21 and Figure 11. The process was

similar for both points. Matlab was used to calculate the area in between adjacent contours

which was then assigned the average Nusselt number of the two contours. Figure 22 shows the

plot of average Nusselt number versus the area for which the average was calculated. As the

area for the average calculation approaches zero the average Nusselt number will approach the

peak value measured. In the opposite direction, as the area for the average Nusselt number

calculation becomes larger and larger the two lines in Figure 22 should theoretical approach

different values. The average Nusselt number for the data without cross flow should approach

zero while the data with cross flow should approach the level which would occur solely due to

the cross flow. It is evident from Figure 22 that the presence of cross flow reduces the peak and

the average jet impingement Nusselt number.

42

Figure 22: Calculated Average Nusselt Number with & without Cross Flow

Kercher [8] conducted experiments involving arrays round holes with the effects of cross

flow. The heat transfer area of his impingement plate was four square inches and he reported

Figure 23 which shows the reduction in average Nusselt number due to the cross flow. Also

shown is the point for the current data evaluated assuming an impingement heat transfer area of

four square inches. It lies just outside the range of data reported by Kercher [8] for the particular

Z/D and mass velocity ratio however there is a fair amount of spread within Kercher’s [8] data to

suggest that there is another correlating parameter not accounted for. A parameter that he reports

as a variable within his experiments but does not attempt to account for is the ratio of jet hole

area to impingement plate heat transfer area which if included with Z/D and mass velocity ratio

may provide a better correlation to average Nusselt number degradation.

43

Figure 23: Degradation of Average Nusselt Number Due to Cross Flow, Kercher [8]

8.6 Impingement Heat Transfer Uncertainty Analysis

Within the data reduction program [5] an uncertainty analysis using the methodology from

Kline & McClintock [9] was used to determine the calculated Nusselt number uncertainty. The

methodology from Kline & McClintock [9] is based on the summation of the product of the

individual variable partial derivative and its assigned uncertainty.

∆� H ��e����� ∆��f1�

�g_ �_1

Equation 22

where

� H linearfunctionof�� ∆� H uncertaintyin�

44

�� H independentvariable ∆�� H uncertaintyin��

Based on Equation 16, Equation 19 and Equation 20 the following partial derivatives were used.

������ H ��6�����6���� b 6��� ������ H ��6�����6���� b 6���

������6���� H b ���6����1�6���� b 6��� �����a/���� P /��&c H b 1�6���� b 6���

�����6���� H b ���6���� b a/���� P/��&c�6���� b 6���1

�����6�� H���6���� b a/���� P /��&c�6���� b 6���1

The assigned variable uncertainties are given in Table 4.

Table 4: Variable Uncertainties

Variable Uncertainty ∆� 0.1 volts ∆� 0.01 amperes

∆�6���� � _u1�1square inches ∆6���� 0.5® ∆6�� 0.5®

45

For test point 3 of Table 1 the uncertainty in the jet impingement heat transfer coefficient and

therefore the Nusselt number ranged from 3.5% at high Nusselt numbers to 5.5% at low Nusselt

numbers. Typically the current measurement was the significant factor affecting the uncertainty

but at lower Nusselt numbers the jet temperature and impingement plate front surface

temperature were of comparable significance.

8.7 Conclusions & Recommendations

This experiment focused on the local impingement heat transfer of a single round jet with

cross flow. Contour plots of Nusselt number for a single jet with a Reynolds number of 15,000

at a Z/D ratio of 0.5 without cross flow, Figure 11, and with cross flow, Figure 21, at a mass

velocity ratio of 0.5 were generated. The located of the peak Nusselt number was shown to shift

downstream by 1 R/D. It was demonstrated that the peak jet impingement Nusselt number was

reduced by 15% with the presence of cross flow for the particular configuration studied. Also

shown was that the average Nusselt number was reduced by 25% which was a larger reduction

than reported by Kercher [8] for an array of holes under similar conditions.

Early on an attempt was made to mask the individual heating elements within the

impingement plate by adding a thin layer of copper foil. This was unsuccessful as there was too

much lateral conduction within the impingement plate violating the necessary one dimensional

heat transfer assumption through its thickness. A more promising approach would be to have a

custom heater made with tight spacing or perhaps layering two heaters offsetting them relative to

one another.

46

Based on the symmetry of the Nusselt number contour plot of the jet with cross flow, no

modifications to the cross circuit are necessary for further testing. It is recommended by this

author to extend the current research to other combinations of jet Reynolds numbers, Z/D ratios

and mass velocity ratios for a single sharp edged hole with a L/D of 4.

One source of uncertainty that has not been mentioned is the manual generation of the 93.6

degree Fahrenheit isotherms from the photographs taken of the liquid crystal within the

impingement plate. A more precise methodology would be to use a program to recognize the

contour in the photographs. An attempt was made to use the standard image processing tools in

Adobe Photoshop or Matlab to do this without success.

47

9 References

[1] J. D. Shapiro, "Experimental Convective Heat Transfer and Flow Discharge Coefficients for

Single Confined Jet Impingement Normal to a Surface at Close Distances," Master's Thesis,

2007.

[2] R. E. Chupp, H. E. Helms, M. P. W. and T. R. Brown, "Evaluation of Internal Heat Transfer

Coefficients for Impingement Cooled Turbine Airfoils," American Institute of Aeronautics

and Astronautics, no. 68-564, 1968.

[3] M. E. Taslim and S. Ugarte, "Discharge Coefficient Measurements for Flow Through

Compound-Angle Conical Holes with Cross-Flow," International Journal of Rotating

Machinery, vol. 10, pp. 145-153, 2004.

[4] L. W. Florschuetz and Y. Isoda, "Flow Distributions and Discharge Coefficient Effects for

Jet Array Impingement with Initial Crossflow," American Society of Mechanical Engineers,

no. 82-GT-156, 1982.

[5] M. E. Taslim, Heat Transfer Data Reduction Program, 2006.

[6] J. E. Chamberlain, "Heat Transfer Between a Turbulent Round Jet and a Segmented Plate

Perpendicular to It," M.S. Thesis, Newark College of Engineering, 1966.

[7] J. Livingood and P. Hrycak, "Impingement Heat Transfer from Turbulent Air Jets to Flat

Plates - A Literature Survey," NASA TM X-2778, 1973.

[8] D. M. Kercher and T. W., "Heat Transfer by a Square Array of Round Jets Impinging

48

Perpendicular to a Flat Surface Including the Effect of Spent Air," ASME Paper 69-GT-4,

1969.

[9] S. J. Kline and F. A. McClintock, "Describing Uncertainty in Single-Sample Experiments,"

Mechanical Engineering, vol. 75, pp. 3-8, 1953.

49

10 Appendix A – Data Reduction Program

C D A T A R E D U C T I O N P R O G R A M C JASON SHAPIRO'S SINGLE JET IMPINGEMENT RIG C M.E. Taslim 8/7/ 2006 C CONTROL PANEL ARANGEMENT C CHANNEL 1 Heater directly against the jet C CHANNEL 2 Gaurd Heater on the top C CHANNEL 3 Gaurd Heater on the right C CHANNEL 4 Gaurd Heater on the left C CHANNEL 5 Gaurd Heater on the bottom IMPLICIT REAL*8(A-H,O-Z) CHARACTER*80 TITLE REAL*8 Mv,Nu,Losses,Mach COMMON Rair,Mv,Tjet,Tamb,Pamb,Tliquid C CORRELATION PROVIDED BY THE MANUFACTURER OF T HE CRITICAL VENTURI C FOR THE AIR MASS FLOE RATE IN lbm/s. F(A,P,T)=0.5215*A*P/SQRT(T) C T H R O A T G E O M E T R Y C PI=4.*ATAN(1.) Dthroat=0.08 ! inches Athroat=PI*(Dthroat**2)/4. Rair=53.34 FAC1=3.412 ! converts Wa tts to BTU/hr Hgtopsi= 0.49083935 ! converts in ches of Hg to psi H2otopsi=Hgtopsi/13.6 ! inches of w ater to psi H2otopsf=H2otopsi*144. ! inches of w ater to lbf/sf.ft Oiltopsi=0.826*H2otopsi ! inches of O il to psi gc=32.17 ! gc=32.17 lb m.ft/(lbf.sec2) C T E S T S E C T I O N G E O M E T R Y C************************************************** *************** C HOLE GEOMETRY C************************************************** *************** Dhole=0.25 ! inche s Dhole=Dhole/12. ! ft. Cross=PI*(Dhole**2)/4. ! sq.ft Perim=PI*Dhole ! ft. Hwidth=3.75 ! inche s

50

Hwidth=Hwidth/12. ! ft. Hheight=4. ! inche s Hheight=Hheight/12. ! ft. CALL OPENFILES write(7,11)12.*Dhole,144.*Cross,12.*Perim,12. *Hwidth, &12.*Hheight 11 FORMAT(/,5x,' GEOMETRY',//, &2x,'Hole Dimension=',f8.4,' inches',/, &2x,'Hole Cross-Sectional Area=',f8.4,' square inches',/, &2x,'Hole Perimeter=',f8.4,' inches',/, &2x,'Heater width=',f8.4,' inches',/, &2x,'Heater height=',f8.4,' inches',/) C READ IN : C # OF LINES and LIQUID CRYSTAL REFERENCE TEMPE RATURE READ(1,*)NP,Tliquid,Z WRITE(2,402)NP 402 FORMAT(I3) WRITE(7,12)Z 12 FORMAT(/,10x,'*** REDUCED DATA FOR THE GAP SI ZE=',f8.2, &' INCHES ****',//) DO I=1,5 READ(1,10)TITLE WRITE(2,10)TITLE WRITE(7,10)TITLE ENDDO 10 FORMAT(A80,//) WRITE(2,450) 450 FORMAT(' Photo Re Nu h Uncer') WRITE(4,*)' Re Pratio' C HEAT TRANSFER AREA HTArea=Hwidth*Hheight ! sq.ft, Middle heater area Reold=7000 DO 1 I=1,NP READ(1,*)ph,Pven,Pplen,flag,Tven,Tplen,Tamb,V 1,A1,V2, &A2,V3,A3,V4,A4,V5,A5,Pamb Pamb=Pamb*hgtopsi if(flag.eq.1)Pplen=Pplen*H2otopsi if(flag.eq.2)Pplen=Pplen*Oiltopsi if(flag.eq.3)Pplen=Pplen*Hgtopsi

51

Pratio=(Pplen+Pamb)/Pamb Tjet=Tplen WRITE(7,*)' ' WRITE(7,*)' ' WRITE(7,*)' ' WRITE(7,100)Ph WRITE(7,*)' ' WRITE(7,406) 406 format('Collected Data:V1,I1,V2,I2,V3,I3,V4,I 4,V5,I5',/, &' Pven,Tven,Tplen,Tamb,Pplen,Pamb', /) WRITE(7,*)' ' WRITE(7,200)V1,A1,V2,A2,V3,A3,V4,A4,V5,A5 WRITE(7,201)Pven,Tven,Tplen,Tamb,Pplen,Pamb 200 FORMAT(4X,F5.2,' ',F6.4,' ',F5.2,' ',F6.4, &' ',F5.2,' ',F6.4,' ',F5.2,' ',F6.4,' ',F5.2, ' ',F6.4) 201 FORMAT(4X,F4.1,' ',F4.1,' ',F4.1, &' ',F4.1,' ',F7.4,' ',F7.4) C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI Mv=F(Athroat,Pven+Pamb,Tven+460) C************************************************** ********************C C ON THE JET PLATE C C************************************************** ********************C C HEAT FLUX, BTU/(sqft.Sec) Flux=(V1*A1*FAC1)/(HTArea) CALL HTCOEFF(Flux,Tm,Tsurf,h,Losses) C************************************************** ****************C C AIR PROPERTIES AT JET TEMPERATURE TjetR=Tjet+460. CALL AIRPROP(TjetR,gam,CON,Vis,PR,Cp) Vis=Vis/3600. C REYNOLDS NUMBER Rejet=4.*Mv/(Perim*Vis) C FILM TEMPERATURE Tf=(Tsurf+Tjet)/2. C DENSITY AT JET TEMPERATURE Rho=144.*(Pplen+Pamb)/(Rair*(Tjet+460.)) C NUSSELT NUMBER

52

Nu=h*Dhole/Con C AVERAGE JET VELOCITY, Um, ft/Sec. Um=Mv/(Cross*Rho) sound=sqrt(1.4*Rair*(Tjet+460.)*gc) Mach=Um/sound C************************************************** ******************** C UNCERTAINTY ANALYSIS CALL UNCERTAIN(A1,V1,HTarea,Tsurf,Tjet,Losses ,Uncer) C************************************************** ******************** write(7,460)mv,rho,Rejet,Pplen,Pamb,Pratio,Um ,sound,Mach,Nu,Uncer write(2,470)i,Rejet,Nu,h,Uncer if(abs((Rejet-Reold)/Reold).ge.0.02)write(5,* )' ' write(5,*)Rejet,Nu,h,Uncer write(4,480)Rejet,Pratio Reold=Rejet 1 CONTINUE write(2,*)' Total Number of Photos:',NP 100 format(' picture #',f3.0,/) 460 format( &5X,'Air mass flow rate=',E13.7,' lbm/s'/, &5X,'Air density=',E13.7,' lbm/ft3',/, &5X,'Jet Reynolds Number=',F10.1,/, &5X,'Plenum Pressure=',F10.5,' psig'/, &5X,'Ambient Pressure=',F10.5,' psi'/, &5X,'Pressure ratio across the hole=',F8.4,/, &5X,'Average Exit Velocity=',F10.3,' ft/s',/, &5X,'Speed of sound=',F10.3,' ft/s',/, &5X,'Jet Mach Number=',F10.3,/, &5X,'Nusselt Number=',F10.3,/, &5X,'%Uncertainty (in h)=',F7.2) 470 format(1x,i3,1x,f9.1,1x,E13.7,1x,E13.7,1x,f6. 2) 480 format(1x,f9.1,1x,E13.7) STOP END SUBROUTINE OPENFILES IMPLICIT REAL*8(A-H,O-Z) OPEN(Unit=7, FILE='output.dat', STATUS='old') OPEN(Unit=1, FILE='input.dat', STATUS='old') OPEN(Unit=2, FILE='ph.in', STATUS='old') OPEN(Unit=3, FILE='uncer.dat', STATUS='old') OPEN(Unit=4, FILE='pressure.dat', STATUS='ol d') OPEN(Unit=5, FILE='ph-plot.dat', STATUS='old ') RETURN END

53

C************************************************** ************** C TARGET PLATE C************************************************** ************** SUBROUTINE HTCOEFF(Flux,Tm,Tsurf,h,Losses) IMPLICIT REAL*8(A-H,O-Z) REAL*8 kinc,kadh,kkap,kmyl,kair,kblack,kliq,k plexi,Mv,Losses COMMON Rgas,Mv,Tjet,Tamb,Pamb,Tliquid C HEATED TARGET PLATE (LIQUID CRYSTALS) C FROM THE CENTER OF HEATING ELEMENT TO THE CEN TER OF Liquid Crystal Layer C 0.75 mil INCONEL HEATING ELEMENT ---- 1 mil AD HESIVE ---- 2 mil KAPTON ---- C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK B ACKGROUND ---- 1.0 mil C LIQUID CRYSTAL (half) C 1/2(tinc1/kinc) -- tadh1/kadh -- tkap/kkap -- tadh2/kadh -- tblack/kblack -- 1/2(tliq/kliq) C FROM THE CENTER OF LIQUID CRYSTALS TO THE AMB IENT AIR C 1.0 mil LIQUID CRYSTAL (half) ---- 5 mil MYL AR COVER --- 1 mil AIR GAP --- C ---- 0.5 inches PLEXIGLASS ---- AMBIENT AIR C 1/2(tliq/kliq) -- tyl/kmyl -- tair/kair -- tp lexi/kplexi -- 1/ho C************************************************** *****************C C Natural Convection Heat transfer coefficient on the outer surface XL=6./12. ! ft, Target plate heig ht gc=32.2 xnu=0.68 ! FIRST GUESS con = 0.0148 ! FIRST GUESS ho=xnu*con/XL C************************************************** *****************C kair = 0.0148 ! BTU/hr.ft.F Air at 75 F kkap = 0.0942 ! BTU/hr.ft.F MINCO ( 0.163 W/m.K) (0.095 BTU/hr.ft.F) kplexi = 0.11 ! BTU/hr.ft.F AIN Pla stics k=1.3 BTU/hr.F.sqft/in (1-800-523-7500) kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19 kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K) kinc = 9.0152 ! BTU/hr.ft.F MINCO ( inconel 600 K=15.6 W/m.K) kblack = 0.165 ! BTU/hr.ft.F Glyceri n kliq = 0.165 ! BTU/hr.ft.F Glyceri n

54

tplexi = 0.5/12. ! United Industries tair = 1.0e-03/12. ! 1 mil gap tkap = 2.5e-03/12. ! MINCO tinc = 1.5e-03/12. ! MINCO tadh1 = 1.0e-03/12. ! MINCO tadh2 = 1.5e-03/12. ! adhesive thickness ( from DAVIS) tblack = 3.0e-03/12. ! absorptive black bac kground (from DAVIS) tliq = 2.0e-03/12. ! liquid crystal thick ness (from DAVIS) tmyl = 5.0e-03/12. ! MYLAR thickness (fro m DAVIS) Rplexi= tplexi/kplexi Rair = tair/kair Rconv = 1./ho Rinc = tinc/kinc Rkap = tkap/kkap Radh1 = tadh1/kadh Radh2 = tadh2/kadh Rblack = tblack/kblack Rliq = tliq/kliq Rmyl = tmyl/kmyl C write(6,*)' Rinc',Rinc,' Rkap ',Rkap C write(6,*)' Radh1',Radh1,' Radh2',Radh2,' Rb lack',Rblack C write(6,*)' Rliq ',Rliq,' Rmyl ',Rmyl C write(6,*)' Rair ',Rair,' Rplexi',Rplexi C Resistance from mid heater to mid Liquid Crysta ls Rbet=0.5*Rinc + Radh1 + Rkap + &Radh2 + Rblack + 0.5*Rliq C Resistance from mid heater to the surface Rfront=0.5*Rinc + Radh1 + Rkap C write(6,*)' ' C write(6,*)' Rbet, Between mid LC to mid Heat er',Rbet C write(6,*)' Rfront, From mid Heater to surfa ce',Rfront C write(6,*)' Tliquid', Tliquid,' Tamb', Tamb C write(6,*)' Flux',Flux C Resistance from mid Liquid Crystals to ambient do kk=1,10 Rconv = 1./ho

55

Rback=0.5*Rliq+Rmyl+Rair+Rplexi+Rconv C************************************************** C C H E A T E D T A R G E T W A L L Fback=(Tliquid-Tamb)/Rback Ffront=Flux-Fback Theater = Ffront*Rbet+Tliquid Tsurf= Theater -Ffront*Rfront Perloss1=100.*(Fback/Flux) Tback=Tliquid-Fback*(Rback-Rconv) Tf=0.5*(Tback+Tamb) TfR=Tf+460. CALL AIRPROP(TfR,gam,con,vis,pr,cp) vis=vis/3600. beta=1./(Tf+460) rho=(Pamb*144.)/(Rgas*(Tf+460)) GrStar=gc*beta*Fback*(XL**4)/(con*(vis/rho)** 2) xnuq=0.6*((GrStar*pr)**0.2) ! Ozisik Page 433 ho=xnuq*con/XL c write(6,*)' Pamb=',Pamb c write(6,*)' Rgas=',Rgas c write(6,*)' Tf=',Tf c write(6,*)' beta=',beta C write(6,*)' Ra=',Ra c write(6,*)' rho,air',rho c write(6,*)' Ffront=',Ffront c write(6,*)' Perloss=',Perloss1 c write(6,*)' Rback=',Rback C write(6,*)' Fback=',Fback c write(6,*)' Rconv=',Rconv c write(6,*)' GrStar=',GrStar c write(6,*)' nu=',xnuq c write(6,*)' ho=',ho C RADIATIONAL LOSSES Emiss=.8 ! Emissivity SIGMA=0.1712E-08 Frad=Emiss*SIGMA*(((Tsurf+460)**4)-((Tjet+460 )**4)) Perloss2=100.*(Frad/Flux) Losses=Fback+Frad Perloss3=100.*(Fback+Frad)/Flux C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING h=(Flux-Fback-Frad)/(Tsurf-Tjet)

56

C FILM TEMPERATURE Tfilm=(Tsurf+Tjet)/2. enddo C ************************************* * WRITE(7,102)Flux,ho,Tjet,Tsurf,Tliquid,Tfilm, Theater,Tback,Tamb,h 102 FORMAT(//, &10x,' T A R G E T W A L L',//, &5X,'Total heat flux on the target wall= ',F8. 3,' BTU/hr.sqft',/, &5X,'heat transfer coefficient on the back sur favce= ',F8.3, &' BTU/hr.sqft.F',/ , &5X,'Jet Temperature = ',F5.1,' F',/, &5X,'Surface Temperature = ',F7.2,' F',/, &5X,'Liquid Crystal Temperature = ',F6.2,' F', /, &5X,'Film Temperature',F7.2,' F',/, &5X,'Heating Element Temperature = ',F7.2,' F' ,/, &5X,'Back of Target wall Temperature = ',F7.2, ' F',/, &5X,'Ambient Temperature = ',F5.1,' F',/, &5X,'Heat Transfer Coefficient = ',F8.3,' BTU/ hr.sqft.F') write(7,180)Fback,frad,Perloss1,Perloss2,Perl oss3 180 FORMAT( &5X,'Flux Losses from the back surface',F10.3, ' BTU/sqft.hr',/, &5X,'Flux Losses by radiation',F10.3,' BTU/sqf t.hr',/, &5X,'% of Flux Losses from the back surface',F 6.2,/, &5X,'% of Flux Losses by radiation',F6.2,/, &5X,'% of total Flux Losses',F6.2) RETURN END C************************************************** ****************** subroutine AIRPROP(t,gamx,kx,mux,prx,cpx) IMPLICIT REAL*8(A-H,O-Z) c physical properties of dry air at one atmosphere c ref: ge heat transfer handbook c c temperature range: 160 to 3960 deg. rankine c -300 to 3500 deg. fahreinheit c c t - temperature, R c gamx - ratios of specific heats c kx - thermal conductivity, BTU/hr.ft.R c mux - viscosity, lbm/hr.ft c prx - prandtl no. c cpx - specific heat, BTU/lbm.R c

57

c dimension tab(34),gam(34),pr(34),cp(34) real*8 k(34),mu(34),kx,mux data nent/34/ data tab/ 160., 260., & 360., 460., 560., 660., 760., 860., 960., 1060., & 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860., & 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660., & 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./ data gam/ 1.417, 1.411, & 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378, & 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336, & 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309, & 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/ data k/ 0.0063,0.0086, & 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220, 0.0243,0.0265, & 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370, 0.0386,0.0405, & 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507, 0.0525,0.0542, & 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702, 0.0740,0.0780/ data mu/ 0.0130,0.0240, & 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627, 0.0679,0.0721, & 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950, 0.0980,0.1015, & 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200, 0.1230,0.1265, & 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535, 0.1595,0.1655/ data pr/ 0.7710,0.7590, & 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820, 0.6790,0.6788, & 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885, 0.6887,0.6890, & 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900, 0.6902,0.6905, & 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921, 0.6925,0.6929/ data cp/ 0.247, 0.242, & 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251, & 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275, & 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293, & 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/ c c if(t.lt.tab(1)) print 510,t,tab(1) 510 format(" in airprop --- temp=",f8.1," is les s than min temp", &" of ",f8.1) if(t.gt.tab(nent)) print 520, t,tab(nent) 520 format(" in airprop --- temp=",f8.1," is gre ater than max", &" temp of ",f8.1) if(t-tab(1))120,120,100 100 if(tab(nent)-t)130,130,110 110 m=2 go to 140 120 j=1 go to 180 130 j=nent go to 180 140 if(t-tab(m))160,170,150 150 m=m+1 go to 140 c

58

c -- Linear Interpolation --- c 160 slp=(t-tab(m-1))/(tab(m)-tab(m-1)) mux= mu(m-1)+(mu(m)-mu(m-1))*slp prx= pr(m-1)+(pr(m)-pr(m-1))*slp cpx=cp(m-1)+(cp(m)-cp(m-1))*slp kx=k(m-1)+(k(m)-k(m-1))*slp gamx=gam(m-1)+(gam(m)-gam(m-1))*slp go to 190 170 j=m go to 180 180 mux=mu(j) prx=pr(j) cpx=cp(j) kx=k(j) gamx=gam(j) 190 return end C************************************************** ********* SUBROUTINE UNCERTAIN(i1,V1,Area,Ts,Tjet,Losse s,Uncer) IMPLICIT REAL*8(A-H,O-Z) REAL*8 i1,Losses dv1=.1 di1=.01 da=1./(32.*32.) dts=0.5 dtjet=0.5 FAC=491.3744 ! (3600 s/hr)(144 sq in/sqft)/(1055 J/BTU) C=0.24*0.5215*1055. ! 0.5215 given by F ox, Cp=0.24 BTU/(lbm.R) and C 1 BTU=1055 J C h UNCERTAINTY a=144*Area Floss=Losses/FAC DFloss=0.1*Floss h=((V1*i1/a)-Floss)/(Ts-Tjet) WRITE(3,*)' ' WRITE(3,*)' h =',h*FAC,' BUT/hr.sqft.F' H2=h*h C C i1 v1 C ------- - Floss C a C h=--------------------- C Ts-Tjet C

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C C1=(i1*v1/a)-Floss C2=(Ts-Tjet) DhDi1=v1/(a*C2) DhDv1=i1/(a*C2) DhDa=-(v1*i1)/(a*a*C2) DhDFloss=-1/C2 DhDTs=-C1/(C2**2) DhDTjet=C1/(C2**2) Zi1=(Di1*DhDi1)**2 Zv1=(Dv1*DhDv1)**2 Za=(Da*DhDa)**2 ZFloss=(DFloss*DhDFloss)**2 ZTs=(DTs*DhDTs)**2 ZTjet=(DTjet*DhDTjet)**2 Uncer=100*SQRT((Zi1+Zv1+Za+ZFloss+ZTs+ZTjet)/ (H2)) WRITE(3,*)' UNCERTAINTY in h %:',Uncer WRITE(3,*)' % Uncer. assoc. with i1 ',100.* sqrt(Zi1)/h WRITE(3,*)' % Uncer. assoc. with v1 ',100.* sqrt(Zv1)/h WRITE(3,*)' % Uncer. assoc. with a ',100.* sqrt(Za)/h WRITE(3,*)' % Uncer. assoc. with Floss',100.* sqrt(ZFloss)/h WRITE(3,*)' % Uncer. assoc. with Ts ',100.* sqrt(ZTs)/h WRITE(3,*)' % Uncer. assoc. with Tjet ',100.* sqrt(ZTjet)/h RETURN END

60

11 Appendix B – Labeling Routine: Nu Plot with Cross Flow

% PICTURE ROUTINE FOR LABELING CONTOURS % READ IN PICTURE I=imread( 'Re15k_ZDpt5_Gpt5.bmp' ); % CONVERT IMAGE TO BINARY I2=im2bw(I); % INVERT THE IMAGE I3=imcomplement(I2); % FIND THE INDIVIDUAL CONTOURS C=bwconncomp(I3); % CREATE LABEL MATRIX FOR CONTOURS L=labelmatrix(C); % MEASURE INTERIOR PIXEL COUNT OF CONTOURS STATS=regionprops(L, 'FilledArea' ); FAREA=[STATS.FilledArea]; % SET COLOR MAP LIMITS Clow=[1 1 0]; % YELLOW Cmid1=[0 0 1]; % BLUE Cmid2=[0 1 0]; % GREEN Cmid3=[1 0 0]; % RED Cmid4=[1 0 1]; % MAGENTA Chigh=[0 1 1]; % CYAN Nulow=0; Numid1=20; Numid2=40; Numid3=60; Numid4=80; Nuhigh=100; CC=[Clow;Cmid1;Cmid2;Cmid3;Cmid4;Chigh]; Nurange=[Nulow Numid1 Numid2 Numid3 Numid4 Nuhigh]; % CONTOUR VALUES Nucont=[21.666 17.089 17.089 17.089 17.089 21.666 28.156 33.372 38.113 43.846

61

46.230 48.872 54.515 65.382]; % CREATE COLOR MAP CM=interp1(Nurange,CC,Nucont); % APPLY COLOR MAP TO THE IMAGE I4=label2rgb(L,CM, 'w' ); % SHOW THE IMAGE imshow(I4); hold on; % JET STAGNATION POINT WITHOUT CROSS FLOW plot(195,161, 'o' , 'MarkerEdgeColor' , 'k' , 'MarkerFaceColor' , 'k' ); % ADD NUSSELT NUMBER LABELS text(35,140, '21.7' , 'Rotation' ,270, 'FontSize' ,6); text(375,140, '21.7' , 'Rotation' ,270, 'FontSize' ,6); text(100,55, '17.1' , 'FontSize' ,6); text(135,75, '17.1' , 'FontSize' ,6); text(100,275, '17.1' , 'FontSize' ,6); text(135,220, '17.1' , 'FontSize' ,6); text(342,170, '28.2' , 'Rotation' ,270, 'FontSize' ,6); text(312,195, '33.4' , 'Rotation' ,270, 'FontSize' ,6); text(292,130, '38.1' , 'Rotation' ,270, 'FontSize' ,6); text(283,150, '43.8' , 'Rotation' ,270, 'FontSize' ,6); text(275,170, '46.2' , 'Rotation' ,270, 'FontSize' ,6); text(267,130, '48.9' , 'Rotation' ,270, 'FontSize' ,6); text(260,150, '54.5' , 'Rotation' ,270, 'FontSize' ,6); text(225,155, '65.4' , 'Rotation' ,270, 'FontSize' ,6);

62

12 Appendix C – Labeling Routine: Nu Plot without Cross Flow

% PICTURE ROUTINE FOR LABELING CONTOURS % READ IN PICTURE I=imread( 'Re15k_ZDpt5_G0.bmp' ); % CONVERT IMAGE TO BINARY I2=im2bw(I); % INVERT THE IMAGE I3=imcomplement(I2); % THIN THE IMAGE I4=bwmorph(I3, 'skel' ); I5=bwmorph(I4, 'spur' ); % FIND THE INDIVIDUAL CONTOURS C=bwconncomp(I5); % CREATE LABEL MATRIX FOR CONTOURS L=labelmatrix(C); % MEASURE INTERIOR PIXEL COUNT OF CONTOURS STATS=regionprops(L, 'FilledArea' ); FAREA=[STATS.FilledArea]; % SET COLOR MAP LIMITS Clow=[1 1 0]; % YELLOW Cmid1=[0 0 1]; % BLUE Cmid2=[0 1 0]; % GREEN Cmid3=[1 0 0]; % RED Cmid4=[1 0 1]; % MAGENTA Chigh=[0 1 1]; % CYAN Nulow=0; Numid1=20; Numid2=40; Numid3=60; Numid4=80; Nuhigh=100; CC=[Clow;Cmid1;Cmid2;Cmid3;Cmid4;Chigh]; Nurange=[Nulow Numid1 Numid2 Numid3 Numid4 Nuhigh]; % CONTOUR VALUES Nucont=[8.782 11.897 16.343 20.959 28.628 35.044

63

43.383 58.406 67.964 76.574]; % CREATE COLOR MAP CM=interp1(Nurange,CC,Nucont); % APPLY COLOR MAP TO THE IMAGE I7=label2rgb(L,CM, 'w' ); % SHOW THE IMAGE imshow(I7); hold on; % JET STAGNATION POINT WITHOUT CROSS FLOW plot(209,241, 'o' , 'MarkerEdgeColor' , 'k' , 'MarkerFaceColor' , 'k' ); % ADD NUSSELT NUMBER LABELS text(209,49, '8.8' , 'FontSize' ,6); text(209,67, '11.9' , 'FontSize' ,6); text(209,89, '16.3' , 'FontSize' ,6); text(209,104, '21.0' , 'FontSize' ,6); text(209,119, '28.6' , 'FontSize' ,6); text(209,130, '35.0' , 'FontSize' ,6); text(209,143, '43.4' , 'FontSize' ,6); text(209,163, '58.4' , 'FontSize' ,6); text(209,192, '68.0' , 'FontSize' ,6); text(209,214, '76.6' , 'FontSize' ,6);

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13 Appendix D – Discharge Coefficient Calculations

A B C Values1 z/d 0.3 0.32 Jet Re =4*E13/(PI()*0.25/12*0.000000382*32.174) 112403 Jet Ven Dia Inches 0.08 0.084 Cross Ven Dia Inches 0.223 0.2235 Tamb F 69.8 69.86 In Hg 30.15 30.157 Psia =E8*0.4911541 14.8088 G Ratio =(E20/(6*0.25*E3))/(E13/(PI()/4*0.25 2̂)) 1.0619 Jet Ven Pres Psig 5 510 Jet Ven Temp F 68 6811 Jet Ven Mdot lb/s =0.5215*PI()/4*E5 2̂*(E9+E11)/SQRT(E12+459.67) 0.002312 In Oil 5.95 5.9513 Psig =0.826*0.0361*E14 0.17714 Jet P Ratio =(E9+E15)/E9 1.01215 Jet Plen Temp F 68.8 68.816 Cross Ven Pres Psig 10 1017 Cross Ven Temp F 68.2 68.218 Cross Ven Mdot lb/s =0.5215*PI()/4*E6 2̂*(E9+E18)/SQRT(E19+459.67) 0.02219 In Oil 4.65 4.6520 Psig =0.826*0.0361*E21 0.13921 In Oil 4.7 4.722 Psig =0.826*0.0361*E23 0.1423 Cross Plen Temp F 68.5 68.524 AA =(E9+E15)*(E9/(E9+E15)) (̂(1.4+1)/(2*1.4)) 14.83425 BB =(2*1.4*32.17)/(1.4-1)/53.35/(E17+459.67) 0.00826 CC =(((E9+E15)/E9) (̂(1.4-1)/1.4))-1 0.003427 DD =PI()/4*0.25 2̂ 0.049128 Mdot Isen =E26*SQRT(E27*E28)*E29 0.003829 Cd =E13/E30 0.595

Cross Cir Pres

Cross Plen Pres

Pamb

Jet Plen Pres

65

14 Appendix E – Discharge Coefficient Data

z/d Jet Re Jet Ven Dia Cross Ven Dia Tamb G Ratio Jet Ven Pres Jet Ven Temp Jet Ven Mdot Jet P Ratio Jet Plen Temp Cross Ven Pres Cross Ven Temp Cross Ven Mdot Cross Plen Temp AA BB CC DD Mdot Isen CdInches Inches F In Hg Psia Psig F lb/s In Oil Psig F Psig F lb/s In Oil Psig In Oil Psig F

Inf 11183 0.08 - 73.4 30.05 14.759 - 5 70.8 0.0022 3.10 0.09 1.006 72.6 0 - - - - - - - 14.772 0.008 0.002 0.049 0.003 0.824Inf 14014 0.08 - 73.4 30.05 14.759 - 10 70.7 0.0028 4.85 0.14 1.010 72.7 0 - - - - - - - 14.780 0.008 0.003 0.049 0.003 0.826Inf 16845 0.08 - 73.4 30.05 14.759 - 15 70.6 0.0034 6.85 0.20 1.014 72.7 0 - - - - - - - 14.788 0.008 0.004 0.049 0.004 0.836Inf 19676 0.08 - 73.4 30.05 14.759 - 20 70.6 0.0040 9.30 0.28 1.019 72.6 0 - - - - - - - 14.798 0.008 0.005 0.049 0.005 0.838Inf 22508 0.08 - 73.4 30.05 14.759 - 25 70.5 0.0045 12.10 0.36 1.024 72.6 0 - - - - - - - 14.810 0.008 0.007 0.049 0.005 0.840Inf 25339 0.08 - 73.4 30.05 14.759 - 30 70.5 0.0051 15.25 0.45 1.031 72.5 0 - - - - - - - 14.823 0.008 0.009 0.049 0.006 0.843Inf 28174 0.08 - 73.4 30.05 14.759 - 35 70.3 0.0057 18.70 0.56 1.038 72.4 0 - - - - - - - 14.838 0.008 0.011 0.049 0.007 0.846Inf 31005 0.08 - 73.4 30.05 14.759 - 40 70.3 0.0062 22.70 0.68 1.046 72.3 0 - - - - - - - 14.854 0.008 0.013 0.049 0.007 0.845Inf 33833 0.08 - 73.4 30.05 14.759 - 45 70.4 0.0068 27.10 0.81 1.055 72.2 0 - - - - - - - 14.872 0.008 0.015 0.049 0.008 0.845Inf 36657 0.08 - 73.4 30.05 14.759 - 50 70.6 0.0074 8.85 0.94 1.064 72.0 0 - - - - - - - 14.890 0.008 0.018 0.049 0.009 0.847Inf 39488 0.08 - 73.4 30.05 14.759 - 55 70.6 0.0079 10.20 1.09 1.074 72.0 0 - - - - - - - 14.910 0.008 0.020 0.049 0.009 0.851Inf 42314 0.08 - 73.4 30.05 14.759 - 60 70.7 0.0085 11.70 1.25 1.084 71.9 0 - - - - - - - 14.931 0.008 0.023 0.049 0.010 0.851Inf 45144 0.08 - 73.4 30.05 14.759 - 65 70.7 0.0091 13.40 1.43 1.097 72.4 0 - - - - - - - 14.955 0.008 0.027 0.049 0.011 0.849Inf 47983 0.08 - 73.4 30.05 14.759 - 70 70.5 0.0096 15.10 1.61 1.109 72.3 0 - - - - - - - 14.979 0.008 0.030 0.049 0.011 0.851Inf 50809 0.08 - 73.4 30.05 14.759 - 75 70.6 0.0102 17.00 1.81 1.123 72.1 0 - - - - - - - 15.005 0.008 0.034 0.049 0.012 0.849Inf 53639 0.08 - 73.4 30.05 14.759 - 80 70.6 0.0108 18.85 2.01 1.136 71.9 0 - - - - - - - 15.031 0.008 0.037 0.049 0.013 0.852

0.30 11240 0.08 0.223 69.8 30.15 14.808 0.00 5 68.0 0.0023 3.10 0.09 1.006 68.7 0 - - - - - - - 14.821 0.008 0.002 0.049 0.003 0.8240.30 14072 0.08 0.223 69.8 30.15 14.808 0.00 10 68.4 0.0028 4.95 0.15 1.010 69.7 0 - - - - - - - 14.829 0.008 0.003 0.049 0.003 0.8170.30 19759 0.08 0.223 69.8 30.15 14.808 0.00 20 67.6 0.0040 9.60 0.29 1.019 69.8 0 - - - - - - - 14.849 0.008 0.005 0.049 0.005 0.8240.30 25536 0.08 0.223 66.4 30.24 14.852 0.00 30 64.5 0.0051 15.75 0.47 1.032 65.9 0 - - - - - - - 14.919 0.008 0.009 0.049 0.006 0.8280.30 31188 0.08 0.223 66.4 30.24 14.852 0.00 40 65.9 0.0063 23.50 0.70 1.047 66.2 0 - - - - - - - 14.951 0.008 0.013 0.049 0.008 0.8280.30 36846 0.08 0.223 66.4 30.24 14.852 0.00 50 66.7 0.0074 9.15 0.97 1.066 66.7 0 - - - - - - - 14.988 0.008 0.018 0.049 0.009 0.8310.30 42391 0.08 0.223 69.8 29.91 14.690 0.00 60 67.8 0.0085 12.15 1.29 1.088 68.4 0 - - - - - - - 14.869 0.008 0.024 0.049 0.010 0.8360.30 48117 0.08 0.223 69.8 29.91 14.690 0.00 70 66.7 0.0097 15.55 1.66 1.113 67.6 0 - - - - - - - 14.916 0.008 0.031 0.049 0.012 0.8390.30 53788 0.08 0.223 69.8 29.91 14.690 0.00 80 66.9 0.0108 19.45 2.07 1.141 68.0 0 - - - - - - - 14.970 0.008 0.038 0.049 0.013 0.8400.30 11240 0.08 0.223 69.8 30.15 14.808 1.06 5 68.0 0.0023 5.95 0.18 1.012 68.8 10 68.2 0.0220 4.65 0.14 4.70 0.14 68.5 14.834 0.008 0.003 0.049 0.004 0.5950.30 14075 0.08 0.223 69.8 30.15 14.808 0.85 10 68.2 0.0028 7.30 0.22 1.015 69.6 10 69.2 0.0220 4.95 0.15 5.00 0.15 69.1 14.839 0.008 0.004 0.049 0.004 0.6730.30 19761 0.08 0.223 69.8 30.15 14.808 0.60 20 67.5 0.0040 11.10 0.33 1.022 69.8 10 70.0 0.0220 5.55 0.17 5.60 0.17 69.7 14.855 0.008 0.006 0.049 0.005 0.7670.30 25541 0.08 0.223 66.4 30.24 14.852 0.47 30 64.3 0.0051 16.95 0.51 1.034 65.9 10 64.5 0.0221 6.15 0.18 6.20 0.18 65.6 14.924 0.008 0.010 0.049 0.006 0.7980.30 31185 0.08 0.223 66.4 30.24 14.852 0.38 40 66 0.0063 23.90 0.71 1.048 66.3 10 66.1 0.0221 6.70 0.20 6.75 0.20 66.2 14.952 0.008 0.013 0.049 0.008 0.8210.30 36839 0.08 0.223 66.4 30.24 14.852 0.32 50 66.9 0.0074 9.25 0.99 1.066 66.7 10 67.1 0.0221 7.40 0.22 7.45 0.22 66.8 14.989 0.008 0.019 0.049 0.009 0.8260.30 42403 0.08 0.223 69.8 29.91 14.690 0.28 60 67.5 0.0085 12.35 1.32 1.090 68.2 10 65.3 0.0219 8.15 0.24 8.25 0.25 68.6 14.871 0.008 0.025 0.049 0.010 0.8290.30 48135 0.08 0.223 69.8 29.91 14.690 0.25 70 66.3 0.0097 15.90 1.69 1.115 67.4 10 64.5 0.0220 8.80 0.26 8.90 0.27 67.0 14.921 0.008 0.032 0.049 0.012 0.8300.30 53793 0.08 0.223 69.8 29.91 14.690 0.22 80 66.8 0.0108 19.90 2.12 1.144 67.6 10 64.9 0.0220 9.50 0.28 9.60 0.29 68.1 14.976 0.008 0.039 0.049 0.013 0.8300.30 11244 0.08 0.223 69.8 30.15 14.808 1.49 5 67.6 0.0023 8.70 0.26 1.018 69.2 20 68.3 0.0309 8.55 0.25 8.65 0.26 68.4 14.845 0.008 0.005 0.049 0.005 0.4920.30 14076 0.08 0.223 69.8 30.15 14.808 1.19 10 68.1 0.0028 10.45 0.31 1.021 69.7 20 69.1 0.0308 8.75 0.26 8.90 0.27 69.3 14.852 0.008 0.006 0.049 0.005 0.5630.30 19761 0.08 0.223 69.8 30.15 14.808 0.85 20 67.5 0.0040 13.95 0.42 1.028 69.7 20 69.8 0.0308 9.45 0.28 9.55 0.28 69.8 14.867 0.008 0.008 0.049 0.006 0.6840.30 25539 0.08 0.223 66.4 30.24 14.852 0.66 30 64.4 0.0051 18.60 0.55 1.037 66.0 20 64.4 0.0310 10.30 0.31 10.40 0.31 65.5 14.930 0.008 0.011 0.049 0.007 0.7620.30 31185 0.08 0.223 66.4 30.24 14.852 0.54 40 66 0.0063 25.70 0.77 1.052 66.3 20 66.2 0.0310 11.15 0.33 11.30 0.34 66.3 14.960 0.008 0.014 0.049 0.008 0.7920.30 36839 0.08 0.223 66.4 30.24 14.852 0.46 50 66.9 0.0074 9.70 1.03 1.070 66.7 20 67.3 0.0309 11.90 0.35 12.00 0.36 66.9 14.996 0.008 0.019 0.049 0.009 0.8070.30 42435 0.08 0.223 69.8 29.91 14.690 0.39 60 66.7 0.0085 12.35 1.32 1.090 67.8 20 65.2 0.0308 12.70 0.38 12.80 0.38 68.2 14.871 0.008 0.025 0.049 0.010 0.8300.30 48135 0.08 0.223 69.8 29.91 14.690 0.35 70 66.3 0.0097 15.80 1.68 1.115 67.1 20 64.5 0.0309 13.55 0.40 13.65 0.41 67.0 14.920 0.008 0.031 0.049 0.012 0.8320.30 53798 0.08 0.223 69.8 29.91 14.690 0.31 80 66.7 0.0108 19.65 2.09 1.142 67.1 20 64.8 0.0309 14.75 0.44 14.85 0.44 67.7 14.973 0.008 0.039 0.049 0.013 0.8350.30 11242 0.08 0.223 69.8 30.15 14.808 1.92 5 67.8 0.0023 12.00 0.36 1.024 69.3 30 68.7 0.0397 13.15 0.39 13.35 0.40 68.5 14.859 0.008 0.007 0.049 0.005 0.4190.30 14076 0.08 0.223 69.8 30.15 14.808 1.53 10 68.1 0.0028 13.95 0.42 1.028 69.6 30 70.0 0.0397 13.50 0.40 13.70 0.41 69.2 14.867 0.008 0.008 0.049 0.006 0.4870.30 19758 0.08 0.223 69.8 30.15 14.808 1.09 20 67.7 0.0040 18.00 0.54 1.036 69.7 30 70.1 0.0397 14.30 0.43 14.50 0.43 69.6 14.884 0.008 0.010 0.049 0.007 0.6020.30 25531 0.08 0.223 66.4 30.24 14.852 0.85 30 64.7 0.0051 22.45 0.67 1.045 66.1 30 65.5 0.0399 15.15 0.45 15.30 0.46 65.2 14.946 0.008 0.013 0.049 0.007 0.6940.30 31182 0.08 0.223 66.4 30.24 14.852 0.69 40 66.1 0.0063 28.30 0.84 1.057 66.4 30 66.7 0.0398 16.00 0.48 16.25 0.48 66.2 14.970 0.008 0.016 0.049 0.008 0.755

Pamb Jet Plen Pres Cross Cir Pres Cross Plen Pres

66

z/d Jet Re Jet Ven Dia Cross Ven Dia Tamb G Ratio Jet Ven Pres Jet Ven Temp Jet Ven Mdot Jet P Ratio Jet Plen Temp Cross Ven Pres Cross Ven Temp Cross Ven Mdot Cross Plen Temp AA BB CC DD Mdot Isen CdInches Inches F In Hg Psia Psig F lb/s In Oil Psig F Psig F lb/s In Oil Psig In Oil Psig F

0.30 36835 0.08 0.223 66.4 30.24 14.852 0.59 50 67 0.0074 10.15 1.08 1.073 66.7 30 67.4 0.0398 17.05 0.51 17.20 0.51 66.9 15.002 0.008 0.020 0.049 0.009 0.7890.30 42435 0.08 0.223 69.8 29.91 14.690 0.51 60 66.7 0.0085 13.00 1.38 1.094 67.7 30 65.3 0.0397 18.40 0.55 18.60 0.55 67.4 14.881 0.008 0.026 0.049 0.011 0.8090.30 48140 0.08 0.223 69.8 29.91 14.690 0.45 70 66.2 0.0097 16.20 1.73 1.117 67.0 30 64.8 0.0397 19.40 0.58 19.65 0.59 66.6 14.925 0.008 0.032 0.049 0.012 0.8220.30 53798 0.08 0.223 69.8 29.91 14.690 0.40 80 66.7 0.0108 19.95 2.12 1.145 67.0 30 65.1 0.0397 20.35 0.61 20.60 0.61 67.2 14.977 0.008 0.039 0.049 0.013 0.8290.30 11242 0.08 0.223 69.8 30.15 14.808 2.34 5 67.8 0.0023 15.60 0.47 1.031 69.4 40 69.4 0.0485 18.60 0.55 18.90 0.56 68.6 14.874 0.008 0.009 0.049 0.006 0.3680.30 14087 0.08 0.223 69.8 30.15 14.808 1.87 10 67.3 0.0028 17.80 0.53 1.036 69.6 40 69.9 0.0485 18.90 0.56 19.25 0.57 69.1 14.883 0.008 0.010 0.049 0.007 0.4320.30 19748 0.08 0.223 69.8 30.15 14.808 1.33 20 68.2 0.0040 22.00 0.66 1.044 69.7 40 70.5 0.0485 19.50 0.58 19.85 0.59 69.6 14.900 0.008 0.012 0.049 0.007 0.5450.30 25527 0.08 0.223 66.4 30.24 14.852 1.04 30 64.9 0.0051 27.15 0.81 1.055 66.1 40 66.4 0.0487 20.70 0.62 21.05 0.63 65.3 14.966 0.008 0.015 0.049 0.008 0.6310.30 31179 0.08 0.223 66.4 30.24 14.852 0.85 40 66.2 0.0063 9.05 0.96 1.065 66.4 40 67.1 0.0487 21.50 0.64 21.85 0.65 66.1 14.987 0.008 0.018 0.049 0.009 0.7070.30 36832 0.08 0.223 66.4 30.24 14.852 0.72 50 67.1 0.0074 11.05 1.18 1.079 66.8 40 67.7 0.0487 22.40 0.67 22.65 0.68 66.8 15.015 0.008 0.022 0.049 0.010 0.7560.30 42443 0.08 0.223 69.8 29.91 14.690 0.62 60 66.5 0.0085 13.70 1.46 1.099 67.7 40 65.6 0.0486 24.30 0.72 24.65 0.74 67.1 14.890 0.008 0.027 0.049 0.011 0.7880.30 48140 0.08 0.223 69.8 29.91 14.690 0.55 70 66.2 0.0097 16.90 1.80 1.123 67.0 40 65.1 0.0486 25.25 0.75 25.50 0.76 66.3 14.935 0.008 0.034 0.049 0.012 0.8050.30 53783 0.08 0.223 69.8 29.91 14.690 0.49 80 67 0.0108 20.40 2.17 1.148 67.1 40 65.3 0.0486 26.15 0.78 26.45 0.79 66.8 14.983 0.008 0.040 0.049 0.013 0.8190.30 11241 0.08 0.223 69.8 30.15 14.808 2.77 5 67.9 0.0023 19.80 0.59 1.040 69.5 50 70.0 0.0574 24.70 0.74 25.05 0.75 68.5 14.891 0.008 0.011 0.049 0.007 0.3270.30 14083 0.08 0.223 69.8 30.15 14.808 2.21 10 67.6 0.0028 22.00 0.66 1.044 69.7 50 70.7 0.0573 24.65 0.74 25.00 0.75 69.1 14.900 0.008 0.012 0.049 0.007 0.3880.30 19743 0.08 0.223 69.8 30.15 14.808 1.57 20 68.5 0.0040 26.45 0.79 1.053 69.7 50 71.2 0.0573 25.30 0.75 25.70 0.77 69.6 14.918 0.008 0.015 0.049 0.008 0.4970.30 25519 0.08 0.223 66.4 30.24 14.852 1.22 30 65.2 0.0051 9.05 0.96 1.065 66.1 50 67.2 0.0575 27.55 0.82 28.00 0.83 65.5 14.987 0.008 0.018 0.049 0.009 0.5780.30 31176 0.08 0.223 66.4 30.24 14.852 1.00 40 66.3 0.0063 10.50 1.12 1.075 66.5 50 67.7 0.0575 27.50 0.82 27.95 0.83 66.2 15.007 0.008 0.021 0.049 0.010 0.6560.30 36828 0.08 0.223 66.4 30.24 14.852 0.85 50 67.2 0.0074 12.35 1.32 1.089 66.7 50 68.5 0.0575 28.40 0.85 28.80 0.86 66.9 15.034 0.008 0.025 0.049 0.010 0.7150.30 42435 0.08 0.223 69.8 29.91 14.690 0.73 60 66.7 0.0085 14.75 1.57 1.107 67.6 50 65.8 0.0575 8.40 0.89 8.50 0.91 66.5 14.905 0.008 0.029 0.049 0.011 0.7600.30 48126 0.08 0.223 69.8 29.91 14.690 0.65 70 66.5 0.0097 17.75 1.89 1.129 67.0 50 65.6 0.0575 8.70 0.93 8.80 0.94 66.0 14.947 0.008 0.035 0.049 0.012 0.7850.30 53783 0.08 0.223 69.8 29.91 14.690 0.58 80 67 0.0108 21.20 2.26 1.154 67.2 50 65.7 0.0575 9.05 0.96 9.20 0.98 66.5 14.994 0.008 0.042 0.049 0.013 0.8040.30 11241 0.08 0.223 69.8 30.15 14.808 3.19 5 67.9 0.0023 24.10 0.72 1.049 69.5 60 70.1 0.0662 8.70 0.93 8.80 0.94 68.6 14.909 0.008 0.014 0.049 0.008 0.2960.30 14073 0.08 0.223 69.8 30.15 14.808 2.55 10 68.3 0.0028 26.20 0.78 1.053 69.7 60 71.0 0.0661 8.55 0.91 8.70 0.93 69.3 14.917 0.008 0.015 0.049 0.008 0.3560.30 19733 0.08 0.223 69.8 30.15 14.808 1.82 20 69.0 0.0040 8.60 0.92 1.062 69.8 60 71.5 0.0661 8.75 0.93 8.90 0.95 69.7 14.936 0.008 0.017 0.049 0.009 0.4610.30 25514 0.08 0.223 66.4 30.24 14.852 1.41 30 65.4 0.0051 10.55 1.12 1.076 66.2 60 67.8 0.0664 9.55 1.02 9.65 1.03 65.6 15.008 0.008 0.021 0.049 0.010 0.5360.30 31170 0.08 0.223 66.4 30.24 14.852 1.15 40 66.5 0.0063 12.00 1.28 1.086 66.5 60 68.2 0.0664 9.45 1.01 9.60 1.02 66.3 15.029 0.008 0.024 0.049 0.010 0.6140.30 36821 0.08 0.223 66.4 30.24 14.852 0.98 50 67.4 0.0074 13.85 1.47 1.099 66.9 60 68.9 0.0663 9.65 1.03 9.85 1.05 67.0 15.055 0.008 0.027 0.049 0.011 0.6760.30 42431 0.08 0.223 69.8 29.91 14.690 0.85 60 66.8 0.0085 16.20 1.73 1.117 67.6 60 66.1 0.0663 10.30 1.10 10.50 1.12 66.3 14.925 0.008 0.032 0.049 0.012 0.7250.30 48121 0.08 0.223 69.8 29.91 14.690 0.75 70 66.6 0.0097 18.85 2.01 1.137 67.2 60 65.9 0.0664 10.55 1.12 10.70 1.14 65.8 14.962 0.008 0.037 0.049 0.013 0.7630.30 53773 0.08 0.223 69.8 29.91 14.690 0.67 80 67.2 0.0108 22.15 2.36 1.161 67.4 60 65.9 0.0664 10.85 1.16 11.00 1.17 66.1 15.006 0.008 0.043 0.049 0.014 0.7870.30 11239 0.08 0.223 69.8 30.15 14.808 3.62 5 68.1 0.0023 29.00 0.86 1.058 69.5 70 70.5 0.0750 10.75 1.14 10.90 1.16 68.6 14.929 0.008 0.016 0.049 0.008 0.2700.30 14073 0.08 0.223 69.8 30.15 14.808 2.89 10 68.3 0.0028 8.55 0.91 1.061 69.7 70 71.5 0.0750 10.50 1.12 10.65 1.13 69.4 14.935 0.008 0.017 0.049 0.009 0.3300.30 19739 0.08 0.223 69.8 30.15 14.808 2.06 20 68.7 0.0040 10.05 1.07 1.072 69.8 70 72.0 0.0749 10.70 1.14 10.85 1.16 69.8 14.957 0.008 0.020 0.049 0.009 0.4270.30 25510 0.08 0.223 66.4 30.24 14.852 1.60 30 65.6 0.0051 11.80 1.26 1.085 66.2 70 68.1 0.0752 11.45 1.22 11.75 1.25 65.8 15.026 0.008 0.023 0.049 0.010 0.5070.30 31167 0.08 0.223 66.4 30.24 14.852 1.31 40 66.6 0.0063 13.40 1.43 1.096 66.7 70 68.7 0.0752 11.45 1.22 11.65 1.24 66.5 15.048 0.008 0.027 0.049 0.011 0.5810.30 36818 0.08 0.223 66.4 30.24 14.852 1.11 50 67.5 0.0074 15.35 1.63 1.110 66.9 70 69.5 0.0751 11.70 1.25 11.90 1.27 67.2 15.076 0.008 0.030 0.049 0.012 0.6420.30 42431 0.08 0.223 69.8 29.91 14.690 0.96 60 66.8 0.0085 17.85 1.90 1.129 67.7 70 66.2 0.0752 21.30 2.27 12.50 1.33 65.9 14.948 0.008 0.035 0.049 0.012 0.6910.30 48117 0.08 0.223 69.8 29.91 14.690 0.85 70 66.7 0.0097 20.35 2.17 1.148 67.2 70 66.4 0.0752 12.65 1.35 12.85 1.37 65.8 14.982 0.008 0.040 0.049 0.013 0.7340.30 53773 0.08 0.223 69.8 29.91 14.690 0.76 80 67.2 0.0108 23.35 2.49 1.169 67.5 70 66.5 0.0752 12.95 1.38 13.15 1.40 66.0 15.022 0.008 0.046 0.049 0.014 0.7670.30 11236 0.08 0.223 69.8 30.15 14.808 4.05 5 68.4 0.0023 9.15 0.97 1.066 69.6 80 71.0 0.0838 12.40 1.32 12.60 1.34 68.7 14.944 0.008 0.018 0.049 0.009 0.2540.30 14072 0.08 0.223 69.8 30.15 14.808 3.23 10 68.4 0.0028 9.95 1.06 1.072 69.8 80 71.8 0.0838 12.50 1.33 12.65 1.35 69.5 14.955 0.008 0.020 0.049 0.009 0.3060.30 19743 0.08 0.223 69.8 30.15 14.808 2.30 20 68.5 0.0040 11.35 1.21 1.082 69.8 80 72.1 0.0837 12.65 1.35 12.90 1.37 69.8 14.975 0.008 0.023 0.049 0.010 0.4020.30 25507 0.08 0.223 66.4 30.24 14.852 1.79 30 65.7 0.0051 13.20 1.41 1.095 66.3 80 68.3 0.0841 13.25 1.41 13.40 1.43 65.9 15.046 0.008 0.026 0.049 0.011 0.4790.30 31164 0.08 0.223 66.4 30.24 14.852 1.46 40 66.7 0.0063 14.90 1.59 1.107 66.7 80 69.0 0.0840 13.35 1.42 13.65 1.45 66.5 15.069 0.008 0.029 0.049 0.011 0.5520.30 36814 0.08 0.223 66.4 30.24 14.852 1.24 50 67.6 0.0074 16.90 1.80 1.121 67.1 80 69.8 0.0840 13.65 1.45 13.85 1.47 67.2 15.097 0.008 0.033 0.049 0.012 0.6120.30 42431 0.08 0.223 69.8 29.91 14.690 1.07 60 66.8 0.0085 19.35 2.06 1.140 67.8 80 66.4 0.0841 14.35 1.53 14.55 1.55 65.7 14.969 0.008 0.038 0.049 0.013 0.6640.30 48112 0.08 0.223 69.8 29.91 14.690 0.95 70 66.8 0.0097 21.90 2.33 1.159 67.4 80 66.7 0.0841 14.65 1.56 14.90 1.59 65.7 15.003 0.008 0.043 0.049 0.014 0.7080.30 53762 0.08 0.223 69.8 29.91 14.690 0.85 80 67.4 0.0108 5.35 2.62 1.178 67.7 80 66.8 0.0841 14.95 1.59 15.20 1.62 66.0 15.038 0.008 0.048 0.049 0.014 0.748

Pamb Jet Plen Pres Cross Cir Pres Cross Plen Pres

67

z/d Jet Re Jet Ven Dia Cross Ven Dia Tamb G Ratio Jet Ven Pres Jet Ven Temp Jet Ven Mdot Jet P Ratio Jet Plen Temp Cross Ven Pres Cross Ven Temp Cross Ven Mdot Cross Plen Temp AA BB CC DD Mdot Isen CdInches Inches F In Hg Psia Psig F lb/s In Oil Psig F Psig F lb/s In Oil Psig In Oil Psig F

0.50 11153 0.08 0.223 70.7 29.65 14.563 0.00 5 63.1 0.0022 3.05 0.09 1.006 70.1 0 - - - - - - - 14.576 0.008 0.002 0.049 0.003 0.8320.50 14033 0.08 0.223 70.7 29.65 14.563 0.00 10 60.9 0.0028 4.80 0.14 1.010 69.7 0 - - - - - - - 14.583 0.008 0.003 0.049 0.003 0.8350.50 19716 0.08 0.223 70.7 29.65 14.563 0.00 20 62.5 0.0040 9.35 0.28 1.019 69.3 0 - - - - - - - 14.602 0.008 0.005 0.049 0.005 0.8400.50 25388 0.08 0.223 70.2 29.65 14.563 0.00 30 63.8 0.0051 15.55 0.46 1.032 68.6 0 - - - - - - - 14.628 0.008 0.009 0.049 0.006 0.8390.50 31035 0.08 0.223 70.2 29.65 14.563 0.00 40 65.5 0.0062 23.00 0.69 1.047 68.9 0 - - - - - - - 14.659 0.008 0.013 0.049 0.007 0.8440.50 36639 0.08 0.223 70.2 29.65 14.563 0.00 50 67.9 0.0074 8.95 0.95 1.065 68.9 0 - - - - - - - 14.695 0.008 0.018 0.049 0.009 0.8450.50 42403 0.08 0.223 69.8 29.65 14.563 0.00 60 65.7 0.0085 11.70 1.25 1.086 67.7 0 - - - - - - - 14.735 0.008 0.024 0.049 0.010 0.8550.50 47980 0.08 0.223 69.8 29.65 14.563 0.00 70 68.1 0.0096 15.10 1.61 1.110 68.1 0 - - - - - - - 14.782 0.008 0.030 0.049 0.011 0.8530.50 53568 0.08 0.223 69.8 29.65 14.563 0.00 80 69.8 0.0108 18.65 1.99 1.136 67.8 0 - - - - - - - 14.831 0.008 0.037 0.049 0.013 0.8580.50 11173 0.08 0.223 70.7 29.65 14.563 0.63 5 61.2 0.0022 3.75 0.11 1.008 69.6 10 67.8 0.0218 2.30 0.07 2.40 0.07 69.4 14.579 0.008 0.002 0.049 0.003 0.7520.50 14029 0.08 0.223 70.7 29.65 14.563 0.50 10 61.2 0.0028 5.15 0.15 1.011 69.5 10 68.9 0.0218 2.45 0.07 2.60 0.08 69.4 14.585 0.008 0.003 0.049 0.004 0.8050.50 19704 0.08 0.223 70.7 29.65 14.563 0.36 20 63.1 0.0040 9.30 0.28 1.019 69.3 10 70.4 0.0217 2.80 0.08 3.00 0.09 69.8 14.602 0.008 0.005 0.049 0.005 0.8420.50 25379 0.08 0.223 70.2 29.65 14.563 0.28 30 64.2 0.0051 14.70 0.44 1.030 68.6 10 70.1 0.0217 3.20 0.10 3.30 0.10 70.2 14.625 0.008 0.009 0.049 0.006 0.8620.50 31020 0.08 0.223 70.2 29.65 14.563 0.23 40 66.0 0.0062 22.20 0.66 1.045 68.8 10 71.3 0.0217 3.50 0.10 3.70 0.11 70.5 14.655 0.008 0.013 0.049 0.007 0.8580.50 36643 0.08 0.223 70.2 29.65 14.563 0.19 50 67.8 0.0074 8.40 0.89 1.061 69.0 10 72.0 0.0217 3.85 0.11 4.00 0.12 70.9 14.687 0.008 0.017 0.049 0.008 0.8730.50 42391 0.08 0.223 69.8 29.65 14.563 0.17 60 66.0 0.0085 11.65 1.24 1.085 67.6 10 68.2 0.0218 4.30 0.13 4.40 0.13 68.7 14.734 0.008 0.024 0.049 0.010 0.8570.50 47962 0.08 0.223 69.8 29.65 14.563 0.15 70 68.5 0.0096 15.15 1.61 1.111 67.2 10 70.0 0.0217 4.65 0.14 4.80 0.14 69.1 14.783 0.008 0.030 0.049 0.011 0.8510.50 53563 0.08 0.223 69.8 29.65 14.563 0.13 80 69.9 0.0108 18.80 2.00 1.137 67.6 10 70.4 0.0217 5.05 0.15 5.15 0.15 69.4 14.833 0.008 0.037 0.049 0.013 0.8540.50 11183 0.08 0.223 70.7 29.65 14.563 0.89 5 60.3 0.0022 4.80 0.14 1.010 70.0 20 68.2 0.0306 4.10 0.12 4.30 0.13 69.2 14.583 0.008 0.003 0.049 0.003 0.6650.50 14029 0.08 0.223 70.7 29.65 14.563 0.71 10 61.2 0.0028 6.30 0.19 1.013 69.4 20 69.4 0.0306 4.30 0.13 4.50 0.13 69.5 14.589 0.008 0.004 0.049 0.004 0.7280.50 19682 0.08 0.223 70.7 29.65 14.563 0.51 20 64.3 0.0040 9.90 0.30 1.020 69.2 20 70.5 0.0306 4.75 0.14 4.90 0.15 69.9 14.605 0.008 0.006 0.049 0.005 0.8150.50 25376 0.08 0.223 70.2 29.65 14.563 0.39 30 64.3 0.0051 14.80 0.44 1.030 68.6 20 70.3 0.0306 5.25 0.16 5.30 0.16 70.2 14.625 0.008 0.009 0.049 0.006 0.8590.50 31014 0.08 0.223 70.2 29.65 14.563 0.32 40 66.2 0.0062 21.60 0.64 1.044 68.9 20 71.4 0.0305 5.70 0.17 5.80 0.17 70.5 14.653 0.008 0.012 0.049 0.007 0.8700.50 36643 0.08 0.223 70.2 29.65 14.563 0.27 50 67.8 0.0074 8.35 0.89 1.061 68.9 20 72.0 0.0305 6.20 0.18 6.30 0.19 70.9 14.687 0.008 0.017 0.049 0.008 0.8750.50 42375 0.08 0.223 69.8 29.65 14.563 0.24 60 66.4 0.0085 11.15 1.19 1.082 67.6 20 68.1 0.0306 6.65 0.20 6.75 0.20 68.7 14.727 0.008 0.023 0.049 0.010 0.8750.50 47958 0.08 0.223 69.8 29.65 14.563 0.21 70 68.6 0.0096 14.60 1.55 1.107 66.1 20 69.7 0.0306 7.25 0.22 7.40 0.22 69.1 14.775 0.008 0.029 0.049 0.011 0.8650.50 53553 0.08 0.223 69.8 29.65 14.563 0.19 80 70.1 0.0108 18.40 1.96 1.135 67.1 20 70.2 0.0306 7.80 0.23 7.95 0.24 69.5 14.828 0.008 0.037 0.049 0.012 0.8630.50 11185 0.08 0.223 70.7 29.65 14.563 1.15 5 60.1 0.0022 6.10 0.18 1.012 69.9 30 69.0 0.0395 6.50 0.19 6.70 0.20 68.9 14.589 0.008 0.004 0.049 0.004 0.5900.50 14026 0.08 0.223 70.7 29.65 14.563 0.92 10 61.4 0.0028 7.80 0.23 1.016 69.4 30 69.5 0.0395 6.80 0.20 7.00 0.21 69.2 14.596 0.008 0.005 0.049 0.004 0.6540.50 19687 0.08 0.223 70.7 29.65 14.563 0.65 20 64.0 0.0040 11.50 0.34 1.024 69.2 30 70.5 0.0394 7.25 0.22 7.40 0.22 69.8 14.611 0.008 0.007 0.049 0.005 0.7560.50 25374 0.08 0.223 70.2 29.65 14.563 0.51 30 64.4 0.0051 16.10 0.48 1.033 68.7 30 70.7 0.0394 7.80 0.23 8.00 0.24 70.1 14.630 0.008 0.009 0.049 0.006 0.8240.50 31011 0.08 0.223 70.2 29.65 14.563 0.41 40 66.3 0.0062 22.15 0.66 1.045 68.8 30 71.4 0.0394 8.35 0.25 8.55 0.25 70.5 14.655 0.008 0.013 0.049 0.007 0.8590.50 36636 0.08 0.223 70.2 29.65 14.563 0.35 50 68.0 0.0074 8.40 0.89 1.061 69.0 30 72.1 0.0394 8.85 0.26 9.10 0.27 71.0 14.687 0.008 0.017 0.049 0.008 0.8730.50 42367 0.08 0.223 69.8 29.65 14.563 0.30 60 66.6 0.0085 11.00 1.17 1.080 67.5 30 69.0 0.0395 9.40 0.28 9.60 0.29 68.6 14.725 0.008 0.022 0.049 0.010 0.8810.50 47958 0.08 0.223 69.8 29.65 14.563 0.27 70 68.6 0.0096 14.30 1.52 1.105 66.0 30 69.7 0.0394 10.15 0.30 10.35 0.31 69.1 14.771 0.008 0.029 0.049 0.011 0.8740.50 53553 0.08 0.223 69.8 29.65 14.563 0.24 80 70.1 0.0108 17.85 1.90 1.131 67.1 30 70.5 0.0394 10.80 0.32 11.00 0.33 69.6 14.820 0.008 0.036 0.049 0.012 0.8760.50 11185 0.08 0.223 70.7 29.65 14.563 1.41 5 60.1 0.0022 7.65 0.23 1.016 69.9 40 69.4 0.0483 9.40 0.28 9.70 0.29 68.8 14.595 0.008 0.004 0.049 0.004 0.5270.50 14023 0.08 0.223 70.7 29.65 14.563 1.12 10 61.6 0.0028 9.30 0.28 1.019 69.4 40 69.9 0.0483 9.60 0.29 9.90 0.30 69.1 14.602 0.008 0.005 0.049 0.005 0.5990.50 19682 0.08 0.223 70.7 29.65 14.563 0.80 20 64.3 0.0040 13.30 0.40 1.027 69.3 40 70.9 0.0482 10.20 0.30 10.40 0.31 69.8 14.619 0.008 0.008 0.049 0.006 0.7030.50 25374 0.08 0.223 70.2 29.65 14.563 0.62 30 64.4 0.0051 18.10 0.54 1.037 68.7 40 71.0 0.0482 10.70 0.32 11.00 0.33 70.0 14.639 0.008 0.010 0.049 0.007 0.7770.50 31014 0.08 0.223 70.2 29.65 14.563 0.51 40 66.2 0.0062 23.80 0.71 1.049 68.8 40 71.8 0.0482 11.40 0.34 11.70 0.35 70.5 14.662 0.008 0.014 0.049 0.008 0.8290.50 36636 0.08 0.223 70.2 29.65 14.563 0.43 50 68.0 0.0074 8.65 0.92 1.063 69.0 40 72.5 0.0482 12.00 0.36 12.30 0.37 70.9 14.691 0.008 0.018 0.049 0.009 0.8600.50 42351 0.08 0.223 69.8 29.65 14.563 0.37 60 67.0 0.0085 11.05 1.18 1.081 67.7 40 69.4 0.0483 12.50 0.37 12.80 0.38 68.6 14.725 0.008 0.022 0.049 0.010 0.8790.50 47953 0.08 0.223 69.8 29.65 14.563 0.33 70 68.7 0.0096 14.30 1.52 1.105 66.6 40 69.9 0.0483 13.35 0.40 1.65 0.05 69.1 14.771 0.008 0.029 0.049 0.011 0.8750.50 53548 0.08 0.223 69.8 29.65 14.563 0.29 80 70.2 0.0108 17.75 1.89 1.130 67.1 40 70.7 0.0483 14.15 0.42 14.45 0.43 69.6 14.819 0.008 0.035 0.049 0.012 0.8780.50 11184 0.08 0.223 70.7 29.65 14.563 1.66 5 60.2 0.0022 9.20 0.27 1.019 69.8 50 69.9 0.0571 12.60 0.38 13.00 0.39 68.8 14.602 0.008 0.005 0.049 0.005 0.4810.50 14017 0.08 0.223 70.7 29.65 14.563 1.33 10 62.1 0.0028 11.10 0.33 1.023 69.4 50 70.7 0.0571 12.90 0.38 13.30 0.40 69.2 14.610 0.008 0.006 0.049 0.005 0.5480.50 19702 0.08 0.223 70.7 29.65 14.563 0.94 20 63.2 0.0040 15.35 0.46 1.031 69.3 50 71.5 0.0571 13.40 0.40 13.80 0.41 69.9 14.627 0.008 0.009 0.049 0.006 0.6560.50 25366 0.08 0.223 70.2 29.65 14.563 0.73 30 64.7 0.0051 20.25 0.60 1.041 68.7 50 71.7 0.0570 1.95 0.06 14.35 0.43 70.1 14.647 0.008 0.012 0.049 0.007 0.735

Pamb Jet Plen Pres Cross Cir Pres Cross Plen Pres

68

z/d Jet Re Jet Ven Dia Cross Ven Dia Tamb G Ratio Jet Ven Pres Jet Ven Temp Jet Ven Mdot Jet P Ratio Jet Plen Temp Cross Ven Pres Cross Ven Temp Cross Ven Mdot Cross Plen Temp AA BB CC DD Mdot Isen CdInches Inches F In Hg Psia Psig F lb/s In Oil Psig F Psig F lb/s In Oil Psig In Oil Psig F

0.50 31011 0.08 0.223 70.2 29.65 14.563 0.60 40 66.3 0.0062 26.05 0.78 1.053 68.8 50 72.5 0.0570 14.7 0.44 15.1 0.45 70.5 14.671 0.008 0.015 0.049 0.008 0.7920.50 36633 0.08 0.223 70.2 29.65 14.563 0.51 50 68.1 0.0074 9.20 0.98 1.067 69.1 50 72.9 0.0570 15.45 0.46 15.90 0.47 70.9 14.699 0.008 0.019 0.049 0.009 0.8340.50 42343 0.08 0.223 69.8 29.65 14.563 0.44 60 67.2 0.0085 11.45 1.22 1.084 67.7 50 70.3 0.0571 16.05 0.48 16.45 0.49 68.7 14.731 0.008 0.023 0.049 0.010 0.8630.50 47944 0.08 0.223 69.8 29.65 14.563 0.39 70 68.9 0.0096 14.50 1.54 1.106 66.8 50 70.8 0.0571 17.00 0.51 17.40 0.52 69.1 14.774 0.008 0.029 0.049 0.011 0.8690.50 53543 0.08 0.223 69.8 29.65 14.563 0.35 80 70.3 0.0108 17.85 1.90 1.131 66.9 50 71.3 0.0571 17.80 0.53 18.20 0.54 69.5 14.820 0.008 0.036 0.049 0.012 0.8750.50 11184 0.08 0.223 70.7 29.65 14.563 1.92 5 60.2 0.0022 10.85 0.32 1.022 69.7 60 70.3 0.0660 16.25 0.48 16.80 0.50 68.9 14.609 0.008 0.006 0.049 0.005 0.4430.50 14014 0.08 0.223 70.7 29.65 14.563 1.53 10 62.3 0.0028 12.95 0.39 1.027 69.4 60 71.1 0.0659 16.55 0.49 17.10 0.51 69.3 14.617 0.008 0.008 0.049 0.006 0.5080.50 19712 0.08 0.223 70.7 29.65 14.563 1.09 20 62.7 0.0040 17.50 0.52 1.036 69.2 60 71.9 0.0659 17.15 0.51 17.65 0.53 70.0 14.636 0.008 0.010 0.049 0.006 0.6140.50 25364 0.08 0.223 70.2 29.65 14.563 0.85 30 64.8 0.0051 22.60 0.67 1.046 68.9 60 72.1 0.0659 17.70 0.53 18.25 0.54 70.2 14.657 0.008 0.013 0.049 0.007 0.6960.50 31000 0.08 0.223 70.2 29.65 14.563 0.69 40 66.7 0.0062 28.55 0.85 1.058 68.9 60 72.7 0.0658 18.40 0.55 18.95 0.57 70.7 14.681 0.008 0.016 0.049 0.008 0.7570.50 36629 0.08 0.223 70.2 29.65 14.563 0.58 50 68.2 0.0074 9.95 1.06 1.073 69.1 60 73.4 0.0658 19.40 0.58 19.95 0.59 71.0 14.710 0.008 0.020 0.049 0.009 0.8020.50 42331 0.08 0.223 69.8 29.65 14.563 0.51 60 67.5 0.0085 12.10 1.29 1.088 67.8 60 70.7 0.0659 20.25 0.60 20.75 0.62 68.7 14.740 0.008 0.025 0.049 0.010 0.8400.50 47940 0.08 0.223 69.8 29.65 14.563 0.45 70 69.0 0.0096 14.90 1.59 1.109 67.1 60 71.0 0.0659 21.05 0.63 21.60 0.64 69.1 14.779 0.008 0.030 0.049 0.011 0.8570.50 53533 0.08 0.223 69.8 29.65 14.563 0.40 80 70.5 0.0108 18.15 1.93 1.133 67.3 60 71.7 0.0659 21.95 0.65 22.45 0.67 69.6 14.824 0.008 0.036 0.049 0.012 0.8680.50 11182 0.08 0.223 70.7 29.65 14.563 2.18 5 60.4 0.0022 12.70 0.38 1.026 69.9 70 70.8 0.0748 20.60 0.61 21.25 0.63 68.8 14.616 0.008 0.007 0.049 0.005 0.4090.50 14013 0.08 0.223 70.7 29.65 14.563 1.74 10 62.4 0.0028 15.05 0.45 1.031 69.4 70 71.6 0.0747 21.05 0.63 21.70 0.65 69.4 14.626 0.008 0.009 0.049 0.006 0.4710.50 19699 0.08 0.223 70.7 29.65 14.563 1.23 20 63.4 0.0040 19.80 0.59 1.041 69.1 70 72.6 0.0747 21.50 0.64 22.15 0.66 70.1 14.646 0.008 0.011 0.049 0.007 0.5770.50 25359 0.08 0.223 70.2 29.65 14.563 0.96 30 65.0 0.0051 25.20 0.75 1.052 68.9 70 72.6 0.0747 22.30 0.66 22.95 0.68 70.2 14.668 0.008 0.014 0.049 0.008 0.6590.50 30988 0.08 0.223 70.2 29.65 14.563 0.78 40 67.1 0.0062 8.70 0.93 1.064 68.9 70 73.5 0.0746 23.05 0.69 23.70 0.71 70.8 14.692 0.008 0.018 0.049 0.009 0.7250.50 36622 0.08 0.223 70.2 29.65 14.563 0.66 50 68.4 0.0074 10.80 1.15 1.079 69.2 70 73.6 0.0746 24.10 0.72 24.75 0.74 71.1 14.722 0.008 0.022 0.049 0.010 0.7700.50 42326 0.08 0.223 69.8 29.65 14.563 0.57 60 67.6 0.0085 12.95 1.38 1.095 68.0 70 71.0 0.0748 24.95 0.74 25.60 0.76 68.7 14.752 0.008 0.026 0.049 0.010 0.8120.50 47935 0.08 0.223 69.8 29.65 14.563 0.51 70 69.1 0.0096 15.60 1.66 1.114 67.3 70 71.8 0.0747 25.85 0.77 26.45 0.79 69.3 14.789 0.008 0.031 0.049 0.012 0.8380.50 53528 0.08 0.223 69.8 29.65 14.563 0.45 80 70.6 0.0108 18.65 1.99 1.136 67.1 70 72.3 0.0747 26.90 0.80 27.55 0.82 69.7 14.831 0.008 0.037 0.049 0.013 0.8560.50 11181 0.08 0.223 70.7 29.65 14.563 2.43 5 60.5 0.0022 14.60 0.44 1.030 69.7 80 71.0 0.0836 25.20 0.75 26.05 0.78 68.8 14.624 0.008 0.008 0.049 0.006 0.3820.50 14010 0.08 0.223 70.7 29.65 14.563 1.94 10 62.6 0.0028 17.05 0.51 1.035 69.4 80 72.0 0.0835 25.60 0.76 26.45 0.79 69.5 14.634 0.008 0.010 0.049 0.006 0.4420.50 19700 0.08 0.223 70.7 29.65 14.563 1.38 20 63.3 0.0040 22.15 0.66 1.045 69.2 80 73.0 0.0835 26.30 0.78 27.10 0.81 70.3 14.655 0.008 0.013 0.049 0.007 0.5460.50 25350 0.08 0.223 70.2 29.65 14.563 1.07 30 65.4 0.0051 27.80 0.83 1.057 69.0 80 73.1 0.0834 27.00 0.81 27.85 0.83 70.4 14.678 0.008 0.016 0.049 0.008 0.6270.50 30988 0.08 0.223 70.2 29.65 14.563 0.88 40 67.1 0.0062 9.55 1.02 1.070 69.1 80 73.9 0.0834 27.90 0.83 28.65 0.85 70.9 14.704 0.008 0.019 0.049 0.009 0.6920.50 36619 0.08 0.223 70.2 29.65 14.563 0.74 50 68.5 0.0074 11.65 1.24 1.085 69.3 80 74.4 0.0833 28.80 0.86 29.60 0.88 71.3 14.734 0.008 0.024 0.049 0.010 0.7410.50 42310 0.08 0.223 69.8 29.65 14.563 0.64 60 68.0 0.0085 13.80 1.47 1.101 68.0 80 71.3 0.0836 29.75 0.89 30.60 0.91 68.9 14.764 0.008 0.028 0.049 0.011 0.7870.50 47917 0.08 0.223 69.8 29.65 14.563 0.57 70 69.5 0.0096 16.45 1.75 1.120 67.8 80 72.0 0.0835 8.55 0.91 8.80 0.94 69.4 14.801 0.008 0.033 0.049 0.012 0.8160.50 53518 0.08 0.223 69.8 29.65 14.563 0.51 80 70.8 0.0108 19.35 2.06 1.142 67.7 80 72.5 0.0835 8.85 0.94 9.10 0.97 69.9 14.841 0.008 0.039 0.049 0.013 0.8410.80 11194 0.08 - 72.5 30.05 14.759 0 5 69.7 0.0023 2.95 0.09 1.006 71.4 - - - - - - - - 14.772 0.008 0.002 0.049 0.003 0.8450.80 14012 0.08 - 72.5 30.05 14.759 0.00 10 70.8 0.0028 4.65 0.14 1.009 72.4 - - - - - - - - 14.779 0.008 0.003 0.049 0.003 0.8430.80 19676 0.08 - 72.5 30.05 14.759 0.00 20 70.6 0.0040 9.05 0.27 1.018 72.5 - - - - - - - - 14.797 0.008 0.005 0.049 0.005 0.8490.80 25334 0.08 - 73.4 30.05 14.759 0.00 30 70.7 0.0051 14.90 0.44 1.030 72.5 - - - - - - - - 14.822 0.008 0.009 0.049 0.006 0.8520.80 30976 0.08 - 73.4 30.05 14.759 0.00 40 71.3 0.0062 22.10 0.66 1.045 72.4 - - - - - - - - 14.852 0.008 0.013 0.049 0.007 0.8560.80 36616 0.08 - 73.4 30.05 14.759 0.00 50 71.8 0.0074 30.80 0.92 1.062 72.4 - - - - - - - - 14.887 0.008 0.017 0.049 0.009 0.8580.80 42250 0.08 - 73.4 30.05 14.759 0.00 60 72.3 0.0085 11.40 1.21 1.082 72.4 - - - - - - - - 14.927 0.008 0.023 0.049 0.010 0.8610.80 47911 0.08 - 73.4 30.05 14.759 0.00 70 72.1 0.0096 14.65 1.56 1.106 72.2 - - - - - - - - 14.973 0.008 0.029 0.049 0.011 0.8620.80 11193 0.08 0.223 72.5 30.05 14.759 0.40 5 69.8 0.0023 2.90 0.09 1.006 71.6 10 69.4 0.0219 0.85 0.03 0.90 0.03 71.0 14.772 0.008 0.002 0.049 0.003 0.8520.80 14012 0.08 0.223 72.5 30.05 14.759 0.32 10 70.8 0.0028 4.40 0.13 1.009 72.4 10 70.8 0.0219 0.90 0.03 0.95 0.03 71.9 14.778 0.008 0.003 0.049 0.003 0.8670.80 19672 0.08 0.223 72.5 30.05 14.759 0.23 20 70.8 0.0040 8.65 0.26 1.017 72.5 10 71.0 0.0219 1.05 0.03 1.10 0.03 72.1 14.796 0.008 0.005 0.049 0.005 0.8680.80 25334 0.08 0.223 73.4 30.05 14.759 0.18 30 70.7 0.0051 14.85 0.44 1.030 72.5 10 69.8 0.0219 1.15 0.03 1.25 0.04 72.5 14.822 0.008 0.008 0.049 0.006 0.8540.80 30979 0.08 0.223 73.4 30.05 14.759 0.14 40 71.2 0.0062 22.00 0.66 1.044 72.5 10 71.0 0.0219 1.35 0.04 1.40 0.04 71.8 14.851 0.008 0.013 0.049 0.007 0.8580.80 36612 0.08 0.223 73.4 30.05 14.759 0.12 50 71.9 0.0074 30.60 0.91 1.062 72.4 10 71.6 0.0219 1.45 0.04 1.50 0.04 72.0 14.886 0.008 0.017 0.049 0.009 0.8600.80 42270 0.08 0.223 73.4 30.05 14.759 0.11 60 71.8 0.0085 11.50 1.22 1.083 72.2 10 71.0 0.0219 1.60 0.05 1.65 0.05 72.9 14.928 0.008 0.023 0.049 0.010 0.8580.80 47807 0.08 0.223 73.4 30.05 14.759 0.09 70 74.4 0.0096 14.55 1.55 1.105 72.9 10 74.5 0.0218 1.75 0.05 1.80 0.05 73.7 14.971 0.008 0.029 0.049 0.011 0.8640.80 11192 0.08 0.223 72.5 30.05 14.759 0.56 5 69.9 0.0023 3.20 0.10 1.006 71.6 20 69.0 0.0308 1.45 0.04 1.55 0.05 71.0 14.773 0.008 0.002 0.049 0.003 0.811

Pamb Jet Plen Pres Cross Cir Pres Cross Plen Pres

69

z/d Jet Re Jet Ven Dia Cross Ven Dia Tamb G Ratio Jet Ven Pres Jet Ven Temp Jet Ven Mdot Jet P Ratio Jet Plen Temp Cross Ven Pres Cross Ven Temp Cross Ven Mdot Cross Plen Temp AA BB CC DD Mdot Isen CdInches Inches F In Hg Psia Psig F lb/s In Oil Psig F Psig F lb/s In Oil Psig In Oil Psig F

0.80 14014 0.08 0.223 72.5 30.05 14.759 0.45 10 70.7 0.0028 4.55 0.14 1.009 72.4 20 70.5 0.0307 1.50 0.04 1.60 0.05 71.8 14.778 0.008 0.003 0.049 0.003 0.8520.80 19674 0.08 0.223 72.5 30.05 14.759 0.32 20 70.7 0.0040 8.30 0.25 1.017 72.4 20 71.2 0.0307 1.65 0.05 1.75 0.05 72.0 14.794 0.008 0.005 0.049 0.004 0.8860.80 25336 0.08 0.223 73.4 30.05 14.759 0.25 30 70.6 0.0051 14.05 0.42 1.028 72.9 20 70.1 0.0308 1.80 0.05 1.95 0.06 72.3 14.818 0.008 0.008 0.049 0.006 0.8780.80 30976 0.08 0.223 73.4 30.05 14.759 0.20 40 71.3 0.0062 21.25 0.63 1.043 72.3 20 71.4 0.0307 2.00 0.06 2.15 0.06 71.7 14.848 0.008 0.012 0.049 0.007 0.8730.80 36616 0.08 0.223 73.4 30.05 14.759 0.17 50 71.8 0.0074 30.10 0.90 1.061 72.3 20 71.8 0.0307 2.20 0.07 2.30 0.07 72.1 14.884 0.008 0.017 0.049 0.008 0.8680.80 42278 0.08 0.223 73.4 30.05 14.759 0.15 60 71.6 0.0085 11.30 1.20 1.082 72.1 20 71.1 0.0307 2.45 0.07 2.55 0.08 72.7 14.925 0.008 0.023 0.049 0.010 0.8660.80 47803 0.08 0.223 73.4 30.05 14.759 0.13 70 74.5 0.0096 14.50 1.54 1.105 72.8 20 74.9 0.0306 2.60 0.08 2.80 0.08 73.7 14.970 0.008 0.029 0.049 0.011 0.8650.80 11191 0.08 0.223 72.5 30.05 14.759 0.72 5 70.0 0.0023 3.60 0.11 1.007 71.7 30 69.6 0.0396 2.25 0.07 2.45 0.07 70.5 14.774 0.008 0.002 0.049 0.003 0.7650.80 14014 0.08 0.223 72.5 30.05 14.759 0.57 10 70.7 0.0028 4.90 0.15 1.010 72.4 30 70.8 0.0396 2.25 0.07 2.45 0.07 71.6 14.780 0.008 0.003 0.049 0.003 0.8210.80 19672 0.08 0.223 72.5 30.05 14.759 0.41 20 70.8 0.0040 8.50 0.25 1.017 72.4 30 71.1 0.0396 2.50 0.07 2.70 0.08 71.7 14.795 0.008 0.005 0.049 0.005 0.8760.80 25331 0.08 0.223 73.4 30.05 14.759 0.32 30 70.8 0.0051 13.75 0.41 1.028 72.9 30 70.1 0.0396 2.60 0.08 2.80 0.08 71.6 14.817 0.008 0.008 0.049 0.006 0.8870.80 30973 0.08 0.223 73.4 30.05 14.759 0.26 40 71.4 0.0062 20.50 0.61 1.041 72.3 30 71.3 0.0396 2.85 0.08 3.05 0.09 71.7 14.845 0.008 0.012 0.049 0.007 0.8890.80 36612 0.08 0.223 73.4 30.05 14.759 0.22 50 71.9 0.0074 29.05 0.87 1.059 72.3 30 71.8 0.0395 3.10 0.09 3.30 0.10 72.0 14.880 0.008 0.016 0.049 0.008 0.8830.80 42282 0.08 0.223 73.4 30.05 14.759 0.19 60 71.5 0.0085 11.05 1.18 1.080 72.1 30 71.5 0.0396 3.40 0.10 3.60 0.11 72.3 14.922 0.008 0.022 0.049 0.010 0.8750.80 47807 0.08 0.223 73.4 30.05 14.759 0.17 70 74.4 0.0096 14.25 1.52 1.103 72.8 30 75.3 0.0394 3.60 0.11 3.80 0.11 73.6 14.967 0.008 0.028 0.049 0.011 0.8730.80 11191 0.08 0.223 72.5 30.05 14.759 0.58 5 70.0 0.0023 4.05 0.12 1.008 71.9 40 770.3 0.0318 3.15 0.09 3.45 0.10 70.4 14.776 0.008 0.002 0.049 0.003 0.7210.80 14015 0.08 0.223 72.5 30.05 14.759 0.70 10 70.6 0.0028 5.35 0.16 1.011 72.4 40 71.0 0.0484 3.20 0.10 3.50 0.10 71.3 14.782 0.008 0.003 0.049 0.004 0.7860.80 19674 0.08 0.223 72.5 30.05 14.759 0.50 20 70.7 0.0040 8.95 0.27 1.018 72.4 40 71.4 0.0484 3.40 0.10 3.70 0.11 71.5 14.797 0.008 0.005 0.049 0.005 0.8540.80 25334 0.08 0.223 73.4 30.05 14.759 0.39 30 70.7 0.0051 13.85 0.41 1.028 72.4 40 70.3 0.0484 3.65 0.11 3.95 0.12 71.4 14.817 0.008 0.008 0.049 0.006 0.8840.80 30970 0.08 0.223 73.4 30.05 14.759 0.32 40 71.5 0.0062 20.25 0.60 1.041 72.6 40 71.7 0.0484 3.85 0.11 4.10 0.12 71.6 14.844 0.008 0.012 0.049 0.007 0.8940.80 36612 0.08 0.223 73.4 30.05 14.759 0.27 50 71.9 0.0074 28.45 0.85 1.057 72.3 40 72.2 0.0484 4.05 0.12 4.35 0.13 71.8 14.877 0.008 0.016 0.049 0.008 0.8920.80 42270 0.08 0.223 73.4 30.05 14.759 0.23 60 71.8 0.0085 10.80 1.15 1.078 72.0 40 72.0 0.0484 4.40 0.13 4.70 0.14 72.1 14.918 0.008 0.022 0.049 0.010 0.8850.80 47812 0.08 0.223 73.4 30.05 14.759 0.21 70 74.3 0.0096 13.85 1.47 1.100 72.7 40 75.4 0.0482 4.65 0.14 4.95 0.15 73.6 14.961 0.008 0.028 0.049 0.011 0.8850.80 11192 0.08 0.223 72.5 30.05 14.759 1.04 5 69.9 0.0023 4.65 0.14 1.009 71.9 50 71.2 0.0572 4.25 0.13 4.65 0.14 70.3 14.779 0.008 0.003 0.049 0.003 0.6730.80 14014 0.08 0.223 72.5 30.05 14.759 0.83 10 70.7 0.0028 5.90 0.18 1.012 72.4 50 71.9 0.0572 4.25 0.13 4.65 0.14 71.0 14.784 0.008 0.003 0.049 0.004 0.7490.80 19674 0.08 0.223 72.5 30.05 14.759 0.59 20 70.7 0.0040 9.50 0.28 1.019 72.5 50 72.1 0.0572 4.45 0.13 4.85 0.14 71.3 14.799 0.008 0.005 0.049 0.005 0.8290.80 25329 0.08 0.223 73.4 30.05 14.759 0.46 30 70.9 0.0051 14.35 0.43 1.029 72.5 50 71.5 0.0572 4.75 0.14 5.15 0.15 71.0 14.820 0.008 0.008 0.049 0.006 0.8680.80 30962 0.08 0.223 73.4 30.05 14.759 0.38 40 71.8 0.0062 20.40 0.61 1.041 72.7 50 72.2 0.0572 5.00 0.15 5.35 0.16 71.3 14.845 0.008 0.012 0.049 0.007 0.8910.80 36612 0.08 0.223 73.4 30.05 14.759 0.32 50 71.9 0.0074 28.20 0.84 1.057 72.3 50 72.7 0.0572 5.25 0.16 5.60 0.17 71.8 14.876 0.008 0.016 0.049 0.008 0.8960.80 42266 0.08 0.223 73.4 30.05 14.759 0.28 60 71.9 0.0085 10.60 1.13 1.076 72.0 50 72.7 0.0572 5.55 0.17 5.90 0.18 71.9 14.915 0.008 0.021 0.049 0.010 0.8930.80 47821 0.08 0.223 73.4 30.05 14.759 0.24 70 74.1 0.0096 13.60 1.45 1.098 72.7 50 75.7 0.0570 5.80 0.17 6.20 0.18 73.6 14.958 0.008 0.027 0.049 0.011 0.8930.80 11192 0.08 0.223 72.5 30.05 14.759 1.20 5 69.9 0.0023 5.25 0.16 1.011 72.0 60 71.6 0.0661 5.45 0.16 6.00 0.18 70.5 14.781 0.008 0.003 0.049 0.004 0.6340.80 14016 0.08 0.223 72.5 30.05 14.759 0.96 10 70.5 0.0028 6.55 0.20 1.013 72.4 60 72.3 0.0660 5.50 0.16 6.00 0.18 71.1 14.787 0.008 0.004 0.049 0.004 0.7110.80 19670 0.08 0.223 72.5 30.05 14.759 0.68 20 70.9 0.0040 10.15 0.30 1.021 72.5 60 72.4 0.0660 5.70 0.17 6.20 0.18 71.2 14.802 0.008 0.006 0.049 0.005 0.8020.80 25329 0.08 0.223 73.4 30.05 14.759 0.53 30 70.9 0.0051 15.00 0.45 1.030 72.4 60 71.9 0.0660 6.00 0.18 6.50 0.19 71.0 14.822 0.008 0.009 0.049 0.006 0.8490.80 30968 0.08 0.223 73.4 30.05 14.759 0.43 40 71.6 0.0062 20.80 0.62 1.042 72.3 60 72.6 0.0660 6.25 0.19 6.80 0.20 71.4 14.846 0.008 0.012 0.049 0.007 0.8820.80 36609 0.08 0.223 73.4 30.05 14.759 0.37 50 72.0 0.0074 28.25 0.84 1.057 72.3 60 73.0 0.0660 6.55 0.20 7.10 0.21 71.8 14.877 0.008 0.016 0.049 0.008 0.8950.80 42258 0.08 0.223 73.4 30.05 14.759 0.32 60 72.1 0.0085 10.50 1.12 1.076 72.0 60 72.9 0.0660 6.80 0.20 7.35 0.22 71.9 14.914 0.008 0.021 0.049 0.009 0.8970.80 47830 0.08 0.223 73.4 30.05 14.759 0.28 70 73.9 0.0096 13.45 1.43 1.097 72.7 60 75.8 0.0658 7.20 0.21 7.70 0.23 73.4 14.956 0.008 0.027 0.049 0.011 0.8990.80 11190 0.08 0.223 72.5 30.05 14.759 1.36 5 70.1 0.0023 6.00 0.18 1.012 72.0 70 72.4 0.0748 6.90 0.21 7.55 0.23 70.6 14.785 0.008 0.003 0.049 0.004 0.5930.80 14014 0.08 0.223 72.5 30.05 14.759 1.09 10 70.7 0.0028 7.30 0.22 1.015 72.4 70 72.7 0.0748 6.85 0.20 7.50 0.22 71.0 14.790 0.008 0.004 0.049 0.004 0.6730.80 19668 0.08 0.223 72.5 30.05 14.759 0.77 20 71.0 0.0040 10.90 0.33 1.022 72.5 70 72.9 0.0748 7.15 0.21 7.80 0.23 71.3 14.805 0.008 0.006 0.049 0.005 0.7730.80 25293 0.08 0.223 73.4 30.05 14.759 0.60 30 72.4 0.0051 15.60 0.47 1.032 72.7 70 74.8 0.0747 7.45 0.22 8.10 0.24 72.4 14.825 0.008 0.009 0.049 0.006 0.8320.80 30968 0.08 0.223 73.4 30.05 14.759 0.49 40 71.6 0.0062 21.60 0.64 1.044 72.7 70 75.2 0.0746 7.75 0.23 8.40 0.25 72.8 14.850 0.008 0.012 0.049 0.007 0.8660.80 36578 0.08 0.223 73.4 30.05 14.759 0.42 50 72.9 0.0074 28.75 0.86 1.058 72.6 70 75.2 0.0746 8.10 0.24 8.75 0.26 72.9 14.879 0.008 0.016 0.049 0.008 0.8870.80 42254 0.08 0.223 73.4 30.05 14.759 0.36 60 72.2 0.0085 10.50 1.12 1.076 72.1 70 73.5 0.0748 8.35 0.25 9.00 0.27 71.8 14.914 0.008 0.021 0.049 0.009 0.8970.80 47839 0.08 0.223 73.4 30.05 14.759 0.32 70 73.7 0.0096 13.40 1.43 1.097 72.6 70 75.8 0.0746 8.70 0.26 9.35 0.28 73.2 14.955 0.008 0.027 0.049 0.011 0.9000.80 11188 0.08 0.223 72.5 30.05 14.759 1.52 5 70.3 0.0022 6.95 0.21 1.014 72.2 80 72.8 0.0836 8.55 0.25 9.30 0.28 70.6 14.789 0.008 0.004 0.049 0.004 0.5510.80 14014 0.08 0.223 72.5 30.05 14.759 1.21 10 70.7 0.0028 8.10 0.24 1.016 72.5 80 73.1 0.0836 8.40 0.25 9.20 0.27 71.1 14.793 0.008 0.005 0.049 0.004 0.6390.80 19666 0.08 0.223 72.5 30.05 14.759 0.86 20 71.1 0.0040 11.70 0.35 1.024 72.5 80 73.3 0.0836 8.65 0.26 9.45 0.28 71.3 14.809 0.008 0.007 0.049 0.005 0.7460.80 25293 0.08 0.223 73.4 30.05 14.759 0.67 30 72.4 0.0051 16.40 0.49 1.033 72.5 80 74.9 0.0835 8.95 0.27 9.80 0.29 72.4 14.828 0.008 0.009 0.049 0.006 0.8110.80 30947 0.08 0.223 73.4 30.05 14.759 0.55 40 72.3 0.0062 22.45 0.67 1.045 72.4 80 74.3 0.0835 9.30 0.28 10.10 0.30 72.0 14.853 0.008 0.013 0.049 0.007 0.8490.80 36599 0.08 0.223 73.4 30.05 14.759 0.46 50 72.3 0.0074 29.40 0.88 1.059 72.3 80 74.3 0.0835 9.65 0.29 10.45 0.31 71.9 14.881 0.008 0.017 0.049 0.008 0.8770.80 42250 0.08 0.223 73.4 30.05 14.759 0.40 60 72.3 0.0085 10.60 1.13 1.076 72.2 80 73.7 0.0836 10.00 0.30 10.80 0.32 71.8 14.915 0.008 0.021 0.049 0.010 0.8930.80 47852 0.08 0.223 73.4 30.05 14.759 0.35 70 73.4 0.0096 13.50 1.44 1.097 72.9 80 76.0 0.0834 10.30 0.31 11.10 0.33 73.1 14.956 0.008 0.027 0.049 0.011 0.897

Pamb Jet Plen Pres Cross Cir Pres Cross Plen Pres

70

15 Appendix F – Jet Impingement Input for Data Reduction Program

Jet Reynolds Number = 15k, Z/D = 0.5 & G = 0

11,93.6,0.125JET HOLE DIAMETER : 0.25 INCHES

NUMBER OF JET HOLES : 1

JET PLATE DISTANCE TO THE TARGET PLATE : 0.125 INCHES

DATE: JUNE 15 ,2010 BRIAN ROBERTS

CAMERA WAS FOCUSSED ON THE BACK SIDE OF THE TARGET PLATE

# Pven Pplen flag Tven Tplen Tamb V1 i1 V2 i2 V3 i3 V4 i4 V5 i5 Pamb5 12.00 5.40 2 70.9 73.1 65.0 28.29 0.1777 30.76 0.0545 30.02 0.0524 29.77 0.0528 30.12 0.0525 30.046 12.00 5.40 2 71.0 73.3 65.0 32.00 0.2007 34.79 0.0614 33.96 0.0589 33.67 0.0596 34.07 0.0587 30.047 12.00 5.40 2 71.0 73.4 65.0 36.75 0.2305 39.96 0.0706 39.00 0.0677 38.67 0.0682 39.13 0.0678 30.048 12.00 5.35 2 71.1 73.6 65.0 41.06 0.2575 44.64 0.0783 43.57 0.0757 43.21 0.0759 43.72 0.0756 30.049 12.00 5.40 2 71.1 73.7 65.0 47.71 0.2982 51.88 0.0914 50.63 0.0876 50.21 0.0881 50.80 0.0873 30.04

10 12.00 5.45 2 71.1 73.7 65.0 52.79 0.3301 57.40 0.1010 56.02 0.0965 55.55 0.0973 56.20 0.0975 30.0411 12.00 5.40 2 71.2 73.8 65.0 58.81 0.3677 63.94 0.1125 62.41 0.1077 61.89 0.1091 62.61 0.1086 30.0412 12.00 5.40 2 71.1 73.8 65.0 69.07 0.4311 75.10 0.1321 73.29 0.1268 72.68 0.1280 73.54 0.1268 30.0413 12.00 5.45 2 71.1 73.8 65.0 75.21 0.4691 81.78 0.1432 79.81 0.1383 79.14 0.1389 80.08 0.1386 30.0414 12.00 5.45 2 71.0 73.8 65.0 80.60 0.5021 87.64 0.1537 85.53 0.1471 84.82 0.1488 85.81 0.1472 30.0415 12.00 5.40 2 71.0 73.8 65.0 84.25 0.5247 91.61 0.1599 89.40 0.1541 88.66 0.1547 89.70 0.1536 30.04

71

Jet Reynolds Number = 20k, Z/D = 0.5 & G = 0

11,93.6,0.125JET HOLE DIAMETER : 0.25 INCHES

NUMBER OF JET HOLES : 1

JET PLATE DISTANCE TO THE TARGET PLATE : 0.125 INCHES

DATE: JUNE 15 ,2010 BRIAN ROBERTS

CAMERA WAS FOCUSSED ON THE BACK SIDE OF THE TARGET PLATE

# Pven Pplen flag Tven Tplen Tamb V1 i1 V2 i2 V3 i3 V4 i4 V5 i5 Pamb16 21.00 9.60 2 71.2 73.2 65.0 27.29 0.1712 29.64 0.0526 0.29 0.0504 28.70 0.0509 29.06 0.0506 30.0417 21.00 9.55 2 71.3 73.3 65.0 32.14 0.2017 34.91 0.0615 0.34 0.0588 33.80 0.0597 34.22 0.0593 30.0418 21.00 9.60 2 71.2 73.4 65.0 36.27 0.2276 39.39 0.0694 0.38 0.0670 38.14 0.0673 38.62 0.0668 30.0419 21.00 9.70 2 71.2 73.4 65.0 41.52 0.2603 45.10 0.0795 0.44 0.0764 43.67 0.0773 44.21 0.0765 30.0420 21.00 9.60 2 71.1 73.4 65.0 46.59 0.2920 50.60 0.0895 0.49 0.0855 49.00 0.0864 49.61 0.0860 30.0421 21.00 9.70 2 71.1 73.4 65.0 52.14 0.3264 56.63 0.0993 0.55 0.0958 54.83 0.0967 55.52 0.0957 30.0422 21.00 9.75 2 71.2 73.5 65.0 59.30 0.3709 64.41 0.1130 0.63 0.1084 62.36 0.1095 63.15 0.1093 30.0423 21.00 9.65 2 71.2 73.5 65.0 67.40 0.4208 73.20 0.1284 0.71 0.1239 70.88 0.1242 71.77 0.1243 30.0424 21.00 9.65 2 71.1 73.4 65.0 75.62 0.4720 82.13 0.1437 0.80 0.1385 79.53 0.1391 80.52 0.1392 30.0425 21.00 9.70 2 71.0 73.4 65.0 85.72 0.5343 93.10 0.1627 0.91 0.1567 90.15 0.1580 91.28 0.1576 30.0426 21.00 9.55 2 71.0 73.4 65.0 89.85 0.5588 97.59 0.1703 0.95 0.1630 94.49 0.1646 95.68 0.1639 30.04

72

Jet Reynolds Number = 15k, Z/D = 0.5 & G = 0.5

18,93.6,0.125JET HOLE DIAMETER : 0.25 INCHES

NUMBER OF JET HOLES : 1

JET PLATE DISTANCE TO THE TARGET PLATE : 0.125 INCHES

DATE: SEPT 25 ,2010 BRIAN ROBERTS

CAMERA WAS FOCUSSED ON THE BACK SIDE OF THE TARGET PLATE

# Pven Pplen flag Tven Tplen Tamb V1 i1 V2 i2 V3 i3 V4 i4 V5 i5 Pamb29 12.00 5.30 2 69.5 71.8 78.0 38.28 0.2405 40.97 0.0749 40.54 0.0757 40.62 0.0756 40.71 0.0754 29.7730 12.00 5.30 2 69.6 71.8 78.0 40.18 0.2523 43.00 0.0786 42.54 0.0794 42.63 0.0793 42.72 0.0791 29.7731 12.00 5.30 2 69.8 71.9 78.0 42.84 0.2687 45.84 0.0837 45.34 0.0846 45.44 0.0845 45.54 0.0843 29.7732 12.00 5.30 2 69.7 72.1 78.0 45.74 0.2867 48.93 0.0893 48.39 0.0903 48.50 0.0901 48.61 0.0899 29.7733 12.00 5.25 2 69.5 72.2 78.0 48.48 0.3037 51.86 0.0946 51.27 0.0957 51.40 0.0955 51.52 0.0953 29.7734 12.00 5.20 2 69.6 71.8 78.0 51.68 0.3235 55.27 0.1008 54.63 0.1020 54.78 0.1017 54.91 0.1015 29.7735 12.00 5.20 2 69.6 71.8 78.0 53.35 0.3338 57.06 0.1040 56.39 0.1053 56.55 0.1050 56.67 0.1047 29.7736 12.00 5.25 2 69.7 71.9 78.0 55.19 0.3452 59.02 0.1076 58.33 0.1089 58.49 0.1086 58.62 0.1083 29.7737 12.00 5.25 2 69.7 71.9 78.0 57.04 0.3567 60.99 0.1112 60.27 0.1125 60.45 0.1122 60.58 0.1119 29.7738 12.00 5.20 2 69.7 72.0 78.0 59.06 0.3692 63.15 0.1151 62.40 0.1165 62.58 0.1161 62.72 0.1159 29.7739 12.00 5.30 2 70.9 72.1 78.0 61.17 0.3822 65.40 0.1192 64.62 0.1206 64.81 0.1202 64.96 0.1200 29.7740 12.00 5.20 2 69.9 72.0 78.0 63.07 0.3940 67.43 0.1228 66.61 0.1243 66.82 0.1240 66.97 0.1237 29.7741 12.00 5.20 2 70.1 71.9 78.0 65.14 0.4068 69.64 0.1268 68.79 0.1284 69.01 0.1280 69.16 0.1277 29.7742 12.00 5.20 2 69.9 72.0 78.0 67.51 0.4215 72.17 0.1314 71.28 0.1331 71.51 0.1326 71.67 0.1323 29.7743 12.00 5.20 2 70.1 72.1 78.0 68.85 0.4298 73.60 0.1340 72.69 0.1357 72.93 0.1352 73.09 0.1349 29.7744 12.00 5.20 2 69.9 72.0 78.0 72.18 0.4504 77.15 0.1405 76.20 0.1422 76.45 0.1417 76.62 0.1414 29.7745 12.00 5.10 2 70.0 72.0 78.0 76.41 0.4766 81.67 0.1486 80.65 0.1505 80.92 0.1500 81.10 0.1497 29.7746 12.00 5.10 2 70.0 72.2 78.0 79.40 0.4951 84.86 0.1544 83.79 0.1564 84.08 0.1558 84.27 0.1555 29.77

73

16 Appendix G – Jet Impingement Photographs

Jet Reynolds Number = 15k, Z/D = 0.5 & G = 0

74

75

Jet Reynolds Number = 20k, Z/D = 0.5 & G = 0

76

77

Jet Reynolds Number = 15k, Z/D = 0.5 & G = 0.5

78