Heat Transfer Experiments in the Internal Cooling Passages ...€¦ · HEAT TRANSFER EXPERIMENTS IN...

NASA Contractor Report 198472

Heat Transfer Experiments in the InternalCooling Passages of a Cooled RadialTurbine Rotor

B.V. Johnson and J.H. Wagner

United Technologies Research Center

East HarO_ord, Connecticut

May 1996

Prepared forLewis Research Center

Under Contract NAS3-25952

f

National Aeronautics and

Space Administration

https://ntrs.nasa.gov/search.jsp?R=19960035825 2020-06-23T05:51:00+00:00Z

FOREWORD

This report covers work performed under NASA Contract NAS-25952 to investigate heat

transfer characteristics of rotating coolant passages of a cooled radial turbine rotor. The NASA Program

Manager is Kestutis Civinskas, NASA Lewis Research Center. Seyf Tanrikut served as the Technical

Program Manager at Pratt & Whitney. Acknowledgments are given to S. Orr, J. Nycz, and the assistance

of colleagues at Pratt & Whitney and UTRC for their contributions to the program.

iii

HEAT TRANSFER EXPERIMENTS

IN THE INTERNAL COOLING PASSAGES

OF A COOLED RADIAL TURBINE ROTOR

TABLE OF CONTENTS

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Summary 1

Introduction 2

2.1 Background 2

2.2 Objectives 3

Description of Apparatus and Experiment3.1 Heat Transfer Model

3.2 Model Instrumentation

3.3 Rotating Heat Transfer Facility

3.4 Experimental Procedures

Experimental Parameters and Test Matrix4. l Flow Parameters

4.2 Geometric Parameters

4.3 Test Conditions

4.4 Outline for Presentation of Results

Heat Transfer Results from Thermocouples5.1 Data and Results for Medium Coolant Flow Rate

5.2 Effects of Rotation on Local Heat Transfer

5.3 Summary of Results from Thermocouple Measurements

Heat Transfer Results from Liquid Crystals

6.1 Results for Stationary Tests

6.2 Results for Rotating Tests

Comparison with Previous AnalysisReferences

Appendix

9.1 Nomenclature

6

6

7

11

16

27

27

28

28

31

32

32

47

58

59

59

64

73

74

79

80

9.2

9.3

9.4

Tablesof Flow Conditions for Full Scale NASA

Radial Turbine and 1.15 Scale Model Coolant Passage

Sample Data Table for Stationary Test Condition and

Medium Flowrate (Test # 6.2, TC 2)

Adjusted Thermocouple Results

ea_ggg

81

93

97

vi

LIST OF TABLES

Table

Table 3-1

Table 4-1Locations of Wall Thermocouples in ModelFlow Conditions for Transient Heat Transfer Tests

14

29

Figure 2-1

Figure 3-1

Figure 3-2

Figure 3-3

Figure 3-4

Figure 3-5

Figure 3-6

Figure 3-7

Figure 3-8

Figure 3-9

Figure 3-10

Figure 3-11

Figure 3-12

Figure 4-1

Figure 5-1

Figure 5-2

LIST OF FIGURES

Sketch of Internal Coolant Passage for NASA LeRC

Cooled High Temperature Radial Turbine Program 5

Internal Passages of NASA LeRC Cooled RadialTurbine Rotor 8

Nomenclature for Internal Passages of NASA LeRCCooled Turbine Rotor 9

Photograph of Leading and Trailing Surfaces

of Coolant Passage Before Assembly 10

Thermocouple Instrumentation for Internal Passagesof NASA LeRC Cooled Turbine Rotor 13

Photograph of Model Mounted in Rotating

Heat Transfer Facility (with cover removed) 15

Schematic of Rotating Heat Transfer Facility 15

Optics Arrangement for Rotating Heat Transfer

Measurements With Liquid Crystals 20

Optical Test Section With Previous Four Pass ModelInstalled 20

Frame of Video Recording Before Startof Transient Heat Transfer Test 21

Frame of Video Recording During TransientHeat Transfer Test 22

Processed Frame of Video Data From Transient

Heat Transfer Test 23

Uncertainty Analysis Results 26

Comparison of Test Matrix With NASA LeRC

Full Scale Operating Conditions 30

Thermocouple Data for Liquid Crystal Test on Leading

Surface with f_ = 0 RPM 33

Results From Thermocouple Data for Liquid Crystal Test

on Leading Surface with I'_ = 0 RIM 34

vii

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

5-3

5-4

5-5

5-6

5-7

5-8

5-9

5-10

5-11

5-12

5-13

5-14

5-15

5-16

5-17

5-18

5-19

6-1

6-2

6-3

6-4

6-5

6-6

Thermocouple Data for Liquid Crystal Test on TrailingSurface with _ = 0 RPM


on Trailing Surface With _ = 0 RPM


Surface with _ = 450 RPM


on Leading Surface with _ = 450 RPM

Thermocouple Data for Liquid Crystal Test on Trailing

Surface with f2 = 450 RPM


on Trailing Surface With f2 = 450 RPM

Thermocouple Data for Liquid Crystal Test on LeadingSurface with f2 = 750 RPM


on Leading Surface with f2 = 750 RPM

Thermocouple Data for Liquid Crystal Test on TrailingSurface with _ = 750 RPM


on Trailing Surface With D = 750 RPMDimensional and Dimensionless Heat Transfer Results

From Thermocouple Data for Region 1

Dimensional Heat Transfer Results From Thermocouple

Data for Region 2 and Re = 13,000

Dimensionless Heat Transfer Results From Thermocouple

Data for Region 2




Data for Region 3




Data for Region 4

Video Records of Liquid Crystal Isotherms for Test 8.1


Nomograph for Evaluating Liquid Crystal Data for

Re = 13,000 and _ = 0 RPM

Heat Transfer Coefficients From Liquid Crystal Isotherms

for Re = 13,000 and D = 0 RPM



35

36

39

40

41

42

43

44

45

46

48

49

50

53

54

55

56

60

61

62

63

65

66

viii

Figure 6-7

Figure 6-8

Figure 6-9

Figure 6-10

Figure 6-11

Figure 6-12

Figure 9.4-1

Figure 9.4-2

Figure 9.4-3

Figure 9.4-4

Figure 9.4-5

Figure 9.4-6

Figure 9.4-7

Figure 9.4-8

Figure 9.4-9

Figure 9.4-10

Figure 9.4-11

Figure 9.4-12


Re = 13,000 and f2 = 450 RPM 67


for Re = 13,000 and f_ = 450 RIM 68

Video Records of Liquid Crystal Isotherms for Test 16.4 69

Video Records of Liquid Crystal Isotherms for Test 12.2 70


Re = 13,000 and _ = 750 RPM 71


for Re = 13,000 and f2 = 750 RPM 72


Surface with f2 = 0 RPM 98


on Leading Surface with f2 = 0 RIM 99

Thermocouple Data for Liquid Crystal Test on TrailingSurface with f2 = 0 RPM 100


on Trailing Surface With f2 = 0 RPM 101

Thermocouple Data for Liquid Crystal Test on LeadingSurface with _ = 450 RPM 102


on Leading Surface with f_ = 450 RIM 103

Thermocouple Data for Liquid Crystal Test on Trailing

Surface with D = 450 RPM 104


on Trailing Surface With f2 = 450 RPM 105

Thermocouple Data for Liquid Crystal Test on LeadingSurface with f2 = 750 RPM 106


on Leading Surface with f2 = 750 RPM 107

Thermocouple Data for Liquid Crystal Test on TrailingSurface with f2 = 750 RPM 108


on Trailing Surface With f_ = 750 RPM 109

ix

1.0 SUMMARY

An experimental study was conducted (1) to experimentally measure, assess and analyze the heat

transfer within the internal cooling configuration of a radial turbine rotor blade and (2) to obtairt heat

transfer data to evaluate and improve CFD procedures and turbulent transport models of internal coolant

flows. A 1.15 times scale model of the coolant passages within the NASA LeRC High Temperature

Radial Turbine was designed, fabricated of Lucite and instrumented for transient heat transfer tests using

thin film surface thermocouples and liquid crystals to indicate temperatures. Transient heat transfer tests

were conducted for Reynolds numbers of one-fourth, one-half, and equal to the operating Reynolds

number for the NASA Turbine. Tests were conducted for stationary and rotating conditions with

rotation numbers in the range occurring in the NASA Turbine.

Results from the experiments showed the heat transfer characteristics within the coolant passage

were affected by rotation. In general, the heat transfer increased and decreased on the sides of the

straight radial passages with rotation as previously reported from NASA-HOST-sponsored experiments.

The heat transfer in the tri-passage axial flow region adjacent to the blade exit was relatively unaffected

by rotation. However, the heat transfer on one surface, in the transitional region between the radial

inflow passage and axial, constant radius passages, decreased to approximately 20 percent of the values

without rotation. Comparisons with previous 3-D numerical studies indicated regions where the heat

transfer characteristics agreed and disagreed with the present experiment.

2.0 INTRODUCTION

NASA Lewis Research Center (LeRC), the US Army and US gas turbine manufacturers have

been developing light weight, radial gas turbines for over 20 years. NASA LeRC and the US ,Army

Aviation Systems Command, in conjunction with gas turbine contractors, have a Cooled High-

Temperature Radial Turbine Program with a cooled turbine designed and manufactured by the Allison

Gas Turbine Division (Snyder, 1992), an analytical and experimental program at the LeRC, and analytical

efforts at ADAPCO and Carnegie Mellon University. The present study supports the NASA LeRC

program by experimentally determining the heat transfer characteristics in the coolant passages of a

model similar to the LeRC rotor (Snyder, 1992).

2.1 Background

Axial Flow Turbines - Heat transfer in rotating radial internal coolant passages, typical of turbine

airfoils of large gas turbine aircraft engines, has been investigated experimentally and analytically for the

past ten to fifteen years. The experimental studies have been sponsored by national and private

laboratories (e.g. USA/NASA, USSR, UK/RAE, France, Germany/DLR, Japan, Taiwan, USA/DOE, and

USA/EPRI) and the large gas turbine manufacturers (e.g. PW, GE, and RR). The pioneering studies

were reported by Morris, 1981.. More recent studies up to 1991, with a wider range of flow and

geometric parameters, are reported in the authors' previous papers by Wagner et al., 1991, and Johnson

et al., 1992, and in NASA contractors reports, Hajek et al., 1991, and Johnson et al., 1993. Other recent

references include Han et al., 1992, E1-Husayni et al., 1992, and Mochizuki et al., 1992, and contain most

references from the studies sponsored by GE, EPRI, and RAE. The results from these studies are

bringing an understanding to the turbine blade durability designer of the effects of many parameters on

heat transfer in rotating radial coolant passages including such flow parameters as Reynolds number,

rotation number, wall-to-bulk density ratio, and buoyancy in addition to such geometric parameters as

trip geometry, passage aspect ratio, and flow direction. The understanding developed by the authors in

their previous studies of heat transfer in rotating internal coolant passages will be used to interpret the

results of the present study.

Radial Flow Turbines - Internal cooling of radial turbines is more complex than that for axial

turbines because of the large surface area of the coolant passages, the large variations in coolant passage

cross-sectional area from inlet to exit, and the changes in flow direction, axially and azimuthally, as the

blade contour varies. A summary of work to 1992 (Roelke, 1992) describes the previous cooled radial

turbine efforts at Garrett (Vershure et al., 1980), Pratt and Whitney (Calvert et al., 1971), and Solar

2

(Hammeret al., 1986). The previous heat transfer studies have been primarily analytic or have measured

the overall performance of the turbine.

The analytical heat transfers studies to date have been conducted with one and three dimensional

analyses. The one dimensional analyses have used heat transfer relationships and a flow network analysis

for multi-path flows. The three dimensional analyses have used 3-D Navier Stokes codes and have been

focused on the configuration used in the NASA LeRC Cooled High Temperature Radial Turbine

Program. The 3-D studies include those by Ippolito, 1991, at ADAPCO using the STAR-CD code,

Dawes, 1992, using a code with an unstructured grid, Steinthorsson et al., 1993, and Stephens et al.,

1993. Results from the analytical studies vary, however, all studies show regions with low convective

velocities which can be expected to produce low heat transfer rates and low heat transfer coefficients.

2.2 Objectives

The principal objectives of this project are (1) to experimentally measure, assess, and analyze the

heat transfer within the internal cooling passage of a radial turbine rotor blade and (2) to obtain heat

transfer data to evaluate and improve CFD procedures and turbulent transport models in internal coolant

flows.

The model used for the experiments was a 1.15 times scale of the coolant passages in the NASA

LeRC Cooled Radial Turbine(Figure 2-1). The model was constructed from a Lucite block and was

instrumented for transient heat transfer experiments with surface and air temperature thermocouples and

liquid crystal paints. Based on (1) UTC previous experience (e.g. Hajek et al., 1991, and Johnson et al.,

1993) in the NASA HOST and in corporate sponsored research programs on heat transfer in rotating

models for axial flow turbines and (2) the flowrates and operating conditions of the LeRC turbine, it is

•expected that the rotation number (Ro = c0d/V) and the coolant passage Reynolds numbers (Re = 9Vd/_t)

will be the principal parameters affecting heat transfer in the model. In addition, because of the

reasonably high Reynolds numbers, it is expected that the heat transfer will scale approximately as Re 0.8

The test matrix was developed using these assumptions.

The transient heat transfer data, which was obtained in this program and which will be used to

evaluate CFD codes, is difficult to present in report form because of its three-dimensional, time

dependent nature. In addition, the data was obtained on a model at flow conditions that were not

identical to those used to predict the performance of the NASA rotor. Therefore, an approximate heat

transfer coefficient was deduced from the results based on the time dependent heat flux from the wail, the

time dependent inlet temperature, and the local wall temperature. This coefficient will be used to

evaluatethe effects of rotation and to make qualitativecomparisonswith the availablenumerical

predictions.

The transient heat transfer results obtained from the surface thermocouple data will be discussed

first. These data obtained at approximately one second intervals for the 150 second tests, are smoothed

and used to produce more accurate results than the liquid crystal data. The liquid crystal data will be

subsequently discussed and used, in conjunction with the surface thermocouple data, to determine

isotherms (at specific times) and iso-heat transfer coefficient contours. These results will be qualitatively

compared with 3-D Navier Stokes calculations.

Figure 2-1. Sketch of Internal Coolant Passage for NASA LeRC Cooled High

Temperature Radial Turbine Program.

3.0 DESCRIPTION OF APPARATUS AND EXPERIMENT

3.1 Heat Transfer Model

A Lucite model of the coolant passages in the NASA LeRC High-Temperature, Cooled, Radial

Turbine was constructed for the experiments. The model was 1.15 times the actual scale and was

constructed using surface coordinates obtained from the LeRC (Roelke, 1991) and drawings from the

Allison Division, General Motors (Anon, 1989).

The views of the coolant passage with the coordinate grid, the flow dividers, and pedestals are

shown in Figure 3-1. The coolant inlet passage of the full-scale rotor was simulated in the 1.15 scale

Lucite model. The coolant exit geometry was modified to account for the relatively small radial pressure

gradient at the model exit plenum due to the larger radial location of the model compared to the full scale

model. The exit plane of the coolant passage was selected to be the streamwise location where the

coolant passage is faired into the trailing edge on the pressure side of the blade (Figure 3-2). Based on

flow estimate information from the LeRC, a discharge flow-control plate with selected orifices was used

at the model exit plane to approximate the exit flow distribution. Twelve orifices were used to regulate

the distribution of trailing edge flow. Six were located at the exit of the inner trailing edge passage and

three were located at each exit of the middle and outer trailing edge passages. The orifices were evenly

spaced in the radial direction in patterns of three. The inner passage required the pattern to be staggered

to obtain a more uniform discharge area distribution. The discharge areas of the inner exit passage was

twice that of the middle and outer exit passages (see Figure 3-2 and table below). Consequently, the

configuration is expected to have 50 percent of the total coolant flow in the inner exit passage and 25

percent of the total coolant flow in each of the middle and outer exit passages.

Inner passage

Middle passage

Outer passage

Exit Plane Orifices

No. Used Diameter, mm(in.)

6 1.5 (0.059)

3 1.5 (0.059)

3 1.5 (0.059)

The leading and trailing surfaces of the coolant passages were machined in blocks of Lucite as

shown in Figure 3-3. The coolant passage was oriented 32.7 degrees from the plane of the test section.

This required that the test section with the model be rotated that amount to conduct the experiment with

the same relative orientation (i.e. axial alignment) as the full scale rotor.

6

The design and fabrication of the model were accomplished using Computer Aided Design and

Computer Aided Machining Technology. The assembly drawing for the model and installation is UTRC

Drawing 1896-30.

3.2 Model Instrumentation

The coolant passage model was instrumented with thermocouples and liquid crystal temperature

indicating paints as discussed in the following paragraphs.

Thermocouple Instrumentation - Chromel-Alumel, thin-film surface thermocouples were installed

on the leading and trailing test surfaces at selected locations as shown in Figure 3-4. The thin-film

thermocouples used were 13 microns (0.0005 in.) thick which resulted in minimal disturbance to the

coolant flow. These surface thermocouples provide an on-board calibration for the liquid crystals and are

also used to obtain local heat transfer rates with numerous time-temperature data points. The locations

of the wall thermocouples are presented in Table 3.1. Fine-wire (36 gage) thermocouples with small

beads were used to measure the inlet air temperature and the exit air temperatures. Four thermocouples

were installed in the inlet duct by suspending the thermocouple from the sides of the duct. A

thermocouple was also suspended in the air stream downstream of a central orifice used to control the

relative tlowrate through each of the three Region 4 channels. Inspection of all the air thermocouples

after the experiments indicated that all the thermocouple junctions were in the same position as at the

onset of the experiments.

Liquid Crystal - Mixtures of encapsulated, chiral-nematic paints for color changes at 47C(116F),

43C(110F), 38C(100F), 32C(90F), and 27C(80F) were sprayed on the test surfaces after the surface

thermocouples were installed. A layer approximately 13 microns (0.0005 in.) thick was used for these

tests. A second layer, approximately 13 microns thick, of black, water-based paint was sprayed over the

liquid crystal to provide optical separation between the leading and trailing surfaces. These thicknesses

provide adequate liquid crystal signals (i.e. color change) and do not require a large correction in the data

analysis due to the temperature drop across the liquid crystal and black paints.

a) Y-Z View

Y

b) Y-X View

X

c) Perspective View

Figure 3-1. Internal Passages of NASA LeRC Cooled Radial Turbine Rotor.

Location C

W c = 5.79 cm2.28 in.

Coolant exit

Outer

Location B

W b = 2.41 cm

I/

Location A

Wa= 0.719 cm0.283 in.

Coolant inlet

location

Middle

Inner

/ [______Region__Orifice / Lir_ 4 ILocations

Exit

Plane

Region1

Figure 3-2. Nomenclature for Internal Passages of NASA LeRC

Cooled Turbine Rotor.

UTRCDrawing 1896-30-66913TrailingSurface

UTRCDrawing 1896-30-66912

Leading Surface

Figure 3-3. Photograph of Leading and Trailing Surfaces of Coolant Passage Before Assembly.

3.3. Rotating Heat Transfer Facility

Rotating Components - The Rotating Heat Transfer Facility (RHTF) (Figures 3-5 and 3-6)

consists of the containment vessel with the integral arm assembly and motor with associated controller.

The containment vessel is 1.83 m (6.0 ft) in diameter and was designed to withstand a destructive failure

of the rotating assembly. The vessel was designed for operation at a pressure of 5 to 13 mm of Hg

absolute to reduce the power required to rotate the arm. The rotating arm assembly is driven by a 11

KW (15 Hp) DC motor via a toothed belt. Shaft RPM is controlled by an adjustable feedback electronic

controller. Maximum shaft speed is approximately 3,500 RPM producing body forces on the model of

approximately 14,000 g's at the tip of the model and approximately 10,000 g's at the root. However, the

flash lamps used to illuminate the model were found to not work properly when the pressure was below

atmospheric. Therefore, the vessel was operated at near atmospheric pressure and the maximum shaft

speed for the present program was 750 RPM. A safety shutdown interlock circuit is used to turn off the

drive motor and model heater power supplies, turn on a magnetic brake and open the containment vessel

vacuum chamber vent. The safety shutdown system prevents damage to the model or the facility in the

event of a leak in the model or an imbalance in the rotating assembly.

The shaft assembly comprises a main outer shaft with two shorter inner shafts. This shaft

arrangement was designed for dual fluid paths from each rotary union mounted on the ends of the shaft to

the rotating assembly. For the present program, a single fluid path was utilized to provide coolant air to

and from the heat transfer model. Grooves located on the exterior surface of the outer shaft allow

instrumentation and power leads to extend from the rotating arm to the rotating portion of the

instrumentation slipring. Two slipring assemblies (a 40 channel unit located on the upper end of the shaft

and a 200 channel unit located on the lower end of the shaft) are used to transfer heater power and

instrumentation leads between the stationary and rotating frames of reference.

Thermocouple Data Acquisition System - The data acquisition system contains two major

components; the computer and the data acquisition control unit. The computer consisted of a DEC PDP

11/03 processor unit with 128k memory, two 20 cm (8 in) floppy disk drives, and a DECWRITER III

terminal. The Hewlett Packard 3497A data acquisition system can be controlled from the front panel or

through the interface connected to the computer. Upon completion of the acquisition of voltage data

through the acquisition control unit and the computer, results are calculated and printed in engineering

units. Flow parameter and raw data are stored on disk for future reduction.

Heater Power Sources - A variable DC power supply was used to provide current to the model

inlet heater assembly. The air inlet, electrical-resistance-type, heater assembly consisted of a thin-wall

11

tube bundle connected in series. Model inlet coolant air flowed through the tubes which were aligned in

the flow direction. The model air was heated to the initial temperature for each experiment by passing

current through the tubes. The thin-wall tubes were subsequently heated by the tube resistance and

provided an efficient method of heating the inlet air. The thin-wall tubes also provided a relatively'short

time constant response due to low total mass of the system. The current from the power supply was

switched on and offby a computer controlled, high current capacity relay. Additional low power supplies

were used to heat resistance film heaters mounted to the model pressure containment shell. These

auxiliary heaters were used to help provide isothermal initial test conditions.

Flow Supply System - Model coolant air is supplied continuously by the UTRC 27 arm (400 psig)

air system which is regulated to approximately 10 arm (150 psig) at the RHTF. The air flowrate to the

model is measured with variable area flow meters. The model coolant return air flows through an

additional flow meter to determine a mass flow balance on the system. Model pressure is controlled by

back pressuring the model air flow system with a return air control valve. The maximum mass flowrate

available is dependent on the model operating pressure and the total pressure loss of the system including

the heat transfer model. For typical models, the maximum air flowrate is approximately 0.02 kg/sec

(0.044 lbm/sec).

The model air is cooled to approximately -12°C(10°F) before flowing to the shaft rotary union

with a chilled-liquid/air heat exchanger. Heat pickup in the shaft and air supply lines on the rotating arm

increase the model air temperature to approximately 10°C(50°F) at the location just before entering the

model inlet heater system.

12

+ Air TC

• Wall TCo Exit orifice locations

a) Leading side viewed fromoutside model

b) Trailing side viewed fromoutside model

e8

o •7o o

0 0 0 00

6•o

o

e32A 4A

17 • oo o

oo o o

o o

°_ 16 _/o 23

O

1 °÷2_?

• 14_o_b

for scaled model

Figure 3-4. Thermocouple Instrumentation for Internal Passages of NASA LeRC

Cooled Turbine Rotor. (Note: model centerline was moved 22.85 inches

from the center of rotation of the test facility.)

13

TABLE 3-t LOCATIONS OF WALL THERMOCOUPLES IN MODEL

NASA LeRC Radial Turbine RotorThermocouple Locations reference to UTRC Drawings Nos. 1896-30-66913 & 66912Note: Axial reference point is the upstream tip of the coolant passage(See Figures 3-1 and 3-4 for coordinate systems)

1.15 Scale Model 1.15 Scale Model

In facility coordinates In rotorcoordinatesx R e x r

Location TC# (in.) (in.) (deg.) (in.) (in.)

Full Scale NASA LeRC Model

LeadingLeadingLeadingLeadingLeadingLeading

_- Leading4==

1 0.125 * 30.145 * -0.530 * 0.125 * 7.300 * -0.5305 0,520 30.160 -0.530 0.520 7.315 -0.530 -0.068 6.361 0.4522 1.169 27.328 -1.010 1.169 3.383 -1.010 -0.079 3.899 1.0177 2.293 27.845 4.370 2.293 5.012 4.370 0.381 4.358 1.9943 2.375 26.369 4.120 2.375 3.532 4.120 0.254 3.071 2.0658 3.380 28.323 19.360 3.380 4.699 19.360 1.558 4.086 2.9394 3.242 25.830 16.120 3.242 3.092 16.120 0.858 2.689 2.819

Trailing 11 0.125 * 30.045 * .57" 0.125 * 7.200 *Trailing 15 0.492 30.077 0.570 0.492 7.232Trailing 12 1.144 27.190 1.550 1.144 4.346Trailing 17 2.340 27.901 6.390 2.340 5.082Trailing 13 2.419 26.016 8.550 2.419 3.202Trailing 18 3.380 27.127 20.710 3.380 4.527Trailing 14 3.278 25.704 19.830 3.278 3.018

0.5700.570 0.072 6.289 0.4281.550 0.118 3.779 0.9956.390 0.566 4.419 2.0458.550 0.476 2.784 2.103

20.710 1.601 3.937 2.93919.830 1.024 2.624 2.850

* = Approximate locationx = axial distance relative tor = radial distance relative to the scaled rotorcenterline before mountingin the rotating facilityR = radialdistance relative to model centedine of rotation after mounted in the rotatingfacility

e = angular location relative to theX,Y,Z = cartesian coordinates for the fullscale NASA LeRC Model

0 X Y Z(deg.) (in.) (in.) (in.)

Dual path _-.2!rotalion union

for airtransfer

Upper slip

ring location

Figure 3-5. Photograph of a Model Mounted in Rotating Heat Transfer Facility.

(Rotating heat transfer facility with cover removed).

E

1.83 m (6 ft) f "Model air in "[Counter- r_ _ . _ I

_ Z_ _ I_ Pressure shell

i ,li 2; 11nstrumen at-ion

slipring assembly _ Motor drive I[

.____ j assembly IIModel air out

Figure 3-6. Schematic of Rotating Heat Transfer Facility.

15

3.4 Experimental Procedures

Thermocouple Data Acquisition - The EMF for each thermocouple was measured and recorded

using laboratory computers and the HP3497A data acquisition system. The data acquisition system was

configured to repeatedly measure the EMF from a sequence of thermocouples in the model. The data

was stored in a memory buffer in the HP3497 and transferred to a data file for the specific test number.

Some unsteadiness was noted for some thermocouples. Typical time variations of measured

temperature are presented in Section 5. The time variations of temperature indicate an approximately +/-

0.5°C(I°F) random noise component added to the expected temperature variation. The probable sources

for this unsteadiness were (1) rotating instrumentation leads through magnetic flux lines generated by the

DC motor, (2) motor power controller noise, and (3) lead, slipring, and instrumentation contact

irregularities. The temperature data were smoothed by performing a second order, least squares fit to the

closest seven data points around each time point of interest. This technique effectively removed the

random noise component but allowed the fit temperature to follow the experimental transient.

Thermocouple Data Reduction - Transient heat transfer measurement techniques are well

documented (e.g., Schultz, et al., 1973, Clifford, et al., 1983, Metzger and Larson, 1986, Saabas et al.,

1987, and Metzger et al., 1989). A typical approach to obtaining transient heat transfer data involves

solving the one-dimensional transient heat conduction equation subject to a semi-infinite wall boundary

condition with a uniform initial wall temperature and a step change in a convection boundary condition on

the surface exposed to the coolant flow (e.g., Kreith, 1973, Metzger and Larsort, 1986, Metzger et al.,

1989). A single, time-temperature pair (typically from phase change paints, wall mounted thermocouples

or liquid-crystal paints) is then used to determine the heat transfer coefficient for each separate point on

the test surface. Different points on a test surface will have differing time-temperature histories. Implicit

in this solution is that the heat transfer coefficient is a constant with time. However, when heat transfer

coefficient is known to be a function of the temperature difference, such as in rotating coolant passages,

this technique may not be appropriate (see Wagner et al., 1989, for more discussion of the combined

effects of Coriolis and buoyancy forces on heat transfer in rotating passages).

The one-dimensional, time dependent heat conduction equation was solved to obtain a time

dependent heat flux and a time dependent heat transfer coefficient. The formulation for time dependent

heat transfer coefficients is required because of the variations in the heat transfer coefficient during the

transient test due to changing buoyancy effects as the wall-to-bulk temperature difference decreases. 2-D

effects of lateral conduction have been studied and reported by Metzger et al., 1989; Metzger and

Larson, 1986, and Saabas et al., 1987, and will not be discussed here. In general, the 1-D assumption has

16

been shown tO be valid for a judicious choice of test surface material and test times. Following is a

description of the UTRC data analysis procedure from Blair et al., 1991, solved to obtain a relationship

for the heat flux from the prescribed surface temperature boundary condition at a particular point in the

coolant passage. The 1-D transient heat conduction equation subject to a semi-infinite wall boundary

condition and a time dependent prescribed surface temperature is shown below.

52T(x, t) 1 6T(x, t)

(_2 a t_t

with boundary and initial conditions:

r(x,0) = m*x +/;,

o¢'T(oo, t)-m

5x

T(0, t) = experimentally determined

Solution:

T(_(O,t- r) at_ m, k

47

An analysis showed that the first temporal derivative of the wall temperature is a continuous

function, therefore, the evaluation of the integral was accomplished by assuming an average derivative,

T' (0, t-x), for a given time increment. This reduced the integral to a series of summations for equally

spaced time increments which were evaluated as shown below.

J

Q(t)= _[_-= _], [T_ (j + 2-i)- T'.(j + 1-i)]

17

A term was included in the solution to allow for an initial temperature gradient in the model wall

due to the difficulty of obtaining a perfect isothermal initial condition during the warm-up phase of the

experiment. For the case of an isothermal wall initial condition, this term is zero.#

These tests had heaters in the space between the model and the Lucite windows which formed the

transparent walls of the Optical Test Section (Figures 3-7 and 3-8). The heaters were used to bring the

average temperature on the outer wall of the model to the same temperature as the inlet air temperature

at the start of the test. In general, isothermal conditions (i.e. inlet flow and model surface temperature

within +/- I°C(2°F)) were obtained for the stationary test conditions. However, test conditions with

rotation had larger temperature variations (i.e. on the order of +/- 3°C(6°F)) especially on the trailing

surface and at the model coolant air exit plane. The procedure to obtain isothermal conditions consisted

of flowing heated air through the model coolant passages with the external auxiliary heaters on for

approximately two hours prior to the initiation of the transient portion of the test. It is likely that the

combination of rotating the model and the thicker model walls on the trailing side resulted in a need for

an increase in the thermal soak time which was not recognized at the time of the test. With limited

external surface instrumentation (3 external thermocouples on each side) and a fairly complex 3-D

thermal initial condition an acceptable initial temperature gradient could not be determined. Therefore,

no initial temperature gradient term was used for the analysis of the data in this study. A discussion of

the effect of initial wall temperature gradient is included in subsequent paragraphs where experimental

uncertainties of the data are presented.

Video Data Acquisition - The typical pre-test procedure consisted of heating the air flowing

through the rotating model coolant passages until the acrylic heat transfer model walls reached

approximately isothermal conditions. Note, the experimental methods described by Metzger and Larson,

1986, and Saabas et al., 1987, utilized an initially cold model wall subject to a suddenly heated

• mainstream flow. However, for the rotating heat transfer problem, the model walls must be hot with a

cold coolant flow in order to give the proper sense to the rotation-induced buoyancy force effects (see

Clifford, 1985, and Wagner et al., 1989). The test was then initiated by switching off the power to the

coolant passage inlet heater. A video imaging system was utilized to record the changing liquid crystal

paint on the coolant passage surface. Concurrently, the inlet and exit coolant temperatures and surface

temperatures were recorded as described in the thermocouple data acquisition section.

The video data was acquired using the optics arrangement shown in Figure 3-7. The video was

recorded on 3/4 inch magnetic tape. The time reference was superimposed on each frame using a

time/date generator. The start of each transient test (Time = 0.0 see) occurred when the heater power

was shut off. Typical test times recorded were 5 seconds prior to the start of the test and 150 to 200

18

seconds after the start. The camera and lighting system were timed by a 1/REV signal such that the

model was recorded in approximately the same position each revolution. (i.e. +/- 1 degree of rotation).

Video Data Analysis - Video imaging processing equipment was used to analyze selected'video

frames. The image processing equipment can display, edit, enhance, analyze, print, and animate images.

The video analysis system supports many standard image processing functions, including histogram

equalization, contrast enhancement, density profiling, smoothing, sharpening, edge detection, median

filtering, and spatial convolution with user defined kernels up to 63x63.

Typical test and data analysis frames are shown in Figures 3-9, 3-10 and 3-11. The video

recording obtained before the start of the test is shown in Figure 3-9. Only the portions of the video

showing a surface of the model are shown. This frame provides a reference that includes shadows and

reflections from the two layers of Lucite. A frame of the video during the test is shown in Figure 3-10.

Although there are differences between Figures 3-9 and 3-10, the liquid crystal contours cannot be readily

discerned from the viewing of one video frame. However, the contours are easier to discern when

viewing the video during playback and the viewer's eye and mind can discern the small changes in video

frames.

A processed video data frame is shown in Figure 3-11. The processing included subtracting the

Figure 3-9 frame from the Figure 3-10 frame, adjusting the location of the pixels to account for small

shifts in the model location, and contrast enhancement. This video frame process enhancement eliminates

extraneous light reflections by "zeroing" portions of the image not associated with the model coolant

passage and enhances the intensity of the liquid crystal isotherms. The processed frame shows a small

liquid crystal contour in Region 1, (see Figure 3-2 for definitions of Regions) two contours in Region 2

with flow radially inward, and contours in Regions 3 and 4 at the entrances to the Inner and Middle

portions of Region 4. Each contour on the frame was identified as to temperature and the time after the

start of the test. See Figure 6-2 for the identifications of video frames used on this video test for the

trailing surface.

Corrections were made to the coolant path wall surface temperature to account for the transient

energy storage in the liquid-crystal paint and temperature gradients through the paint. The transient

energy storage corrections were obtained by estimating the temperature at the paint/air interface based on

the calculated heat flux and the measured temperature at the paint/acrylic interface. The average internal

paint temperature was then calculated for each time step. Differences in the temporal response of the

average paint temperature and the paint/acrylic interface temperature (measured with the liquid-crystal

19

. Counterweigh_

Flash '/ w_,,,,_ II \\

1/rev signal }

_ Xybion B/W _"_u_'__ _ iii I

| m_ed -1 ,_ "11 __ Rotating optical

|._l__r-_J ..:...._..__.. _-- Lucite model

]P°y_m_gabt_r] _'_ C°°NN_-Lucite window lant Passage

Time/date L__ Vide° ___ Monitor Igenerator [_ recorder I I

Figure 3-7. Optics Arrangement for Rotating Heat Transfer Measurements

With Liquid Crystals.

UTRC Drawing 1896-20

Figure 3-8. Rotating Optical Test Section With Previous Four PassModel Installed.

2o

Superimposed on NASA LeRC cooled turbine rotor outline

;!::!ii':!ii::iii::i!!!ili::!i_::!

:::::::::::::::::::::

:::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::

" ........................._:i:_:i:i:!:_:i:i:i:i:i:i:!:i:i:!:i:i:i:iiii_::.':':::: .... .

_!_::i:J::!iiiiiiii!iiiiiiiiiiii::::::::::;

Figure 3-9. Frame of Video Recording Before Start of Transient Heat Transfer Test.

21


.... :::i_!!!iiii_:i!iiiii!_

.::i!i!iiiii_i_iiii_::.... "

Figure 3o10. Frame of Video Recording During Transient Heat Transfer Test.

22


Figure 3-11. Processed Frame of Video Data From Transient Heat Transfer Test

23

paint) were associated with the transient energy storage in the paint. The corrections associated with the

energy storage and temperature gradient in the paint were typically on the order of 3 to 5 percent aider 10

seconds.

A rotation induced calibration shift was also observed in this series of experiments. Comparison

of the surface temperatures obtained with the liquid crystal paints with the thin film thermocouples

showed that a calibration correction was necessary when the model was rotating. The temperatures

measured with the liquid crystals on the stationary model were in good agreement, i.e. +/- 0.5°C (I°F),

with the thermocouple measurement for stationary test conditions. The temperature calibration of the

liquid crystals changed considerably during rotation. The liquid crystals are known to be sensitive to

shear stresses which will occur due to the centrifugal force on the liquid crystals due to its own weight

and that of the black overcoat on the liquid crystal paint. The experimental results showed a 2 to 7°C(4

to 14°F) difference between the liquid-crystal surface and thin film thermocouples mounted on the test

surface at the 450 and 750 RPM test conditions. This calibration shift is attributed to stresses in the paint

under conditions of rotation which are not present when stationary. The surface thermocouples provide

an on board calibration required to resolve these variations.

Heat transfer coefficients at specific locations were calculated by dividing the instantaneous heat

flux with the wall-to-coolant inlet temperature difference for a given test time.

Accuracy of Results - A number of factors can affect the accuracy of the reduced heat transfer

coefficient data. Typically, uncertainties in absolute and relative temperature differences are the largest

contributors to uncertainties in calculated heat transfer coefficients. In this section the effect of

temperature measurement error, noise in the temperature data, time resolution error, initial wall

temperature gradient, paint thickness, and material property errors are presented.

A baseline test condition (Run 6.2) at a midpassage location (TC02) was used for the uncertainty

analysis. The baseline wall temperature data was perturbed as noted and reduced to evaluate the effects

listed. The temperature measurement error was simulated by adding I°C(2°F) to the raw data. Noise in

the data was simulated by applying a random function ranging +/-I°C(2°F) to the smoothed data. The

effect of time resolution was simulated by adding 1 second to the raw data. The effect of an initial wall

temperature gradient was determined by assuming the outside of the model was approximately 6°C(10°F)

lower than the coolant passage surface at the start of the test. The effect of uncertainty of the Lucite

model material properties was determined by adjusting the thermal conductivity 10 percent. The

perturbations were applied to the measured data set and reduced to obtain heat flux and heat transfer

coefficient results.

24

The inlet coolant temperature, wall temperature, heat flux, and heat transfer coefficient records

are shown in Figure 3-12. The results show that random noise on the wall temperature data causes

significant fluctuations in the resulting heat flux and heat transfer coefficient histories (Figure 3-12_ and

d) and that fluctuations in the heat transfer results are more likely related to less-than-ideal smoothing

rather than flow-induced oscillations. Aside from the application of random offsets to the wall

temperature data, the perturbation analysis indicates that the results are fairly insensitive to the effects

studied. The percent change in heat transfer coefficient at Time = 50 seconds is listed below. As

previously noted, the uncertainty in measuring temperature results in the largest contribution to the

uncertainty in the heat transfer coefficient results although the temperature offset had a minimal effect on

the heat flux distribution.

Percent Change in Heat Transfer Coefficient

Percent Change

Twall + I°C(2°F)

Twan +/- (random) I°C(2°F)

Time + 1 second

With initial gradient

Without paint corrections

10 percent increase in model conductivity

-8

NA

+1

-3

-3

+5

25

a) T_.

140 1

120_

R06T02 Data

eeeee Baseline_.se Tw w/ offset

Tw w'/ randomTime + 1 secondw/. gradient

w'/o paint_v 1.1 * K

100

°_E__80-

60.

4O o ......... s'o........ i66 ....... i5oTime, see

140

120

100

80

60'

4O0

b) T_.

RO6T02 Data

eeeee Baselineseeee Tw w/ offset

Tw w/ random(HHH_ Time + 1 second

w/ gradientw/o paint

........bb........i6o.......isoTime, sec

1000

c)Qw

R06T02 Data

5

i000 50 100

Time, sec

i000

2

100

1

lO

5"

Z

150

d) nr

R06T02 Data

oeeee Baseline_eeee Tw w/ offset

Tw w/ randomTime + i secondw/. gradient

w/o paint_1.1 *K

0 50 I00 150Time, sec

Figure 3-12. Uncertainty Analysis Results (Run 6.2, TC02)

26

4.0 EXPERIMENTAL PARAMETERS AND TEST MATRIX

The present study of heat transfer from a 1.15 times scale model was conducted at several

dimensionless flow parameters in or near the range of the NASA LeRC rotor. Following is discussion of

the flow and geometric parameter test conditions, and an outline of the presentation of results.

4.1 Flow Parameters

A dimensional analysis study performed at UTRC (Section 10 ofHajek et al., 1991, similar to that

of Guidez, 1989), showed that the flow patterns and convective heat transfer in rotating radial passages

would be influenced by four dimensionless flow parameters and several geometric parameters. The

dimensionless flow parameters are as follows:

Reynolds number (Re) pVd/_t

Rotation Number (Ro) c0d/V or oH/V

Density Ratio (Ap/p) (Pb - Pw)/Pb = (Tw - Tb)/Tw

Buoyancy Parameter (BUOY) [(Pb - pw)/Pb](c0R/V)(od/V)

For flow in rotating radial coolant passages, Coriolis forces, represented by the dimensionless

parameter, c0d/V, and the dimensionless streamwise velocity gradients, produce secondary flows in the

plane perpendicular to the radial direction. These secondary flows are produced by the viscous

force/Coriolis force interaction. Buoyancy also produces secondary flows in the radial direction. For

flow in rotating radial coolant passages with walls hotter than the bulk fluid, the buoyancy effects drive

the heated flow inward. Thus, the buoyancy flow direction is opposite the mean velocity direction for

flow radially outward and is in the same direction for flow radially inward. From previous studies, both

the Coriolis and buoyancy forces can be expected to produce significant changes to the coolant passage

flowfield and heat transfer. Rotating constant-temperature flow studies by Johnston, et al., 1972, have

shown that the Coriolis forces can dampen turbulent fluctuations and laminarize flow in portions of a

channel. Combined free and forced convection studies in stationary systems have shown that the

turbulent shear structure and heat transfer is significantly altered with co-flowing or counter-flowing

buoyancy effects ( e.g., Eckert et al., 1953).

27

4.2 Geometric Parameters

The flow and heat transfer in stationary coolant passages are also strong functions of the

geometric parameters (e.g., Johnson et al., 1993). All parameters except the radial location of the model

are identical to the NASA LeRC rotor.

4.3 Test Conditions

The test conditions for the heat transfer experiments are listed in Table 4-1. The variations of

Reynolds number and rotation numbers are shown in Figure 4-1. Tests were conducted for three

flowrates (Reynolds numbers indicated in the figure) and three nominal rotation rates (0, 450, and 750

RPM). Tests were conducted at the Reynolds number range and approximately one-half and one-fourth

the Reynolds number of the Full Scale Rotor. Due to the Reynolds number variation in the coolant

passage for a given flowrate, subsequent references to flowrate will be as low, medium, and high flowrate

test conditions. A tabulation of the test conditions for which thermocouple and liquid crystal data were

obtained and the Full Scale NASA LeRC Radial (Full Scale) Turbine operating conditions are presented

in Section 9.2. The characteristic dimensions used for the representation of the Reynolds and rotation

numbers are shown in Figure 3-2. The channel width dimensions, W, were determined from the model

drawings. The channel depth dimensions, H, at each location indicated on Figure 3-2 were obtained

from the tabulated coolant passage coordinates supplied by the LeRC. Because of the flow distribution

uncertainty, the average results anticipated for Regions 3 and 4 are represented by the single Location C.

Results are presented for all of the available locations. The Nusselt and Reynolds numbers

(nominal values noted in the figures where appropriate) were calculated based on the geometry of

Location B (see Appendix 9.2 and Figure 3-2). The viscosity and thermal conductivity of the coolant

were based on the film properties where the coolant temperature was assumed to be the lowest

temperature obtained for a given test condition (Tc, Appendix 9.2) and the wall temperature was

assumed to be the initial temperature of the coolant (i.e. the ideal initial wall temperature, Tw in

Appendix 9.2). Flow properties, velocity and Reynolds number, were based on the coolant temperature

described above. Whereas the Nusselt and Reynolds numbers used the hydraulic diameter of the passage

for a characteristic dimension, the separation distance, H, was used for the calculation of Rotation

number. Local Rotation, Reynolds, and Nusselt numbers at a given location can be obtained using the

local geometry and applying adjustments to the parameters presented based on ratios of the local and

Location B dimensions. Normalizing the data in this manner (i.e. using a common representative model

location) resulted in plots with similar scales so that results could be compared more easily. Note that the

location designations in the figures refer to thermocouple (TC) locations shown in Figure 3-4.

28

Table 4-1

Flow Conditions for Transient Heat Transfer Tests

Test Flow Video

No. Date Rate RPM Surface Comments

5.1 4/13/92 H 0 Trailing (11)

5.2 4/13/92 H 0 Trailing (11)

6.1 4/13/92 M 0 Trailing (11)

6.2 4/13/92 M 0 Trailing

7.1 4/14/93 H 0 Leading (11)

8.1 4/14/93 M 0 Leading (11)

9.1 6/1/93 H 453 Trailing

9.2 6/1/93 M 453 Trailing

10.1 6/2/93 H 450 Trailing

10.2 6/2/93 M 450 Trailing

11.1 6/3/93 H 756 Trailing

12.1 6/24/93 H 749 Trailing

12.2 6/24/93 M 751 Trailing

12.3 6/24/93 L 749 Trailing

Low Quality Video

Low Quality Video

14.1 6/26/93 H 750 Trailing No Video

14.2 6/26/93 H 750 Trailing Low Quality Video

14.3 6/26/93 M 750 Trailing Low Quality Video

14.4 6/26/93 L 750 Trailing Low Quality Video

15.1 8/12/93 H 753 Leading (1,8,11)

16.1 8/13/93 H 450 Leading (1,11)

16.2 8/13/93 H 753 Leading (1,8)

16.3 8/13/93 M 750 Leading (1,8)

16.4 8/13/93 M 450 Leading (1)

16.5 8/13/93 L 452 Leading (1,11)

16.6 8/13/93 L 751 Leading (1)

Data

TC

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

N

Y

Y

Y

Y

Y

Y

N

Y

Y

Y

Y

Y

Y

Y

ReducedVideo

N

Y

N

Y

Y

Y

N

N

Y

Y

N

Y

Y

Y

N

N

N

N

N

Y

Y

Y

Y

Y

Y

Note: Numbers in ( ) indicate thermocouple locations where data is not available.

29

o

0

c_

o

0.08

a) Location A

0 Full scaleX Test point

0.04 --

0.00

0.20

0

X OX

X

20000 40000 60000 80000

b) Location B

Re d

0.15 --

0.i0--

0.05--

0.00

1.00

X

X

0

X<

i l>_<t

0 i0000 20000 30000

Re d

c) Location C

0.80 --

0.60 --

0.40--

0.20-

0.00

X

X

X

>X<

0 4000 8000 12000

Re d

Figure 4-I. Comparison of Test Matrix With NASA LeRC Ful!

Scale Operating Conditions.3o

The combinations of Re and Ro for the tests and for the Full Scale turbine are shown in Figure 4-

1 for Locations A, B, and C. The figure shows the maximum rotation numbers obtained during this series '

of tests with the scaled UTRC model for Locations A and B (see Figure 3-2) near the entrance of the

airfoil coolant passage were approximately half that of the Full Scale model at the design Reynolds

number. The low test rotation numbers for these locations were due to facility limitations. However, the

design rotation numbers for these locations were obtained at Reynolds numbers half the Full Scale

operating conditions.

Design rotation numbers were obtained for Location C as a result of the large pressure drop

through the Full Scale model coolant passage (1.66 to 0.82 atmospheres) and the relatively small pressure

drop through the UTRC model (11.0 to 10.9 atmospheres). The large pressure drop in the Full Scale

model results in a significant increase in coolant velocity and a commensurate decrease in Full Scale

rotation numbers compared to little pressure drop in the UTRC model. Therefore, due to the relatively

low pressure drop in the coolant passage of the scaled UTRC model the same relative decrease in the

rotation number which occurs in the Full Scale model with streamwise distance does not occur in the

UTRC model.

4.4 Outline for Presentation of Results

A total of twenty-five tests were conducted with models as shown in Table 4-1 (repeat runs were

obtained under different test numbers). These tests consisted of eight different combinations of coolant

flowrate and rotation rate as noted. Repeat runs and runs where one portion of the data system was

unsatisfactory are also noted. In order to make the presentation of the principle results for this program

tractable and discernible to the reader, the heat transfer data is presented in several stages.

The local heat transfer results obtained from the thermocouple data are presented in Section 5.0

These results show the range of heat flux and heat transfer coefficients based on the inlet air temperature,

the local wall temperature, and the local wall heat flux for three sets of rotating conditions and the

medium flowrate. The results for each thermocouple location at this flowrate are compared to show the

effects of rotation. To summarize the effects of flow and rotation, the heat transfer ratio, Nu/Re 0.8,

versus rotation number, Ro, is used to compare all of the data acquired.

Liquid crystal data and regions of constant heat flux will be presented in Section 6.0.

31

5.0 HEAT TRANSFER RESULTS FROM THERMOCOUPLES

Six sets of thermocouple data are presented in detail to identify the range of wall temperature

responses, heat fluxes, and heat transfer coefficients based on measured inlet coolant temperatureS. All

six cases were at the same approximate coolant flowrate, 3.4 gm/sec (0.0075 Ibm/see) and the same

model pressure, approximately eleven atmospheres. These data were obtained during transient heat

transfer tests at 0, 450, and 750 RPM with concurrent video recording of the leading or trailing coolant

passage surfaces (one side per test). These thermocouple data facilitate the interpretation of the results

from the video records of the liquid crystal color changes. Data and results are available on computer

disk. A sample table is provided in Appendix 9.3.

5.1 Data and Results for Medium Coolant Fiowrate

Measured temperature, heat flux, and heat transfer coefficient results are presented. The

temperature records shown in the figures are not smoothed. Note that not all of the temperature records

were available for analysis. During the testing it was speculated that the thin film thermocouples were

intermittently failing. However, the test-to-test variations in the quality and availability of the

thermocouple data suggest that lead and switch contact irregularities may have been contributing factors.

The temperature data was smoothed with a "running" second order fit of the nearest seven data points.

The smoothed data was used to obtain heat flux and heat transfer coefficient results. Using more points

resulted in smoother heat flux and heat transfer coefficient plots but was not deemed necessary. The

major purpose of the smoothing was to reduce the large variations which tended to obscure the general

trends (see discussion of uncertainty in Section 3). It is the authors' recommendation that using the

relative smoothness of the heat flux and heat transfer coefficient data to contemplate the unsteadiness of

the coolant flow should be done with much care.

Stationary Tests - The data and results for the two medium flow, stationary tests are presented in

Figures 5-1 through 5-4. The leading and trailing wall temperature histories (Figure 5-1c and d) are used

to determine their respective wall heat flux histories (e.g., Figure 5-2a and b)as described in Section 3.4.

The inlet air temperature histories (e.g., Figure 5-1a), the wall temperature histories, and the heat flux

histories are used to determine a heat transfer coefficient, Hr, (e.g., Figure 5-2c and d) based on the

difference between the local wall temperature and the inlet temperature. Note that the calculated heat

transfer coefficients are essentially independent of time aider 10 seconds of test time for these stationary

tests.

32

140

120

100

8O

60

40-50

a) Tin

Re = 13,000

140'R08T01 Data oOOOOTC02

_TC03_TC010_0_TC04

II IIIIIlllll,l,llllll,llt,ll,llllllllll

0 50 100 150Time, see

120

i00

60-

b) Tou t

40-50

R08T01 Data eeeeeTC21_TC22_TC23----- Tout. avg

IIt111,111 II, I,1111|1,1,111tlIII1,11111

0 50 100 150Time, sec

E-_

140

120

I00

c) Leading Surface

8O

60

R08T01 Data eeeeeTC01meBe_TC02a_TC03_TC04_TC05B-B-B_TC07

0 I I I, ,I l ,1 Illll II tI111 II III I-I1 II IIIII III

-50 0 50 100 150Time, sec

d) Trailing Surface140

R08T01 Data

120

100

_e_s.eTC12_a_,a-,aTC13v'_w-vTCl4

_a.,_TCl5_9-9-_TC17

60

4°-5_ ....... 6........ g_ ....... i66....... i5oTime, see

Figure 5-1. Thermocouple Data for Liquid Crystal Test on Leading Surface

With fi = 0 rpm.

33

Re = 13,000

a) Leading Surface b) Trailing Surface ,

looo I/'_ .o_.o,oa_a _G%' I 1000I ..- .o,_o,D_,o/ / \ _ TC12 [

I U _ a-a-a-6-a TC03 I 1 ] _ _ TC18 II I _ _ TC04 I "_ I _ _ TCl4 III _ _TC05 I |1 N-A _TCl5 I

II _-_-._ % _ =o_ i - I _ _ _ TC17 I

I00 100__

0 50 100 150 0 50 100 150Time, sec Time, sec

1000c) Leading Surface

R08T01 Data

1000

2

O

"6 .00

o ......... 5'o........ i66 ....... i50Time, see

2

10

d) Trailing Surface

R08T01 Data

eeseeTCl2_TCI3w_TCl4

_TC15_TCI7

_TCI8

,4Lill*-,,li*ll,tillllll,lli'I

50 100 150Time, see

Figure 5-2. Results From Thermocouple Data for Liquid Crystal Test on

Leading Surface With f2 = 0 rpm

34

140"

120"

100'

._ 80

6O

a) Tin

Re = 13,000

140

40--50

R06T02 Data eeeeeTC02eeeeeTC03

a_TC01_TC04

.... Tin, avg

,11111,111111111111 IIIIIIIIIIIIIIIIIIII

0 50 i00 150Time, sec

P

120

i00

8O

b) Tou t

60

40-50

RO6T02 Data

eeOeeTC21eeee_TC22_TC23

------ j

I,t,nnl,,I II,ll,n, I1,1 II_ll ,,I ,,I,II, II

0 50 I00 150Time, sec

140'

120

I00

c) Leading Surface

RO6T02 DataeeeeeTC01eememTC02

a._a.a_TC03_TC04

_k ,_-_TC05

l_ t_-_-DTC07

8O

6O

40 ......... t ......... t ......... _ .........-50 0 50 I00 150

Time, sec

140d) Trailing Surface

120

I00

=_ 80'

6O

R06T02 Dataeeeee TCIIeeeem TCI2ac_ec_m TCI3

_ TCI4TCI5TCI7

4°-5'd ....... 6........ b'd ....... {6b ....... {50Time, sec

Figure 5-3. Thermocouple Data for Liquid Crystal Test on Trailing Surface

With f2 = 0 rpm.

35

Re = 13,000

a) Leading Surface b) Trailing Surface '

1000 1 _ ROeT02 Data oeeeozc01 "I 1000 _ . R0eT0Z Data oooooTC11i a "_ _Booe TC02 [ | _ _TC12III Tco3 11 Tcls• " _ _ TC04 -I / -_ _ TCI4

5

i00 z 100

0 50 i00 150 0 50 100 150Time, sec Time, sec

c) Leading Surface d) Trailing Surface

i000 _ i 1 RO6T02Data eeeeeTCllRo6r02 Data eeeee TC01 [ 000

5-[ Dos_o TC02 _ _. _ TCI2"I _ TC03 [ _ TCI3TCI4J _ TC04 [ _ _ TC15t _ TC05 I -

o I00 _ tOO

_ -

i0[_ i0 '_2

1 10 50 I00 150

Time, see

_i,is,lJlii_,lililillt,i,lltl

0 50 i00 150Time, sec


Trailing Surface With f2 = 0 rpm.

36

The data indicate a quick decrease in inlet flow temperature when power to the inlet heater is

switched off at Time=0 (Figures 5-1a and 5-3a). For this medium flowrate the time constant of the inlet

heater system is approximately 5 seconds. The outlet temperature response (Figure 5-1b) is much slower

due to the heat transfer to the coolant from the model walls. The dashed lines in the figures are the

smoothed average of the measured inlet and exit flow temperature data. The average coolant

temperature records were used for determination of the heat transfer coefficients. The wall temperature

records by definition are slower responding than the inlet flow temperature due to the heat capacity of the

model walls and the finite heat transfer coefficient. Note that the wall temperature records are not bound

by the limits of the outlet coolant temperature. In general, as the shape of a wall temperature trace

approaches that of the inlet coolant temperature trace the heat transfer coefficients become large (i.e.

towards infinity in the limiting case). Conversely, as the model wall temperature records approach a flat

distribution (i.e. constant wall temperature) the heat transfer decreases to zero,

The wall temperature records represent a wide range of time temperature responses indicating

various levels of heat flux and, therefore, heat transfer coefficient. The heat flux records (Figure 5-2a and

b and Figure 5-4a and b) are characterized by a large increase in heat flux near the start of the test

(Time=0) and a general decline as the model wall temperatures approach the coolant temperature.

The heat flux histories are somewhat sensitive to the smoothness of the temperature records. For

example, the temperature record for TC08 in figure 5-1c results in heat flux and heat transfer coefficient

records which are not as smooth as the other records associated with this test. The unsteadiness of this

thermocouple trace is attributed to lead, slip ring, and switch contact irregularities. The unsteadiness was

intermittent and was not restricted to specific channels (note TC08 in Figure 5-1 c and TC07 in Figure 5-

3c). Smoothing of the raw data reduced the effects of the unsteadiness as discussed in Section 3.

The results for the stationary tests show a 10 fold variation in heat transfer in the model

depending on the relative location from the inlet. Heat transfer is highest near the two inlet locations

(TC01, TC05, TC11, and TC15) and lowest near the exit in the outer passage of Region 4. The large

variations noted are due to large differences in local Reynolds numbers and redistribution of flow near the

exit of the model passage.

Rotating Tests - The data and results for two rotation rates (450 and 750 RPM) are presented in

Figures 5-5 through 5-12 in the same format as the results from the stationary tests. Several differences

between the operating condition of the stationary and rotating tests should be noted.

37

It is clear from the thermocouple data for times less than zero (i.e. the initial conditions before the

start of the transient portion of the test) that the model did not attain the same level of temperature

uniformity for the rotating tests as for the stationary tests. Whereas the initial inlet temperature

uniformity was good for all tests, the range of exit temperatures increased from +/- I°C(2°F) for the

stationary tests to approximately +/- 3°C(6°F) for rotating test conditions. The variations noted for the

exit flow temperatures are representative of the level at which isothermal conditions were attained in the

model prior to the start of the test. This was also indicated in the plots showing the wall temperature

data.

Rotation decreased the range of the inlet flow temperature variation alter the inlet heater was

switched off. The inlet temperature varied from 52 to 27°C(125F to 80°F) in the rotating tests and from

52 to 13°C(125 to 55°F) in the stationary tests. The decrease in range is due to increased heat pick up in

the rotating air supply system to the model. The combination of rotation and a fixed attainable minimum

coolant supply temperature resulted in reduced temperature differences and, consequently, lower values

of buoyancy parameter.

The temperature records for the tests with rotation were used to calculate the heat flux histories

at each thermocouple location as outlined above. The results shown in Figures 5-5 through 5-12 show

that heat transfer was significantly affected by rotation. The most notable effect is the reduction in heat

flux from locations in Regions 3 and 4 on the leading surface, (e.g. TC07, see Figures 3-2 and 3-4). The

outer portion of Region 3 was especially slow in thermal response which resulted in very low heat flux

and heat transfer coefficient.

Some heat transfer coefficient results from tests with rotation show some uncharacteristic

behavior, principally, a sharp increase in heat transfer coefficient as time increases from the start of the

test (TC01 and TC 11) even though the heat flux traces for these locations are consistent compared to the

other traces associated with a given test. This characteristic is typically associated with the outer

locations of Regions 1 and 2 (i.e. near the inlet of the passage). The sharp increases in the heat transfer

coefficient traces are attributed to nonisothermal initial test conditions combined with high heat transfer

rates. The wall temperatures for locations in the model with high heat transfer decrease rapidly from the

onset of the transient portion of the test. This results in small temperature differences between the wall

and the inlet coolant which increases heat transfer coefficients. Additionally, the measured wall

temperatures were corrected for conduction and heat storage effects associated with the liquid crystal

paint which also contributed to smaller temperature differences. Therefore, results where the temperature

difference is greater are expected to be more useful for analyzing the effects of rotation.

38

140

120

100

P

__ 80

Re = 13,000

a) Tin140

60

RI6T03 Data EM_eeeTC02_TC03a_-_TC01

_TCO4

405'6 ....... 8........ '5_....... f Sb....... i5oTime, sec

120

i00

p_

b) Tou t

RI6T03 Data e_eeeTC21sseesTC22_._TC23

Tout, avg

60'

4°-s_ ....... 6 ........ 5'd ....... ido ....... i50Time, see

140

120

100

-_ 8o

c) Leading Surface

RI6T03 DataTC02TC03

TC04

60

4°--5i_ ....... 6........ '_iJ....... i db....... i aoTime, see

140

d) Trailing Surface

120

100

P

60 ¸

RI6T03 Data eeeee TCIIe_se_TCl2

_TCI3w_,_TC14

TCI8

4°-5'd....... 6 ........ 5'd....... fbb....... fsoTime, sec


With f2 = 450 rpm.39

Re= 13,000

a) Leading Surface

i000 I RI6T03 Data moses TC02

TC03_ TC04

/ ",, rco5

d

1000 50 100

Time, sec

b) Trailing Surface

I000 I R16T03 Data eeeee TCll

TC12TCI3

vvv_v TC14_ TC15

5 _ TC18

100150 0 50 100 150

Time, sec

i000

._0

loo8

10

10

c) Leading Surface

TC02 RI6T03 Data . [A/ITC04 . ! '_ ,

a_ad_ad TC05 t-_ _ "

i.l i i i s i I i I i i _ i _ i i i i 1 4 i J _ i i i i i

5O

1000

100 150Time, sec

=

100_Do

_D

=

d) Trailing Surface

8-

10

2

10

TCI3v'_q_TCl4

_TCI5_9_9_TC17

_TCI8

i_l,IIJ,,l,lli,lt0111111111J_

50 I00 150Time, see


Leading Surface With f2 = 450 rpm.

40

Re= 13,000

a) LeadingSurfacemR1000

]//_ R10T02 Data eeeee TC01'I If \_t _ TC024 II x__\ _ TC08II1 _ _ TC0411 A \"_ _Tco_J I of" _ _x^ _ TC07

lOOZ_

0 50 100Time, see

b) Trailing Surface1000

T RIOT02 Data c_eee TCI 1j Qeeee 'l'C 12

_ _ TC13-_ _ _ TC14

[ I _ _ TC15-I! _ _ TClV

O' z

10050 0 50 i00 150

Time. sec

c) Leading Surface

- eeeeeTC01 R10T02 Data / _[ 1000TC02 A /k/ U

6-- _ TC03 I _ I "

TCO5 ._ ../ _. / _,/ :_

2 _ TC07 _ / _ pv ,v-e-

d) Trailing Surface

_I000 sI 1 _.BeeeTCII_BBee_Tc15Tc14Tcz3TC12R10T02 Data//_j_j_ l_J'":_ |illj'

? /

_ lo_C,_-_- _ lO"_ t_ -_ " " " I_

i i , i i i i i l '_ i i i i _ _ i i i L _ D i iI o 5o ioo 15o o 5'o' 166 i50Time, see Time, see


Trailing Surface With _ = 450 rpm.

42

Re = 13,000


"__ R10TO_Data _ TC01'] 1000 7 Rlcroa D_ _ Ten1000

• BBBOB TC02 | J _ TC12_f/ _ _*_ =03i _ -- _ =_34U "_ _ Tco4 ! _ [ "_ _ Tc14If _ \_s. _ TCO5 | | | _ _ TC15

I _f" _ _ _TC07 | "1 I _ _TC17

d

i002 10021 ......................

o so loo 15o o 'sb' i66 i5oTime, see Time, see


1000 bl--_j_ oeeeeTC01_ Tc03TC02TC04R 10T02 Data t!_\ d!/_l-vl_L/_[ ]G_j_/]I _:_ 1000 5_ °_eee TC111_ Tc14Tc13TC12 R 10T02 Dat_^ ,_Y-_//_J'a _ //|t_'_ -I _ TC05 / _ I _ / i _ TC15 /x,._. |

_ lOO _ loo _

_ _o_f_ • _ _o_'_

='_ i_Id-_ .... 1_ [I1 I ......... J, ........ _ ......... '

0 50 100 150 0 50 100 150Time, see Time, see


Trailing Surface With f) = 450 rpm.

42

Re = 13,000

o

140

120

100

80

a) Tin

60 ¸

40-50

R16T04 Data _TC02meemmTC03_TC01_TC04

i i,ii,lllllllllll,lll,,lllll_lllllll*ll

0 50 i00 150Time, sec

140

120

i00

8o.

b) Tou t

60

40-50

R16T04 Data_TC21mmmmmTC22

Tout, avg

ill tii Sill i illllllil I,II,IL iii iII1_11,1

0 50 100 150Time, sec

140

120

100.

c) Leading Surface

80 ¸

60-

40 :-50

R16T04 Data_TC02_,_-_TC03_TC04

_ TC05

'-,4_,.__. _ TC07

illltlll[lllll II,lll,l**''al'lllll III[I

0 50 100 150Time, sec

140

120

IO0

60

d) Trailing Surface

40-50

RI6T04 Data eeee_TCll

eeeeeTCl2

_TCI3

v_v_TCi4

,_TC15_-_-_TC17_TCI8

IILiIIIl III IllllllIllllll lllalllllll'll

0 50 100 150Time, sec


With f2 = 750 rpm.

43

Rc = 13,000


1000 _ R16T04 Data _ TO02 4 _ TC12 |

] r.. _,co, I looo I RI,,_D._ ____,, ]- " _ TCO3 • _ TCI3 l

. , R _4444 TC05 {[ _ _ TC07 I ] Y X"_x a.a-,ma-a TC15 |/ I "x.',_ _ TCl"t /

100 1000 50 100 150 0 50 100 150

Time, see Time, see

c) Leading Surfacei000

i00

1o

2

i

.o

ssseeTC02

_TC03v_wTC04

_TC05_TC07

_TC08

0

d) Trailing Surface

_J sesse TC12TC13TCI4TCI5

21 _ TCl7._o__ _ TC18

lO

1......... 5b........ i 66 ....... i 50 o 50 1oo 15oTime, sec Time, see


Leading Surface With f_ = 750 rpm.

44

Re--- 13,000

a) Tin140

120

100

__ 80E-.,

60

R12T02 Data eoeeoTC02BBBB_TC03_TCOI

_T904

405'0 ....... 6 ........ '5_ ....... /66 ....... ,50Time, sec

140

120

i00

P

_ eoE-_

60

b) Tou t

RI2T02 Data eeeeeTC21_TC22_TC23

------ Tout, avg

"X

4o5'6 ....... 6 ........ _'6 ....... f66 ....... %0Time, see

o_

E-_

140

120

100

BO

c) Leading Surface

R12T02 Data eeeeeTCOl_BBe_TC02_TC03

_-,_TC05_-_-_TC07

60

405'6 ....... 6 ........ i'd ....... 1'66 ....... i50

Time, see

140

120

_100

80

60

d) Trailing Surface

RI2T02 Data _TC11_TC12_TCI3_TC14

_-_TC15

_TCI7_TCI8

405'6 ....... 6 ........ 5'd ....... 1'66 ....... ]'50

Time, see

Figure 5-11. Thermocouple Data for Liquid Crystal Test on Trailing Surface

With £2 = 750 rpm.

45

Re = 13,000

a) Leading Surface b) Trailing Surface '

•1ooo _ R12zo2 Dat_ o_oTC01"l 1000 _ RIaZ02Data _ZCn ]• eeeee TC02 4 eeeee TCI8 ["_ _TC03 [ • _TC13 [

I _ _ zco4 I 4 _ Tc,4 IJ" "" _ TC05 I / _ _ TCI5 I

I00 I000 50 i00 150 0 50 I00 150

Time, sec Time, sec


RI2T02 Data eeeee TCll

seeee TCI2TCI3TC14TC15TC17TC18

0 50 1oo 1_o o ......... 5'o........ i 66 ....... isoTime, sec Time, see


Trailing Surface With f2 = 750 rpm.

46

An adjustment was applied to the measured temperature data. Offsets were applied to normalize

the thermocouple results with rotation to the same initial temperature variation as shown for the

stationary tests. Temperature offsets from mean model surface and flow temperatures for each

thermocouple were calculated from the tests with stationary conditions. These offsets were subsequently

applied to the mean model surface and flow temperatures determined for tests with rotation. The

corrected results are presented in Appendix 9.4. Note that the heat flux records were essentially

unaffected by the temperature offset adjustments.

The adjusted heat transfer coefficient results shown in the appendix are less affected by the small

temperature differences associated with the high heat transfer areas as evidenced by the flatter heat

transfer coefficient records for TC01, TC05, TC11, and TC15. The effects of rotation on heat transfer

are shown in the figures. In general, lesser increases in heat transfer coefficient as a result of rotation are

shown in the adjusted results compared to the nonadjusted results. However, the large decrease in heat

transfer in certain model areas with rotation are still predicted for the low heat transfer areas (i.e. TC07).

The effects of rotation on heat transfer are more clearly shown in the following section for two elapsed

times atter the beginning of the transient portion of the test.

5.2 Effects of Rotation on Local Heat Transfer

The adjusted heat transfer coefficient records for the medium (0.0075 lbm/sec) coolant flowrates

for all rotation rates are presented in Figures 5-13 through 5-18. Additionally, the heat transfer ratio,

Nu/Re 0.8, at 10 and 30 seconds from the start of the test are compared as a function of rotation number

for the three coolant flowrates and the three rotational rates, i.e. stationary, 450 RPM, and 750 RPM.

Adjusted results, as described above, are presented in this section and subsequent sections.

Region 1 - Tip Section - The adjusted heat transfer coefficients for Location 1 (Figure 5-13a,

leading surface) with medium flow and RPM = 0 are essentially identical, indicating repeatability for this

flow condition. The heat transfer coefficients for the two tests with medium flow and rotation are

approximately 60 to 100 percent greater than those for RPM = 0. The effect of rotation on heat transfer

ratio is shown in Figure 5-13c. These results show an increase in heat transfer (consistent with the

medium flow heat transfer coefficient results, Figure 5-13a) at moderate values of rotation number (i.e.

Ro less than 0.1) and then a subsequent decrease for larger Rotation numbers. The increase in heat

transfer coefficient is not consistent with the previous results from Guidez, 1989, or Wagner et al., 1991,

where the heat transfer on the leading surface of coolant passages with flow outward decreased with

rotation. It is likely that the increase in heat transfer at the moderate to high flowrates results from

secondary flows in the inlet duct and the continuation of these secondary flows in the coolant passage.

47

a) Location 1, Tip Region,Leading Surface

i lO00 i_

100

9

10

s-

Q Runeeeee 0 0602eeeee 0 0801

+450 1002+750 1202

Surface

TrailingLeading

TrailingTrailing

11o"'3'o"'5b'"vb'"9'o"''"_d'k5o,10

_[le, see

b) Location 11, Tip Region,Trailing Surface

I000

ool16'

10

1I0

D Run Surface

oeeee 0 . 0602 Trailing+450 1002 Trailing

+750 1202 Trailing

I'l'II'il'H'HIlil'l'iIII"l'I""'"l''lll'lill"''''lq''''"H30 50 70 90 110 130 150

T'h'n e, sec

0.1

0.01

c) Location 1, Tip Region,

Leading Surface

• 08'

$

0 0

Re

ooooo 6,000ooooo 13,00000000 27,000

Solid symbol - 10 secOpen symbol 30 see

o.OOlo.od.....o'._.....o'.d_.....o'A_.....o'.15Ro (B)

0.1

_. 0.01

Z

d) Location 11, Tip Region,Trailing Surface

00

0 =$ $$ B •

0 O0

Solid symbol - 10 secOpen symbol 30 sec

Re

ooooo 6,000

oDooo 13,000o0oo0 27,000

ii i=1_ ill= i_l°'°°lo.od" 'o'.6_ ......o.o8 o.12'" '0.16go (B)

Figure 5-13. Dimensional and Dimensionless Heat Transfer Results From

Thermocouple Data for Region 1.

48

1000

.__ 100o

c.)

s

I0

a) Location 5,Tip Region,

Leading Surface

Run Surface

o_ee.e 0 0602 Trailingv_eee 0 0801 Leading

_-_+4501002_a'._+450 1604

+750 1202 Trailing+750 1403 Trailing+750 1603 Leading

IIl|lll,l|ll,ll,l,ll,llllllllllll'lll'ltlnllllll|llllll'll|''''l'll|

10 30 50 70 90 110 130 150

TiII1e, sec

b) Location 15, Tip Region,

Trailing Surface

1000 ol

._ I00 /o

0

10 Q Run Surface

eeeee 0 0602 Trailing0 0801 Leading

+450 1002 Trailing+450 1604 Leading+750 1202 Trailing+750 1403 Trailing+750 1603 Leading

I IIIIIII II,lln,I, IIII IIIIIIIII1,,11 IIII1,, I,II Illllll IIII III III1,11,

I0 30 50 70 90 110 130 150

Time. sec

1000

c) Location 2, Root Region,

Leading Surface1000

=_ 100 o 100

_ I0'

I0 4

:1 0 0802 =_ aveee 0 0801 Leading-1 _ +450 1002 Trailing

_ +450 1604 Leading.J _ +750 1202 Trailing-| _ +750 1403 TraiLing

_ +750 1603 Leading1 I,,,,,,,,,,,,,,,,,,,.,,,,,,,,,,,,,,,,,,.,,,,,,,,.,,,,,",."'"'" 110 30 50 70 90 II0 130 150

TilIle, sec

d) Location 12, Root Region,Trailing Surface

eeeee 0 0602 Trailing

aeeev 0 0801 Leading+450 1002 Trailing

+450 1604 Leadingv_v_v +750 1202 Trailing

+750 1403 Trailing

+750 1603 Leading1,11, Ill, Ill I,I, Ill III, Ill ,,,1 Illl,llllll IIII II,.1|111111 |111111 IIIIII

I0 30 50 70 90 110 130 150

Tin'_ e, sec

Figure 5-14. Dimensional Heat Transfer Results From Thermocouple Data for

Region 2 and Re = 13,000.

49

0.1

0

0.01

Z

0.001


00

Solid symbol - 10 secOpen symbol - 30 sec

Re

ooooo 6,000

aaaao 13,000OOO00 27,000

o.od ..... 0..d_...... 0.._ .... '0..I_.... '0..16Ro (B)

0.1

0.01

Z

0.001


Trailing Surface

6-

0

gg

Solid symbol - i0 secOpen symbol 30 sec

Re

ooooo 6,000oaooo 13,00000000 27,000

,o6.....0..6,_......od_.....o'i_.....0:18Ro (B)

0.1

0.01

c) Location 2, Root Region,Leading Surface

00

• iP o

Solid symbol -- I0 sec

Open symbol 30 sec

Re

ooooo 6,000ooooo 13,00000000 27,000

o.ool 0.06 ...... o.o4'...... o'._ ..... o'._. ..... o'.16Ro (B)

0.I

._ 0.01

Z

0.001

d) Location 12, Root Region,

Trailing Surface

o O

## •

O

O@

Solid symbol - i0 sec

Open symbol 30 sec

• Re

ooooo 6,000ooooo 13,000

00000 27,000

0.06 ..... 0'.0'_ ..... 0'.()8..... 0..I_-..... 0.16

Ro (B)

Figure 5-15. Dimensionless Heat Transfer Results From Thermocouple Data

for Region 2.

5o

The results for Location 11 (Figure 5-13b and d, trailing surface, tip region) are generally similar

to previous studies (e.g., Hajek et al., 1991). Heat transfer coefficient and heat transfer ratio are shown

to increase, on the order of 50 percent, with increases in rotation number, especially for the low to

moderate flowrates.

The general conclusion from the analysis of the heat transfer results from Region 1 are that the

effect of rotation is consistent with earlier results where heat transfer decreases on the low pressure side

of the passage and increases on the high pressure side. However, this only appears to be consistently true

for the low flowrate. Note that the previous experience is generally limited to Reynolds numbers of

50,000 and below. The high flowrate case of the present program results in a local Reynolds number

significantly greater than previous experience (over 70,000). Considering that inlet flow effects may be

convecting into the coolant passage for the high flowrate cases, it is inappropriate to generalize the effect

ofrotation on the heat transfer results for Region 1.

Region 2 - Tip Section - The calculated heat transfer coefficient, Hr, for the medium flowrate

(Figure 5-14a) increased significantly with rotation for TC Location 5 (tip leading surface). The

calculated coefficients at 10 seconds were approximately 25 percent greater then the stationary values

and generally increased with time. Heat transfer on the trailing surface (TC Location 15, Figure 5-14b)

for the medium flowrate is much less affected by rotation. Heat transfer is shown to increase and

decrease with rotation compared to the stationary results. Additionally, the results are uncorrelated with

rotation rate. The effect of rotation number on heat transfer is shown in Figure 5-15a and b. Heat

transfer ratio is shown to increase with increases in rotation number on the leading and trailing surfaces.

Whereas the increase in heat transfer on the leading surface is pronounced at the low and moderate

rotation numbers, the effect of rotation on heat transfer on the trailing surface is minimal. In general,

heat transfer ratio for all flowrates increased or stayed the same with rotation. These results had high

heat transfer coefficients as expected from previous results. The local streamwise velocities are high and

a great deal of turbulence and vorticity downstream of the turn is expected. The conclusion from these

comparisons is that the vorticity in the channel is increased significantly due to rotation.

Region 2 - Root Section - The results from TC Location 2 at the root on the leading surface with

the medium flowrate and radially inward flow (Figure 5-14c) are compatible with Hajek et al., 1991.

Heat transfer coefficients increase on the leading surface approximately 50 percent with rotation. The

results for TC Location 12 at the root on the trailing surface appear anomalous (as discussed above for

51

the tip section) compared with the values for stationary conditions. Heat transfer coefficient is shown to

increase and decrease with rotation but is uncorrelated with the rotation rate. The effect of rotation

number on the heat transfer ratio is shown in Figure 5-15c and d for the root section of Region 2. The

results on the leading surface generally increase with rotation number for low to moderate valtles of

rotation number and then subsequently decrease to the same level of heat transfer ratio measured for the

stationary tests. The trend of the trailing surface results is opposite to that of the leading surface such

that heat transfer ratio generally decreases with rotation number for low to moderate values of rotation

and then subsequently increases to the same level of heat transfer ratio measured for the stationary tests.

The conclusion from the analysis of the heat transfer coefficient and heat transfer ratio results

from Region 2 is that heat transfer increased and decreased significantly with rotation on the leading and

trailing surfaces especially for the medium to high flowrate test conditions.

Region 3 - Tip Section - The tip, leading surface of Region 3 (TC Location 7, Figures 5-16a and

5-17a) was the only region that had consistently lower heat transfer with rotation. The heat transfer in

this region with rotation was as low as 10 to 30 percent of that with no rotation. Heat transfer on the

trailing surface (TC Location 17, Figures 5-16b and 5-17b) is less affected by rotation compared to the

leading surface. However, heat transfer is shown to increase slightly and then decrease with an increase

in the rotation number.

Region 3 - Root Section - The heat transfer in the root region of Region 3 (Figures 5-16c and d

and 5-17c and d) is shown to increase slightly and then decrease with rotation number on the leading and

trailing surfaces. These results are inconsistent with Coriolis driven secondary flows and are likely

affected by more complex rotation induced flow structures.

The general conclusion from the analysis of the heat transfer results obtained in Region 3 is that

the heat transfer is strongly affected by rotation especially in the tip section where heat transfer was

substantially reduced.

Region 4 - Tip section - The heat transfer on the leading and trailing surfaces in the tip region of

Region 4 (TC Location 8 and 18, Figures 5-18a and b and 5-19a and b) was relatively unaffected by

rotation. This relative insensitivity to rotation would be expected when the flow is axial and the stream

tubes do not change radius.

52

1000

.-_ 100o

a) Location 7, Tip Region,

Leading Surface

fl Run Surface

eeee-e 0 0602 Trailing

eeeee 0 0801 _a'._+450 1002+450 1604 Leading

+750 1202 Trailin E+750 1403 Trailing+750 1603 Leading

10 -

I

1 •

10 30 50 70 90 110 180 150

Ti.lIle, sec

1000

o 100

b) Location 17, Tip Region,Trailing Surface

fl Run Surface

e_e_e 0 0602 Trailing0 OflOl Lea.di'.ng

+450 1002 Trailing+450 1604 Leading

+750 1202 Trailing+750 1403 Trailing'"+750 1603 Leading

2

10 30 50 70 90 110 130 150

TiIne. sec

I000

100

10


Leading Surface

0 Run Surface

eeeee 0 0602 _Le "aa_'_0 0801

+450 1002 Trailing+450 1604 Leading+750 1202 Trailing+750 1403 Trailing+750 1603 Leading

iHi,,,, lilll,, "*IIH'II''III|I*IIII'IHII' "lllilllill|'l|lli''i"

10 30 50 70 90 110 130 50

TiIne, sec

1000

8"


Trailing Surface

0 Run Surface

0 0602 Trailingseeee 0 0801 Leading

+450 1002 Trailing+450 1604 Leading+750 1202 Trailing+750 1403 Trailing+750 1603 Leading.2 I00

o

8

:11 ii1||;111 ill i¢11111|1115IH|I|II|IIIII 1|1114¢¢H II;I HII II¢illlll|51

10 30 50 70 90 110 130 150

Time. sec

Figure 5-16. Dimensional Heat Transfer Data From Thermocouple Data for

Region 3 and Rc = 13,000.

53

0.01

0.001

Z

0.0001

a) LocationT, TipRegion,Leading Surface

SoLd symbol -- 10 seeOpen symbol - 30 sec

Re

ooooo 6,000ooooo 13,00000000 27,000

,.,o• •

0 o O

oo

oO

@

iL=l=tlt===ll i|=1 i===o.oo 0.04 '6.d_ 'd.i_ 'd.1.Ro (B)

0.01

0.001

z

5-


Trailing Surface

O

0 *t_' 8 o• _ eo

Solid symbol - 10 secOpen symbol - 30 sec

Re

ooooo 6,000Maoonn 13,00000000 27,000

o.ooo10.06.....o'.6_.....o'.d_.....o'.i_......o.16Ro (B)

0.1

0

_ 0.01

Z

0.001

c) Location3, RootRegion,LeadingSurface

Solid symbol - I0 seeOpen symbol -- 30 sec

Re

ooooo 6,000

ooooo 13,000OOOOO 27 000

o 0

• i o

• 0 0

i i i D i i s i i i _ e = i i i e i io.o6 'o'.d_..... o.os o.1_ 'o'.16Ro (B)

0.1

30.01

Z


Trailing Surface

SoLd symbol - 10 secOpen symbol -- 30 sec

Re|-

)oooo 6,000ooooo 13,00000000 27,000

,! = oo

o.ool d......'......o'd_......'......o.o 0.o¢ . o.12 o.16Ro (B)

Figure 5-17. Dimensionless Heat Transfer Data From Thermocouple Data for

Region 3.

54

1000

"_ 1000

8

_ 1o

a) Location 8, Tip Region,

Leading Surface

0 Run Su_ace

oeoee 0 0602 TrailingVHaee_ 0 0801 Leading

+450 1002 Trailing+450 1604 Leading+750 1202 Trailing+750 1403 Trailing

+750 1603 Leading

llUlllUll[llllll,ll iiiiiii 1111111 iiii iiii iiii iiiiiiiiiiiiiiiii IIII III I

10 30 50 70 90 110 130 150

TiIne, Sec

1000

o 100

8cD

"_ 10


Trailing Surface

0 Run Surface

oeeee 0 0602 Trailing0 0801 Leading

+450 1002 Trailingee#-o-0 +450 1604 Leading


,.11,,,,|..1,, H, 1111.11|11, II.1.1| ,SIIH,,+I+II]+I+'I+IHI''''I+H '

10 30 50 70 90 110 130 150

Tinle, sec

I000


Leading Surface

Run Su_ace

eeoeo 0 0602 Trailingeeeee 0 0801 Leading

+450 1002 TrailinE+450 1604 Leading+750 1202 Trailing+750 1403 Trailing+750 1603 Leading

.2 1000

8

_ 10 .

10 30 50 70 90 110 130 150

rilne, SeC

1000

o 100"3

8C.)

1o


Trailing Surface

Q Run Surface

eeeee 0 0602 Trailingeeeee 0 0801 Leading

+450 1002 Trailing(H_H_ +450 1604 Leading


llll llllll I lllllll III IIII IIII IIIIIIIIIII IIII III IIII IIII III 1111 IIIII

10 30 50 70 90 110 130 150

TiIne, sec

Figure 5-18. Dimensional Heat Transfer Data From Thermocouple Data for

Region 4 and Re = 13,000.

55

0.1

0.01

2_

0.001


Solid symbol -- 10 secOpen symbol -- 30 sec

Re

)oooo 6,000ooooo 13,000

00000 27,000

O

13

• • 0

).0(_, , , , , , i , _ , , , , , , , , , , , , ,0.04 '0'.6fi '0'.I_. 0.16Ro (B)

0.1

0.01

Z


Trailing Surface

Solid symbol -- 10 secOpen symbol 30 sec

Re

ooooo 6,000ooooo 13,000

ooo00 27,000

IIk

@@

o.OOlo.o6..... o'.di..... o'.dg..... o'.i_..... o'.16Ro (B)

0.1

0.01

0.0010.00


Leading Surface

Solid symbol - 10 seeOpen symbol -- 30 sec

Re

ooooo 6,000ooooo 13,00000000 27,000

00O o*! '_ I, .

I

i;i illll# t i llll 1111 ll;i ii1_ ii ii

0.04: 0.08 0.12 0.16

Ro (B)

0.1

0.01

Z


Trailing Surface

Solid symbol - 10 secOpen symbol -- 30 sec

Re

ooooo 6,000iooooo 13,00000000 27,000

i °6

. $ 0 •

0

0

e

o.oo, 06.....o'd_......'.......'......o'O. . 0.08 0.12 .16

Ro (B)

Figure 5-19. Dimensionless Heat Transfer Data From Thermocouple Data for

Region 4.

56

Region 4 - Root Section - The heat transfer for TC Locations 4 and 14 (Figures 5-18c and d and

5-19c and d) are also relatively unaffected by rotation. One could conjecture that an increase in heat

transfer ratio occurred with an increase in rotation number at low rotation numbers on the leading

surface. However, the increased heat transfer ratio results are for the high flowrate case only which

might suggest a flow redistribution effect rather than a rotation induced flow phenomena.

The conclusion from the analysis of the heat transfer results from Region 4 is that rotation effects

are minimal when the flow is predominately axial. Any heat transfer differences with rotation are more

likely to be the result of a flow redistribution between the three exiting flow streams rather than by a

rotation induced secondary flow.

57

5.3 Summary of Results from Thermocouple Measurements

[] The heat transfer coefficients in the tip section of Regions 1 and 2 are at least twice as much as those

in other regions of the coolant passage.

[] Heat transfer in Regions 1 and 2 are significantly affected by rotation. The results are generally

consistent with previous studies where heat transfer increases on the high pressure side of a passage

and decreases on the low pressure side.

[] The affects of rotation are most pronounced on the leading surface of the tip section of Region 3.

Heat transfer decreased to a level of 10 to 30 percent of stationary levels when the model was

rotating. The consequence of this result is that this region of the airfoil is essentially uncooled. The

low heat transfer in this region is attributed to a redistribution of the coolant flow which results in a

large recirculating stall cell.

[] The heat transfer in Region 4 with axial flow was less affected by rotation than Regions 1, 2, or 3.

58

6.0 HEAT TRANSFER RESULTS FROM LIQUID CRYSTALS

The video records for fitteen combinations of model orientation and flow conditions of transient

heat transfer tests are available from the NASA LeRC. Used in conjunction with the thermocouple'data

for the same tests, such as that presented in Section 5, these video data might be used to evaluate codes

for predicting conjugate heat transfer in complex coolant passages. The results also show the shapes of

the constant heat flux contours and provide insight, through inference of the flow structure in the coolant

passages.

Because the transient heat flux and temperature distributions do not lend themselves to easy

interpretation, those data were used, along with the thermocouple data, to develop heat transfer

coefficient contours. Corresponding flow parameters for the selected tests for several locations in the

model coolant passage (Figure 3-2) are presented in Appendix 9.2.

The temperatures measured with the liquid crystals on the stationary model were in good

agreement, i.e. +/- 0.5C (IF), with the thermocouple measurement for stationary test conditions. The

temperature calibration of the liquid crystals changed considerably during rotation. The liquid crystals are

known to be sensitive to shear stresses which will occur due to the centrifugal force on the liquid crystals

due to its own weight and that of the black overcoat on the liquid crystal paint.

6.1 Results for Stationary Tests

The video records of liquid crystal isotherms for the leading and trailing surfaces of the model for

the middle flowrate are presented in Figures 6-1 and 6-2, respectively. The contours noted were drawn

from processed frames of video data like that shown in Figure 3-11. The identification system uses the

isotherms, 1 through 6, and the video times, 1 through 4, for test 8.1 (Figure 6-1).

Nomographs were constructed from surface thermocouple data, obtained concurrently, to aid in

the interpolation of each set of liquid crystal data (Figure 6-3). The heat transfer coefficients, determined

for each thermocouple, are plotted as a function of local wall temperature for selected times into the test.

The heat transfer coefficients at selected times after the start of the test (Times 1, 2, 3, and 4) for wall

temperatures (Isotherms 1 through 6) are determined by intersecting a vertical wall temperature isotherm

line with a selected test time shown as dashed lines in the nomograph figures. Heat transfer coefficients

greater and less than the range of data are obtained by extrapolation.

59

Isotherms

1 - 46.7 °C (116 °F)

2 - 43.3 °G (110 °F)

3 - 37.8 °C (100 °F)

4 - 32.2 °C ( 90 °F)

5 - 26.7°C ( 80 °F)

6 - 21.1 °C ( 70 °F)

Video Times ID System

1 - 5.8 sec

2- 9.2sec D [-7

3- 17.4sec I _---4 - 33.3 sec Time ,Isotherm

32

43

23, 34

12, 34

o o21

11,22,33,44

13

23 34 _ _-1224

22,33

11,44

Figure 6-1. Video Records of Liquid Crystal Isotherms for Test 8.1.

6O

Isotherms

1 - 46.7 °C (116 °F)

2 - 43.3 °C (110 °F)

3 - 37.8 °C (100 °F)

4 - 32.2 °C ( 90 °F)

5 - 26.7°C ( 80 °F)

6 - 21.1 °C( 70 °F)

Video Times

1 - 4.7 sec

2 - 7.8 sec

3 - 15.4 sec

4 - 29.4 sec

ID System

Time

Isotherm

23

13, 1234

23

23

13


61

. "tuda 0 = ET pue 000'EI = o_I _oj _31eG IelS,(aD p!nb!l _u.q_nleA_ .mj qde:_otuo N "g-9 aang!tt

0_I 00I 09 09 0_I 00I 09

Og x_01, -H-H-Fgg _ \

08

o__'_..... \ \

iiI\ L_ a\ \_ f:l:t:t:_

\'\

'\ \, \ '\ _ "_ \'v

\ \ \atur.,L 1. \ _\ £ ___ IA___

-[-'_--_--_5--9"

su_saq_osI:

(:6 9_ ) Do _'_l_ = (pua) uT.I.

(90 0_I) Do 8"8_ = (]ae_s) m.L

_;'9 _,saLa_jsn S _[.n_s.I. (q

000!

O9

og x_Of,

gg P_Ogq_

/. ta..U.L_

_o N

"_N"., o\ _ _.",b"k\ \ N

N% •

"" ",, 'x 00I _

\ \\ \

,, \ \ \_

au_..I, I'x- gx- -_ k I, _-

stu:;aq]oslI 000I

_-5_ I_-5"s_.T_Iuaosj _G

(_To9_ ) Do _'_ = (pua) _L(_qo0_0 Do 9"9D= 0s_ s) _..L

178 %saL

a3ejsn s _pea'-I (e

Note: Dotted iso-coefficients

from TC data

O',

a) Leading SurfaceTest 8.1

II

/

b) Trailing SurfaceTest 6.2

3

Figure 6-4. Heat Transfer Coefficients From Liquid Crystal Isotherms for Re = 13,000 and f2 = 0 rpm.

The iso-heat-transfer coefficients at the intersections of the times and wall temperatures are

plotted on Figure 6-4. In Regions 1 and 2, the heat transfer coefficient contour shapes and levels on the

leading and trailing surfaces are similar. Variations in the results between the leading and trailing surfaces

(+/- 15 percent at the same location in the coolant passage) are indicative of the precision with whi6h the

heat flux and heat transfer coefficients can be determined using the liquid crystal and transient heat

transfer measurement system. The heat transfer on the leading and trailing surface in Region 4 are also

approximately the same on both sides of the channel, although the shapes of the contours in the middle

and root passages have significantly different shapes. The leading surface heat transfer contour shapes

indicate centerflowing coolant in the middle and root passages while the trailing surface contours suggest

the coolant flow is biased to the side of the passage. These differences are attributed to the curvature in

the coolant passage as the gas paths changes from radial (Region 1) to axial (Region 4).

6.2 Results from Rotating Tests

The apparent calibration of the liquid crystal paint changed appreciably due to rotation.

Consequently, an effort was made to evaluate isotherms which were adjacent to or passed over the

surface thermocouples. The isotherms selected are shown in Figures 6-5 and 6-6 for tests at 450 RPM

and in Figures 6-9 and 6-10 for tests at 750 RPM. Nomographs were constructed for the four data sets

required for the leading and trailing surfaces at 450 and 750 RPM (Figures 6-7 and 6-11). However,

comparison of the liquid crystal contours with thermocouple data indicated that the liquid crystal paint

calibration had shifted as much as 7.8°C (14°F) (e.g., in one instance the 46.6°C (116°F) liquid crystal

paint calibration had shifted to 38.9°C (102°F)). Consequently, the contours passing through the surface

thermocouple locations were used to characterize the heat transfer. Analysis of the liquid crystal and

thermocouple results suggested a constant shit_ in the paint calibrations was appropriate to compensate

for the effects of rotation. Therefore, a shi_ of 6°C(10°F) was applied to the liquid crystal paint

calibrations for tests with rotation (Figures 6-7 and 6-11) to help in the interpretation of the nomographs.

Iso-heat-transfer coefficient results for the medium flowrate at 450 and 750 RPM are presented in

Figures 6-8 and 6-12, respectively. As noted in the discussions of the thermocouple results, the largest

effects of rotation occurred on the leading surface in the tip section of Region 3 where the heat transfer

decreased by a factor of approximately 5 at the thermocouple location. The large decrease in heat

transfer is the result of a rotation induced flow redistribution in the exiting, Region 4, passages.

Comparing the contours of heat transfer coefficient with rotation (Figures 6-8 and 6-12) with those from

the stationary test (Figure 6-4) the flow structure is significantly different on the leading surface. The

flow structure in the outward passage of Region 4 is centerflowing when stationary and skewed when

rotating as a result of the blockage in the Region 3 tip section.

64

Isotherms

1 - 46.7 °C (116 °F)

2 - 43.3 °C (110 OF)

3 - 37.8 °C (100 OF)

4 - 32.2 °C ( 90 °F)

5 - 26.7 °C( 80 °F)

6 - 21.1 °C( 70 °F)

Video Times

1 - 18.9 sec2 - 30.9 sec

ID System_

Jl Time '

Isotherm

12

12

11

22

11


65

Isotherms

1 - 46.7 °C (116 OF)

2 - 43.3 °C (110 OF)

3 - 37.8 oc (100 °F)4 - 32.2 °C ( 90 °F)

5 - 26.7 °C ( 80 °F)

6 - 21.1°C( 70 °F)

Video Times1 - 17.0 sec

2 - 26.0 sec

3 - 49.7 secTime

Isotherm

32

\

11, 22, 33

11, 22, 33

11, 22

3312

13

12

21

11, 22, 33

O

23

12, 23

12

23

13


66

tO00


Tin (start) = 51.7 °C (125 °F)

Tin (end) = 23.9 °C ( 75 °F)Data from Figs. 5-5 & 5-6

[-Iso erms I I [3 2--1

i000


Tin (start) = 52.8 °C (127 °F)


Isotherms - I [3 2--1

8

tO0

I0

160

2 1 Time100

\\\\'"'_ \ \ 8

\'_ x\\,\ , XX

t 0\\\ . \ \. _ _ F.)¢_..

\",Y ,%\ _111 s,o"<&\/111See _5

t3B_ 7 a_,_ I0

_ _o __ 25

25 ',_MI 8O884) 30

O'88"84) 30 _ _ _5

35 • -H-H-F 4040 >aa+x_ 50

50 I

80 tO0 t20 60

Twall, deg F

,..3--:2-1- Time

\ N,_ X

80 100

Twall, deg F

t20

Figure 6-7. Nomograph for Evaluating Liquid Crystal Data for Re = 13,000 and f) = 450 rpm.

Notes: Dotted iso-coefficients from TC data.

Iso-coefficients interpolated between values at TC locations

due to liquid crystal calibration shift with rotation.

O_

8


O

V


® 10

7

9

5

10

Figure 6-8. Heat Transfer Coefficients From Liquid Crystal Isotherms for Re = 13,000 and f2 = 450 rpm.

Isotherms

1 - 46.7 °C (116 °F)

2 - 43.3 °C (110 °F)

3 - 37.8 °C (100 °F)

4 - 32.2 °C ( 90 °F)

5 - 26.7 °C ( 80 °F)

6 - 21.1 °C ( 70 °F)

Video Times

1 - 15.6 sec

2 - 23.8 sec3 - 43.9 sec4 - 58.0 sec

ID System

Time

Isotherm

2311

33

22


69

Isotherms

1 - 46.7 °C (116 °F)

2 - 43.3 °C (110 °F)

3 - 37.8 °C (100 °F)

4 - 32.2 °C( 90 °F)

5 - 26.7°C( 80 °F)

6 - 21.1 °C ( 70 °F)

Video Times1 - 19.4 sec

2 - 32.9 sec

3 - 99.0 sec

ID System

Time _

Isotherm

32

11

22, 33

\

21

12

o

o

o o

o o

13

12, 23

1213

11, 22, 33

12

12

13

12


7O

t000


Tin (start) = 51.1 °C (124 °F)



Tin (start) = 51.1 °C (124 °F)

Tin (end) = 25.0 °C ( 77 °F)

Data from Figs. 5-11 & 5-12

I I000 I

Isotherms-- Isotherms--4._ 3 _ 2 --1 - -- 3 2--1

.,4

8

100

I0

t60

4_3 __2_1_ Time _ _. too 3:_2 -- 1--Time-

\\

G'K'% '

_ See' ,_\,X&\l [I _5Sec

'° \NI_ 25

25 _"Pa,k_ 08.0_0 30

30 l_ _ 35

35 _ 40

-H-'H-+ 40 _ 50

x-x-w.w-K50 I

80 100 120 60 80 tOOTwall, deg F Twall, deg F

,, \ XI_

120

Figure 6-11. Nomograph for Evaluating Liquid Crystal Data for Re = 13,000 and f_ ---750 rpm.

Notes: Dotted iso-coefficients from TC data.

Iso-coefficients interpolated between values at TC locations

due to liquid crystal calibration shift with rotation.

.,,abo

6

12

6

a) Leading Surface b) Trailing SurfaceTest 16.4 Test 12.2

I _

/50

\

10

®

Figure 6-12. Heat Transfer Coefficients From Liquid Crystal Isotherms for Re -- 13,000 and f2 = 750 rpm.

7.0 COMPARISON WITH PREVIOUS ANALYSIS

Only general heat transfer characteristics can be compared due to the differences in operating

conditions and the lack of velocity and pressure data within the model. The largest noticeable difference

in the flow fields and heat transfer between the four sets of calculations, Ippolito, 1991, Dawes, 1992,

Steinthorsson et al., 1991, and Stephens et al., 1993, occurs in Region 2 where the flow is radially

inward. The results of Ippolito, 1991, and Steinthorsson 1991, show higher velocities along the outer or

tip section of Region 2 and along the divider between Region 2 and Region 3. The results of Dawes,

1992, and Stephens, et al., 1993, show higher velocities in the center of the Region 2 passage. High heat

transfer accompanied the higher velocities in the preceding calculations. The results from both the

rotating and stationary heat transfer experiments show the highest heat flux in the center of the channel

with the characteristic predicted by Dawes, 1992, and Stephens et al., 1993. More recent work by

Steinthorsson, 1993, with a finer grid also produced (unpublished) results with the flow tending toward

the center of the Region 2 passage.

A second region in which general characteristics can be compared is the tip section of Region 3.

All the analyses showed low velocities and low heat transfers in this region. However, from the

numerical results presented, it does not appear that a significant difference was predicted by any of the

analyses in the heat transfer between the leading and trailing surface.

The heat transfer contours predicted by Ippolito, 1991, in the root section of Region 3 also

resemble the contours measured and have larger heat transfer coefficients on the leading surface than the

trailing surface. Recall that the experimental results from the leading and trailing surfaces of the root

section, Region 3, indicated increased levels of heat transfer with rotation for certain rotation numbers.

The shapes of the Region 4 heat transfer contours predicted by Ippolito, 1991, in the root, middle,

and tip passages resemble the contours measured.

Several of the heat transfer characteristics measured in the 1.15 scale model of the NASA LeRC

High Temperature Radial Turbine appear to be predicted by one or more of the numerical studies.

However, a more complete evaluation of the numerical procedures by direct comparison with the present

experiments requires that calculations be made using the boundary conditions of the experiment,

including possibly the conjugate heat transfer condition of the transient heat transfer experiment.

73

8.0 REFERENCES

Anon, 1989, "Rotor Assy-Air-Cooled Radial Turbine: Drawing Ex159092", Allison Gas Turbine

Division, July 12, 1989.

Blair, M.F., Wagner, J.H., and Steuber, G.D., 1991, "New Applications of Liquid Crystal

Thermography in Rotating Turbomachinery Heat Transfer Research", ASME Preprint 91-GT-354.

Calvert, G.S., Beck, S.C., and Okapuu, E., 1971, "Design and Experimental Evaluation of a

High-Temperature Radial Turbine", USAAMRDL TR 71-20.

Clifford, R.J., Jones, T.V., and Dunne, S.T., 1983, "Techniques for Obtaining Detailed Heat

Transfer Coefficient Measurements Within Gas Turbine Blade and Vane Cooling Passages," ASME

Paper 83-GT-58.

Clifford, R.J., 1985, "Rotating Heat Transfer Investigations on a Multipass Cooling Geometry",

AGARD Conference Proceedings, No. 390: Heat Transfer and Cooling in Gas Turbines.

Dawes, W.N., 1992, "The Solution-Adaptive Numerical Simulation of the 3D Viscous Flow in

the Serpentine Coolant Passage of a Radial Inflow Turbine Blade", ASME Paper 92-GT-193.

Eckert, E.R.G., Diaguila, A.J. and Curren, A.N., 1953, "Experiments on Mixed - Free and

Forced-Convective Heat Transfer Connected with Turbulent Flow Through a Short Tube", NACA

Technical Note 2974.

EI-Husayini, H.A., Taslim, M.E. and Kercher, D.M., 1992, "Experimental Heat Transfer

Investigation of Stationary and Orthogonally Rotating Asymmetric and Symmetric Heated Smooth and

Turbulated Channels", ASME Paper 92-HT-189.

Guidez, J., 1989, "Study of the Convective Heat Transfer in Rotating Coolant Channel", ASME

Turbomachinery, Vol 111, pp. 43-50.

Hajek, T.J., Wagner, J.H., Johnson, B.V., Higgens, A.W., and Steuber, G.D., 1991, "Effects of

Rotation on Coolant Passage Heat Transfer: Volume 1 - Coolant Passages with Smooth Walls", NASA

Contractors Report 4396.

74

Hammer, A.N., Aigret, G.G., Psichogios, T.P., and Rodger, C., 1986, "Fabrication of Cooled

Radial Turbine Rotor", (SR 86-R-4938, Solar Turbines, Inc.,) NASA CR- 179503.

Han, J.C., Zhang, Y.M., and Lee, C.P., 1992, "Influence of Surface Heating Condition on Local

Heat Transfer in a Rotating Square Channel with Smooth Walls and Radial Flow Outward,", ASME

Paper 92-GT-188.

Han, J.C., Park, J.S. and Ibrahim, M.Y., 1986, "Measurement of Heat Transfer and Pressure

Drop in Rectangular Channels with Turbulence Promoters", NASA Contractors Report 4015.

Ippolito, J., 1991, "Three Dimensional Flow Analysis of the Internal Passage of a Cooled Radial

Rotor", Analysis and Design Application Company, LTD., Report Number 30-02-004, April 26, 1991.

Johnson, B.V., Wagner, J.H., Steuber, G.D. and Yeh, F.C., 1992, "Heat Transfer in Rotating

Serpentine Passages with Trips Skewed to the Flow", ASME Paper 92-GT-191.

Johnson, B.V., Wagner, J.H., and Steuber, G.D., 1993, "Effect of Rotation on Coolant Passage

Heat Transfer: Volume II - Coolant Passages with Trips Normal and Skew to the Flow", NASA

Contractors Report 4396.

Johnston, J.P., Halleen, R.M., and Lezius, D.K., 1972, "Effects of Spanwise Rotation of the

Structure of Two-Dimensional Fully Developed Turbulent Channel Flow", J. Fluid Mech., Vol 56, Part 3,

pp 533-557;

Kreith, F., 1973, "Principles of Heat Transfer" 3rd Edition, Intex Press, Inc., pp 177.

Kumar, G.N. and Deanna, R.G., 1998, "Development of a Thermal and Structural Analysis

Procedure for Cooled Radial Turbines", ASME Paper 88-GT-18.

Kumar, G.N, and Deanna, R.G, , 1989, "A Generalized One Dimensional Computer Code for

Turbomachinery Cooling Passage Flow Calculations", NASA Technical Memorandum 102079.

Metzger, D.E. and Larson D.E., 1986, "Use of Melting Point Surface Coatings for Local

Convective Heat Transfer Measurements in Rectangular Channel Flows with 90-deg Turns", ASME J.

Heat Transfer, Vol 108, pp 48.

75

Metzger, D.E., Bunker, R.S., and Bosch, G., 1989, "Transient Liquid Crystal Measurement of

Local Heat Transfer on a Rotating Disk with Jet Impingement", ASME Paper 89-GT-287.

Mochizuki, S., Takamura, J., Yamawaki, S., and Yang, W.J., 1992, "Heat Transfer in Serpentine

Flow Passages with Rotation", ASME Paper 92-GT-190

Morris, W.D., 1981, Heat Transfer and Fluid Flow in Rotating Coolant Channels, Research

Studies Press.

Roelke, R.J, 1991, Coordinates for Coolant Passage Core of NASA LeRC High-Temperature

Cooled Radial Turbine, Private Communication.

Saabas, J., Arora, S.C., and Abdel Messeh, W., 1987, "Application of the Transient Test

Technique to Measure Local Heat Transfer Coefficients Associated with Augmented Airfoil Cooling

Passages", ASME Paper 87-GT-212.

Schultz, D.L., Jones, T.V., Oldfield, M.L.G., and Daniels, L.C., 1973, "Heat Transfer

Measurements in Short-Duration Hypersonic Facilities", Agardograph 165.

Snyder, P.H., 1992, "Cooled High-Temperature Radial Turbine Program", NASA CR 189122,

USAACSCOM TR-92-C-010, Allison Report No. EDR 15982, May 1992.

Snyder, P.H. and Roelke, R.J., 1988, "The Design of an Air-Cooled Metallic High Temperature

Radial Turbine," Conference Preprint AIAA-88-2872.

Steinhorsson, E., Shih TI-P and Roelke R.J., 1991, "Computation of the Three-Dimensional Flow

and Heat Transfer Within a Coolant Passage of a Radial Flow Turbine", Conference Preprint AIAA-91-

2238. 1991.

Steinthorsson, E., Liou, M.S., and Povinelli, L.A., 1993, "Development of an Explicit

Multiblock/Multigrid Flow Solver for Viscous Flows in Complex Geometries", Conference Preprint

AIAA-93-2380.

Steinthorsson, E., 1993, "Private Communication", July.

76

Stephens, M.A.., Rimlinger, M.J., and Shih T.I-P, 1993, "Chimera Grids in the Simulation of

Three-Dimensional Flowfields in Turbine-Blade-Coolant Passages", Conference Preprim AIAA-93-2559.

Vershure, R.W., Large, G.D., Meyer, L.J., and Lane, J.M., 1980, "A Cooler Laminated Radial

Turbine Technology Demonstration", AIAA Paper 80-0300.

Wagner, J.H., Johnson, B.V., and Hajek, T.J., 1991, "Heat Transfer in Rotating Passages with

Smooth Walls and Radial Outward Flow", ASME Turbomachinery, Vol. 113 pp 42-51, January (ASME

Paper 89-GT-272).

77

9.0APPENDIX

79

9.1 Nomenclature

d

H

Hr

k

QwR

Re

Ro

t

T

V

W

x

(X

_t

£0

P

Hydraulic diameter, 2HW/(H+W)

Leading to trailing surface separation difference

Heat transfer coefficient, Btu/Ft2/hrFF

Thermal conductivity

Heat flux, Btu/Ft2/hr

Radial position

Reynolds number

Rotation number

Time

Temperature

Coolant velocity

Width of coolant passage

Distance into model wall

Thermal diffiasivity

Dynamic viscosity

Rotation rate rad/sec

Density

Subscripts:

b, c

w, wall

d

h

Bulk fluid property

Fluid property at the wall

Parameter based on hydraulic diameter

Parameter based on separation distance

80

9.2 Tables of Flow Conditions for Full Scale NASA Radial Turbine and 1.15 Scale Model

Coolant Passage

Note:

Model pressures noted are derived from an average of the measured pressures at the flowmeter locations

upstream and downstream of the rotating facility. Temperatures were measured in the model coolant

passage. For parametric analysis the wall temperature, Tw, was assumed to be the initial coolant

temperature prior to the transient portion of a test and the coolant temperature, To, was assumed to be

the inlet coolant temperature at 150 seconds. These two temperatures provided the ideal heat transfer

potential used for comparisons of the test results.

81

NASA RadialTurbine Full Scale

LocationFlowratcRadius

H

WPc

TcTwROh

REdBUOY

DensityVelocityRPM

Omegad

area

visc(mu)k

A0.0154

6.8

0.1100.246

24.5600

7500.02872949

0.00960.110742.6

215962261.5

0.1520.0001881.42E-05

0.0180

B

0.01546.8

0.1100.826

18.0650750

0.06427086

0.03330.075326.2

215962261.5

0.1940.0006311.46E-05

0.0186

C

0.01546.8

0.1701.983

12.0

700750

0.22611506

0.1356

0.046142.1

215962261.5

0.313

0.0023411.49E-05

0.0191

#1secin

inin

psiadeg R

degR

#/ft^3ft/sec

rad/secinin^2

lb/sec-ftBTU/ft-hr-F

82

1.15 Full Scale Model

Median Coolant Flow Rate

Stationary Model

Test # : 6.2 Date:

Location AFlowrate 0.0073

Radius 19.0H 0.127W 0.283

Pc 164.2Tc 514.5

Tw 579.9KOh 0.000REd 34676

BUOY 0.0000

Density 0.862Velocity 34.2RPM 0

Omega 0.0d 0.175area 0.000249

visc(mu) 1.24E-05k 0.0152

Test # : 8.1 Date:

Location A

Flowrate 0.0073Radius 19.0

H 0.127W 0.283

Pc 164.0Tc 514.9

Tw 580.7ROh 0.000

REd 34745

BUOY 0.0000

Density 0.861

Velocity 34.3RPM 0

Omega 0d 0.175

area 0.000249

visc(mu) 1.24E-05k 0.0152

B0.0073

19.00.127

0.950164.2514.5

579.90.000

131910.0000

0.86210.2

00.0

0.2230.0008351.24E-05

0.0152

B0.0073

19.00.1270.950

164.0

514.9580.70.000

13217

0.0000

0.86110.2

00

0.223

0.0008351.24E-05

0.0152

C0.0073

16.50.1962.280

164.2514.5

579.90.000

57360.0000

0.8622.7

00.0

0.3600.003095

1.24E-050.0152

C0.0073

16.5

0.1962.280

164.0514.9

580.7

0.0005748

0.00000.861

2.8

00

0.360

0.0030951.24E-05

0.0152

#/sec

ininin

psiadeg P.

deg R

#/ft^3ft/sec

rad/sec

inin^2


#/sec

in

in

in

psia

deg Rdeg R

#/ft^3ft/sec

rad/sec

inin^2


83


High Coolant Flow Rate

Stationary Model

Test # : 5.2 Date:

Location A

Flowrate 0.0151

Radius 19.0H 0.127W 0.283

Pc 161.0Tc 503.3

Tw 580.7ROh 0.000REd 72196

BUOY 0.0000

Density 0.864Velocity 70.5KPM 0

Omega 0.0d 0.175area 0.000249

visc(mu) 1.23E-05k 0.0151

Test # : 7.1 Date:

Location A


H 0.127W 0.283

Pc 160.2Tc 504.6

Tw 581.8ROh 0.0000REd 71033

BUOY 0:0000

Density 0.858

Velocity 69.98RPM 0

Omega 0.0d 0.175area 0.00025

visc(mu) 1.23E-05k 0.0151

B0.0151

19.00.1270.950

161.0503.3

580.70.00027463

0.0000

0.86421.0

0

0.00.223

0.0008351.23E-05

0.0151

B

0.014919.0

0.127

0.950160.2

504.6581.8

0.000027021

0.00000.858

20.850

0.00.223

0.00083

1.23E-050.0151

C

0.015116.5

0.1962.280161.0

503.3580.7

0.00011943

0.00000.864

5.70

0.0

0.3600.0030951.23E-05

0.0151

C

0.014916.5

0.1962.280

160.2504.6

581.80.0000

117500.0000

0.8585.62

00.0

0.3600.00310

1.23E-05

0.0151

#/sec

inin

in

psiadeg Rdeg R

#/fl^3

ft/sec

rad/secin

in^2lb/see-ft

BTU/ft-hr-F

#/see

inin

in

psia

deg Rdeg R

#/fl^3fl/sec

radlsecinin^2


84


Low Coolant Flow Rate

450 rpm

Test # : 16.5 Date:


Radius 19.0H 0.127

W 0.283Pc 165.3

Tc 536.8Tw 579.2

ROh 0.027REd 17642BUOY 0.0082


Omega 47.1d 0.175

area 0.000249

visc(mu) 1.25E-05k 0.0155

B

0.003819.0

0.1270.950

165.3536.8

579.20.0916711

0.09190.832

5.4450

47.10.223

0.000835

1.25E-050.0155

C0.0038

16.5

0.1962.280165.3

536.8579.2

0.5242918

1.69650.832

1.5

45047.1

0.3600.003095

1.25E-050.0155

#/sec

inin

in

psiadeg R

deg R

#/ft^3IVsec

racl/secin

in^2lb/sec-ft

BTU/ft-hr-F

85



450 rpm

Test # : 10.2 Date:

Location A

Flowrate 0.0073Radius 19.0I-I 0.127

W 0.283Pc 164.2

Tc 518.9Tw 581.9ROh 0.014

REd 34650

BUOY 0.0034

Density 0.855

Velocity 34.6RPM 450

Omega 47.1d 0.175area 0.000249

visc(mu) 1.24E-05k 0.0153

Test # : 16.4 Date:


Radius 19.0

I-I 0.127W 0.283

Pc 164.4Tc 528.5Tw 580.3

ROh 0.014REd 34971

BUOY 0.0026


Omega 47.1d 0.175area 0.000249

visc(mu) 1.25E-05k 0.0154

B

0.007319.0

0.1270.950164.2

518.9581.9

0.04813181

0.03790.855

10.3450

47.10.223

0.0008351.24E-05

0.0153

C0.0073

16.5

0.1962.280164.2

518.9581.9

0.2775732

0.6991

0.8552.8450

47.10.360

0.0030951.24E-05

0.0153

B

0.007419.0

0.1270.950

164.4528.5

580.30.047

133030.0293

0.840

10.6450

47.10.223

0.000835

1.25E-050.0154

C

0.007416.5

0.1962.280

164.4528.5

580.30.268

57850.5415

0.840

2.9450

47.10.360

0.003095

1.25E-05

0.0154

#/secin

inin

psia

deg RdegR

#/ft^3ft/sec

rad/secin

in^2lb/sec-ft

BTU/ft-hr-F

#/secin

inin

psiadeg Rdeg R

#/ft^3

ft/sec

md/secin

in^2

lb/sec-ftBTU/t_-hr=F

86

1.15Full Scale Model


450 rpm

Test # : 10.1 Date:

Location A

Flowrate 0.0150

Radius 19.0H 0.127

W 0.283Pc 159.2

Tc 511.2Tw 579.3ROh 0.007

71036BUOY 0.0009


Omega 47.1d 0.175area 0.000249

visc(mu) 1.23E-05k "0.0152

Test # : 16.1 Date:

Location A


H 0.127

W 0.283Pc 161.7

Tc 512.7Tw 581.8

ROh 0.007REd 71417

BUOY 0.0009


Omega 47.1d 0.175area 0.000249

visc(mu) 1.24E-05k 0.0152

B

0.0150

19.00.127

0.950159.2

511.2579.3

0.02327022

0.00960.841

21.3

45047.1

0.2230.0008351.23E-05

0.0152

C

0.0150

16.50.196

2.280159.2

511.2579.3

0.13411751

0.17720.841

5.7

45047.1

0.3600.0030951.23E-05

0.0152

B

0.0151

19.00.127

0.950161.7

512.7581.8

0.02327167

0.0098

0.85221.2450

47.1

0.2230.0008351.24E-05

0.0152

C

0.0151

16.50.196

2.280161.7

512.7581.8

0.13411814

0.1808

0.8525.7450

47.1

0.3600.0030951.24E-05

0.0152

#/secin

in

in

psiadeg RdegR

#/ft^3ft/sec

rad/sec

inin^2lb/sec-ft

BTUIR-hr-F

#/secin

in

in

psiadeg R

deg tt

#/fl^3ft/sec

md/sec

inin^2

Ib/sec-ftBTU/ft-hr-F

87


Low Coolant Flow Rate

750 rpm

Test # : 12.3 Date:


Radius 19.0H 0.127W 0.283

Pc 164.3Tc 546.4

Tw 581.8ROb 0.043REd 18127

BUOY 0.0168


Omega 78.5d 0.175

area 0.000249

visc(mu) 1.26E-05k 0.0156

Test # : 16.6 Date:

Lo_tion A

Flowrate 0.0038

Radius 19.0H 0.127

W 0.283Pc 165.2

Tc 542.6Tw 581.6

ROh 0.045REd 17556BUOY 0.0203

Density 0.823


Omega 78.5d 0.175area 0.000249

visc(mu) 1.26E-05k 0.0155

B0.0039

19.00.127

0.950164.3

546.4581.80.144

68960.1888

0.8125.8

750

78.50.223

0.0008351.26E-05

0.0156

C

0.0039

16.50.196

2.280164.3546.4

581.80.8242999

3.4866

0.8121.6

750

78.50.360

0.0030951.26E-05

0.0156

B0.0038

19.00.127

0.950165.2

542.6581.6

0.1516678

0.2285

0.823

5.5750

78.5

0.223

0.0008351.26E-05

0.0155

C0.0038

16.50.196

2.280165.2

542.6581.6

0.8632904

4.2197

0.823

1.575078.5

0.3600.003095

1.26E-050.0155

#/sec

ininin

psia

deg Rdeg R

#/ft^3ft/sec

racl/secinin^2

lb/sec-ft

BTUlft-hr-F

#/sec

inin

in

psiadeg R

deg R

#/ft^3

ft/sec

rad/secin

in^2lb/sec-ft

BTU/fi-hr-F

88



750 rpm

. Test#:

Location

FlowrateRadiusH

WPc

TcTw

ROhREd

BUOY

DensityVelocityRPM

Omegad

area

visc(mu)k

12.2 Date:

A B C0.0075 0.0075 0.0075

19.0 19.0 16.50.127 0.127 0.196

0.283 0.950 2.280164.1 164.1 164.1533.9 533.9 533.9

581.0 581.0 581.0

0.023 0.076 0.43835097 13351 58060.0063 0.0712 1.3146

0.830 0.830 0.83036.3 10.8 2.9

750 750 75078.5 78.5 78.5

0.175 0.223 0.3600.000249 0.000835 0.003095

1.25E-05 1.25E-05 1.25E-050.0154 0.0154 0.0154

Test # : 16.3 Date:


Radius 19.0H 0.127

W 0.283

Pc 164.1Tc 529.0

Tw 580.8ROh 0.023REd 34899

BUOY 0.0072


Omega 78.5d 0.175area 0.000249

visc(mu) 1.25E-05k 0.0154

B C

0.0074 0.007419.0 16.5

0.127 0.1960.950 2.280

164.1 164.1529.0 529.0

580.8 580.8

0.078 0.44613275 5773

0.0812 1.49910.838 0.838

10.6 2.9750 750

78.5 78.50.223 0.360

0.000835 0.0030951.25E-05 1.25E-05

0.0154 0.0154

#/secinin

in

psiadeg R

deg R

#/ft^3

ft/sec

rad/secinin^2


#/secin

inin

psia

deg Rdeg R

#/ft^3

ft/sec

rad/secin

in^2lb/sec-ft

BTU/ft-hr-F

89



750 rpm

Test # : 14.3 Date:

Lo_tion A


H 0.127W 0.283Pc 164.4

Tc 542.0Tw 584.1

ROb 0.023REd 34376

BUOY 0.0056

Density 0.819


Omega 78.5d 0.175area 0.000249

visc(mu) 1.26E-05k 0.0156

B

0.007419.0

0.1270.950164.4542.0

584.10.077

130760.0634

0.81910.8750

78.50.223

0.0008351.26E-05

0.0156

C

0.007416.5

0.196

2.280164.4542.0

584.10.4395686

1.17080.819

2.9750

78.50.360

0.0030951.26E-05

0.0156

#/secin

inin

psiadeg R

degR

#/ft^3

ft/sec

rad/secinin^2

Ib/sec-ft

BTUfft-hr-F

9O



750 rpm

Test # : 12.1 Date:


Radius 19.0

H 0.127W 0.283Pc 163.6

Tc 522.4Tw 582.2

ROb 0.012REd 70633

BUOY 0.0021


Omega 78.5d 0.175area 0.000249

visc(mu) 1.24E-05k 0.0153

Test # : 16.2 Date:

Location A

Flowrate 0.0151

Radius 19.0H 0.127

W 0.283

Pc 161.7Tc 516.3Tw 581.3

ROh 0.012REd 71349

BUOY 0.0022


Omega 78.5d 0.175

area 0.000249

,,isc(mu) 1.24E-05k 0.0153

B

0.0150

19.00.127

0.950163.6

522.4582.20.039

268690.0234

0,84621.2

75078.5

0.223

0.0008351.24E-05

0.0153

B

0.015119.0

0.127

0.950161.7

516.3581.3

0.03927141

0.02520.846

21.4750

78.50.223

0.000835

1.24E-050.0153

C

0.0150

16.50.196

2.280163.6522.4

582.20.223

116840.4325

0.8465.7

75078.5

0.3600.003095

1.24E-050.0153

C

0.015116.5

0.196

2.280161.7

516.3581.3

0.22211803

0.46540.846

5.8

750

78.50.360

0.003095

1.24E-050.0153

#/secin

inin

psia

deg RdegR

#/ft^3ft/sec

rad/secinin^2


#/secin

in

in

psiadegR

deg R

#/ft^3ft/sec

rad/secinin^2

lb/sec-ftBTU/ft-ltr-F

91



750 rpm

Test # : 14.2 Date:


Radius 19.0H 0.127

W 0.283Pc 161.9Tc 523.5

Tw 583.6

ROb 0.011REd 70508BUOY 0.0020

Density 0.835


Omega 78.5d 0.175area 0.000249

visc(mu) 1.25E-05k 0.0154

B0.0150

19.00.127

0.950145.0

523.5583.60.034

268210.0184

0.748

24.075078.5

0.2230.000835

1.25E-050.0154

C0.0150

16.50.196

2.280145.0523.5

583.60.198

116640.3394

0.748

6.5750

78.5

0.3600.003095

1.25E-050.0154

#/sec

inin

in

psiadeg R

degR

#/ft^3

It/sec

rad/secinin^2

Ib/sec-ftBTU/ft-hr-F

92

9.3 Sample Data Table for Stationary Test Condition and Medium Flowrate

(Test # 6.2, TC 2)

Time

O1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

2O21

22

23

24

25

26

27

28

29

3O

31

32

33

34

35

36

3738

39

4O

41

42

43

44

45

46

47

45

49

50

51

52

5354

55

55

57

58

59

6O

61

62

63

64

65

66

67

T¢

119.9115.5

106.997.2

90.985.4

80.3

77.5

75.1

72.8

70.9

69.6

68.5

67.5

66.6

65.9

65.3

64.6

63.9

63.4

63.162.7

62.3

62.0

61.7

61.4

60.9

60.6

60.6

60.4

60.2

60.2

60.0

59.8

59.4

59.3

59.2

59.0

58.8

58.858.6

58.5

58.3

58.3

58.2

58.1

57.9

57.8

57.7

57.6

57.4

57.5

57.5

57.457.3

57.2

57.2

57.157.0

56.958.9

58.958.8

59.758.6

56.5

58.4

56.4

Tw

120.7

120.6

119.5

118.0

115.8

113.9

111.6109.9

108.3

108.9

105.4

104.1

103.0

101.9

100.6

99.5

98.5

97.6

96.5

95.6

95.0

94.393.5

92.8

92.1

91.4

90.7

90.2

89.8

89.4

88.8

88.3

87.8

87.3

86.8

86.4

86.1

65.7

65.3

64.9

64.6

84.283.9

63.663.3

63.0

82.6

82.3

82.0

81.8

81.6

81.4

81.2

81.0

80.7

80.4

80.2

79.9

79.6

79.4

79.2

79.1

78.7

78.5

78.4

78.2

78.1

78.0

• To

119.9

119.4

117.8

115.1

113.2

111.3

109.0107.5

108.1

104.7

103.2

100.1

101.1

100.1

99.0

98,2

97.5

96.7

95.8

95.2

94.6

94.0

93.392.8

92.3

91.9

91.4

90.9

90.5

90.1

89.7

89.3

89.0

88.6

88.2

87.9

87.6

87.3

86.9

86.7

86.4

86.165.8

65.565.3

65.1

64.8

54.6

84.5

84.2

63.9

83.7

83.6

83.4

83.1

83.0

82.9

82.7

82.4

82.3

82.1

81.9

81.7

81.6

81.4

81.2

81.1

80.9

Tw'

O.O00E+O0

-1.818E+03

-4.499E+03

-6.693E+03

-5.995E+03

-6.476E+03

-6.638E+03

-6.077E+03

-5.648E+03

-5.310E+03

-4.933E+03

-4.580E+03

-4.372E+03

-4.195E+03

-4.109E+03-3.829E+03

-3.630E+03

-3.355E+03

o3.257E+03

-2.870E+03

-2.752E+03

-2.745E+03

-2.616E+03

-2.535E+03

-2.388E+03-2.236E+03

-2.195E+03

-1.899E+03

-1.768E+03

-1.826E+03

-1.771 E+03-1.703E+03

-1.755E+03

-1.647E+03

-1.615E+03

-1.493E+03

-1.427E+03

-1.315E+03

-1.397E+03

-1.322E+03

-1.223E+03

-1.221 E+03

-1.132E+03

-1.119E+03

-1.167E+03

-1.185E+03-1.063E+03

-9.698E+02-9.076E+02

-8.724E+O2-7.656E+O2

-7.797E+00-7.692E+O2

-8.988E+02

-9.489E+02

-9.166E+02

-9.125E+02

-9.013E+02

-8.588E+O2

-7.174E+02

-7.829E+02

-7.736E+02

-7.501E+02

-6.513E+00

-5.626E+02

-5.411E+O2

-5.620E+02

-5.171E+02

Q

1.0(X)E-02

3.020E+01

1.175E+022.390E+02

3.292E+02

3.888E+02

4.517E+02

4.960E.H)2

5.209E+02

5.4O6E+02

5.567E+02

5.667E+02

5.748E+00

5.829E+02

5.915E+02

5.975E+02

6.000E+026.001E+02

5.998E+02

5.965E+02

5.908E+025.895E+02

5.888E+02

5.871E+02

5.846E+02

5.803E+02

5.768E+02

5.706E+02

5.617E+02

5.509E+02

5.543E+02

5.506E+02

5.486E+02

5.465E+02

5.432E+02

5.393E",'02

5.342E+925.288E+02

5.253E+02

5.230E+02

5.164E+02

5.141E+02

5.100E+02

5.058E+02

5.033E+02

5.004E+02

4.998E+02

4.945E+02

4.888E+O2

4.637E+02

4.762E+02

4.729E+02

4.689E+02

4.676E+024.685E+02

4.680E+024.667E+02

4.654E+024.635E+02

4.592E+02

4.5,56E+02

4.541E+024.519E+02

4.481E+02

4.426E+O2

4.375E+02

4.339E+02

4.305E+02

H NUR NU QW &T HR Z_o/p1.000E-02 1.000E-O2 1.000E-02 1.000E-02 8.020E-01 1.000E-02 -O.0014 *

5.913E+00 3.209E+01 3.063E+01 3.133E+01 5.057E+00 6.195E+O0 -0.0088

9.319E+00 5.387E+01 4.863E+01 1.280E+02 1.240E+O1 1.032E+01-0.0017

1.150E+01 6.559E+01 6.052E+01 2.539E+02 2.037E+01 1.246E+01 -0.0360

1.320E+01 7.597E+01 6.994E+01 3.495E+02 2.437E+01 1.434E+01 -0.0433

1.363E+01 7.769E+01 7.261E+01 4.064E+02 2.787E+01 1.458E+01-0.0497

1.440E+01 8.278E+01 7.717E+01 4.726E+02 3.060E+01 1.545E+01 -0.0549

1.532E+01 8.732E+01 8.24OE+01 5.119E+02 3.153E+01 1.624E+01 -0.0568

1.571E+01 8.955E+01 8.477E+01 5.356E+02 3.227E+O1 1.660E+01 -0.0583

1.586E-=,O1 9.021E+01 8.562E+01 5.530E+02 3.317E+01 1.667E+O1 -0.0601

1.614E+01 9.215E+01 8.755E+01 5.700E+02 3.356E+01 1.699E÷01 -0.0610

1.640E+01 9.361E+O1 8.914E+O1 5.786E+02 3.361E+01 1.722E+01-0.0613

1.670E+01 9.529E+01 9.093E+01 5.85,4E+02 3.346E+01 1.750E+01 -0.0612

1.695E+01 9.681E+01 9.248E+01 5.928E+O2 3.341E+01 1.775E+01 -0.0612

1.739E+01 9.984E+O1 9.505E+01 6.031E+02 3.3O2E+01 1.827E+01 -0.0607

1.780E+01 1.O21E+02 9.743E+01 6.075E+02 3.256E+01 1.866E+01 -0.0600

1.806E+01 1.036E+02 9.897E+O1 6.089E+02 3.221E+01 1.890E+01 -0.0595

1.821E+01 1.045E+02 9.995E+01 6.083E+02 3.194E+01 1.905E+01 -0.0591

1.842E+01 1.061E+02 1.012E+02 6.096E+02 3.156E+O1 1.932E+01 -0.0585

1.850E+01 1.064E+02 1.018E+02 6.041E+02 3.124E+01 1.934E+01 -0.056O

1.652E+01 1.063E+02 1.020E+O2 5.968E+02 3.091E+01 1.931E+01 -0.05751.863E+01 1.070E+02 1.026E+02 5.954E+O2 3.066E+01 1.942E+01 -0.0571

1.886E+01 1.08BE.H02 1.041E+02 5.961E+O2 3.022E+01 1.972E+01 -0.0564

1.906E+01 1.099E+O2 1.052E+O2 5.935E+02 2.982E+01 1.990E+01 -0.0557

1.922E+01 1.108E+02 1.062E+02 5.906E+02 2.944E+01 2.006E+01 -0.0551

1.932E+01 1.116E+O2 1.068E+02 5.867E+02 2.907E+01 2.018E+01 -0.0545

1.934E+01 1.117E+02 1.070E+02 5.827E+02 2.886E+O1 2.019E+01 -0.0542

1.933E+01 1.116E+02 1.071E+02 5.757E+02 2.856E+01 2.016E+01 -0.0536

1.922E+01 1.107E+02 1.065E-H)2 5.650E+02 2.628E+01 1.998E+01 -0.0531

1.920E+01 1.106E+02 1.064E+02 5.603E+02 2.807E+O1 1.996E+01 -0.6528

1.943E+01 1.125E+02 1.078E+02 5.6O0E+02 2.76OE+01 2.029E+01 -0.0520

1.958E+01 1.132E+00 1.086E+O2 5.549E+02 2.720E+O1 2.040E+01 -0.0513

1.972E+01 1.14OE+O2 1.094E+02 5.528E+02 2.691E+01 2.054E+01 -0.0508

1.990E+01 1.154E+02 1.165E+02 5.515E+02 2.655E+01 2.077E+01 -0.0502

1.978E+01 1.145E+02 1.099E+02 5.471E+02 2.656E+01 2.060E+O1 -0.0502

1.988E+01 1.152E+O2 1.106E+02 5.431E+02 2.623E+01 2.071E+01 -0.0496

1.984E+01 1.148E+02 1.104E+02 5.372E+02 2.6O3E+01 2.064E+01 -0.0493

1.979E+01 1.145E+02 1.101E+02 5.319E+02 2.584E+01 2.059E+01 -0.0490

1.987E+01 1.153E+O2 1.107E+02 5.293E+02 2.556E+01 2.071E+01 -0.0485

2.000E+01 1.16OE+O2 1.114E+02 5.264E+O2 2.528E+O1 2_083E+O1 -0.0480

1.995E+01 1.156E+02 1.112E+02 5.211E+O2 2.512E+01 2.074E+01 -0.0477

1.999E+01 1.161E+02 1.114E+02 5.177E+02 2.486E+01 2.082E+01 -0.0473

1.987E+01 1.152E+O2 1.108E+02 5.124E+02 2.482E+01 2.065E+01 -0.0472

1.995E+01 1.158E+02 1.113E+02 5.034E+02 2.449E+01 2.076E+01 -0.0466

2.003E+01 1.163E+O2 1.118E+02 5.059E+02 2.428E+01 2.083E+01 -0.04622.018E+01 1.173E+02 1.126E+02 5.055E+02 2.4O6E+01 2.101E+01 -0.0459

2.025E+01 1.179E+O2 1.131E+02 5.032E+02 2.384E+01 2.1tlE+01 -0.04552.019E+01 1.173E+02 1.128E+02 4.971E+02 2.367E+01 2.100E+01 -0.0452

2.010E+01 1.168E+02 1.123E+02 4.913E+02 2.350E+01 2.090E+01 -0.0449

2.000E+01 1.162E+02 1.118E+02 4.658E+02 2.338E+01 2.078E+01 -0.0446

1.975E+01 1.145E+02 1.104E+02 4.797E+02 2.342E+01 2.O48E+01 -0.0447

1.977E+01 1.148E+O2 1.106E.HT2 4.749E+02 2.313E+01 2.053E+01 -0.0442

1.973E+01 1.145E+02 1.103E+02 4.704E+02 2.299E+01 2.046E+01 -O.04391.979E+01 1.149E+02 1.107E+O2 4.694E+02 2.285E+01 2.055E+01 -0.0437

2.001E+01 1.165E+02 1.120E+02 4.716E+02 2.263E+01 2.084E+01 -0.0433

2.018E+01 1.175E+02 1.129E+02 4.704E+02 2.242E+01 2.098E+01 -0.0429

2.03OE+01 1.182E+O2 1.137E+02 4.689E+02 2.221E+01 2.111E+01 -0.0426

2.040E+01 1.189E+02 1.143E+02 4.677E+02 2.204E+01 2.122E+01 -0.0423

2.O48E+01 1.196E+O2 1.145E+O2 4.664E+O2 2.186E+O1 2.134E+01 -0.0419

2.O44E+01 1.191E+02 1.146E+02 4.612E+O2 2.170E+01 2.126E+01 -0.0416

2.044E+01 1.190E+02 1.145E+02 4.570E+O2 2.153E+01 2.123E+01 -0.0413

2.046E+01 1.191E+02 1.147E+02 4.555E+O2 2.144E+01 2.125E+01 -0.0412

2.057E+01 1.202E+O2 1.153E+02 4.548E+O2 2.121E+01 2.144E+01 -0.0408

2.047E,_'-O1 1.193E+02 1.148E+02 4.498E+02 2.114E+01 2.128E+01 -0.0406

2.031E+01 1.183E+02 1.139E+02 4.440E+02 2.105E+01 2.109E+01 -0.0405

2.016E+01 1.174E+02 1.131E+02 4.387E+O2 2.097E+01 2.092E+01 -0.0403

2.002E+01 1.165E+02 1.123E+02 4.351E+02 2.095E+01 2.077E+01 -0.04031.994E+O1 1.161E+02 1.119E+02 4.318E+02 2.087E+01 2.069E+01 -0.0401

94

68 56.3

69 56,570 56.4

71 56.3

72 56.3

73 56.3

74 56.3

75 56.276 56.3

77 56.2

78 56.3

79 56.280 56.1

61 56.0

82 56.8

83 56.7

84 55.6

85 55.8

86 55.8

87 56.888 55.7

89 55.5

90 56.4

91 55.4

92 55.4

93 55.4

94 56.4

95 55.4

95 55.497 56.4

98 55.4

99 55.5

100 55.5

101 56.3

102 56.4

103 55.3

194 55.3

105 56.3

106 55.2

107 55.2

108 55.2

109 55.2

110 55.2111 55.1

112 55.1

113 55.2

114 55.0

115 55,0

116 55.0

117 55.0

118 54.9

119 54.9

120 54.9

121 55.0

122 54.9

123 54.8

124 54.8

125 54.9

126 54.8127 54.9

128 54.9

129 54.9

130 54.9131 54.8

132 54.7

133 54.8

134 54.7135 54.6

136 54.7

77.9 80.8-3.976E+02 4.249E+02 1.968E+01

77.8 80.7-5.041E+02 4.209E+02 1.969E+01

77.7 80.5-6.535E+02 4.219E+02 1.979E+01

77.4 80.4-5.239E+02 4.210E+02 1.994E+01

77.3 80.3-6.696E+02 4.200E+02 2.004E+01

77.1 80.1-6.430E+02 4.208E+02 2.026E+0176.9 79.9-5.712E+02 4.189E+02 2.033E+01

76.7 79.8-4.873E+02 4.151E+02 2.027E+01

76.6 79.7-4.861E+02 4.115E+02 2.027E+01

76.5 79.6-4.742E+02 4.089E+02 2.018E+01

76.4 79.4-5.279E+02 4.074E+02 2.022E+01

76.2 79.4-6.012E+02 4.078E+02 2.035E+01

76.2 79.3-6.022E+02 4.083E+02 2.036E+01

75.8 79,2-5.620E+02 4.077E+02 2.054E+01

75.7 79.1-5.246E+02 4.058E+02 2.038E+01

75.5 79.0-5.599E+02 4.043E+02 2.043E+01

75.3 78.8-5.169E+02 4.030E+02 2.046E-',-01

75.3 78.7-4.422E+02 3.999E+0_ 2.054E+01

75.1 78.6-4.566E+02 3.971E+02 2,053E+01

75.0 78.5-3.559E+02 3.937E+02 2.045E+01

74.9 76.4-3.779E+02 3.900E+02 2.031E+01

74.8 78.2-4.184E+02 3,885E+02 2.015E+01

74.6 78.1-3.230E+02 3.857E+02 2.008E+01

74.6 78.0-2.835E+02 3.814E+02 1.989E+01

74.5 77.9-2.646E+02 3.776E+02 1.972E+01

74.5 77.9-2.809E+02 3.747E+02 1.962E+01

74.4 77.8-3.251E+02 3.731E+02 1.960E+0174.3 77.8-,4.563E+02 3.741E+02 1.981E+01

74.2 77.7-4.069E+02 3.748E+02 1.997E+01

74.0 77.5-4,100E+02 3.737E÷02 2.006E+01

73.9 77.4 -3.032E+02 3.711E+02 2.006E÷01

73.8 77.3-3.888E+02 3.692E+02 2.012E+01

73.7 77.2-3.530E+02 3.685E+02 2.022E+01

73.7 77.1-3.127E+02 3.662E+02 1.998E+01

T3.6 77.1-3.583E+02 3.647E+02 2,007E+0173.5 77.0-2.434E+02 3.922E+02 1.996E+01

73.4 76.9-3.775E+02 3.607E+02 1.996E+01

73.2 76.6-3.524E+02 3.611E+02 2.013E+01

73.1 76.7-2.657E+02 3.586E+02 1.995E+01

73.1 76.6-1.670E+02 3.540E+02 1.977E+01

73.1 76.5 -2.148E+02 3.505E+02 1.965E+01

73.0 76.5-1.851E+02 3.482E+02 1.946E+01

73.0 76.4 -2.271E+02 3.462E+02 1.944E+01

72.9 76.3-2.903E+02 3.460E+02 1.945E+01

72.9 76.2-3.322E+02 3.467E+02 1.946E+01

72.7 76.1-4.062E+02 3.481E+02 1.989E+01

72.6 76.0 -3.604E+02 3.488E+02 1.991E+01

72.5 75.9-3.445E+02 3.479E+02 1.989E+01

72.4 75.9 -3.560E+02 3.473E+02 1.993E+01

72.3 75.8-3.126E+02 3.462E+02 2.001E+01

72.2 75.7-2.528E+02 3.438E+02 1.987E+01

72.1 75.7-2.551E+92 3.419E+02 1.987E+01

72.1 75.6-3.240E+02 3.417E+02 1.990E+01

72.0 75.5-4.108E+02 3.430E+02 2.022E+01

71.8 75.5-4.385E+02 3.450E+02 2.036E+0171.7 75.4-2.946E+02 3.438E+02 2.033E+01

71.6 75.3-2.329E+02 3.400E+02 2.018E+01

71.5 75.2-2.746E+02 3.379E+02 2.026E÷01

71.5 75.1-1.671E+02 3.352E+02 2.009E+0171.5 75.1-1.658E+02 3.316E+02 1.994E+01

71.5 75.0-1.230E+02 3.285E+02 1.980E+01

71.5 75.0-1.585E+02 3.261E+02 1.967E+01

71.4 75.0-2.783E+02 3.266E+02 1.971E+01

71.3 74.9-2.879E+02 3.279E+02 1.986E+01

71.2 74.9-3.084E+02 3.283E+02 1.994E+01

71.1 74.8-2.690E+02 3.279E+02 2.017E+01

71.0 74.7-1.726E+02 3.252E+02 1.994E+01

71.0 74.6-1.619E+02 3.221E+02 1.974E+01

70.9 74.6-1.913E+02 3.205E+02 1.970E+01

1.143E+02 1.195E+02 4.252E+02 2.088E+01 2.037E+01 -0.0401

1.145E+02 1.105E+02 4.216E+02 2.068E+01 2.039E+01 -0.03971.153E+02 1.111E+02 4.233E+02 2.061E+01 2.054E+01 -0.0396

1.165E+02 1.120E+02 4.233E+02 2.041E+01 2.074E+01 -0.0393

1.168E+02 1.126E+02 4.211E+02 2.025E+01 2.079E+01 -0.0390

1.183E+02 1.138E+02 4.227E+02 2.007E+01 2.106E+01 -0.0387

1.168E+02 1.142E+02 4.209E+02 1.991E+01 2.114E+01 -0.03841.183E+02 1.139E+02 4.164E÷02 1.978E+01 2.105E+01 -0.0381

1.183E+02 1.139E+02 4.129E+02 1o961E+01 2.105E+01 -0.0378

1.175E+02 1.134E+02 4.093E+02 1.958E+01 2.090E+01 -0.0376

1.179E+02 1.137E+02 4.083E+02 1.947E+01 2.098E+01 -0.0376

1.189E+02 1.144E+02 4.092E+02 1.935E+01 2.114E+01 .0.0374

1.187E+02 1.145E+02 4.090E+02 1.937E+01 2.112E+01 -0.0374

1.205E+02 1.155E+02 4.107E+02 1.916E+01 2.143E+01 -0.0370

1.191E+02 1.147E+02 4.072E+02 1.923E+01 2.117E+01 -0.0372

1.195E+02 1.150E+02 4.062E+02 1.911E+01 2.126E+01 -0.0369

1.196E+02 1.152E+02 4.041E+02 1.903E+01 2.124E+01 -0.0368

1.199E+02 1.156E+02 4.006E+02 1.880E+01 2.131E+01 -0.0364

1.200E+02 1.156E+02 3.982E+02 1.868E+01 2.132E+01 -0.0361

1.195E+02 1.152E+02 3.946E+02 1.859E+01 2.123E+01 -0.0360

1.186E+02 1.144E+02 3.909E+02 1.855E+01 2.107E+01 -0.0359

1.179E+02 1.135E+02 3.899E+02 1.863E+01 2.093E+01 .0.03601.173E+02 1.131E+02 3.866E+02 1.857E+01 2.082E+01 .0.0359

1.160E+02 1.121E+02 3.816E+02 1.854E+01 2.059E+01 -0.0359

1.151E+02 1.111E+02 3.782E+02 1.852E+01 2.042E+01 -0.0358

1.144E+02 1.105E+02 3.751E+02 1.847E+01 2.031E+01 -0.0357

1.144E+02 1.104E+02 3.739E+02 1.841E+01 2.030E+01 -0.03561.157E+02 1.116E+02 3.750E+02 1.826E+01 2.053E+01 -0.0354

1.168E+02 1.125E+02 3.759E+02 1.814E+01 2.072E+01 -0.0351

1.176E+02 1.131E+02 3.756E+02 1.800E+01 2.086E+01 -0.0349

1.173E+02 1.131E+02 3.720E+02 1.788E+01 2.080E+01 .0.0347

1.175E+02 1.134E+02 3.697E+02 1.774E+01 2.085E+01 .0.0344

1.183E+02 1.140E+02 3.697E+02 1.762E+01 2.098E+01 .0.0342

1.156E+02 1.126E+02 3.565E+02 1.772E+01 2.068E+01 .0.0344

1.174E+02 1.132E+02 3.656E+02 1.756E+01 2.081E+01 -0.0341

1.167E+02 1.125E+02 3.630E+02 1.755E+01 2.069E+01-0.0340

1.167E+02 1.126E+02 3.616E+02 1.747E+01 2.070E+01 .0.0339

1.180E+02 1.135E+02 3.625E+02 1.733E+01 2.091E+01 .0.0336

1.167E+02 1.125E+02 3.593E+02 1.738E+01 2.068E+01 .0.0337

1.154E+02 1.115E+02 3.541E+02 1.731E+01 2.045E+01 -0.0336

1.148E+02 1.109E+02 3.511E+02 1.725E+01 2.035E+01 -0.0335

1.134E+02 1.098E+02 3.482E+02 t.732E+01 2.011E+01 -0.0336

1.135E+02 1.097E+02 3.467E+02 1.723E+01 2.012E+01 -0.03341.137E+02 1.098E+02 3.468E+02 1.721E+01 2.015E+01 -0.0334

1.135E+02 1.098E+02 3.467E+02 1.724E+01 2.012E+01 -0.03341.168E+02 1.123E+02 3.502E+02 1.692E+01 2.070E+01 -0.0329

1.166E+02 1.124E+02 3.497E+02 1.694E+01 2.065E+01 -0.0329

1.165E+02 1.123E+02 3.489E+02 1.691E+01 2.063E+01 -0.0328

1.168E+02 1.125E+02 3.480E+02 1.685E+01 2.065E+01 -0.03271.172E+02 1.130E+02 3.473E+02 1.673E+01 2.076E+01 -0.0325

1.163E+02 1.122E+02 3.445E+02 1.673E+01 2.060E+01 -0.03251.162E+02 1.122E+02 3.423E+02 1.664E+01 2.057E+01 -0.0323

1.163E+02 1.124E+02 3.421E+02 1.681E+01 2.060E+01 -0.0323

1.168E+02 1.142E+02 3.443E+02 1.639E+01 2.100E+01 -0.0319

1.194E+02 1.150E+02 3.461E+02 1.637E+01 2.114E÷01 -0.0319

1.193E+02 1.149E+02 3.449E+02 1.634E+01 2.112E+01 -0.0318

1.182E+02 1.140E+02 3.407E+02 1.628E+01 2.092E+01 -0.0317

1.168E+02 1.145E+02 3.387E+02 1.611E+01 2.102E+01 -0.0314

1.176E+02 1.135E+02 3.357E+02 1.613E+01 2.082E+01 -0.0314

1.155E+02 1.127E+02 3.314E+02 1.607E+01 2.062E+01 -0.0313

1.158E+02 1.119E+02 3.287E+02 1.504E+01 2.049E+01 -0.0312

1.149E+02 1.111E+02 3.260E+02 1.603E+01 2.033E+01 -0.0312

1.154E+02 1.114E+02 3.271E+02 1.602E+01 2.042E+01 -0.0312

1.166E+02 1.122E+02 3.292E+02 1.596E+01 2.062E+01 .0.0311

1.168E+02 1.127E+02 3.289E+02 1.591E+01 2.067E+01 -0.0310

1.185E+02 1.140E+02 3.292E+02 1.571E+01 2.096E÷01 -0.0306

1.168E+02 1.127E+02 3.256E+02 1.577E+01 2.066E+01 .0.0307

1.155E+02 1.116E+02 3.223E+02 1.578E+01 2.042E+01 .0.0307

1.153E+02 1.114E+02 3.209E+02 1.573E+01 2.040E+01 --0.0306

95

137 54.7 70.9 74.5 -9.681E+01 3.179E+02138 54.7 70.9 74.4-1.440E+02 3.153E+02

139 54.7 70.9 74.3 -2.480E+02 3.158E+02

140 54.7 70.8 74.2 -3.249E+02 3.181E+02141 54.9 70.6 74.2 -3.718E+02 3.206E+02

142 54.7 70.5 74.2 -3.068E+02 3.212E+02

143 54.5 70.4 74.1 -2.303E+02 3.193E+02

144 54.5 70.4 74.1 -2.605E+02 3.179E+02

145 54.6 70.3 74.0 -2.215E+02 3.168E+02

145 54.5 70.2 74.0-1.541E+02 3.143E+02

147 54.6 70.2 73.9-1.226E+02 3.112E+02

148 54.6 70.2 73.8-1.761E+02 3.096E+02

149 54.6 70.1 73.8 -2.568E+02 3.103E+02

150 54.5 70.1 73.8 -2.739E+02 3.115E+02

1.953E+01 1.141E+02 1.104E+02 3.178E+02 1.575E+01 2.018E+01 -0.03071.947E+01 1.139E+02 1.101E+02 3.156E+02 1.567E+01 2.014E+01 -0.0305

1.959E+01 1.147E+02 1.108E+02 3.163E+02 1.560E+01 2.028E+01 -0.0304

1.979E+01 1.159E+02 1.119E+02 3.184E+02 1.554E+01 2.049E+01 -0.03032.038E+01 1.199E+02 1.151E+02 3.225E+02 1.521E+01 2.121E+01 -0.0297

2.031E+01 1.192E+02 1.148E+02 3.221E+02 1.528E+01 2.107E+01 -0.0298

2.007E+01 1.177E+02 1.135E+02 3.200E+02 1.538E+01 2.081E+01 -0.0300

2.0(X)E+01 1.17;2E+02 1.131E+02 3.184E+02 1.537E+01 2.072E+01 -0.0300

2.014E+01 1.182E+02 1.140E+02 3.176E+02 1.520E+01 2.089E+01 -0.0297

2.000E+01 1.172E+02 1.131E+02 3.147E+02 1.519E+01 2.072E+01 -0.0296

1.983E+01 1.160E+02 1.122E+02 3.111E+02 1.517E+01 2.051E+01 -0.0296

1.975E+01 1.155E+02 1.117E+02 3.096E+02 1.516E+01 2.042E+01 -0.0296

2.000E+01 1.174E+02 1.132E+02 3.112E+02 1.499E+01 2.076E+01 -0.0293

2.005E+01 1.176E+02 1.135E+02 3.121E+02 1.501E+01 2.079E+01 -0.0293

Where:

Time

Tc

Tw

To

Tw'

Q

H

NUR

NU

QWAT

HR

Ap/p

Seconds past start of transient portion of the test

Average coolant inlet temperature, °F

Wall temperature, F

Average coolant outlet temperature, OF

Temporal derivative of the wall temperature variation, OF/hr

Heat flux without paint correction, Btu/ft2/hr

Heat transfer coefficient without paint correction, Btu/ft2/hrFF

Nusselt number with paint correction based on d=l inch, HR*d/k

Nusselt number without paint correction based on d=l inch, HR*d/k

Heat flux with paint correction, Btu/ft2/hr

Temperature difference with paint correction, Tw-Tc, OF

Heat transfer coefficient with paint correction, Btu/ft2/hrFF

Density ratio, -(Pb - Pw)/Pb =-(Tw- Tb)/Tw

96

9.4 Adjusted Thermocouple Results

97

Re = 13,000

a) Tin

140'

120'

100

8O

60'

40-50

RO8T01 Data eeeeeTC02 '

eeeeeTC03_TC01{k@_{_TC04

Tin, avg

i i 1 | 61 i i * I

0 50 100 150Time, sec

0

E-,

140

120

I00'

80 ¸

b) Tou t

R08T01 Data eeeeeTCZ1_eeTC22a_.sTC23

--Tout, avg

6O

4°s'd.......6........s'd.......ido.......isoTime, sec

c) Leading Surface

140

120

100

so

RO8T01 Data eeeeeTC01s_eeeTC02a_a_TC03

_ewTC04

_TC05

_TC07

60

4°s_ .......6........5_.......i60.......i_oTime, sec

d) Trailing Surface

140'

120

I00

80

60

40-50

R08T01 Data

_8TC12_a_aTC13

v_"_vTC14

,J-&a-_TC15BH_-_TC17

Illllll_llJllllll|ll,lllllll

0 50 I00 150

Time, sec

Figure 9.4-1. Thermocouple Data for Liquid Crystal Test on Leading Surface

With _ = 0 rpm.

98

Re= 13,000


__,_ °eeeeTC01" I i000 I ROBT01 Data _eee TC121000 R08T01 Data eeeee TC02

-4 // "%. _ TC03 l -I I -a. _.s_.s TC13I V _ _ zco4 1 I I \. _'rc14

J I _ _ TCI5

I I _ _ TCOS i _ J __ _. _ TClV

Ic Iz

c_ c_ i0 50

I00 0 50 I00 150 0 50 I00Time, sec Time, sec

c) Leading Surface

I000 _ ROBT01 Data eeeeeTC01

seeeeTC02

5_ A-_,_TC031 _v_,TC04

_TCO5z_ e_B-_TC07

t _TC08

100

10

t_

o

8

0 50 100Time, sec

d) Trailing Surface

1000 _ R08T01 Data

TCl2_ TC13

_ TCI4TCI5

._ _ _ TC17TCI8

"5

I00

1 i s i i i i i i t _ , i i i i i i i i i i , _ i15o o 5o i66Time, sec

1

50

Figure 9.4-2. Results From Thermocouple Data for Liquid Crystal Test on Leading

Surface With _ = 0 rpm.

99

Re = 13,000

140

120

100

a) Tin

R06T02 Data eoOOOTC02eem_e_TC03_,_TC01_TC04

--- Tin. avg

80'

oo

4°-ag ....... 6........ bg ....... idb ....... iaoTime, see

"d0

(-_

b) Tou t

140

120

100

80,

6O

R06T02 Data_TC21_TC22_r_TC23

*

0 III I''ll'i''ll' '1611 '|'l'll'|i ' ' I ' I I I I I

-50 0 50 100 150Time, sec

c) Leading Surface

140.

120'

100

0

80E._

R06T02 DataeeoeoTC01_TC02_TC03

, v_v_vTC04,_-_TC05e-e-e_TC07

60'

O fllll iliM Jl IIlll4 5_ ....... 6.... 5b "16b' 'i5oTime, see

d) Trailing Surface

140 _ RO6T02 Data

120

100

j so

60 ¸

40-50

eeeeeTCll_TC12_a_TC13_TC14_TCl5

_'_ _ TC17

Illllll_lll#111111#1|llllll#

0 50 100 150Time, see

Figure 9.4-3. Thermocouple Data for Liquid Crystal Test on Trailing Surface

With _ = 0 rpm.

I00

Re = 13,000


.1 1ooo --1ooo _ _ roszo2pat. _ _ r \ _ TcI_-i II _x\ _ TC03 [ | ] _ _ TCI3| I/ _ v-v_vv TC04 [ -] [ _ vvv_v TCI4J I "_. _ TC05 I -, "_ _ zcts

_ I00

I00 0 50 100 150 0 50 i00 150Time, see Time, sec

c) Leading Surface

looo i_1_o_o_ pat,, ooo__C01

_eeee TC02TC03

v_,eee TC04_a-a-aa TC05_ TCO7_ TC08

100

[-.. 10

50 100Time, sec

i50

I000

°_

I00

2

10

d) Trailing Surface

R06T02 Data eeeeeTClltmeeeTCl2_TCI3v_TCl4_-_TCI5_TCI7_TCI8

....... ' sb ........ i66 ....... isoTime, see

Figure 9.4-4. Results From Thermocouple Data for Liquid Crystal Test on Trailing


I01

EOI

•rods O_Tz= U q:l!M

a_ejan S _u!p_o'- I uo ]so/. I_ISSaD p!nb!q aoj _eCl oldno:_omuou, i "S-_r'6 aan_!..4

oos 'otu!.I. oos 'owt!j_ogl 00_ og 0 Og- Og_ OOI og 0 og--

......... ' ......... ' ......... ' ......... 0_' ......... ' ......... ' ......... ' ......... O_

8IO&mnnnn

.O9

og0

"x"J

OOI

.08I

a_3_Tns _.m_. sl (p

80D&3031

_l_(I 8019_H

09

0

'-z'J

OOI

.08I

O_zI

oos 'or, n_logI OOI og 0 Og-

......... '............................. O_

09

.og

-4

OOI

08__A_ '_no& --

88D_88D&_ISD_ooooo _fl g0&9IH

O_I

_n° l (q

oos 'ou.q,LOgl OOI og 0 og--

tllllllll|lili'Ittllt'It_it'tllt Ittllit O_

IOO&__OD_80o&oeeee _':t_G _0&glH

.09

-0g

OOI

08I

O_'I

_4

000"£I = o'tl

Rc = 13,000

a) Leading Surface

1000

I RlflT03 Data _ TC02

TC03

_ TC04_s_-DTC07

5-

d

:I

II oolt.........,.........,.........0 50 100

Time, see

b) Trailing Surface

i000 j R16T03 Data eeeee TC11

I TC12

TC13TC14

I "_. _ TC17

d

10150 0 50 100 150

Time, see

I000

o

8_J

c) Leading Surface

R16T03 Data_eee_ TC02

TC03TC04TC05

z _ TC07

100

2-

lO

2

10 50 100

Time, see

i000

8_J

150

2

100

10

d Trailing Surface

RI6T03 Data

TC14

2 _ TCI5TC17TC18

1 o ......... 5b........ i66 ....... i5oTime, see



.103

Re = 13,000

a) Tin140

120

100

aO,E--,

R10T02 Data eeeeeTC02_TC03_._a_-_TC01(H),0,_TC04

°

60

405'6 ....... 6........ gb ....... i6o ....... i5oTime, see

b) Tou t140

P

E-*

120

100

80

60

40-50

R10T02 Data GeeeeTC21eeeesTC22

il lllll i Itllllllll.illIl lll|lililIllll!

0 50 100 150Time, seo

c) Leading Surface

140 _ RIOT02 Data

I120

100

80,

60

eeeeeTC01_TC02_a_TC03

v_vTC04

A-a_TC05H-B_eTC07

4o_5_ ....... 6........ 'if) ....... i 6b....... i5oTime, sec

140

120

100

d) Trailing Surface

R10T02 Data eeeeeTCll_TCI2a_._TC13

_TCI4

_TC15_TC17

60"

4°5_ ....... 6........ _b ....... idb ....... i50Time, see

Figure 9.4-7. Thermocouple Data for Liquid Crystal Test on Trailing Surface

With £_ = 450 rpm.

104

Re = 13,000


1000 _ RIOT02 Data _eeTC017 1000 _ R10T02 Data oeeeeTC11 imn \_. 8eeee TC02 | / seeee TC12 I

q I/ x,k.._ _ TC03 [ 1 a _ TC13 JJ U x_x v._v ZC04 } | (=_- _ TC14 II! _ \"_ _TCOS/ ][ _ _TCtSl41 _ _ _TC071 d I _ _TClV I ',

C_ 5

100 0 O0 100 150 i00" 0 50 i00 150

Time, sec Time, sec


1000 I oeeee TC01_seeeTC02

_TC04_TC05_-_TC07_TC08

100

8q_

RIOT02 Data I000 _eeeeeTCll R10T02 Datal -IE_eee TC12

l l_ TCI4I_ I_ zclsI z4 _ TC17

10 10

0 50 100 150 0 50 100 150Time, sec Time, sec

Figure 9.4-8. Results From Thermocouple Data for Liquid Crystal Test on Trailing


105

Re = 13,000

a) Tm

140.

120'

100

80E-.,

6O

40-50

R16T04 Data eeeeOTC02_TC03_TC01_TC04

I IIIIII II _111111 ] III1 III IIII I IIIII ,1111

0 50 100 150Time, see

b) Tou t

140

F_0

0

120

i00"

80'

6O

40-50

R16T04 Dataeeeee TC21

TC22TC23

ii i lllliil ii ii lllll i lll*ImlIllllllllJEl

0 50 100 150Time, see

c) Leading Surface140

120

100

BO

60

40-50

R16T04 Data_eeeeTC02_TC03vv_v_TC04

___ _TC05_e_TC07

I, IIII, II ]11 II II IIIII III IIII I|1 IIIIII11

0 50 100 150Time, sec

140'

120

100

6O

d) Trailing Surface

40-50

R16T04 Data _eOTC11_TC12_TC13v_TC14

_TC15b_-B-HTC17

II II I11tl II I II II II I II II It1111tl II Iltll I

0 50 I00 150Time, sec

Figure 9.4-9. Thermocouple Data for Liquid Crystal Test on Leading Surface

With _ = 750 rpm.

106

Re = 13,000


I000 _ R16T04 Data "[ 1000 _ RI6T04 Data _ TCll

JTC02 [ t _ TC12TC03

/AN.- _ TC04 _ TC13_ _ TC14

l I _t _ TC05 I _._. _ TC15

d d

100 ...... _ 1000 50 100 150 0 50 I00 150

Time, sec Time, sec


i000

°..,

o 100

[...

I R16T04 Data

TC04TC05TC07

TC08

i000?

110 50 100 150

Time, see

RI6T04 Data oeeee TCI1

_eae TCI2

TC13TCI4TC15

TC17(HHH_ TC18

0 50 i00 150Time, see



107

E-,

140

120

100"

Rc = 13,000

a) Tin

80.

6O-

40"-50

R12T02 Data oeeeeTc02_TC03_TC01

i ; , | , ; . , , ii , s, ,, , * iil ,* , ,, , i i i, , | , ,. , s i

0 50 100 150Time, see

140

120

i00

ao.E-,

b) Tou t

60.

4O-50

R12T02 Data eeeee TC21TC22TC23

0 50 100 150Time, sec

c_

140

120

100"

c) Leading Surface

BO

6oi

R1RT02 Data eeeeeTC01_TC02_a_TC03vv_vTC04_,_-aTC05

40 'I'''' 'fill' 'IIL ''' If'' 'i''' 'ii''l' ' if'

--50 0 50 100 150Time, sec

d) Trailing Surface

140

120

100'

BO'

6oi

R12T02 Data eeeeeTCllmmeeeTCl2_TC13_v_,_TCl4

_TC15_TC17

0' ,,i;,l, ,, IS,,, ,,If| I, II,,, ,ili,|lillill

--50 0 50 100 150Time, sec

Figure 9.4-11. Thermocouple Data for Liquid Crystal Test on Trailing Surface With

= 750 rpm.

108

Re = 13,000

a) Leading Surface

I000 i000Rl_r02 Data _ TC01

eeeee TC02TC031IK _ zco4

1 I N, _ TC0SIf %. _ Tco7

d d

2_ 2-

100 1000 50 100 150 0

Time, see

b) Trailing Surface

R12T02 Data oeeee TC11

seeee TC12TC13

TC14

_ TC15[ _ _ TC17

.........s'o........ idd ....... isoTime, see

"5

8

c) Leading Surface

1000 _ eeeeeTC01 R12T02 Data

-I_ TC02 A5-I _ TC03 It

-I _ TC04 A ]A_t_J _ TC05 i,_ n_u_

z _ TC07

i00

10

1 10 50 150I00

Time, sec

d) Trailing Surface

i000

o 100 _

-

h_ I0 :

2-

R12T02 Data oeeee TC11

8_eee TC12TC13TCI4

TC15TC17

¢_¢d_ TCIB

o.........5b........i6d ........i5oTime, see

Figure 9.4-12. Results From Thermocouple Data for Liquid Crystal Test on Trailing Surface

With f_ = 750 rpm.

109

Form ApprovedREPORT DOCUMENTATION PAGE OMBNo. 0704-0188

Public reportingburdenfor this collectionof Infomlatic_lb esti.maled.to average 1.h_. r I_. rW, Includingthe._._Umel.or_revk__ng ins=_, s_,_,;,,_ e_..ist_=.__c_rC_..l_gatheringand maintainingthe data needed, ano _,ng ano reviewingme comc_ono_ immrrmm., oeno _vrr.,_=.* ,.t_u,.,_ .,? uuff,=, m,,_.w _=,I y.__._"_,_ -_k_o, o__nforma,en.induulngsu0ge_nsforredu_ng_ bumn.tow_in_en Hpa_,a_-s Sm_. 0y_e3_."for2_.Opy..rp_..._a_. Rep0aMS._.'"en_Davis Highway,Suite 1204, Arlington,VA _:".'J02-4302,and to the Office ¢4Managementarm uudget, P,apem_omHeou_uoflr'roje_ (u,'u4-ulee), wasnr, gzm'_,_., ,:u._.

1. AGENCY USE ONLY (Leave blanlO 2. REPORTDATE 3. P,_PORTTYPEANDDA]_SCOVERED

May 1996 Final Contractor Report

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Heat Transfer Experiments in the Internal Cooling Passages of a CooledRadial Turbine Rotor

e. AUTHOR(S)

B.V. Johnson and J.H. Wagner

7. pERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

United Technologies Research CenterSilver Lane

East Hartford, Connecticut

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS{ES)

National Aeronautics and Space AdministrationLewis Research Center

Cleveland, Ohio 44135-3191

WU-505-452-10

C-NAS3-25952

8. PF.IqFORMING ORGANIZATIONREPORT NUMBER

E-10155

10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

NASA CR-198472

11. SUPPLEMENTARY NOTES

Project Manager, Kestutis C. Civinskas, Prop_ion Systems Division, NASA Lewis Research Center, organization code

2760, (216) 433-3944.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified -Unlimited

Subject Category 07

This publication is available from the NASA Center for AeroSpace Information, (301 ) 621--(I390,

12b. DI:SlHIBUTION CODE

13. ABSTRACT (Maximum 200 words)

An experimental study was conducted (1) to experimentally measure, assess and analyze the heat transfer within theinternal cooling configuration of a radial turbine rotor blade and (2) to obtain heat transfer data to evaluate and improve

CFD procedures and turbulent transport models of internal coolant flows. A 1.15 times scale model of the coolant

passages within the NASA LeRC High Temperature Radial Turbine was designed, fabricated of Lucite and iustmmentedfor transient heat transfer tests using thin film surface thermocouples and liquid crystals to indicate temperatures. Tran-

sient heat transfer tests were conducted for Reynolds numbers of one-fourth, one-half, and equal to the operating

Reynolds number for the NASA Turbine. Tests were conducted for stationary and rotating conditions with rotationnumbers in the range occurring in the NASA Turbine. Results from the experiments showed the heat transfer characteris-tics within the coolant passage were affected by rotation. In general, the heat transfer increased and decreased on the sides

of the straight radial passages with rotation as previously reported from NASA-HOST-sponsored experiments. The heattransfer in the tri-passage axial flow region adjacent to the blade exit was relatively unaffected by rotation. However, theheat transfer on one surface, in the transitional region between the radial inflow passage and axial, constant radius

passages, decreased to approximately 20 percent of the values without rotation. Comparisons with previous 3-D numeri-cal studies indicated regions where the heat tmusfer characteristics agreed and disagreed with the present experiment.

14. SUBJECT TERMS

Radial turbine; Cooling; Internal cooling; Cooling passages; Heat transfer

17. SECURITY CLASSIFICATIONOF REPORT

Unclassified

_ISN7540-01-280-5500

;18. SECURITY CLASSIFICATIONOF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATIONOF ABSTRACT

Unclassified

15. NUMeE_i OF PAGES

11816. PRICE CODE

A0620. LIMITATION OF AB:_/Z-LACT

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