NASA Contractor Report 174667

Investigation of the Effects of Pressure Gradient, Temperature, and Wall

Temperature Ratio on the Stagnation Point Heat Transfer for Circular Cylinders

and Gas Turbine Vanes

H. T Nagamatsu and R. E. Duffy

Rensselaer Polytechnic Institute

Troy, New York

April 1984

Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Lewis Research Center

Under Grant NAG 3-292

https://ntrs.nasa.gov/search.jsp?R=19840015581 2019-06-28T13:37:14+00:00Z
FOREWORD

This report was prepared under Contract No. NASA Grant No. NAG 3-292

for the NASA Lewis Research Center under the technical direction of Dr. R.W.

Graham. The high temperature heat transfer research in the shock tubes was

initiated under the sponsorship of National Science Foundation, Dr. W. Aung,

and NASA Lewis Research Center, Dr. R.W. Graham, under the NSF Grant No. MEA

80-06806. The work was conducted at the Gas Dynamics Laboratory, Rensselaer

Polytechnic Institute in Troy, New York.
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TABLE OF CONTENTS

Page

FOREWORD i

1. INTRODUCTION 1

2. EXPERIMENTAL APPARATUS 3

2.1 Low and High Pressure Shock Tubes 3

2.2 Square Test Section With Adjustable Walls and Reflection Wedges.. 5

2.3 Gas Turbine Nozzle Airfoil Cascade 7

2.4 Instrumentation 8

3. DATA REDUCTION 9

3.1 Determination of Test Conditions 9

3.2 Heat Transfer Gage Data Analysis 10

4. EXPERIMENTAL AND ANALYTICAL RESULTS 13 .

4.1 Heat Flux for Laminar, Transition, and Turbulent Boundary Layers

and Transition Phenomenon on a Shock Tube Wall 13

4.2 Stagnation Point Heat Transfer 15

4.3 Flat Plate Heat Transfer 18

4.4 Heat Transfer in the Junction Region of a Circular Cylinder Normal

to a Flat Plate 25

4.5 Shock Induced Turbulence 30

4.6 Investigation of Steady-Flow Establishment Time in a 15° HalfAngle Concial Nozzle 31

5. CONCLUSIONS 34

6. LITERATURE CITED 36

m
1. INTRODUCTION . . ,

The increased cost of fuel for the jet engines on transport aircraft and

for generating electrical power with gas turbines has made it necessary to reduce

fuel consumption by operating the turbines at higher temperatures and pressures

to increase the efficiency [1]. The gas temperatures in the operational jet

engines require turbine film cooling and for high gas temperatures more advanced

cooling schemes will be required. With a water-cooled gas turbine it seems

possible to operate with gas temperatures of 1900°K and higher, and combining

this with a steam turbine it appears possible for power generators to have an

overall thermal efficiency of over 50% [2].

To achieve the higher efficiencies for the jet engines and gas turbines,

it is essential in the design of turbines to have an accurate estimate of the

local gas-side heat flux loads on the blades and vanes. For this purpose it

is necessary to understand more quantitatively the local heat transfer rates

at the stagnation region for the turbine vanes and blades as well as the heat

fluxes for laminar, transition, and turbulent boundary layers over the pressure

and suction surfaces under the influence of pressure gradients with gas temperatures as high as 2200°K and pressures to 40 atm. Also, it is necessary to

know the heat flux distribution at the junction of the vanes with the shroud

at these anticipated high temperatures. The available experimental and theoretical literature on the local gas-side heat transfer rates at high temperatures

and pressures are very limited for the stagnation and end-wall regions and along

the pressure and suction surfaces.

With these realizations, a basic heat transfer investigation to study the

heat flux at the stagnation region for circular cylinders and over a flat plate

with and without pressure gradient with gas temperature as high as 2200°K was

initiated. This research was initially sponsored by NSF and NASA under NSF
-2-

Grant No. MEA80-06806, "Investigation of the Effects of Pressure Graident, Temperature and Wall Temperature Ratio on Heat Transfer Over Blunt and Streamlined

Bodies," and continued under NASA Grant NAG 3-292. The objectives of the program

were to obtain heat transfer data at high temperatures for circular cylinders

and flat plates and correlate with the available theories to develop prediction

methods for the external heat transfer at the stagnation region for circular

cylinder, over a flat plate, and a turbine nozzle airfoil.

To produce shock heated air to 2500°K and to measure the local heat flux

over bodies it was necessary to design and construct low and high pressure shock

tubes with an internal diameter of 10.16 cm and a length of 21.34 m to cover

the range of temperatures and pressures anticipated for the advanced jet engines

and gas turbines. A square test section was designed and constructed to produce

pressure gradient over a flat plate. Thin-film platinum heat gages were developed

and calibrated to measure the local heat flux. The experimental heat transfer

and analytical results obtained for the initial phase on the high temperature

heat transfer program will be discussed in some detail in the body of this report.

The results from the new shock tubes and instrumentation have been published

in two Ph.D. theses [3,4] and seven Masters theses [5-11], and in three publications [12,13,14] which were presented at technical society meetings. A paper

[15] on the hot-wire measurements of turbulence level and temperature fluctuations

behind incident and reflected shock waves will be presented at the AIAA 13th

Aerodynamic Testing Conference, March 5-7, 1984. The stagnation point heat

transfer results [16] for circular cylinders at high temperatures and Reynolds

number has been submitted to the AIAA 19th Thermophysics Conference, June 16-18,

1984. High temperature heat transfer results [17] for a flat plate with and

without pressure, for an inlet flow Mach number of 0.45 and over a range of Reynolds

numbers has been submitted to the AIAA/SAE/ASME 20th Propulsion Conference,

June 11-13, 1984. The heat flux distributions in the junction region between
-3-

the flat plate and a circular cylinder mounted normal to the plate have been

obtained and the paper [18] and has been submitted to the AIAA 19th Thermophysics

Conference, June 16-18, 1984. Another paper [19] on the heat transfer distribution over a flat plate with a flow Mach number of 0.12 for laminar, transition,

and turbulent boundary layers over a range of Reynolds number and gas temperature

has been submitted to the same Conference.

2. EXPERIMENTAL APPARATUS

2.1 Low and High Pressure Shock Tubes

The initial heat transfer investigations for the circular cylinders, flat

plates and shock tube wall were conducted in the RPI Low Pressure Shock Tube,

and some of the results from these investigations are presented. This shock

tube which has an operating pressure limit of 7.8 atm with a diameter of 10.16

cm and a length of 21.34 m is shown in Figure 1 and is described in Refs. [5,6].

In this facility it is possible to study the heat transfer over a temperature

range of 350°K to 2600°K, as well as to calibrate the thin film platinum heat

gages and piezoelectric pressure transducers [12,14].

High Pressure Shock Tube

Low Pressure Shock

Tube

Figure 1 RPI Low and High Pressure Shock Tubes
-4-

A high pressure shock tube with a maximum driver pressure of 410 atm and

driven tube maximum pressure of 128 atm with a diameter of 10.16 and a length

of 21.34 m was designed and constructed, Figure 1. With this facility it is

possible to produce shock heated air after reflected shock wave to 2800°K at

high pressures and Reynolds numbers. Stagnation point heat transfer data for

circular cylinders have been obtained at high Reynolds numbers [4,10*16].

A 5 hp compressor is installed near the 3.05 m long, 4 in. diameter driver

sections for the low and high pressure shock tubes to pressurize the air to

205 atm in the storage bottles. This high pressure air is used to charge the

driver section for both shock tubes.

A 5.67 m3 dump tank was obtained from the General Electric Research and

Development Center as surplus equipment. The dump tank is installed at the

end of the high pressure shock tube as shown in Figure 2, and a 60.96 cm diameter

Figure 2 Dump Tank and Nozzle

conical nozzle can be attached to the dump tank for investigating hypersonic

flow phenomena. A square test section with adjustable top and bottom walls
-5-

to produce pressure gradient over a flat plate can be attached to the end of

the tube with the exit of this test section located within the dump tank as

discussed in Refs. [3,8]. Vacuum pumps are connected to the dump tank for evacuating the tank to the desired pressure.

2.2 Square Test Section With Adjustable Walls and Reflection Wedges

To increase the efficiency of jet engines and gas turbines, the combustion

temperature and pressure must be increased to approximately 2200°K and 40

atm, respectively. At present there is no available heat transfer data at these

extreme flow conditions in the literature [20-24]. For the vanes the inlet

flow Mach number is about 0.15 and the flow accelerates to nearly sonic velocity

at the trailing edge. But for the blades the inlet Mach number is approximately

0.45 with an exit Mach number of about 0.85.

An investigation was initiated in Ref. [8] to design, construct and test

a square test section with either a reflection wedge or adjustable top and bottom

wall, as shown in Figure 3, for producing high temperatures after the reflected

shock waves. The adjustable top and bottom walls reflect the incident shock

IUSTIIK. ?;I:BKW H>K ADJUSTABLE UALLX ]

Flow

Figure 3 Square Test Section with Flat Plate Model
-6-

wave from the trailing edge of the plate to increase the gas temperature [3,8,25],

as well as to produce a pressure gradient over the flat plate with the desired

inlet flow Mach numbers of 0.15 and 0.45 after the reflected shock wave. The

square test section with a dimension of 9.00 cm was connected to a transition

section with an inlet diameter of 10.16 cm and square exit cross section, which

was machined out of solid aluminum block by a numerically controlled milling

machine [8]. The cross-sectional area in the transition section was kept constant.

Reflection wedges with various total open areas to produce reflected flow

Mach numbers of 0.15 and 0.45 were constructed and installed in the square test

section with a flat plate as shown in Figure 3. The variation of the static

pressure with time for the four pressure gages located in the test section and

over the flat plate (Figure 3) were measured for the flow Mach number of 0.15

after the reflected shock wave produced by the reflection wedges, Fig. 4a, and

mimm

Figure 4a Square Test Section with Wedges

converging walls, Figure 4b, respectively. These results with the converging

walls in the test section to simulate the flow through the gas turbine vane

section at high temperatures indicate that the technique of adjustable wall

will permit the measurement of the heat flux over a flat plate at temperatures
-7-

up to 2600°K [3,14], with the desired pressure gradients existing in gas turbine

vanes and blades.

Figure 4b Square Test Section with Converging Walls

2.3 Gas Turbine Nozzle Airfoil Cascade

In Ref. [23] the heat transfer measurements were made on a gas turbine

nozzle airfoil in a cascade (Figure 5) over a temperature range of 470° to 1780°K

in the hypersonic shock tunnel [25] for the pressure and suction surfaces.

Unfortunately, only a limited number of tests were conducted at Reynolds numbers

much lower than that for the full-scale water-cooled gas turbine [2]. Thus,

the cascade model can be attached to the high pressure shock tube (Figure 1)

and heat transfer measurements can be obtained over the pressure and suction

surfaces for a temperature range of 540° to 2200°F, various wall-to-gas temperature ratios and a range of Reynolds numbers. The wall temperature ratio on

the laminar boundary layer transition Reynolds number for pressure and suction

surfaces can be investigated. This cascade tunnel was loaned to RPI by the

Department of Energy for use by the graduate students for their heat transfer

research projects.
-8-

Figure 5 Shock Tunnel Configuration with the Flat

Plate and Nozzle Cascade Test Section

2.4 Instrumentation

The General Electric Research and Development Center donated ten Tektronix

scopes, scope cameras and peripheral equipment to RPI. These scopes have a

response time of 1 usec, which is adequate to measure the local heat transfer

rates with the thin-film heat gages and static pressures with the piezoelectric

pressure transducers.

Six Tektronix 122 low-level preamplifiers have been purchased and are being

used with the heat gages and four piezoelectric quartz Kistler gages are used

to measure the dynamic, static, and reflected pressures in the shock tube.

Lead-zirconate-titanate crystals were purchased to construct dynamic pressure

gages for use as a time-of-arrival instrumentation to monitor the shock velocity

in the shock tube.

initial static pressure in the driver and the driven tubes have been measured

with mercury manometers and Heise pressure gages. Instrument panels to house

these pressure gages have been constructed for the low and high pressure shock

tubes (Figure 6).
-9-

Figure 6a Loading Panel -

Driver Tube

Figure 6b Loading Panel

Driven Tube

Painted thin-film platinum heat gages have been fabricated for measuring

the local heat transfer rates at the stangation point for circular cylinders

[4,10,16] on a shock tube wall [6,12] and to flat plates [3,11,14]. The response

time for these heat gages is approximately 1 psec, and a detailed description

for these heat gages is presented in Ref. [10].

A Schlieren system consists of two 20.32 cm diameter parabolic mirrors

and two flat mirrors with a 0.4 psec spark light source. This system can be

used to take Schlieren and shadowgraph photographs of the boundary layer flow

over a flat plate and at stagnation region for circular cylinders.

3. DATA REDUCTION

3.1 Determination of Test Conditions

The flow conditions in the test section are determined from the measured
-10-

incident shock Mach number, initial pressure, P , and temperature, T , in the

shock tube and the ratio of the area between the test section and total open

area in the reflection wedges [26]. The pressure, P , behind the reflected

shock wave from the wedges was measured with a Kistler quartz gage, and the

corresponding reflected temperature, T , was calculated using the known shock

velocity at the end of the driven tube and the equilibrium thermodynamic properties for air [27,28], For the straight-through flow condition in the test section

without the reflection wedges, the pressure, P , after the incident shock wave

and the shock wave velocity were measured and the temperature, T , of the shock

heated gas was calculated by using the normal shock wave equations as discussed

in Ref. [26].

Stagnation point heat transfer investigations [4,10,16] were conducted

in the low and high pressure shock tubes, Figure 1, over a range of pressure,

P , from 5 to 250 psia and corresponding temperature, T , from 390 to 1000°K.

The heat flux distribution over flat plates with and without pressure gradient

[3,11,14], over shock tube wall [6,12] and in the junction region between a

flat plate and a normal circular cylinder [18] were determined for laminar,

transition, and turbulent boundary layers in the low pressure shock tube over

a range of pressure, P , from 5 to 150 psia and corresponding temperature,

T , from 670°K to 2800°K. At high temperatures the real gas effects were significant and the gas properties were calculated using the equilibrium thermodynamic

properties presented in [27] and [28].

3.2 Heat Transfer Gage Data Analysis

The platinum film on the backing material of the heat transfer gage is

thin enough such that the thermal effects of the platinum can be neglected in

comparison to the backing material. Furthermore, the backing material can be

treated as a semi-infinite solid having the property & = (pCpk)].,, where p,
-11-

C-, and k are the density, specific heat, and thermal conductivity of the backing

material respectively.

The change in gage resistance, AR, due to a surface temperature change,

AT = Tf - To, is

AR = Rf - R0 = R0a AT, (1)

where R0 and Rf are the gage resistances at temperatures To and Tf, and a is

the resistivity. The gage is operated at a constant current I and hence the

voltage change AE across the gage for a temperature change AT is

AE = I AR = I R0a AT (2)

When AT = AT(t) = AE(t)/aI Ro is a function of time, the heat transfer q(t)

to the gage is given in Ref. [29] as

q(t) = 2a IR0

t

|AE(t) 1 f A/t AE(t) - AE(-r)1

— ;= — + - — 770 — "I

|_/t ^ J (t -T)3/2

The heat transfer rate can be calculated from Eq.(3) using the voltage-time

trace gage when the values of (3^ and a are known. The constant coefficient

/6b/a for each gage can be obtained by a dynamic calibration.

To find the coefficient, the gages were mounted in the flat plate and placed

in the center of a 10.16 cm diameter low pressure shock tube [3]. A piece

of plexiglass which extended forward from the leading edge and from the plate

edges to the tube walls was used to produce surface conditions for the gages

which simulate a plate of infinite extent. When the shock passes over the plate

a boundary layer forms behind the shock and there is a small step rise in the

gage surface temperature evidenced by the voltage-time traces of the gage.

The change in temperature is generally .1 to .2°C which is small compared to

the plate surface temperature of approximately 300°K but adequate enough to

give a voltage change of approximately .1 to .2 millivolts. For a step rise
-12-

in temperature, the heat transfer rate qt,(t) for assumed semi-infinite solid

backing material is

r / a I R0 /t

For a constant wall temperature, Tw, the local heat transfer rate q(t)

at the wall from the gas in the boundary layer formed by a normal shock passage

over a plate is given by [30]

q(t) = "k« (TW

 ~

 TW'I> s<(0>

where kw and vw are the gas conductivity and kinematic viscosity at the wall

temperature, Tw ^ is the insulated wall temperature, uj., and ua are the free

stream velocities before and after the normal shock, and S' (0) is a coefficient

tabulated in Ref. [30].

Since at the gage surface AT « Tw, the gage surface temperature changes

have a negligible effect on the heat trasnfer rate q(t). Furthermore, since

the effect of the shock passage on the gage is to give a step rise in the surface

temperature, Eq.(4) and (5) can be equated and the gage coefficient /Bfc/a can

be found by

(6)

S'(0)

The constants associated with the gas are accurately known and depend only

on the wall temperature.

The heat gages were calibrated in this manner over a shock Mach number

range of 1.5 to 3, with the actual pressure rises on the surface of the plate

corresponding to the estimated pressure rises that the plate would experience
-13-

in the actual test section flows. This permitted the gage calibration to absorb

any strain gage effects that the thin platinum film might exhibit under pressure

loading.

4. EXPERIMENTAL AND ANALYTICAL RESULTS

4.1 Heat Flux for Laminar, Transition, and Turbulent Boundary Layers and

Transition Phenomenon on a Shock Tube Wall

Dillon [6,12] conducted an investigation in the low pressure shock tube

(Figure 1) over an incident shock Mach number range of 1.16 to 3.0, with a corresponding total temperature range of 331°K to 909°K, to study the local heat flux

to the shock tube wall for laminar, transition and turbulent boundary layers

and to observe the transition phenomenon and the transition Reynolds number

HORIZONTAL: 1 msec./cm

VERTICAL: Pressure

11.5 cm. Hg/cm; Temp.

1.0 mv/cm

Figure 7 Heat and Pressure Gage Output Against Time

Fully Laminar Boundary Layer, M2 = .70,

T2 = 410°K, Re/cm = 2481

in the shock induced flow. Representative heat gage oscilloscope traces for

a laminar boundary layer are presented in Figure 7. In this figure P is the

shock tube wall pressure and H's are the heat gage located along the wall. For

a laminar boundary layer the heat gage traces are smooth without fluctuations.

The heat gage traces were integrated on a computer to determine the local

heat flux as a function of time. For a laminar boundary layer the local heat
-14-

flux variation with time is presented in Figure 8 together with Mirels1 [30]

theoretical prediction for a laminar boundary layer. The agreement between

the experimental data and the theory is very close.

O.I

mi/ft: uc.

o.i

e.i

• urauicn

KIMLS

O.S 1.0 I.S 2.0 2.S 1.0

Figure 8 Local Heat Transfer Rate Against Time, Laminar Boundary

Layer, M2 = .70, T2 = 410°K, Re/cm = 2481

For the case of fully developed turbulent boundary layer following the

shock wave, the local heat flux variation with time is presented in Figure 9.

i.otgu»TI» (I) (UJUJTCD b)

0.5 1.0 I.S 2.0 2.S 1.0

Figure 9 Local Heat Transfer Rate Against Time, Turbulent Boundary

Layer, M2 = .72, T2 = 415°K, Re/cm = 30,000
-15-

In this figure the heat fluxes calculated by the modified von Karman equation

[31] for compressible turbulent boundary layer are presented for the cases with

and without adjusted flow Reynolds number. The agreement between the experimental

and the theoretical heat transfer rates are reasonable.

4.2 Stagnation Point Heat Transfer

Experiments have been conducted in the low pressure and high pressure shock

tubes at low gas temperatures to investigate the stagnation point heat transfer

for circular cylinders of various diameters (Figure 10) which simulate the leading

edge of turbine vanes and blades. By using cylinders of different diameters,

the effects of the pressure gradient on the stagnation heat transfer were investigated. The results for the low temperature heat transfer data are presented

in Figure 11 as a function of Reynolds number [4,10,16] for flow Mach numbers

of 0.15 and 0.45.

Figure 10 Different Heat Gage Units
-16-

Two known theories (laminar by Eckert [32] and turbulent by Van Driest

[33]) respectively are plotted on Figures 11 and 12 with some typical test results

obtained from the four different diameter heat gages. All data have been corrected

for the effects of tunnel blockage according to the methodology of Ref. 34.

For low temperatures of 422°K at both flow Mach numbers of 0.15 and 0.45

the stagnation point heat transfer measurements were in very good agreement

with Eckert's predicted laminar stagnation point heat transfer on a cylindrical

capped flat plate for the Reynolds number range of 1Q3 < RN < 106, as shown

in Figures 11 and 12.

1000.

N

y taa.

n

10.

-{- 6W GRUGE

A snn GAUGE

Qiznn cnuce

Qisnn GAUGE

THEORY-.992-SORT(RE)

THEORY-.889-SORT <R£)

1000.

i i i nir*

10000. 100000.

REYNOLDS NUHBGR

1000000.

Figure lla Stangation Point Heat Transfer Results for

M

FLOW '

 TFLOW

At higher flow temperature of 922°K the experimental heat flux measurements agree with Eckerts theory at low Reynolds. However, at Reynolds number

of approximately 5 x lO'* a marked increase in the heat transfer exists. The

data show a trend predicted by Van Driest's turbulent stagnation point heat
-17-

J000.

-f- enn

A am GAUGE

12tV1 GAUGE

( 1 ism cnuce

THEORY-.992-SORT(R£>

THEORY-.eo3-SORTCRE>

10.

10000. 100000.

REYNOLDS NUMBER

1000000.

Figure lib Stagnation Point Heat Transfer Results for

MFLOW - °'45' TFLOW = 422°K

10'

<u

ca

10

10-

6 mm gage

mm gage

015 mm gage

Van Driest Turbulent Theory

Eckert Laminar Theory

10 10

Reynolds Number

10

Figure 12 Stagnation Point Heat Transfer Nusselts Number vs

Reynolds Number, MFLQW = 0.15, TpLQw = 922°K
-18-

transfer theory although approximately twenty percent higher than theory. Typical

measurements illustrating this effect at a flow Mach number and temperature

of 0.15 and 922°K respectively are shown in Figure 12. Some preliminary measurements

have been made to access the turbulence level in the shock induced flow [9].

Indications are that the level of observed turbulence intensity is not sufficient

to explain the high measured heat transfer.

The data gathered will contribute to a fundamental heat transfer data file

which will be useful in the design of future jet engines and gas turbines.

4.3 Flat Plate Heat Transfer

Two flat plate models were constructed to measure the heat flux for laminar,

transition, and turbulent boundary layers as fucntions of Mach number, Reynolds

number, gas temperature, and wall temperature ratio. The first model was 10.16 cm

wide, 60.96 cm long, and 6.35 mm thick with eight heat gages located along the

surface for testing in the 10.16 mm diameter low pressure shock tube (Figure

13). The second plate model was 30.48 cm long, 9.02 cm wide and 6.35 mm thick

for use in the square test section shown in Figure 3. The leading edge was

machined round and the plate housed five thin-film platinum heat gages spaced

along the plate ahead of the reflection wedges [3,11].

The heat gage constants were determined in the low pressure shock tube

for Reynolds number per inch range of 0.20 x 10^ to 2.3 x 105. The flow Mach

number after the incident shock wave varied from 0.45 to 0.87. The response

time of these gages is a few microseconds [12,23,25]. Heat gage traces on the

oscilloscope for laminar, transition, and turbulent boundary layers are presented

in Figure 14. For the laminar boundary layer the trace is relatively smooth.
-19-

Figure 13 Circular Test Section and Flow Plate

but for the transition flow the fluctuation due to the turbulent bursts as they

traverse across the heat gage produce relatively large oscillations. For nearly

fully turbulent flow, the heat gage trace returned to reasonably smooth parabolic

variation with a superimposed high frequency oscillation due to the turbulent

eddies. Similar results were obtained by Nagamatsu, Graber and Sheer [35] for

hypersonic flow over a 10° cone.

Figure 14 Heat Gage Traces for Laminar, Transition and

Turbulent Boundary Layers

The local heat flux distributions over the 60.96 cm long flat plate, with

cylindrical leading edge (Figure 13) using the wedges to produce a flow Mach
-20-

number after the reflected shock wave of 0.15, for laminar, transition, and

turbulent boundary layers were determined in Refs. [3,14], and the results for

laminar and turbulent boundary layers are presented in Figures 15a and b, respectively. The Reynolds numbers per inch for these flow conditions were 8.05 x

and 7.6 x 104 for a gas temperature of approximately 440°K. In these

Reynolds Nutter

Figure 15a Heat Transfer for Partial Reflection - Laminar Flow.

Re/cm = 199, !„ = 517°K, MOO = -15

figures the theoretical and experimental laminar and turbulent boundary layer

heat flux variations with Reynolds number [36] are presented. The experimental

Stanton numbers are slightly greater than the laminar boundary layer prediction

but the variation of the Stanton number with Reynolds number agrees reasonably

well with the theoretical variation. The higher heat flux at a given gage location from the leading edge is due mainly to the blunt leading edge. In Figure

15b the experimental Stanton numbers are presented for a Reynolds number range

of 3.84 x 104 to 1.65 x 106 and a temperature of 420°K. The variation of Stanton

number with Reynolds number is close to the turbulent boundary layer prediction

which indicates that the boundary layer is turbulent. Higher experimental heat

flux at a given location is due primarily to the blunt leading edge which makes

the boundary layer thinner at a fixed distance from the leading edge than the

flow over a plate with a sharp leading edge.
-21-

KEY I

• LfitllNP* Th ,

• TURBULENT Th

oEXPERIHENTRy

Utf

Reynolds Nuiber

Figure 15b Heat Transfer for Partial REflection - Turbulent Plow.

Re/cm = 30,197, T^ = 416°K, M^ = .15

The local heat transfer rates over a flat plate were measured for various

Reynolds numbers with the top and bottom walls converged (Figures 3, 4b) to

produce pressure gradient and flow Mach number after the reflected shock wave

of 0.10 and 0.15 and temperature of 400°K and 2570°K. The variations of

Nusselt number with Reynolds number for these representative flow conditions

were reported in Refs. [3,14] and are presented in Figures 16a and b. The Nusselt

numbers for a Reynolds number of 7.84 x 104 over the initial one inch of the

plate at a temperature of 406°K are close to the turbulent theory as shown in

Figure 16a. For this flow conditions the Reynolds number varied from 7.84 x

104 to 2.35 x 105 over the heat gages. Preliminary high temperature heat transfer

measurements were conducted for a temperature of 2575°K with the converging

walls and the results are presented in Figure 16b. The Reynolds number over

the initial one inch of the plate was 2.93 x 104 and a wall temperature ratio

of 0.11. For this flow condition after the reflected shock wave, the Nusselt

numbers and the variation with Reynolds number agree reasonably well with the

turbulent theory. Additional heat transfer investigations will be conducted

to determine the effects of high temperatures and wall temperature ratios with
-22-

» '+ * w

"Reynold' H"***1"

Figure 16a Converging Wall - Turbulent Flow Heat Transfer.

Re/cm = 30,806, TOT = 406°K, MO, = .15

REYNOLDS NUMBER

Figure 16b High Temperature - Converging Walls Heat Transfer.

Re/cm = 11,535, T^ = 2575°3c, H» = .15
-23-

and without pressure gradient on the heat transfer. •••"_.

An investigation was initiated to study the effects of large temperature

gradient and corresponding density fluctuations on the turbulent boundary layer

heat transfer [37,38] for flow Mach number of 0.12, which is the flow Mach

number after the combustor in gas turbines. For water cooled gas turbines to

generate power [2] the gas temperature may be as high as 2220°K with the vanes

and blades surface temperature of approximately 830°K. Under these conditions

there will be large temperature gradient in the laminar and turbulent boundary

layers.

The square test section was used with the top and bottom walls in the horizontal position to measure the heat flux distribution over the flat plate, as

shown in Figure 3. Reflection wedges were used to reflect the incident shock

wave to produce flow Mach after the shock wave of 0.12. This flow Mach number

was produced by selecting the ratio of the throat area in the reflecting wedges

to the test section area ahead of the flat plate. Six thin-film platinum heat

gages were mounted flush on the plate surface to measure the local heat flux.

The heat transfer results for laminar, turbulent and transition boundary

layers are presented in Figures 17a and b, respectively for a gas temperature

TM 1 COO .

s

s

E

v

N

o leg

B :

:

i .

LfiniNRR flNO TURBULENT HEftT

••• • •• T

M^-0.12 To>-42S°K —-.7 0

g

Test No. Re/cm

X 38 434

D 39 475

B 50 1710 ,f

+ 51 698 jfsg*

0 32 26700 a/0

« 33 27300 x^

fl 59 93200 ^ **

* 60 94700 a^d*'

^^^ ""

^-"^ **

«oa. iceo. IBOCSO. leaooo.

TRANSFER .

X

_x*

•c*

Turbulent Theory

Laminar Theory

1000030. icsecooo.

ncrNCXOS

Figure I7a Heat Transfer for Laminar and Turbulent Boundary Layer

T = 425°K, M = .12
-24-

of 370°K, Mach number of 0.12, and wall to gas temperature ratio of 0.70 [11,19].

For unit Reynolds number, Re/cm of 434 to 1710, the Nusselt numbers agree with

laminar boundary layer prediction, but for unit Reynolds number greater than

2.67 x 104, the heat flux rates are close to the turbulent prediction.

In Figure 17b the heat transfer rates are for the transition region from

laminar to turbulent boundary layer and the Nusselt numbers lie between the

laminar and turbulent predictions. The unit Reynolds numbers for these tests

ranged from 3.0 x 103 to 1.36 x 104.

s

s

E

L

T

N

y 100.

fl

a

TRRMSITJON HEOT

M_-0.12 T^-42

Test No. Re/cm

O 34 13600

O 35 13100

•f- 37 3000

& W 3110

lose.

Turbulent Theory

— Laminar Theory

1B2JO0. IOOO0O.

REYNOLDS NUMBER

Figure 17b Heat Transfer for Transition Boundary Layer

T = 425°K, M = .12

The Nusselt numbers over the flat plate for a gas temperature of 1000°K,

flow Mach number of 0.12, and wall to gas temperature ratio of 0.33 are presented

in Figure 18. At low unit Reynolds number the Nusselt numbers are close to

the laminar predictions, but at higher unit Reynolds number of 2.09 x 104 the

Nusselt numbers are greater than for the turbulent prediction which indicate

that the turbulent boundary layer was not fully developed.

Additional experiments will be conducted at higher unit Reynolds numbers
-25-

and temperatures to achieve fully developed turbulent boundary layer and to

determine the effects of large density gradient in the boundary layer on the

heat transfer at low Mach numbers.

HIGH TEnPERRTURE HERT TRRNSFER

n

a

. E

R

M -0.12 T • 1000 K ^- .33

Turbulent Theory

Laminar Theory

100.

i i i i i i ii—

IB00. I0O0B. 103003.

Figure 18 Heat Transfer for Laminar and Turbulent Boundary Layers

T = 1000°K, M = .12

4.4 Heat Transfer in the Junction Region of a Circular Cylinder Normal to a

Flat Plate ;

An experimental investigation was conducted to measure the heat transfer

rate in the junction region of a circular cylinder mounted normal to a flat

plate [18]. This geometrical configuration was selected to simulate the endwall

of a gas turbine vane. To achieve higher efficiency for jet engines and gas

turbines, higher temperatures and pressures are required. Because of the smaller

span for the vanes at high pressures, the interaction between vanes and the

endwall on the heat transfer becomes increasingly important. For adequate and

efficient cooling of the endwall and the vanes, the heat flux distribution in

the junction region is required. Only limited experimental heat transfer data

are available and an analytical treatment of the problem is difficult due to

the nonlinearity of the viscous interaction phenomena.

A low pressure 21.34 m long shock tube with a diameter of 10.16 cm, shown

in Figure 1, was used to generate the shock heated air. Partial reflection
-26-

of the incident shock wave by a slotted plate shown in Figure 19 was used to

obtain the desired flow Mach number of 0.14 over the flat plate, which is approximately

the inlet flow Mach number for the first stage vanes in the jet engines. Since

the flow Mach number after the reflected shock wave is determined by the ratio

of the slotted throat area to the test section area, the flow Mach number is

very consistent. About 10 to 15 ms of steady flow was observed after the reflected

shock wave [18].

The sketch of the flat plate with a circular cylinder mounted normal to

the surface is presented in Figures 19. A slotted wall is placed downstream

of the 1.59 cm inch diameter cylinder and the total opening in the plate is ;

determined to achieve flow Mach number after the reflected shock wave of approximately

0.14. Two rows of heat gages are mounted on a rotatable circular plate inserted

«| Cyllndrlcally Capped Plate

Figure 19 Flat Plate with Heat Gages (Side View)

flush with the flat plate with the cylinder placed on the axis as shown in Figure

19. The center of the cylinder was located 15.2 cm from the leading edge of

the flat plate and the heat gages were located on the horizontal plane 0.2,

0.4, 0.6, 0.8, 1.0 and 1.5 diameters from the leading edge of the cylinder. In
-27-

the vertical plane the heat gages are located at similar distances from the ;

edge of the cylinder. Fast response thin-film platinum heat sensors were painted

on pyrex glass and baked in an oven to get good bonding to the glass. The change

in the surface heat temperature produces a change in the voltage which was recorded

on an oscilloscope. A computer program was used to calculate the heat flux

from the voltage variation with time as discussed in Refs. 6 and 14. The response

time of the platinum heat gages is fast enough to resolve the passage of turbulent

eddies over the plate.

To determine the effects of the circular cylinder on the flat plate heat

transfer rate in the junction region, Figure 19, experiments were conducted

for the same flow conditions for both the flat plate with and without the circular

cylinder of 1.59 cm diameter. The heat flux distributions on the flat plate

were measured in the horizontal plane ahead of the cylinder and perpendicular

to the flow as shown in the figure. For the present tests the temperature after

the reflected shock wave was approximately 450°K and a flow Mach number of about

0.14.

The Stanton number variations with Reynolds number for the heat gages located

in the horizontal plate ahead of the cylinder are presented in Figures 20a to

c for gages located at 0.2, 0.6, and 1.5 diameter from the cylinder, cf. Figure

19. In these figures the theoretical heat flux variation with Reynolds number

for laminar and turbulent boundary layers are presented to correlate the experimental data.

For the heat gage located 0.2 diameter ahead of the cylinder the Stanton

number at low Reynolds number for the flat plate only is close to the laminar

theory and for Reynolds number greater than 10^ the Stanton numbers are close

to the turbulent prediction as shown in Figure 20a. But with the cylinder the

Stanton number is increased nearly 300% for a Reynolds number of 3.0 x
-28-

Q Without Cylinder

A With Cylinder

Turbulent

Reynolds Number

Figure 20a Heat Transfer for Flat Plate with and without Cylinder

for Heat Gage at x = -2D

Similar Stanton number variation with Reynolds number is presented in Figure

20b for the heat gage located 0.6 diameter from the cylinder. With the cylinder

the heat flux is increased approximately 200% for a Reynolds number of 3.5 x

10^. For the heat gage located 1.5 diameter from the cylinder, the Stanton

numbers with and without the cylinder are presented in Figure 20c, and the heat

flux is increased approximately 15% by the cylinder.

The Stanton numbers at the three heat gage locations are normalized by

the Stanton number for a turbulent flow over a flat plate and the results are

presented in Figure 21. For the present test conditions, the heat flux increase

by the circular cylinder is appreciable near the stagnation region of the cylinder

and the increase in the heat flux decreases for the gages located farther from

the leading edge. A new set of experiments has just been completed to extend

the range of Reynolds number. The heat transfer data are being reduced and

will be correlated with the existing results.
-29-

D Without Cylinder

A With Cylinder

Turbulent

Reynolds Number

Figure 20b Heat Transfer for Flat Plate with and without Cylinder

of x = .6D

D Without Cylinder

With Cylinder

Turbulent

Reynolds Number

Figure 20c Heat Transfer for Flat Plate with and without Cylinder

at x* = 1.5D
-30-

•P

CO

•P

W

a

4J

to

•o

v

M

1-1

o

2:

>.e

.20

.40

.60

Reynolds Number

Figure 21 Normalized Heat Transfer Rate for Heat Gages Located at

Various Distances from the Circular Cylinder Leading Edge

4.5 Shock Induced Turbulence

The purpose of this investigation is to determine the free stream turbulence

intensity generated by shock induced flows. Inasmuch as heat transfer measurements are strongly influenced by free stream turbulence level, an accurate determination of the turbulence present in the test environment must be made to satisfactorily interpret heat transfer data.

The experimental measurements of shock induced turbulence utilizes a hot

wire anemometer. Two tungsten hot wires with a diameter of 0.0038 mm are being

used as sensors with two TSl Model 1050 anemometer modules. By operating these

wires at different temperatures it is possible to obtain two separate time histories

of density, velocity, and temperature, from which the turbulence intensities

can be calculated.
-31-

Initial hot wire results have been obtained for a shock Mach number range

of 1.1 and 1.6 which corresponds to induced flow Mach numbers between 0.15 and

0.70, static temperatures between 310° and 415°K, and static pressures between

0.014 and 1.70 atm. The unit Reynolds number range for these conditions span

between 7800 and 78,000. Tests are being conducted with tungsten sensors in

nitrogen to permit the operation of the wire to 1370°K. Since air is composed

largely of nitrogen and has a ratio of specific heat very close to that of nitrogen,

turbulence tests in nitrogen are anticipated to closely resemble turbulence

tests in air. Preliminary hot-wire results indicate low turbulence intensity

after the incident shock wave and the turbulence intensity increased after the

reflected shock wave [9,15].

4.6 Investigation of Steady-Flow Establishment Time in a 15° Half-Angle Concial

Nozzle

The shock tunnel facility [25] was modified to obtain local heat flux distribution "over gas turbine nozzles [23]. One of the problems associated with facilities of this type is the loss of the testing time due to the transient flow

produced by the passage of the starting shock wave system through the nozzle,

as shown in Figure 22.

In an effort to clarify the nature of the flow starting process and to

obtain experimental values of the starting times, an investigation was conducted

and the results are presented in Refs. [7,13]. A computer model similar to

the finite difference scheme used by Takayama [39] was developed and extended

in Refs. [40,41] to include effects of variable geometry and shock reflecting

diaphragm. The computer program was adopted for the particular geometry of

the test section used in the investigation (Figure 22) and a range of shock

Mach numbers and nozzle pressure ratios were computed and tests were then conducted
-32-

using this test section. The passage times of the primary and secondary shock

waves were measured with a thin-film platinum heat gage probe.

cum so'semes

e i * j

SCALS(in)

Figure 22 Test Section With Conical Nozzle

Tests were conducted in the RPI Low Pressure Shock Tube (Figure 1), and

the test section is shown in Figure 22. Tests were made with and without the

reflection diaphragm for an incident shock Mach number range of 1.25 to 3.0,

and the heat gage probe was located at various distances from the nozzle throat.

The computer results [40,41] for the flow starting process without the

diaphragm and for an incident shock Mach number of 2.5 are presented in Figure

23. The variation of pressure with axial distance and time in this figure indicates the movement of the primary and secondary shock waves down the conical

nozzle with time.

The passage times for the primary and secondary shock waves at various

distances from the nozzle throat were determined for an incident shock Mach

number of 2 and without a reflection diaphragm [39,40], and the results are

presented in Figure 24. The agreement of the experimental data with the computer
-33-

LU -0.20 0.60 w<.40 3.20 103 ISO

Figure 23 Nondimensional Pressure Distribution for Various Times

Following Deblocking

A EtPQtlKDITiL Pom

O MLCUUTEO HOIST

Figure 24 Interval Between Shock Waves - Nozzle Pressure Survey
-34-

results for the time interval between the shock wave is quite close, as well

as the predictions of the shock wave location. Thus, it can be seen that the

computer program [40,41] can predict the primary shock wave velocities through

the nozzle.

 ;

5. CONCLUSIONS

Low Pressure (7.80 atm) and high pressure (124 atm) shock tubes with an

inside diameter of 10.16 cm and a length of 21.34 m were designed and constructed

for measuring heat transfer over a temperature range of 390° to 2500°K and pressures of 1.68 to 42 atm in the test section. Heat transfer data for circular

cylinders and flat plate with and without pressure gradient have been obtained

and heat flux data over flat plate have been measured up to 2580°K.

A square test section with adjustable top and bottom walls was constructed

and the experimental pressure data indicated that the converging top and bottom

walls produced the desired favorable pressure gradient over the flat plate. Plow

Mach numbers of 0.15 and 0.45 after the reflected shock wave were produced by

varying the deflection of the walls.

Painted thin-film platinum heat gages with response time of a few microseconds were fabricated and used to measure the local heat transfer rate and

to determine the type of boundary layer existing over the surface. A computer

program was developed to determine the heat flux from the heat gage output.

Department of Energy loaned to RPI a water cooled gas turbine nozzle cascade

which is attached to the high pressure shock tube within the dump tank. Heat

transfer distributions over the pressure and suction surfaces for the nozzle

airfoil can be determined at high temperatures and pressures.

Laminar, transition, and turbulent boundary layer heat fluxes were determined

on the low pressure shock tube wall with the platinum heat gages. The variation

with time of the heat flux for laminar boundary layer after the shock agreed
-35-

with Mirel's prediction.

Stagnation point heat flux was measured for various diameter circular cylinders in the low. and high pressure shock tubes for a range of Reynolds numbers

and free stream Mach numbers of 0.15 and 0.45 at temperatures of 420°K and 920°K

temperatures. The heat flux data indicated no significant pressure gradient

effect at low temperatures and agreed reasonably well with Eckerts laminar theory.

But at high temperature the stagnation heat fluxes were greater then Van Driest's

turbulent theory.

Flat plate heat transfer measurements were made for free-stream temperatures

of 350° to 2580°K, pressure gradients, Reynolds numbers, and Mach numbers anticipated in advanced gas turbines. Preliminary local fluxes for laminar, transition

and turubulent boundary layers were determined for various flow conditions and

correlated with the laminar and turbulent theories.

Heat fluxes over a flat plate without pressure gradient were determined

for laminar, transition, and turbulent boundary layers for a flow Mach number

of 0.12 and temperatures of 370° and 1000°K. At the low temperature the heat

fluxes agreed well with the laminar and turbulent theories. For the high temperature the heat fluxes were greater than the turbulent theory but this difference

may be due to the fact that the Reynolds numbers were too low to produce fully

developed turbulent boundary layer. Additional tests are necessary to determine

the contribution of the turbulent density fluctuations to the heat transfer

at high temperatures.

The heat flux distributions were determined in the junction region of a

circular cylinder mounted normal to a flat plate for various Reynolds numbers

and a flow Mach number of 0.14, which corresponds to the vane inlet Mach number

for jet engines. Large effects of the cylinder on the flat plate heat transfer

were felt in the region 1/4 to 3/4 diameter ahead of the cylinder which depended

on the Reynolds number.
-36-

A probe with two hot wires was developed and used to measure the turbulence

intensity behind the incident and reflected shock waves. Turbulence level is

necessary to correlate the heat transfer data for circular cylinders and flat

plates with existing theories. Preliminary hot wire results indicated low turbulence intensity behind the incident shock wave and higher intensity after the

reflected shock wave.

Measurements of the time intervals of passage of the primary and secondary

shock waves in the convergent-divergent nozzle of a shock tunnel were made and

the data correlated well with the finite difference computer program predictions.

The flow starting process in the nozzle depended on the pressure ratio across

the nozzle.

6. LITERATURE CITED

1. Graham, R.W., "Fundamental Mechanisms that Influence the Estimate of Heat

Transfer to Gas Turbine Blades," NASA TM 79128, Presented at the National

Heat Transfer Conference, San Diego, August 1979.

2. Kydd, P.H. and Day, W.H., "An Ultra High Temperature Turbine for Maximum

Performance and Fuels Flexibility," ASME Paper No. 75-GT-81, March 1975.

3. Pedrosa, A.C.F., "An Investigation of the Effect of Pressure Gradient, Temperature Ratio on Flat Plate Heat Transfer," Ph.D. Thesis, Rensselaer Polytechnic

Institute, August 1982.

4. Gahmouse, A., "An Investigation of the Effect of Pressure Gradient, Temperature

and Temperature Ratio on Stagnation Point Heat Transfer," Ph.D. Thesis,

Rensselaer Polytechnic Institute, August 1982.

5. Bouck, S., "Design of a Low Pressure Shock Tube," M.S. Thesis, Rensselaer

Polytechnic Institute, May 1980.

6. Dillon, R.E., Jr., "Heat Transfer Rate for Laminar, Transition and Turbulent

Boundary Layers and Transition Phenomena on a Shock Tube.Wall," M.S. Thesis,

Rensselaer Polytechnic Institute, May 1981.

7. Schaefer, L.M., "An Investigation of the Steady Flow Establishment Time

in a 15° Half Angle Conical Nozzle," M.S. Thesis, Rensselaer Polytechnic

Institute, May 1981.
-37-

8. Nunn, T.C., "Reflected Shock Wave Technique for Producing High Temperatures

and Pressure Gradients in Shock Tubes," M.S. Thesis, REnsselaer Polytechnic

Institute, December 1981.

9. Trolier, J., "Preliminary Studies of Shock Induced Turublence," M.S. Thesis,

Rensselear Polytechnic Institute, September 1981.

10. Zaffuts, P.J., "Stagnation Point Heat Transfer for Circular Cylinders of

Various Diameters," M.S. Thesis, Rensselaer Polytechnic Institute> August

1982.

11. Brostmeyer, J.D., "Flat Plate Heat Transfer for Laminar, Transition, and

Turublent Boundary Layer Using a Shock Tube," M.S. Thesis, Rensselaer

Polytechnic Institute, December 1983.

12. Dillon, R.E., Jr. and Nagamatsu, H.T., "Heat Transfer Rate for Laminar,

Transition, and Turbulent Boundary Layer on Shock Tube Wall," AIAA Paper

No. 12-0032, January 1982.

13. Schaefer, L.M., Leone, S.A., and Nagamatsu, H.T., "An Investigation of

the Steady-Flow Establishment Time in a 15° Half-Angle Conical Nozzle,"

AIAA Paper No. 80-0186, January 1982.

14. Pedrosa, A.C.F., and Nagamatsu, H.T., "Convective Heat Transfer on Flat

Plate at VEry High Temperature and Pressure Gradient," ASME Paper No. 83-GT-113,

March 1983.

15. Trolier, J., and Duffy, R.E., "Shock Induced Turbulence," Paper for AIAA

13th Aerodynamic Testing Conference, San Diego, March 5-7, 1984.

16. Dales, K., Duffy, R., and Zaffuts, P., "Stagnation Point Heat Tansfers

At Flow Mach Numbers of 0.15 arid 0.45 and Temperatures of 3460°R," Submitted

to AIAA 19th Thermophysics Conference, Snowmass, June 25-28, 1984.

17. Pedrosa, A.C.F., and Nagamatsu, H.T., "Convective Heat Transfer Studies

at High Temperatures with Pressure Gradient for Inlet Flow Mach number

of 0.45," Submitted to the AIAA/ASME/SAE Propulsion Conference, June 1984.

18. Hinckel, J. and Nagamatsu, H.T., "Experimental Investigation of Heat Transfer

in the Junction REgion of a Circular Cylinder Normal to a Flat Plate," Submitted

to AIAA 19th Therophysic Conference, Snowmass, June 25-28, 1984.

19. Brostmeyer, J.D., and Nagamatsu, H.T., "Flat Plate Heat Transfer for Laminar,

Transition, and Turbulent Boundary Layer Using a Shock Tube," Submitted

to AIAA 19th Thermophysics Conference, Snowmass, June 25-28, 1984.

20. Turner, A.B., "Local Heat Transfer Measurements on a Gas Turbine Blade,"

Journal of Mechanical Engineering Science, Vol. 13, No. 1, 1971.

21. Lander, R.P., Fish, R.W., Suo, M., "The External Heat Transfer Distribution

on Film Cooled Turbine Vanes," AIAA 72-a, January 1972.

22. Schultz, D.L. and Jones, T.V., "Heat Transfer Measurements in Short Duration

Hypersonic Facilities," Agardograph, No. 165, 1973.
-38-

23. Kercher, D.M., Sheer, R.E., Jr., and So, R.M.C., "Short Duration Heat Transfer

Studies at High Free-Stream Temperatures," ASME 82-GT-129, March 1982. .

24. Dunn, M.G., Rae, W.J., and Holt, J.L., "Measurement and Analyses of Heat

Flux Data in a Turbine STage: Part II - Discussion of Results and Comparison

with Predictions," ASME 83-GT-122, March 1983.

25. Nagamatsu, H.T., Geiger, R.E., and Sheer, R.E., Jr., "Hypersonic Shock

Tunnel," Am. Rocket Soc. Jour., Vol. 29, May 1959, pp. 332-340.

26. Ferri, A., Fundamental Data Obtained From Shock Tube Experiments, Pergamon

Press, 1961.

27. Gilmore, F.R., "Equilibrium Composition and Thermodynamic Properties of

Air to 24,000°K," Rand Rept. RM-1543 (1953). :

28. Hilsenrath, J. et al., "Tables of Thermal Properties of Gases," National

Bureau of Standards Circular 564, November 1955.

2.9. Carslow, H.S. and Jaeger, J.C., Conduction of Heat in Solids, University •

Press, 1961.

30. Mirels, H., "Laminar Boundary Layer Behind Shock Advancing into Stationary

Fluids," NACA TN 3401 (1955).

31. White, F., Viscous Fluid Flows, McGraw-Hill, 1974.

32. Eckert, E.R.G., Introduction to the Transfer of Heat and Mass, FjLrst Edition

1950, McGraw-Hill Book Company, Inc.

33. Van Driest, E.R., "The Problem of AErodynamic Heating," Aeronautical Engineering

Review, Vol. 15, October 1956, pp. 26-41.

34. Vincenti, W. and Graham, D., "The Effect of Wall Interence Upon the Aerodyanmic

Characteristics of an Airfoil Spanning a Closed Throat Circular Wind Tunnel,

NACA Report No. 849, 1952.

35. Nagamatsu, H.T., Graber, B.C. and Sheer, R.E., Jr., "Roughness, Bluntness,

and Angle of Attack Effects on Hypersonic Boundary Layer Transition," Jour.

Fluid Mech., Vol 24, 1966, pp. 1-31.

36. Young, A.D., Modern Developments in Fluid Dynamics, Vol. 1, High Speed

Flow, Oxford Univ. Press, 1953.

37. Li, T.Y., and Nagamatsu, H.T., "Effects of Density Fluctuations on the

Turbulent Skin Friction of an Insulated Flat Plate at High Supersonic Speeds,"

Jour. Aeronautical Sciences, Vol. 18, Oct. 1953, pp. 606-607.

38. Nagamatsu, H.T., and Sheer, R.E., Jr., "Hypersonic Laminar Boundary-Layer

Transition on 8-Foot-Long, 10° Cone, M^ = 9.1-16," AIAA Jour., Vol. 5,

July 1967, pp. 1245-1252.

39. Takayama, K., "Studies on the Flow in Shock Tubes - Report 1; Propagation

of a Shcok Wave Along a Duct of Diverging Cross-Section." Univ. of Jendai,

Inst. of High Speed Rept. Vol 28, No. 261, 1973.
-39-

40. Leone, S.A., "Analysis of Cold Flow Establishment Time in A Circuit Breaker

Nozzles," Ph.D. Thesis, Rensselaer Polytechnic Institute, May 1982. .

41. Leone, S.A. and Nagamatsu, H.T., "Analysis of Cold Flow Establishment Time

in a Circuit Breaker Nozzle," AIAA Paper No. 83-1749, July 1983.
1. Report No.

NASA CR-174667

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

Investigation of the Effects of Pressure Gradient,

Temperature, and Wall Temperature Ratio on the

Stagnation Point Heat Transfer for Circular Cylinders

and Gas Turbine Vanes

5. Report Date

April 1984

6. Performing Organization Code

7. Authors)

H. T. Nagamatsu and R. E. Duffy

8. Performing Organization Report No.

None

10. Work Unit No.

9. Performing Organization Name and Address

Rensselaer Polytechnic Institute

Dept. of Mechanical Engineering Aeronautical

Engineering and Mechanics

Troy, New York 12181

11. Contract or Grant No.

NAG 3-292

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D. C. 20546

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

505-31-42

15. Supplementary Notes

Final report. Project Manager, Robert W. Graham, Aerothermodynamics and Fuels

Division. NASA Lewis Research Center, Cleveland, Ohio 44135.

1«. Abstract

Low and high pressure shock tubes were designed and constructed for the purpose of obtaining heat

transfer data over a temperature range of 390 to 2500 K, pressures of 0.3 to 42 atm, and Mach numbers of 0.15 to 1.5 with and without pressure gradient. A square test section with adjustable top

and bottem walls was constructed to produce the favorable and adverse pressure gradient over the flate

plate with heat gages. A water cooled gas turbine nozzle cascade which is attached to the high pressure shock tube was obtained to measure the heat flux over pressure and suction surfaces. Thin-film

platinum heat gages with a response time of a few microseconds were developed and used to measure the

heat flux for laminar, transition, and turbulent boundary layers. The laminar boundary heat flux on

the shock tube wall agreed with Mirel's flat plate theory. Stagnation point heat transfer for circular cylinders at low temperature compared with the theoretical prediction, but for a gas temperature

of 922 K the heat fluxes were higher than the predicted values. Preliminary flat plate heat transfer

data were measured for laminar, transition, and turbulent boundary layers with and without pressure

gradients for free-stream temperatures of 350 to 2575 K and flow Mach numbers of 0.11 to 1.9. The

experimental heat flux data were correlated with the laminar and turbulent theories and the agreement

was good at low temperatures which was not the case for higher temperatures. The heat flux distributions were determined in the junction region of a circular cylinder mounted normal to a flat plate

for various Reynolds numbers and a flow Mach number of 0.15. Large effects of the cylinder on the

flate plate heat transfer were felt in the region close to the cylinder. A hot-wire probe was used to

measure the turbulence level after the incident and reflected shock wave and after the reflected shock

wave the turbulence increased to six percent. Measurements of the time intervals of passage of primary and secondary shock waves in the convergent-divergent nozzle were made and the results agreed

with a finite difference computer program prediction.

17. Key Words (Suggested by Authors))

Heat transfer

Turbine

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