N I STIR 89-3926

APPARATUS FOR MEASURING

HIGH-FLUX HEAT TRANSFER

IN RADIATIVELY HEATED

COMPACT EXCHANGERS

Douglas A. Olson

National Institute of Standards and Technology

U.S. Department of Commerce

Boulder, Colorado 80303-3328

October 1989

NISTIR 89-3926

APPARATUS FOR MEASURING

HIGH-FLUX HEAT TRANSFER

IN RADIATIVELY HEATED

COMPACT EXCHANGERS

Douglas A. Olson

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

October 1989

Sponsored by

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23665

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director

CONTENTS

Page

List of tables iv

List of figures v

Nomenclature vii

Abstract 1

1. Introduction 2

2. Description of experimental apparatus 2

2.1. Flow loop 3

2.2. Instrumentation 4

3. Methods of data analysis 6

3.1. Friction factor 6

3.2. Heat transfer coefficient 7

4. Summary 10

5. References , 11

Appendix A. Calibration of the heat-flux distribution within the

furnace 12

A.l. Description of the calibration apparatus 12

A. 2. Operation of the heat flow meters 13

A. 3. Methods of data analysis 14

A. 4. Results of the calibration 16

A. 5. Uncertainty in the furnace heat flux calibration 19

iii
List of tables

Table 1 . Uncertainties in experimental measurements and gas properties

at a 95% confidence interval. 4

Table A.l. Summary of furnace calibration experiments 17

Table A. 2. Furnace heat flux distribution function, f

q

19
List of figures

Figure 1. Pin-fin heat exchanger for NASP application (separated view).. 20

Figure 2. Helium flow loop 21

Figure 3. Specimen furnace. Inlet and outlet gas temperatures are

measured at points 0 and 1; upstream and downstream pressures

are measured at points A and B 22

Figure 4. Technique for mounting thermocouples on pin- fin specimens 23

Figure A.l. Calibration specimen in furnace 24

Figure A. 2. Lay-out of heat flow meters on calibration specimen 25

Figure A. 3. Traverse of normalized heat flow along y direction at x=0

.

Shown are data from tests 2 and 3, heater voltages 35.3%

and 19.9%. is meter 1, and "o" is meter 2 26

Figure A. 4. Traverse of normalized heat flow along x direction at y=0

for heater voltages greater than 29%. Shown are data from

test 2 (35.3% voltage, "*"), test 4 (50.8% voltage, "o"),

and test 11 (29.3% voltage, "A"). The smooth curve is the

curve fitted to the normalized heat flow data (j function)

,

which has a standard deviation of 0.5% 27

Figure A. 5. Traverse of normalized heat flow along x direction at y=0

for heater voltages less than 29%. Shown are data from

test 6 (20.4% voltage, "*"), test 9 (20.2% voltage, "o"),

and test 10 (24.5% voltage, "A")- The smooth curve is the

curve fitted to the normalized heat flow data (j function)

,

which has a standard deviation of 0.3% 28

v
•V-

.
Nomenclature

A = upstream location of pressure tap

Af = flow normal area = V0 /L

A^ = specimen normal area

= wetted wall area (total wall area exposed to fluid)

B = downstream location of pressure tap

c

p = specific heat at constant pressure

Dh = specimen hydraulic diameter

= ^o/K

f = friction factor

f = normalized heat flux on target

f (x,y,v) = heat flux distribution function

G = mass flow rate per unit flow normal area

= m/Af = pV

h = heat transfer coefficient

h = enthalpy

j(x,y,v) = normalized heat flow through heat flow meter

j t (x,y,v) = heat flow through heat flow meter

k = thermal conductivity

K = heat flow meter calibration constant

L = length of specimen

m = mass flow rate

Nu = Nusselt number = h-Dh /k

P = pressure

Pr = Prandtl number = p-cp

/k

q(x,y,v) = local heat flux based on area normal to the furnace target

Qm = heat leak to manifolds through insulation

Qm , ,

„

= heat leak to inlet manifold

Qpx = fraction of total heat flow on specimen added up to position x = integration of furnace calibration function f

q

, 0 to x

Qt = total heat transfer to specimen

qw - local heat flux (heat flow per unit area) into the cooling fluid based on

total wetted-wall area of the specimen

r = recovery factor = Pr 1/3 for turbulent flow

Re = Reynolds number = pVDh /p

T = temperature

Taw = cooling fluid adiabatic wall temperature

Tf = local bulk fluid temperature

Tr = Eckert reference temperature

Tw = specimen wall temperature

v = heater voltage

V = velocity

V(x,y,v) = measured heat flow meter voltage

VQ = open volume in specimen

w = heat flow meter half-width

x = position coordinate parallel to flow direction

x0 = furnace target half-width = L/2

y = position coordinate perpendicular to flow direction

/3 = coefficient of thermal expansion

a = standard deviation

vii
/i = dynamic viscosity

p = density

0 = location in inlet manifold of PRT

1 = location in outlet manifold of PRT

viii
Apparatus for Measuring High-Flux

Heat Transfer in Radiatively Heated Compact Exchangers

Douglas A. Olson

Chemical Engineering Science Division

National Institute of Standards and Technology

Boulder, CO 80303-3328

We describe an apparatus which can deliver uniform heat flux

densities of up to 80 W/cm2 over an area 7.8 cm by 15.2 cm for use

in measuring the heat transfer and pressure drop in thin (6 mm or

less), compact heat exchangers. Helium gas at flow rates of 0 to

40 kg/h and pressures to 6.9 MPa (1000 psi) is the working fluid.

We describe the instrumentation used in the apparatus and the methods

for analyzing the data. We will use the apparatus initially to

test the performance of prototype cooling jackets for the engine

struts of the National Aerospace Plane (NASP)

.

Key words: apparatus; compact heat exchanger; convection heat

transfer; friction factor; high temperature; National Aerospace

Plane; pin-fin; radiative furnace.

This work was funded by NASA Langley Research Center under contract L7400C.

1
1. Introduction

Research at NASA on vehicles for hypersonic flight has been active since

the 1960's (Shore, 1986). The renewed interest in developing a National

Aerospace Plane (NASP) requires solving many demanding heat transfer problems

associated with the anticipated high heat fluxes on various components. The

problem of interest motivating this work is the cooling of the engine struts.

Due to aerodynamic heating associated with the combustion of the hydrogen

fuel, along with radiation from the fuel combustion, the engine struts are

expected to receive a heating load in excess of 2000 W/cm2 (Scotti et al .

,

1988). NASA plans to cool the struts by attaching a cooling jacket heat

exchanger to the surface facing the high heat flux. Hydrogen gas will flow

through the cooling jacket, absorbing the heat before entering the engine.

The anticipated conditions are that the hydrogen gas will enter the heat

exchangers at 56 K and 6.9 MPa (1000 psi) , and exit at 890 K and 4.8 MPa (700

psi) . The heat exchangers are expected to be thin perpendicular to the flow

direction (6 mm or less) to add minimal weight and thickness to the struts.

Small flow passages will also produce high rates of convective heat transfer,

which will reduce the exchanger temperatures. Reynolds numbers are expected

to be in the range 10000 to 30000, with the variation due to the flow rate

and the specific design of the flow passage. Because of the small flow

passages and high heating rates, the heat transfer performance of the

prototype heat exchangers is beyond the range of past experimental work and

correlations

.

A leading candidate for the cooling jacket is the "pin-fin" heat

exchanger (fig. 1). This design is being considered based on fabrication

techniques, structural considerations, and the anticipated heat transfer

performance (Buchmann et al., 1985). Nickel 201 is one of the proposed

materials, due to its high ductility and high thermal conductivity. A pin- fin

heat exchanger consists of a closely spaced channel with pins connecting the

top and bottom surfaces. The pin-fins increase the heat transfer area; by

promoting turbulence they also increase the local heat transfer coefficient.

Compared to other compact heat exchangers, the pin-fin configuration has high

heat transfer per unit volume, but also a large pressure drop (Kays and

London, 1964) . Pin-fin heat exchangers have been used for cooling turbine

blades in gas turbines, and most of the existing correlations are based on

work for that application (Armstrong and Winstanley, 1987).

The objective of this work was to design and build an experimental

apparatus which could test prototype heat exchangers at some of the conditions

anticipated for the NASP application. Test results would be heat transfer

performance and pressure drop as a function of Reynolds number, heating rate,

and flow geometry. The apparatus will be used initially to test pin-fin heat

exchangers, and in the future will be capable of testing any flat, compact

heat exchanger which can conform to the furnace dimensions.

2. Description of the experimental apparatus

The experimental apparatus has been designed to initially test a subset

of the conditions required for the NASP application. Those conditions are (1)

2
a heating rate of 0-80 W/cm2

; (2) an inlet temperature of 300 K; (3) a cooling-gas pressure of 6.9 MPa at the inlet; and (4) an outlet temperature of

810 K. The size of specimen which can be tested is 7.8 cm wide by 15.2 cm

long. Because of the similarities in specific heat, thermal conductivity, and

dynamic viscosity between helium and hydrogen, helium will be the first

cooling gas tested. The Reynolds numbers and temperature rise from specimen

inlet to outlet can be matched between helium and hydrogen. As the taking of

data progresses, indicating the critical experimental parameters, flow loop

components can be added which yield cryogenic inlet conditions or higher

heating rates. Hydrogen gas will be tested after moving the apparatus to a special site for hazardous tests and adding hydrogen-safety features.

2.1. Flow loop

The helium flow loop is shown in figure 2, with the details of the

specimen furnace section in figure 3. Helium gas at 13.8 MPa (2000 psi) is

supplied from a tube trailer outside the laboratory. The tube trailer

contains 1100 m

3 of gas (STP) . Valve #1 at the trailer isolates the gas from

the 1.2 cm diameter high pressure copper piping to the laboratory. A second

shut-off valve (#2) within the laboratory isolates the inlet piping from the

portion within the laboratory. With valves #1 and #2 open, gas flows from the

trailer, through the inlet piping, and is filtered before entering the domeloaded pressure regulator (valve #3) . The regulator sets the flow pressure

downstream of the regulator to the value of an external control pressure, 6.9

MPa (1000 psi) or less. A pressure relief valve downstream of the regulator,

set at 8.3 MPa (1200 psi), prevents system over-pressure. The gas flows

through stainless steel tubing, 1.9 cm OD and 0.21 cm wall, from the pressure

regulator to the furnace.

Within the furnace (fig. 3), the gas flows into an inlet distribution

manifold (347 stainless steel) which directs the gas to the heat exchanger

specimen. A similar distribution manifold collects the gas exiting the

specimen and directs it to the outlet tubing. The heat exchanger specimen is

brazed into the space between the manifolds. The specimens are located in the

target area of the furnace, which delivers radiant heat to the specimens and

raises the temperature of the helium as it flows through the specimen.

The furnace consists of a high- intensity radiant infrared heater,

surrounded by refractory insulation, 5 cm thick or greater, which directs and

re-radiates the heat from the heater to the specimen. The heater contains six

high- temperature infrared lamps mounted in an aluminum housing. Filtered shop

air at 0.85 m

3 /min (30 cfm) or greater cools the heater lamps, and water at 4

kg/min (1 gpm) or greater cools the housing. The radiant heater is powered by

a phase-angle power controller which uses 480 VAC, single phase, and 75 A at

full power setting. At the maximum heat flux setting, the refractory walls

reach an estimated temperature of 1760°C (3200°F).

Downstream of the furnace section, the hot gas flows through more

stainless steel tubing (1.9 cm OD, 0.21 cm wall) to a cooling coil (5.5 m of

the same tubing) immersed in a water bath. The water bath cools the helium

temperature to 30°C or less. The rate of gas flow is manually adjusted at

the bath outlet by valve #4, which also drops the gas pressure to atmospheric

3
pressure. Beyond the valve, helium flow rate is measured with a heated-tube

thermal mass flow meter, with ±1% uncertainty in the reading (at a 95%

confidence level) . After exiting the flow meter the gas flows into an exhaust

line of 5 cm copper tubing, and is vented outside the laboratory.

2.2. Instrumentation

Measurements are made of temperature of the gas in the inlet and outlet

manifolds, gas pressure in the specimen, specimen temperatures, and the

aforementioned gas flow rate. Uncertainties in the measured quantities are

summarized in Table 1.

Table 1 . Uncertainties in experimental measurements and gas properties

at a 95% confidence interval

Measurement /Proper tv Technique

Major Source

of Uncertaintv

Magnitude

of Uncertaintv

Gas Flow Rate Thermal Mass Flow

Meter

Meter Calibration ±1%

Heat Flux Calibration of

Furnace

Heat Flow Meter ±4%

Gas Inlet and

Outlet Temperatures

Platinum Resistance Thermometer

Radiation ±0.5 K

Gas Pressure Pressure TransducerCalibration ±0.25% of

full scale

Specimen Temperature Type-N Thermocouple

Wire Calibration,

Installation

greater of

±0.4% or 1.1 K

Gas Temperature in

Specimen

Integrate Energy

Equation

Heat Flux

Uncertainty

±1% of T : -T0

Gas Density Thermodynamic

Function

Function Accuracy ±0.1%

Gas Enthalpy Thermodynamic

Function

Function Accuracy ±0.2%

Gas Specific Heat Thermodynamic

Function

Function Accuracy ±5%

Gas Viscosity Thermodynamic

Function

Function Accuracy ±10%

Gas Thermal

Conductivity

Thermodynamic

Function

Function Accuracy ±3%

4
We determined the heat flux distribution on the specimen by calibrating

the furnace prior to inserting the specimen. The heat flux distribution is

defined as the local heat flux as a function of position over the furnace

target and as a function of heater lamp voltage. Details of the furnace

calibration are given in appendix A. The uncertainty in the heat flux is

estimated as ±4%.

The gas inlet and outlet temperatures are measured with platinum

resistance thermometers (PRTs) , 0.48 cm diameter, inserted in the gas

manifolds at locations 0 and 1 of figure 3. The uncertainty in the

thermometer calibration is ±0.08 K; the uncertainty introduced by the digital

voltmeter is ±0.036 K. Radiation errors in the thermometers are estimated as

less than ±0.5 K, while conduction errors in the thermometers are estimated as

less than ±0.01 K. The gas pressure at the specimen inlet (location A in

figure 3) is measured with a variable-reluctance pressure transducer.

Pressure difference between the specimen inlet and outlet (A to B) is measured

with a second pressure transducer, also a variable-reluctance type with

interchangeable diaphragms. The uncertainty in the calibration of both is

±0.25% of full scale. Uncertainty introduced by the voltmeter is ±0.011% of

the pressure reading.

Specimen temperatures will be measured with type-N thermocouple wire,

wire diameter 0.25 mm. An array of thermocouples, 25 or more depending on the

specimen design, will be spot-welded to the side opposite the radiant heat

flux (insulated-side). Temperatures measured at the insulated-side

thermocouples will be used to determine the heat transfer coefficient. The

relative uncertainty from pair-to-pair is ±0.4% of the reading or ±1.1 K,

whichever is greater. At the maximum expected specimen temperature this is

±2.1 K. Estimates of the heated-side temperature will be made with type-N

thermocouples mounted in a fashion shown in figure 4, which is the method for

the pin-fin specimen. Each wire of the pair is spot-welded to the heated

surface, with the lead extending out a hole drilled through the specimen. For

the pin-fin specimen, the holes will be drilled through the center of a pin.

The thermocouple circuit is completed by the specimen wall between the two

wires. A quartz sleeve, 0.5 mm diameter, electrically insulates the wire from

the wall of the hole. Because a portion of the pin is removed and replaced

by wire plus quartz, each of which has a lower thermal conductivity than the

pin (nickel) , a pin with a wire mounted in it will be hotter than a pin with

no wire mounted in it. We estimated the magnitude of this temperature rise

from a finite-element analysis as 2-5 K at a radiant heat flux of 50 W/cm2

.

All type-N thermocouples will be connected to an isothermal reference

box. We measured the temperature uniformity of the reference box as ±0.05 K

or better. Copper conductor wire runs from the reference box to the data

scanner. The temperature of the reference box is measured with a platinum

resistance thermometer (PRT) . Using the box PRT sensor for the reference

temperature, we compared temperatures indicated by thermocouples connected to

six terminals in the reference box with temperatures indicated by the gas

inlet and outlet PRTs. All sensors were immersed in a stirred water bath at

20-30°C. This provided a system accuracy for the reference box plus PRT.

The agreement in temperature between the thermocouples and gas PRTs was better

than ±0.06 K.

5
All instrument signals are multiplexed through an automated scanner and

measured on a digital voltmeter. The scanner and voltmeter are controlled

with a personal computer through an IEEE 488 bus. Raw signals are stored on a

hard disk and copied to floppy disk for backup. Signals are converted to

engineering units and the data analyzed at the completion of an experimental

run. Some signal readings are converted immediately to engineering units and

displayed on the video terminal to assist in monitoring and operating the

experiment. The measurement uncertainties introduced by the data acquisition

system have been included in the stated uncertainties of each sensor.

3. Methods of data analysis

The data required to evaluate the performance of the heat transfer

specimens are the heat transfer coefficient, h, and the friction factor, f.

3.1. Friction factor

The friction factor results from an integration of the one-dimensional

momentum equation in the flow direction:

Pfl -PB = G

2

( l/p B- l/pA ) + (2G2 /Dh )

fB

( f/P ) dx

,

( 1 )

where P =

G =

A =

B =

pressure

mass flow rate per unit flow normal area

m/Af = pV;

flow normal area = open volume/specimen length;

density

velocity

specimen hydraulic diameter;

upstream location of pressure tap;

downstream location of pressure tap.

The first term on the right hand side of the equation is the pressure change

due to flow acceleration, and the second term is the pressure drop due to

frictional effects. For the pin-fin specimens, the hydraulic diameter is

given by (VanFossen, 1982):

Dh “ ^VQ /

w , (2)

where VQ = open volume in specimen;

= wetted wall area (total wall area exposed to fluid)

This definition is appropriate when the pin height, pin diameter, and pin-topin separation are of the same order, as all are likely significant in

generating turbulence which drives the pressure drop and heat transfer.

If the density change is small compared to the absolute density, and the

pressure drop through the specimen is linear, then the integral can be

approximated as a constant and the resulting equation for f is:

6
PA -PB

- G

2

( l/pB- 1/pA )

2 (G2 /p )

• (L/Dh )

f = (3)

with p = (pA + p B )/2

.

The density change criterion is met when the gas flows through the

specimen without being heated, but when the specimen is heated the exit

density can be less than half the entrance density and eq (3) is not valid.

The friction factor is calculated for a series of tests with flow rate as the

variable but with no heating, and a functional dependence of f on Reynolds

number is developed, where the Reynolds number is defined as

Re = pVDh /p . (4)

Then, for experiments with specimen heating, the density and Reynolds number

(evaluated using the local gas temperature and pressure) are calculated as a

function of x. The integral in eq (1) is evaluated to calculate the pressure

drop from A to B, which is checked against the measured pressure drop. This

provides a technique for evaluating if f depends on more than Reynolds number

alone

.

3.2. Heat transfer coefficient

The heat transfer coefficient, h, is defined through the equation

qw = h • (Tw -Taw ) , (5)

where qw = local heat flux (heat flow per unit area) into the cooling

fluid based on total wetted-wall area of the specimen;

h = heat transfer coefficient;

Tw = specimen wall temperature;

Taw = adiabatic wall temperature of the cooling fluid.

The adiabatic wall temperature is used in gas flows whenever the kinetic

energy is significant compared to enthalpy changes (Rohsenow and Choi, 1961).

Friction can cause the local wall temperature to exceed the bulk fluid

temperature for an adiabatic specimen, and the adiabatic wall temperature

approximates this effect. It is defined as

Tau = Tf + rV2 /(2c

p ), (6)

where Tf = local bulk fluid temperature;

r = recovery factor = Pr 1/3 for turbulent flow.

Adiabatic heating can be on the order of 1 K for the anticipated conditions.

The local heat flux in eq (5) is expressed in terms of the total heat

transfer to the specimen, QT , the total wetted wall area, and the furnace

calibration function, f

q

, which is a dimensionless expression of the local

normal heat flux:

q„ = (QI /An )-£

q -(An /Aw ). (7)

7
The wall temperature used in eq (5) is measured with a thermocouple on the

insulated side of the specimen.

In the defining equation of h we assume (1) that the heat flux is uniform

into the cooling fluid at a particular location (the same at the top and

bottom surfaces and at the pins joining the top and bottom), (2) that the wall

temperature is uniform, and hence (3) that the heat transfer coefficient is

constant. However, since the specimen is heated from one side only and heat

must flow through the specimen structure to enter the fluid from the pin and

insulated wall, wall temperatures will not be constant. The dimensions of the

specimen prevent instrumenting around the perimeter of a pin, and imbedded

thermocouples alter the specimen temperature distribution, so the insulatedside thermocouple is used as the wall temperature. A finite-element

conduction analysis using anticipated values of the heat transfer coefficient

and the pin-fin configuration of figure 1 indicated that the temperature along

the insulated side varies by 0.1 K or less with respect to pin position (for

50 W/cm2 hot side heat flux) . In addition, the analysis indicated that the

temperature of the insulated side is very close to the fluid-wall interface

temperature along the bottom surface (within ±1 K for a pin-fin specimen with

50 W/cm2 hot side heat flux) . This compares with a temperature difference

between the wall and bulk fluid of at least 10 K for the same conditions.

These conclusions could change for specimen geometries and materials different

from those of the pin-fin configuration.

Combining eqs (5), (6) and (7) and rearranging, we get

(QT /^w )

' fq

(Tw -[T f +(rV2 )/(2c

p )]

}

( 8 )

We will calculate the heat transfer coefficient at all locations where

temperature of the insulated side is measured with a thermocouple. We will

measure the wall temperature directly, while the furnace calibration function

f is a function of location and heater voltage. The flow direction energy

equation is used to calculate QT (to follow). Gas temperature T f is

calculated using the flow direction energy equation along with the furnace

calibration (also to follow)

The total heat absorbed by the heat transfer specimen equals the total

heat absorbed by the specimen plus manifolds, less the heat leak through the

furnace insulation into the manifolds, . It is calculated from the

temperatures of the gas inlet and outlet, the gas pressure drop, and an

estimation of the manifold heat leak. Or

Qt = in- (h : -h0 )

- Qm , (9)

where h = enthalpy;

0 = location in inlet manifold of PRT

1 = location in outlet manifold of PRT;

Qm = heat leak to manifolds through insulation.

Heat absorbed by the manifold is typically 2-5% of the total heat flow, which

we measured during calibrations on the furnace prior to inserting the test

8
specimens. We neglect kinetic energy changes from 0 to 1 since they are

insignificant compared to the uncertainties of the temperature measurement.

The enthalpy change is given by

Ih-ho = Cp-dj-Tj) + P [ (l-/3T)/p]dP, (10)

where (5 = coefficient of thermal expansion.

The pressure term is significant since helium is not an ideal gas at these

temperatures and pressures. The integral is evaluated using the virial

equation of state for the gas (McCarty, 1973) and is included as a subroutine

in the data analysis program. For that evaluation, pressure in the inlet and

outlet manifold is required, although it is measured only at locations A and

B (fig. 3) . Since the pressure term is usually less than 1% of the

temperature term, pressure is assumed to vary linearly along the specimen and

to be constant within the end manifolds. The ratio of the specimen length

between taps A and B to the length between A and 0 (the specimen inlet) is 8.

Thus, P0 and P : are estimated as

Po = Pa + (Pa-PB )/8.

Pi = PB

- (PA -PB )/ 8 - (ID

Combining eqs (9) and (10) yield for QT

:

Qt = mlCp-dj-To) + J[(l-/3T)/p]dP} - Qm . (12)

The fluid temperature, Tf , is calculated by integrating the flow energy

equation from the inlet manifold up to the location of interest (designated as

x) , now including kinetic energy:

f X T0 +

Qt ‘Qp me. +Qm > i n mc„

[u-/m/P ]dP

Yxl

2 S’

(13)

where Qpx = fraction of total heat flow on specimen added up to

position x; = integration of furnace calibration function f , 0 to x;

Qm , in = heat leak to inlet manifold.

The fluid temperature requires the velocity at x, given by

Vx = m/(Af px ), (14)

and the density is given by the equation of state (McCarty, 1973):

Px = MTfx> Px).

The pressure at x is estimated by

9

( 15 )
(Pa -Pb P„ = P, )-x/L. (16)

With eq (16) substituted into eq (13) to evaluate the pressure term, eqs

(13), (14), and (15) form a system of three equations in the unknowns of

temperature, velocity, and density. They are solved through iteration by

first neglecting velocity in eq (13) to calculate temperature; eq (15) is used

to calculate density, eq (14) is used to calculate velocity, and temperature

is re-calculated from eq (13) with velocity included. The iteration continues

until convergence (<0.01 K change in successive computations of temperature).

Only two or three iterations are usually required since the kinetic energy is

about 1% of the enthalpy change.

With Tf and V determined at location x, the heat transfer coefficient is

calculated using eq (8). The Nusselt number, Prandtl number, and Reynolds

number are then calculated:

Nu = h •

h /k

,

Pr = M-cp /k. (17)

The Eckert reference temperature is used to calculate the fluid properties due

to the large wall to fluid temperature difference, as done by VanFossen

(1982):

Tr = 0 . 5 •

w + 0 . 28Tf + 0.22Taw . (18)

Fluid properties are calculated from the functions given in McCarty (1973).

4

Summary

We have described an apparatus which can measure the heat transfer and

friction factor in thin, compact heat exchangers which are radiatively heated

in a furnace at heat fluxes of up to 80 W/cm2

. Instrumentation and methods of

data analysis are described. The apparatus will be used initially to test a

compact heat exchanger of the pin-fin configuration using helium gas as the

heat transfer fluid.

We acknowledge the assistance of Robert R. Wilson in performing the

furnace calibration, developing data acquisition programs, and constructing

the apparatus. We appreciate the assistance of David E. Daney in designing

the apparatus. The thermocouple mounting technique for the pin-fin

configuration was developed by NASA Langley Research Center.

10
5. References

Armstrong, J., and Winstanley, D., 1987, "A Review of Staggered Array Pin Fin

Heat Transfer for Turbine Cooling Applications," ASME paper 87-GT-201 .

Buchmann, 0. A., Arefian, V. V. , Warren, H. A., Vuigner, A. A., and Pohlman,

M. J., 1985, "Advanced Fabrication Techniques for Hydrogen-Cooled Engine

S true ture s

, " NASA CR-3949 .

Kays, W. M. , and London, A. L. , 1964, Compact Heat Exchangers . McGraw-Hill,

New York, 2nd. edition.

McCarty, Robert D., 1973, "Thermodynamic Properties of Helium 4 from 2 to 1500

K at Pressures to 10 8 Pa," J. Phvs . Chem, Ref. Data . Vol. 2, no. 4, pp . 923-

1042.

Rohsenow, W. M. , and Choi, H. , 1961, Heat. Mass, and Momentum Transfer . Prentice-Hall, Inc., Englewood Cliffs.

Scotti, Stephen J., Martin, Carl J., and Lucas, Stephen H. , 1988, "Active

Cooling Design for Scramjet Engines Using Optimization Methods," NASA TM100581.

Shore, Charles P., 1986, "Review of Convectively Cooled Structures for

Hypersonic Flight," NASA TM-87740 .

VanFossen, G. J., 1982, "Heat Transfer Coefficients for Staggered Arrays of

Short Pin Fins," J. Eng, for Power . Vol. 104, pp . 268-274.

11
Appendix A. Calibration of the heat-flux distribution within the furnace

Evaluation of the heat transfer performance of the specimens requires

values for gas temperature inside the flow passages and for the local heat

flux incident on the specimen. Neither of these will be measured directly

during a test run with the specimen in place; the local gas temperature can be

inferred from an energy balance on the gas if the heat flux to the specimen is

known. Variations in heat flux across the furnace target area, the "heat flux

distribution" are measured prior to the tests on the pin-fin specimens through

tests on a "calibration specimen." For specimens with the same emissivity

and thermal conductance to the heat sink, the furnace performance will not

depend on the type of specimen receiving the heat flux.

A.l. Description of the calibration apparatus

To calibrate the furnace, the calibration specimen was placed in the

target area of the furnace (see fig. A.l). Three heat flow meters soldered to

the specimen measured the heat flow over the meter area, approximately 2.52

cm2

. With the radiant heater at a steady voltage and with water cooling the

specimen, the plate with meters attached was traversed over the furnace target

area to measure variations in the x and y directions at that voltage. The

readings from the meters were used only up to the point where the outer edge

aligned with the furnace wall. The voltage was then changed and the x-y

traverse was repeated. The measured meter heat flow was then analyzed to give

a heat flux , and a function for the heat flux was developed with inputs x, y,

and heater voltage.

The calibration specimen consisted of a lower brass plate, 2.5 cm thick,

and an upper copper plate, 0.64 cm thick. Cooling channels for water flow

were machined in the brass piece. The plates were 12.7 cm wide and 33 cm

long. The three heat flux meters were each 1.59 cm by 1.59 cm and 0.16 cm

thick, and were located as shown in figure A. 2. The signal lead wires lay in

shallow channels machined in the top copper plate, and copper shading shims,

also 0.16 cm thick, covered the leads to prevent overheating. The top surface

of the assembled piece, including shims and heat flow meters, was spraypainted a flat black to provide a uniformly high absorptivity.

The calibration specimen was placed in a traversing mechanism which

moved the specimen in the x and y directions in the plane of furnace target.

In the x direction (parallel to the axis of the heater) , the traversing

mechanism could move all heat flow meters from one end of the furnace to the

other. In the y direction (perpendicular to the axis of the furnace), motion

was limited to about 3.8 cm, sufficient to allow meters 2 and 3 to align with

the +y wall, and meter 1 to align with the -y wall. This allowed about 1.9 cm

of meter overlap in the center; however each meter did not traverse the full y

width. Position was read to ±0.5 mm. At maximum specimen displacement in the

traversing mechanism (meters aligned with the furnace wall) , coverage of the

target by the specimen was 100%.

The temperature of the calibration specimen was monitored with a type K

thermocouple placed under the left-side shim of figure A. 2. Type K

12
thermocouples monitored temperatures at an interior location of the furnace

insulation, on the housing of the heater, and in the cooling air as it exited

the heater. The heater voltage was also measured (as a percent of maximum

voltage) . The cooling water flow rate was monitored with a rotameter

flowmeter, and the water temperature rise across the specimen was measured

with thermistors.

A. 2. Operation of the heat flow meters

The heat flow meters generated a DC voltage proportional to the heat flow

through them. They consisted of three layers of metal; the top and bottom

were the EP thermoelement, thermoelectrically different from the EN

thermoelement in the middle layer. Flow of heat through the meter generated a

temperature difference across the middle layer. Due to the alternating

materials of construction, the temperature difference produced a voltage

difference across the middle layer. Leads of the EP thermoelement were spotwelded to tabs on the top and bottom layers.

The manufacturer listed the uncertainty in the calibration of the meters

as ±5%, with a linear relationship between heat flow and measured voltage

output. As used in this application, though, they were not interchangeable.

That is, if the plate was positioned such that each meter was exposed to the

same heat flow, the output varied between meters by as much as 20%. This

variability was not due to an uncertainty of an individual meter calibration

constant, but rather to differences in the calibration constant between

meters. We found individual meters to be linear and repeatable to better than

±1%, over a range of heat fluxes from 0 to 44 W/cm2

, from calibrating the

meters in a simple guarded hot plate apparatus. The calibration constant was

also estimated with the meters attached to the calibration specimen. Using

the heat absorbed in the cooling water as an estimate of the heat flow through

the meter, the linearity for a single meter was about ±2.5% for heat fluxes of

18 to 52 W/cm2

, which was the same as the uncertainty in the measurement of

heat absorbed in the cooling water.

We believe differences in the calibration constants between meters are

caused by: (1) variations in the thickness or thermal conductivity of the

meter; (2) differences in the absorptivity between the meters; (3) variations

in the thermal contact between the meter and copper plate for different

meters. We think that (3) is the most likely; in the guarded hot plate

apparatus we found that the agent bonding the meter to the cold sink affected

the meter calibration. For example, the calibration constant differed by 15%

for a meter soft-soldered to the cold sink and for a meter with indium

compressed between the meter and cold sink.

As used in the furnace calibration, we obtained a relative calibration

by assuming each meter was exposed to the same heat flow when located at the

center of the furnace target. The voltage obtained at the center location was

then used to normalize readings at locations off center. Based on the

linearity and repeatability of the meters, the basic accuracy of the

normalized reading was taken as ±1%. The uncertainty in the over-all heat

flux distribution is evaluated below.

13
A. 3. Methods of data analysis

The heat flow meters measured the heat flow over a 2.52 cm2 area. For

the specimen heat transfer experiments, heat flux (heat flow over an

infinitesimal area) is required as a function of x position, y position, and

the heater lamp voltage. It is more convenient to express this as

q(x,y,v) = f

q

(x,y,v) -Qt/Ah

,

(A.l)

where q(x,y,v) = local heat flux based on the normal area;

A^ = specimen normal area;

v = heater voltage;

f

q

(x,y,v) = heat flux distribution function.

The quantity Qx/A^ is the average heat flux over the specimen. As re-stated,

the problem now is to find f

q

. The steps in determining the distribution

function are

1) Measure the heat flow meter output (heat flow) over the target area

(vs x and y) for several heater voltages.

2) For each voltage, normalize the readings by the value of the meter

output at the center of the target.

3) Fit a curve to the normalized data vs. x and y.

4) Using the fitted curve, transform the data to extract the local

normalized heat flux.

These steps are now explained in more detail.

The meter heat flow is equal to the measured voltage times a calibration

constant, K, or:

j t (x,y,v) =K-V(x,y,v), (A. 2)

with j t (x,y,v) = heat flow;

V(x,y,v) = the measured meter voltage.

By normalizing all the readings by the reading at the center of the furnace

(x=0,y=0), we can define another function:

j (x,y , v) = V(x,y,v)/V(0,0,v) = j t (x,y , v)/j t (0 , 0 , v) . (A. 3)

This function, through the linearity of the meter, is also the ratio of heat

flow at x and y to the heat flow at the furnace center. With values j(x,y,v)

at a few discrete points, typically a scan of x at constant y or a scan of y

at constant x, we fit a curve to the data using a least squares regression

scheme to develop a polynomial function for j(x,y,v). The data show that the

variation in j with y is less than the uncertainty in the heat flow meter, so

we neglect it and determine only a dependence of j on x. For simplicity in

the notation, the v argument is dropped also, with the understanding that the

operations which follow occur at a constant voltage.

14
We now define a function f(x) which is the local heat flux normalized to

he heat flux at x=0

.

f (x ) = q(x)/q(0)

.

(A. 4)

The function j is thus the integration of f over the meter area, or

j (x) • 2w f(Ddr, (A. 5)

where w is the half -width of the meter. If f is constant or linear over the

meter area, eq (A. 5) will show that j = f. The relationship between f and f

q is found by combining (A.l) and (A. 4):

f (x) • q(0) = q(x) = f

q

(x) •

Q

t /

.

(A. 6)

By integrating (A. 6) over the total target area and equating to Qt , it can be

shown that

f(x)

+x0

[ 1/ (2x0 )

]

• v f(r)dr

-xo

(A. 7)

where x0 is the half width of the target. Hence if we can find f(x) through

eq (A. 5), eq (A. 7) can be used to find the distribution function f

q

and eq

(A.l) is used to find q(x).

To find f(x), we define a function g such that

j (x) • 2w = g(x+w) - g(x-w) = j d[g(0]- (A. 8)

J X - w

From eqs (A. 5) and (A. 8) we see that

f (x) = d[g(x) ]/dx. (A. 9)

Considering for the moment x>0 , from eq (A. 8), we can substitute z=x+w, and

then

g ( z ) = g(z-2w) + 2w- j (z-w) . (A. 10)

The function g at z-2w can be evaluated by recursion of eq (A. 10), or

g(z) = 2w-j(z-w) + 2w-j(z-3w) + g(z-4w). (A. 11)

And for an expansion of n terms,

n

f(z) = g'(z) = 2w-

£

( j' [z- (2i-l)w] } + f (z-2nw)

,

i=l

(A. 12)

15
where eq (A. 9) has been used where appropriate. The number of terms n is

chosen such that -w<z-2nw<w; that is, f(z-2nw) is evaluated around the center

of the furnace target. The measurements show that j (x) is nearly linear near

the target center, and f can be taken equal to j with little error. Or,

replacing z with x,

n

f(x) = 2w-^{j'[x-(2i-l)w]} + j (x-2nw) . (A. 13)

i=l

To evaluate f at a location x, one sums up j' evaluated at x-w, x-3w, ... and adds to j near x=0 . It is easily shown that for x<0

,

n

f(x) = -2w- (j * [x+(2i-l)w]

}

+ j (x+2nw) , (A. 14)

i=l

and n is chosen so that -w<x+2nw<w.

In summary, j (x) is calculated from the meter voltages for the measured

points from eq (A. 3) and fitted to a polynomial. The function f(x) is

calculated from eqs (A. 13) and (A. 14), and also fitted to a polynomial.

Finally, f is calculated from eq (A. 7). The major advantages for using this

technique (as opposed to using j (x) directly) to determine the calibration

function are two- fold. First, if the actual heat flux varies with x in a nonlinear manner, the measured j is not equal to f. This occurs near the end

walls in the furnace, as the results of the next section will show. Second,

the method allows for extrapolating to the furnace wall (x=±x0 ) , even though

the heat flow meter, when aligned with the wall, gives a heat flow centered at

distance w from the wall. This is because j ' (x) represents the change in heat

flux between (x+w) and (x-w)

,

and j at a meter half-width from the wall gives

f at the wall.

A. 4. Results of the calibration

We calibrated the furnace at a range of heater lamp voltages from 20% of

full voltage to 50% of full voltage. Very roughly, the heat flux on the

target is linear with heater voltage; 50% of full voltage corresponds to about

50 W/cm2 of heat flux on the target. At a single calibration, we held the

heater voltage constant and measured heat flow through the meters over a

representative portion of the furnace target. Voltages below 20% were not

calibrated as they corresponded to heat fluxes lower than necessary for the

heat transfer experiments, and voltages above 50% were not calibrated to

avoid overheating the heat flow meters. The calibration tests are summarized

in table A.l. We repeated the tests at voltages of 20%, 35%, and 50% to

assess the reproducibility of the data. At the 35% voltage level, we

conducted calibrations at several levels of air cooling of the heater to

determine whether the cooling rate had an effect on the calibration.

We present results in terms of the measured normalized heat flow through

the heat flow meters (j of the previous section) plotted as a function of the

16
position variables x and y. This indicates the trends of the data. Curve

fits of the heat flow data are plotted where appropriate, and the calibration

equations (f

q function) for the dimensionless heat flux are presented.

Table A.l. Summary of furnace calibration experiments

Test

Number Date

Heater

Voltage

Type of

Scan

Comments

1 6/13/88 35.3%

35.3%

x-scan

y- scan

Scan at y=0 and both

side walls.

Scan at x=0 and both

end walls

.

2 6/22/88 35.3% x-scan

y- scan

y~o

;

flow

x=0.

3 cooling air

settings

.

3 6/23/88 19.9% x-scan

y-scan

oo

II

II

>•, X

4 6/23/88 50.8% x-scan

y-scan

o

o

II

II

5 8/16/88 35.4% x-scan •- £

o

o

II

-

1

M-l

2 cooling air

settings

.

6 8/18/88 20.4% x-scan y=0.

7 8/18/88 35.2% x-scan y=o.

8 8/18/88 50.0% x-scan y=o.

9 9/06/88 20.2% x-scan y=o.

10 9/06/88 24.5% x-scan y=o.

11 9/06/88 29.3% x-scan y=o.

12 9/06/88 35.2% x-scan y=o.

Traverses in the y (short) direction of the furnace indicated uniform

heat flow at all voltages tested. This can be seen in figure A. 3, which

shows the normalized meter heat flow (j function) from tests 2 and 3, voltages

35% and 20% respectively. The scan was done near x=0 , the midpoint of the

furnace. Data from meters 1 and 2 are shown; the data overlap near y=0

.

There is about a 5% drop off in the meter output near the side-walls (±2.5% of

the mean) , but since this is of the same order as the meter calibration

uncertainty, we neglect this effect in developing the calibration functions.

In test 1, the furnace was scanned in the y direction close to both end walls

17
(large x and small x) . The results indicated the same uniformity in the heat

flux for the y direction as in figure A. 3. Hence, we found no significant

variation in heat flux in the y direction, regardless of heater voltage or x position in the furnace.

Scans in the x (long) direction showed variations with position and in

some cases the heater voltage. Figure A. 4 shows meter heat flow data for

tests 2, 4, and 11 using heat flow meter #3, at voltages of 35%, 51%, and 29%.

This distribution was unsymmetric; the heat flow gradually increased from the

negative x end to the positive x end, with a drop-off near both end walls. We

measured this asymmetry for all voltages above 29%, which we believe is due to

the air cooling characteristics of the radiant heater. In the heater, cooling

air flows around the lamp elements to prevent overheating; the cooling air

flow direction is from the negative x end to the positive x end. In flowing

along the lamps, the air heats up significantly. Hence the cooler lamps at

the air inlet (negative x) produce lower heat flux that the hotter lamps at

the air outlet. Reversing the position of the heater relative to the furnace

produced reverse asymmetry in the heat flow distribution.

A curve fitted to the data from tests 1, 2, and 4 is also shown in figure

A. 4, and the standard deviation of the residuals between the measured heat

flow and the curve value is 0.5%. Although the heat flow varies with x

position, we found no significant change in the distribution above 29%

voltage. When data from later tests at voltages above 29% (tests 7, 8, 11,

and 12) was compared to the curve-fit from figure A. 4, the standard deviations

to the curve for these later tests ranged from 0.9% for test 11 to 1.3% for

test 7, indicating the repeatability of the furnace. In test 2 we varied the

cooling air flow rate such that the temperature of the air exiting the heater

changed from 175°C to 250°C (lower cooling air flow corresponding to higher

air temperature) . This had no significant effect on the heat flow

distribution.

For heater voltages of 25% and lower, the furnace produced a symmetric

heat flow distribution in the x direction. Figure A. 5 shows scans in the x

direction from tests 6, 9, and 10 for heater voltages of 20% and 25%. Also

shown is the curve fitted to the meter heat flow data (j function) , which had

a standard deviation of 0.3% from the measured data. The heat flow drops to

about 85% of the maximum at the end walls. The variation in the y direction

was again no greater than that shown in figure A. 3. We believe that at the

low voltages, the heater lamps remain cool along their entire length, which

results in the symmetric distribution.

The measured heat flow data for tests 1, 2, and 4 were analyzed to give

the furnace distribution function (fa ) for the unsymmetric profile (voltages

greater than 29%), and heat flow data from tests 6, 9, and 10 were analyzed to

give the distribution function for the symmetric profile (voltages less than

29%)

The sixth-order polynomial curve-fit and the region of validity are

summarized in table A. 2. The actual heat flux at any x and y for a heater

voltage v is then given by eq (A.l).

18
Table A. 2. Furnace heat flux distribution function, fq

Type of Profile Region of Validity Coefficients of

Polynomial, f

a

Symmetric Lamp Voltage < 29%

Unsymmetric Lamp Voltage > 29%

a where f = A0 + A1 -x + A2 -x

2 + A3

• x

3 + Aa -x

4 and x is in cm.

A-0 — 1.053 205

A, -- 6.291 236 E-5

a2 — -1.770 100 E-3

a3 = -6.021 114 E-5

A* — 4.450 009 E-5

a5 = 1.028 527 E-6

a6 — -1.750 378 E-6

A0 — 1.035 180

Ai = 2.761 752 E-3

a2 = -1.480 886 E-3

a3 = 4.125 198 E-4

A, = 7.524 066 E-5

a5 = -8.586 921 E-6

a6 — -2.047 184 E-6

+ a5 x

5 + A6 •x6

A. 5. Uncertainty in the furnace heat flux calibration

The uncertainty in the heat flux distribution is estimated from the

uncertainty in the heat flow meter measurement, a, the uncertainty in the

calibration function when compared to the measured heat flow data (3a), and

from the reproducibility of the furnace calibration (3a). The square root of

the sum of the squares of these individual uncertainties results in an

uncertainty of about ±4%.

19
1 .3 mm

0.4 mm

Figure 1. Pin- fin heat exchanger

/ for NASP application (separated view)

20
480 VAC

75 A

Single Phase

Figure 2

.

Helium flow loop.
Cooling Air Cooling Air

Figure 3. Specimen furnace. Inlet and outlet gas temperatures are

measured at points 0 and 1; upstream and downstream pressures

are measured at points A and B.

22
Thermocouple

0.89

1.27

0.13 mm

Glass Sleeve,

0.51 —!

Nickel 20

1

Nicrosil Nisil

0.25

NOTE:

All dimensions in mm

Figure 4. Technique for mounting thermocouples on pin-fin specimens.

23
Figure A.l. Calibration specimen in furnace.

24
Thermocouple

< 15.4 cm

33 cm

Heat Flow

Meters (3)

(1.6 x 1.6 cm)

12.7 cm

4.6 cm

I

thick)

A +Y

Copper Shading

Shims

Signal Leads

Figure A. 2. Lay-out of heat flow meters on calibration specimen

25
Normalized

Meter

Heat

Flow

Y Position (cm)

Figure A. 3. Traverse of normalized heat flow along y direction at x=0

Shown are data from tests 2 and 3, heater voltages 35.3%

and 19.9%. is meter 1, and "o" is meter 2.

26
Normalized

Meter

Heat

Flow

1.5

0.0 m i i i i - 8.0

r r | i i i - 4.0

X

I i i i i i

| i i i i I I I I I 1 ~T" I I I I I I I I

|

( 0.0 4.0 8.0

Position (cm)

Figure A. 4. Traverse of normalized heat flow along x direction at y=0

for heater voltages greater than 29%. Shown are data from

test 2 (35.3% voltage, test 4 (50.8% voltage, "o"),

and test 11 (29.3% voltage, "A")- The smooth curve is the

curve fitted to the normalized heat flow data (j function)

,

which has a standard deviation of 0.5%.

27
Normalized

Meter

Heat

Flow

*

X Position (cm)

Figure A. 5. Traverse of normalized heat flow along x direction at y=0

for heater voltages less than 29%. Shown are data from

test 6 (20.4% voltage, test 9 (20.2% voltage, "o"),

and test 10 (24.5% voltage, "A"). The smooth curve is the

curve fitted to the normalized heat flow data (j function)

,

which has a standard deviation of 0.3%.

28
IST-114A

!EV. 3-89)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NISTIR 89-3926

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBLICATION DATE

October 1989

TITLE AND SUBTITLE

APPARATUS FOR MEASURING HIGH-FLUX HEAT TRANSFER IN RADIATIVELY HEATED COMPACT EXCHANGERS

AUTHOR(S)

Douglas A. Olson

PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURG, MD 20899

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23665

SUPPLEMENTARY NOTES

DOCUMENT DESCRIBES A COMPUTER PROGRAM; SF-185, FIPS SOFTWARE SUMMARY, IS ATTACHED.

. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

We describe an apparatus which can deliver uniform heat flux

densities of up to 80 W/cm2 over an area 7.8 cm by 15.2 cm for use

in measuring the heat transfer and pressure drop in thin (6 mm or

less), compact heat exchangers. Helium gas at flow rates of 0 to

AO kg/h and pressures to 6.9 MPa (1000 psi) is the working fluid.

We describe the instrumentation used in the apparatus and the methods

for analyzing the data. We will use the apparatus initially to

test the performance of prototype cooling jackets for the engine

struts of the National Aerospace Plane (NASP)

.

!. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

apparatus; compact heat exchanger; convection heat transfer; friction factor;

high temperatures; National Aerospace Plane; pin-fin; radiative furnace.

1. AVAILABILITY UNLIMITED

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS).

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ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

40

15. PRICE

LECTRONIC FORM

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