nasa technical note nasa tn d-6028

NASA TECHNICAL NOTE

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NASA TN D-6028

HEAT-TRANSFER RATE AND

PRESSURE MEASUREMENTS OBTAINED

DURING APOLLO ORBITAL ENTRIES

by Dorothy B. Lee, John J. Bertin,

and Winston D. Goodrich

Manned Spacecraft Center

Houston, Texas 77058

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • OCTOBER1970

I,REPORT NO, 2, GOVERNMENT ACCESSION NOD

NASA TN D-6028

4, TITLE AND SUBTITLE

HEAT-TRANSFER RATE AND PRESSUREMEASUREMENTS OBTAINED DURING APOLLO

ORBITAL ENTRIES

7, AUTHOR (5)

Dorothy B. Lee, John J. Bertin, andWinston D. Goodrich, MSC

9, PERFORMING ORGANIZATION NAME AND ADDRESS

Manned Spacecraft CenterHouston, Texas 77058

IZ, SPONSORING AGENCY NAME AND ADDRESS

National Aeronautics and Space AdministrationWashington, D.C. 20546

3, RECIPIENT'S CATALOG NO,

So REPORT DATE

October 1970

6, PERFORMING ORGANIZATION CODE

8. PERFORMING ORGANIZATION REPORT NO,

MSC S-159

|0o WORK UNIT NO,

914-11-20-10-72

II, CONTRACT OR GRANT NO.

I

|3, REPORT TYPE AND PERIOD COVERED

Technical Note

14. SPONSORING AGENCY CODE

IS, SUPPLEMENTARY NOTES

16. ABSTRACT

Measurements of local pressures and heating rates were made on the Apollo command moduleduring entry from orbital velocities at Mach numbers from 28.6 to 11.5 on Apollo mission 1and from 31.2 to 2.2 on Apollo mission 3. Flight pressure measurements were found to com-pare well with wind-tunnel results. Comparisons showed that laminar and turbulent heat-transfer theories augmented by wind-tunnel data can be used to predict the heating rates tothe conical section of the spacecraft. Analysis of the heat-transfer-rate measurements indi-cated that transition to turbulent flow occurred on the conical section at local Reynolds num-bers between 20 000 and 102 000, based on distance from the stagnation point. No validheat-transfer data were obtained on the blunt entry face.

17. KEY WORDS (SUPPLIED BY AUTHOR)

"Heat Transfer Rate

• Apollo Flight Data• Aerothermodynamtcs

IS. DISTRIBUTION STATEMENT

Unclassified - unlimited

19. BECURITY CI.ASSIPICATION

(THIS REPORT)

None

ao, SECURITY CLASBIPICATION

(THIS PAGE)

None

21, NO, OF PAGES

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*For sale by the Clearinghouse for Federal Scientific and Technical Information

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CONTENTS

Section Page

SUMMARY ..................................... 1

INTRODUCTION .................................. 1

SYMBOLS ................................... . . 2

SPACECRAFT CONFIGURATION AND FLIGHT TEST .............. 3

Entry Vehicle .................................. 3

Instrumentation ................................. 3

Entry Trajectory ................................ 4

RESULTS AND DISCUSSION ............................ 4

Flow Patterns of Spacecraft 009 ........................ 4

Pressure .................................... 5

Heating Rates .................................. 6

CONCLUSIONS ................................... 10

REFERENCES ................................... 11

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III

Table

I

Figure

1

TABLE

LOCATIONS AND RANGES OF PRESSURE SENSORSAND CALORIMETERS

(a) Aft Compartment ...........................(b) Conical section ...........................

FIGURES

Apollo entry vehicle

(a) Leeward view of the command module configuration ........

(b) Sketch of forward and crew compartments showinginstrumentation location ......................

(c) Pressure sensor and calorimeter locations on the aft

compartment and conical section of spacecraft 009 ........(d) Pressure sensor and calorimeter locations on the aft

compartment and conical section of spacecraft 011 ........

Schematic of calorimeters on spacecraft 009 and 011.Dimensions are in inches

(a) Asymptotic calorimeter .......................(b) High-range calorimeter wafer assembly ..............

Entry conditions of spacecraft 009

(a) Altitude and relative free-stream velocity .............(b) Free-stream density .........................(c) Total pressure and free-stream Mach number ...........

Entry conditions of spacecraft 011

(a) Altitude and relative free-stream velocity .............(b) Free-stream Mach number and Reynolds number

based on body diameter ......................(c) Free-stream density .........................

Photograph showing streak patterns on aft heatshield of spacecraft 009 ........................

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Figure

6

10

II

12

13

Photograph of conical section showing char demarcation

(a) +Yc' e = 0 ° • ............................

(b) 9 = 45 ° ................................

(c) e = 135 ° . ..............................

(d) -Yc' ? = 180°" ...........................

Illustration of char pattern on conical section .............

Photograph of char pattern around the umbilical housing .......

Wind-tunnel distributions of local-to-total pressure ratio

(a) a = 18 ° . ...............................

(b) a = 20 ° . ...............................

Time histories of pressures measured on spacecraft 009

(a) Y =0, ZC C

(b) Y = 2.25,C

(c) Y = 2.25,C

(d) Y = 71.8,C

(e) Y =0, ZC C

(f) Y :0, ZC C

(g) Y =2.1,C

(h) Y = 34.3,C

(i) Y = 36.7,C

(j) Y =6.0,C

(k) X = 45.5,C

(1)(m)

--75 ...........................

Z : -71.8 .....................C

Z = 70.5, S/R= 0.94 ................C

Z = -0.8 ........................C

= 58.4 .........................

=54.4 ........................

Z --35.2 .......................C

Z = -2.1 ........................c

Z = -3.8 .......................c

Z = -2.5 ........................C

o =88 °, S/R = 1.44 ..................

Toroid-conical tangency point ...................Conical section .......................... ,.

Photograph of flow pattern around windward scimitar antenna .....

Comparison of spacecraft 009 pressure distributionwith wind-tunnel results

(a) Pitch plane,

(b) Yaw plane,

-Z to +Z .....................C C

-Y to+Y .......................C C

Stagnation pressure measured on spacecraft 011 ............

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Figure

14Comparison of spacecraft 011 pressure distribution with

wind-tunnel results

15

16

(a) Pitch plane,(b) Yaw plane,

e =90 ° and 270 °e = 0 ° and 180 ° ....................

• . . . . ° . ..... . . . . . ° . . •

Wind-tunnel distribution of local heating rate divided by zero angle-of-attack stagnation-point heating rate

(a) a = 18 °(b) a : 20 ° ''''°°°°'°°o°•.o°°o°°..•o°...°.°

°l..° .... *'°'°°°°°°°•'°°°''°*°.°

Histories of local Reynolds number and heating rates onconical section of spacecraft 009

(a) X c =45.5, _ =85.3 ° , S/R=I 475• . • . . o . • . . • . . . . . •

(b) X c = 64.8, o =92 °, S/R =1.775 ..................

(c) X c = 78.9, o = 115 ° , S/R = 1.99. . . . ° ° . • . ° . . . . . . •

(d) X c =114, o =83.4°, S/R=2.5 ..................

(e) Apex

(f) x c = 3"8 s/ "='1.16............(g) X c = 19.4, a = 178.5 ° , S/R = 1 071

• . , , • , , . , , . , , • , , .

(h) X c = 19.4, e = 270 ° , S/R = 1. 071 .................

(i) X =88, 0 = 182.9 ° , S/R = 2. 135C ' ........ . . . . o * . .

O

(j) X c = 78.9, _ = 191.3 , S/R = 1 97• ..... . . . . . . .....

(k) X c = 40, o = 215.3 ° S/R 1 39, _--- . ....... . . .........

(1) X c = 25.3, e = 225.5 ° S/R 1 16, ---- . . ° . . . • . . . . . . . . . .

(m) X = 51.7, 0 = 229.8 ° , S/R= 1.57C " * * . • • * * ° . . . . ° • .

(n) X = 58, e = 234 ° , S/R= 1 67C ..... " • . * • • • . . .... * .

(o) X c = 70.5, 0 = 276.4 °, S/R= 1 865. . . . . . . . . . . . . . . . .

(p) X = 114, e = 265 ° , S/R = 2.5C " " " " ...... * .... . • • .

17Histories of local Reynolds number and heating rates on

conical section of spacecraft 011

(a) X = 45.5,C

(b) X =64.8,C

(c) x c=78.9,

(d) X = 114,C

=85.3 ° , S/R= 1.475• . . • . . . ° . . . • . • . .

e =92 ° , S/R= 1.775 ..................

o = 115, S/R = 1.99 ..................

= 83.4 °, S/R= 2.5 ..................

P ag e

4243

4445

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Figure

I8

19

2O

(e)

(g) xC

(h) XC

(i) xC

(j) xC

(k) XC

(1) xC

(m) XC

(n) xC

(o) xC

(p) xC

(q) xC

(r) xC

(s) xC

Apex ........

X =25.3, _ =138°_ "S/R-l" i6" i i i i i i i i i ........C

= 61.5, _ =142.8 °, S/R= 1.723• , • • • . , . . . . • . . .

= 19.4, e = 178.5 °, S/R= 1. 071• . • , ° • • • . • • . . • •

= 19.4, o = 270 ° ,

= 35, 9 = 178.6 ° ,

= 60, _ = 177• 5 ° ,

=88, e = 182.9 ° ,

= 40, e = 215• 3 ° ,

S/R = 1. 071• • , • • . . • • • . . • , • •

S/R = 1 31• • • , . . • • . . • • • • •" • • .

S/R = 1. 696• • . . . • • . • • . • ° ° • •

S/R = 2. 135• • o • • • • . • • • • . • • •

S/R = 1.39• . . , . . , • • • • , . . , • .

= 25.3, e =225.5 °, S/R= 1 16• • . , . , • • ° • . , • • . . •

= 51.7, e =229.8 °, S/R= 1.57• . • . • , . . • • , , • . • •

= 58, e = 234 ° , S/R = 1.67• • . o • • . , . • . • • • • . . •

=70.5, _ = 276.4 °, S/R = 1.865• . • . • • , . • . • . , • .

= 78.9, e = 267.8 ° , S/R = 1.99• , • • . . . . . , . • • • • .

= 114, e = 265 °, S/R= 2.5• . . * , • • . , • • • • • . . . •

Wind-tunnel heating rate measurements on windward conical

section (e = 90 °) at Mach numbers from 7.42 to 10.18 .......

History of total angle of attack measured during entry ofspacecraft 011

• . , • • • • • • . . . . . . • • . . . . . ° • • • . •

Leeward heating as a function of local Reynolds number

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vii

HEAT-TRANSFER RATE AND PRESSUREMEASUREMENTS

OBTAINED DURING APOLLO ORBITAL ENTRIES

By Dorothy B. Lee, John J. Bertin,and Winston D. Goodrich

Manned Spacecraft Center

SUMMARY

Measurements of local pressures and heating rates were made on the Apollo com-mand module during entry from orbital velocities at Mach numbers from 28.6 to 11.5on Apollo mission 1 and from 31.2 to 2.2 on Apollo mission 3. Flight pressure meas-urements compared well with wind-tunnel results. Comparisons showed that laminarand turbulent heat-transfer theories augmented by wind-tunnel data can be used to pre-dict the heating to the conical section of the spacecraft. Analysis of the heat-transfer-rate measurements indicated that transition to turbulent flow occurred on the conical

section at local Reynolds numbers between 20 000 and 102 000, based on distance fromthe stagnation point. No valid heat-transfer data were obtained on the blunt entry face.

INTRODUCTION

The design of the thermal protection system for the Apollo command module wasbased on theory augmented by wind-tunnel data. Final qualification of the system towithstand entry from orbital missions required flight tests of the command module.During the entry portion of the tests, local pressure and heat-transfer measurementswere obtained on the spacecraft. The trajectories for the flight tests were so chosenas to subject the vehicles to a high heating-rate environment and to a high heat-loadentry. The first flight test, Apollo mission 1, was conducted with spacecraft 009 onthe Saturn IB launch vehicle. The spacecraft was launched from Cape Kennedy,Florida, on February 26, 1966. After a flight of approximately 37 minutes, the com-mand module landed near Ascension Island, and recovery was achieved approximately

3 hours later. The second flight test was conducted with spacecraft 011 on Apollo mis-sion 3. This high heat-load test was launched with the Saturn IB vehicle on August 25,1966, and later recovered in the Pacific Ocean near Wake Island.

Measurements of local pressure and heating rates were obtained with pressuretransducers and surface-mounted calorimeters installed on the command module. Datawere obtained at free-stream relative velocities between 25 300 and 12 000 ft/sec on

spacecraft 009 and between 27 300 and 2080 ft/sec on spacecraft 011. Histories of themeasured pressures and heating rates compared with theoretical predictions and with

wind-tunnel results are presented in this report.

tests are given in references 1 to 6.

SYMBOLS

Data from some of the wind-tunnel

h

M

Pr

P

Pt

qt, a =0

R

R_,X

S

t

V

Xc' Yc' Zc

X

P

P

enthalpy, Btu/lb

Mach number

Prandtl number

pressure, psia

total pressure behind normal shock, psia

heating rate, Btu/ft 2-sec

stagnation-point heating rate at zero angle of attack, Btu/ft2-sec

command module maximum radius measured from the X -axis, 6. 417 ftc

local Reynolds number based on distance from flight stagnation point

distance measured from center of aft compartment, ft

time, sec

velocity, ft/sec

command module body coordinates, in.

. distance measured from flight stagnation point, ft

angle of attack, deg

angle about the command module Xc-aX!s , deg

viscosity, lb/ft-sec

density, lb/ft 3

2

Subscripts:

aw adiabatic wall

CW cold wall

D diameter

fp flat plate

lain laminar

turb turbulent

WB with blowing

w wall

local

_o free stream

SPACECRAFT CONFI GURATI ON AND FLIGHT TEST

Entry Vehicle

The general configuration of the Apollo command module is shown in figure 1.The heat shield or thermal protection system, which covers the entire vehicle, is di-

vided into three parts: the aft compartment, the crew compartment, and the forwardcompartment (fig. 1 (a)). The aft compartment is a segment of a sphere with a radiusof curvature of 184.8 inches. A toroidal section with a 7.7-inch radius forms the fair-

ing between the spherical segment and the crew compartment. As shown in fig-ure l(b), the crew compartment extends from the toroid-conical tangency pointat X = 23.2 inches to X = 81 inches. The forward compartment extends from

C C

X = 81 inches to X = 133.5 inches and is blunted to a 9.1-inch radius. The maximumC C

body diameter of the command module is 154 inches and the axial length is 133.5 inches.

Instrumentation

Pressure transducers and surface-mounted calorimeters were installed on thecommand module to measure the local pressures and the heat-transfer rates on the

vehicle. The locations and ranges of these sensors, which were the same for bothspacecraft, are given in table I and are shown in figure 1 (c). Sensors that did not op-erate or that gave questionable data are indicated by solid symbols in figure 1 (c) for

spacecraft 009 and in figure l(d) for spacecraft 011.

Two types of calorimeters were used to measure heating rates on the spacecraft.Asymptotic calorimeters, designedto measureheating rates less than 50 Btu/ft2-sec,were located on the conical section. The design of these instruments is shown sche-

matically in figure 2(a) and the principle of operation is discussed in reference 7.High-range slug calorimeters, developed specifically for the Apollo Program, were

located on the aft compartment to measure heating rates greater than 50 Btu/ft2-sec.These slug calorimeters consist of several graphite wafers that are stacked to allow

continuous heating measurements during recession of the surrounding ablator. The

detail of one such wafer is shown schematically in figure 2(b). The wafer temperatureand the rate of change of temperature are used to determine the heat flux to the sur-face. T.he operation and design of these calorimeters are discussed in reference 8.

Flight measurements were recorded on magnetic tape on board the spacecraft.A malfunction occurred in the electrical power subsystem on spacecraft 009 that re-sulted in permanent loss of heating-rate data approximately 86 seconds after initiationof entry. Heating data were obtained for the entire entry time of spacecraft 011.

Entry Trajectory

The desired high-heating-rate entry was achieved with spacecraft 009 enteringthe atmosphere at a flight-path angle of -9.03 ° and at a velocity of 25 173 ft/sec meas-ured relative to the earth. Initial entry conditions, ass_ ned to occur at an altitude of400 000 feet, correspond to 1565.6 seconds after launch. The histories of altitude and

velocity for spacecraft 009 are given in figure 3(a), and the atmospheric density used inthe data analysis is given in figure 3(b). The calculated Mach number and total pres-sure are shown in figure 3(c).

The high-heat-load entry was achieved with spacecraft 011 entering the atmos-

phere at a relatively shallow flight-path angle of-3.53 ° and at a velocity of 27 200 ft/secmeasured relative to the earth. Initial entry conditions occurred at 4348 seconds after

launch. The trajectory parameters and the ambient conditions during entry of space-craft 011 are shown in figure 4.

RESULTS AND DISCUSSION

Flow Patterns of Spacecraft 009

Asymmetric flow patterns were observed on spacecraft 009 because of the rolledattitude of the vehicle. Accelerometer data showed that spacecraft 009 entered at anangle of attack of 19.7 ° to 21.3 ° until 1649 seconds after launch, when the vehicle be-gan rolling rapidly. For an angle of attack of 20 °, wind-tunnel tests indicated that the

spacecraft stagnation point should be located approximately 50 inches from the centerof the aft compartment on the +Z-coordinate axis at n = 90 ° (fig. l(c)). However,postflight examination of the streak pattern on the aft compartment of spacecraft 009(fig. 5) revealed a rotation of approximately 10 ° in the flight pitch plane which mayhave been caused by a lateral offset position of the center of gravity. Thus, the stag-nation point was presumed to be in the +Z to +Y quadrant at e _ 80 ° .

e c

The effect of the rolled attitude on the conic_ ection of spacecraft 009 can beseen in figures 6(a) to 6(d). Examination of the char interface in the yaw plane (evidentin figs. 6(a) and 6(d)) reveals the asymmetry of the char pattern on the spacecraft. Acomposite drawing from these photographs (fig. 7) illustrates the char pattern on theconical section. The shaded area represents the surface which was charred during en-try. Because the forward compartment was jettisoned before parachute deploymentand was not recovered intact, the region of charring is not defined for this compart-ment. As seen in figure 7, the char pattern is rotated approximately 11 ° toward the+Y-axis when measured at various points along the char interface. This angular dis-placement corresponded to the flight pitch plane at _ -_ 79 °, which is consistent withthe flow patterns in figure 5.

In figure 7, the shaded areas on either side of the umbilical housing were foundto consist mostly of scorched paint and not of charred ablator material. A photographof this pattern is shown in figure 8.

Spacecraft 011 entered at an angle of attack of 18 ° and did not appear to have ex-perienced off-nominal roll. The ablator on the conical section of spacecraft 011 wasnot charred since the flow was separated over the entire conical region because of thelow angle-of-attack attitude during entry.

Pressure

Pressure distributions over the basic command module have been measured at

various angles of attack in several wind-tunnel facilities. Selected data have beenpresented in reference 2 as the ratio of the measured pressure to the calculated total

pressure behind a normal shock. Faired curves of these pressure ratios are shown infigure 9 for angles of attack of 18 ° and 20 °. Estimates of flight pressures were madeby using these ratios and normal-shock calculations of total pressure for actual flightconditions.

Spacecraft 009.- Flight-test data were obtained from 19 pressure transducers(10 on the aft heat shield and nine on the conical section) on spacecraft 009. Historiesof the measured values are shown in figure 10. The measured pressures have not beencorrected for possible zero shifts, although it is evident that such corrections are ap-propriate for several of the sensors. There is very good agreement between the flightmeasurements and the estimates based on the wind-tunnel data for the aft heat shield

(figs.lO(a) to 100)).

The pressures on the conical section of spacecraft 009 (figs. 10(k) to 10(m)) weremeasured with 3-psia transducers (minimum range available in suitable flight-qualifiedsensors), although the maximum pressure was anticipated to be between 0.5 and1.0 psia. As a result of the low magnitude of the measurements, the quantitative andqualitative analyses of the data are limited. The pressure history measured immedi-ately downstream of the windward scimitar antenna is shown in figure 10_). The ir-regular behavior of this pressure measurement suggests strong local influence of thescimitar antenna on the flow. In figure 11, which displays the flow pattern around theantenna, the sensor is indiscernible.

The pressure histories for most of the sensors on the toroid and conical sections(figs. 10(1)and 10(m)) are in reasonableagreementwith wind-tunnel predictions if cor-rections for zero shift are considered.

The irregular drop in pressure that occurred at approximately 1635secondsateach measurement location on spacecraft 009 coincides with a drop in signal strengthnoted oil oscillograph records. Although full signal strength returned shortly after1635seconds, the signal faded again. As a result, the data obtainedafter 1660secondswere considered questionableandwere subsequentlydiscarded.

The flight pressure measurementsshownin figure 10were corrected for the es-timated zero shift andthen divided by the maximum pressure measuredat S/R = 0.72in the stagnation region. The resultant pressure distribution is shown as bars in fig-ure 12. The bars show the range of data in the Mach number interval M = 21.9 to 11.5

where the measured values were at least 50 percent of the full-scale reading. Theflight measurements are compared with wind-tunnel data obtained at a Mach number of10 (ref. 2) for angles of attack of 20 ° and 25 °. The flight measurements fall between

the two wind-tunnel curves, which differ most near the leeward corner. Although thedifference in the wind-tunnel curves was as much as 20 percent, only a 5-percent dif-ference resulted in the calculated Reynolds numbers based on local conditions.

Spacecraft 011. - Flight-test data were obtained from 10 of the 12 pressure trans-ducers on the aft compartment of spacecraft 011 and from one transducer located on the

toroid. No discernible pressure rise was detected and, in some cases, no data wereobtained on the conical section until just before parachute deployment.

The maximum pressure was measured at S/R = 0.775, which is in the stagnationregion. The excellent agreement between this measurement and the calculated total

pressure is evident in figure 13. Pressure distributions for the pitch and yaw planesof spacecraft 011 are shown in figure 14. The flight data have been normalized by themaximum pressure measurement and compared with wind-tunnel distributions for theApollo command module at 18 ° and 20 ° angles of attack. The spacecraft changed angleof attack during entry (ref. 9), and thus the two fairings are presented to illustrate thesmall angle-of-attack effect on the pressure distribution. The comparison of the flightdata with the wind-tunnel pressure distribution is good considering the accuracy asso-ciated with these measurements. This accuracy was assumed to be _*3 percent of full

scale, which resulted in a P/Pt uncertainty as high as 0.20.

Heating Rates

Wind-tunnel heat-transfer-rate measurements obtained on the smooth-body con-figuration of the Apollo command module at various angles of attack are described inreferences 1 and 2. Figure 15 shows wind-tunnel data obtained at a = 18 ° and 20 ° ref-erenced to the measured zero angle-of-attack stagnation-point value. These measureddistributions were used with a stagnation-point theory (ref. 10) to predict the cold-wall

laminar local heating rates over the surface of the command module during entry.Turbulent heating to the aft compartment, the toroid, and the leeward conical section

6

was estimated using the theory advancedby VanDriest in reference 11where the ratioof turbulent to laminar heating is expressedas

• bvx\qturb_ 0.055_'_ _ J

qlam

O. 301

(1)

Turbulent heating to the windward conical section was estimated with the flaf-platetheory and expressed as

o.o3op w- "w)qturb, fp - pr2/3(R,,x)l/5

(2)

The local Reynolds number was calculated with the assumption of an isentropicexpansion from the stagnation conditions behind the normal shock to the local pressureobtained from figure 9. For the predictions of flight heat-transfer rates, transitionfrom laminar to turbulent flow was assumed to occur at a local Reynolds number of

150 000 in attached flow and at a local Reynolds number of 20 000 in separated flow.

Aft compartment heating rates.- Six of the high-range calorimeters located onthe aft compartment of spacecraft 009 were operational, and temperatures of the outer-most wafers were measured for approximately 54 seconds from the initial entry time.An attempt was made to deduce heat-transfer rates from these measured temperaturesand from the thermal properties of the sensor. However, calibration tests showedthat heat losses to subsequent wafers and surrounding material were so large that anal-ysis was impossible when only the temperature of the top wafer was monitored. There-fore, no results from these sensors are presented.

Numerous malfunctions were observed in the wafer temperature measurements

on spacecraft 011. No meaningful data were obtained because of thermocouple shortingand premature switching from each recording wafer.

Spacecraft 009 conical-section heating rates.- Histories of the heating rates

measured with the asymptotic calorimeters on the conical section are shown in fig-

ure 16. Predictions of heating rates based on theory and on wind-tunnel data are in-cluded for comparison with the experimental flightdata. The local l_eynolds number is

shown above the heating-rate history.

The heating-rate histories shown in figures 16(a) to 16(f) show an apparently ir-regular increase in heating between 1580 and 1595 seconds• All these sensors shareda common recording circuit. Because the increase did not occur for the two sensors(figs. 16(g) and 16(h)) that were connected to a different recording circuit, it is be-lieved that an electrical disturbance in this circuit may have caused the irregular in-crease. Some of the sensors indicated significant heating rates before entry when the

7

heating rate is knownto be low. Becausethese rates approachedvalues near zero afterthe aforementioned irregularity, no corrections for zero shift were made. At the timeof maximum heating (1635seconds), the main electrical busesbeganto showtransientexcursions from nominal values. The excursions continued until approximately1650seconds, whenan electrical short resulted in loss of data.

Whenthe ablator is subjected to sufficiently high heating rates to cause charring,local mass injection or outgassingmust be consideredin the dataanalysis. A charringand ablation computer program, designatedSTABII (ref. 12), was used to calculate theheat-transfer rates adjusted for blowing qWB" Theseadjusteddata are comparedwiththe flight data in figure 16. Wherewarranted, the data havebeencorrected for discon-tinuous mass injection as presented in reference 13and for nonisothermal wall effectsas discussed in reference 14. The corrections were 6 to 12percent near the toroidand 2 to 4 percent ,lear the apex. Although the scatter of the data prevents precisecomparisons for most calorimeters, both flight measurements and theory show similarcharacteristics at most locations.

The heating analysis for the spacecraft conical section can be classified accord-ing to three areas: the windward and the toroid sections (both of which are in attachedflow) and the leeward conical section (which is in separated flow). On the windwardconical section (figs. 16(a) to 16(f)), the laminar cold-wall predictions adequately de-scribe the flight data during the laminar portion of the flight. The flat-plate turbulenttheory (eq. (2)) adjusted for local blowing overpredicts the measurements obtainednear the scimitar antenna (figs. 16(a) and 16(b)) but is in excellent agreement with thedata obtained farther downstream (fig. 16(d)). Transition was observed at a local

Reynolds number as low as 40 000 in this attached-flow region. The low level of heat-ing at the apex suggests that the flow is separated when the command module is at a20 ° angle of attack.

The toroid is in a region of rapidly accelerating flow and experiences severepressure and heating gradients. Histories of the measured heating rates for the toroidarea are shown in figures 16(g) and 16(h). The slope change observed in the measure-ments is presumed to be caused by the onset of transition and corresponds to a localReynolds number of approximately 30 000 at both locations. The temporary loss ofdata indicated in figure 16(h) occurred when the heating rates exceeded the sensor de-

sign limit of 10 Btu/ft2-sec.

The leeward conical section, which was in separated flow, remained uncharred.Therefore, the cold-wall predictions shown in figures 16(i) to 16(p) were not adjustedfor blowing. At all of the locations except the one near the apex (fig. 16(p)), the lami-nar predictions based on 2 percent of the stagnation-point theory adequately describethe flight data. Where the data exceed the laminar predictions, the turbulent theory(eq. (1)) is adequate for the separated-flow region. The flat-plate turbulent theory(eq. (2)), even when lowered by 60 percent to account for separated flow, yielded heat-ing rates that were 3 to 4 times the measurements. Curves obtained from the twotheories are shown in figure 16(i). Transition on the leeward conical section was ob-

served to occur at local Reynolds numbers varying from 40 000 to 102 000. No transi-tion was observed at some measurement stations even though local Reynolds numberswere as high as 270 000. The higher heating near the apex (fig. 16(p)) may be due tocrossflow or wake effects.

Spacecraft 011 conical-section heating rates.-Histories of the heating ratesmeasured on the conical section of spacecraft 011 are shown in figure 17. The lowmagnitude of the measurements at all locations suggests that the flow was separatedover the entire conical section. The spacecraft entered at an angle of attack of 18 ° ,which is consistent with the possibility that the windward side was at the threshold of

flow attachment. The wind-tunnel data shown in figure 18 as a function of angle ofattack illustrate the effect of separated and attached flow on the heating. The dashedline at 18 ° denotes the extent of measured separated flow as a function of angle of at-

tack. The separated-flow laminar predictions of 3.5 and 4 percent of stagnation-pointtheory are in excellent agreement with the measurements on the windward conical sec-tion (figs. 17(a) to 17(f)) during the first heat pulse. The flat-plate turbulent theory

adjusted for separated flow agrees closely with measured values during the secondpulse. Transition was assumed to occur at a local Reynolds number of 20 000. Thespacecraft changed angle of attack during entry, increasing from 18 ° to 20 °, whichmay have caused the flow to attach to the windward conical section after the peak of thesecond heat pulse. A history of the total angle of attack obtained from the accelerom-eter data (ref. 9) is shown in figure 19.

The measured values shown in figure 17(g) were obtained on the windward side ofthe coni c a 1 section. Although the wind-tunnel-based prediction of 3 p e r cent ofstagnation-point theory is twice the measured value during the first heat pulse, thewind-tunnel data are of the same magnitude as the flight data during the second heatpulse.

The measured values obtained on the toroid (figs. 17(h), 17(i), and 17(n)) indicatethe flow remained laminar throughout the heating portion of the entry. The cold-walllaminar predictions agree very well with the flight data. The temporary loss of datanoted in figure 17(i) occurred when the heating rates exceeded the sensor design limit

of 3 Btu/ft2-sec.

All of the leeward conical measurements, with the exception of the one near the

apex (fig. 17(s)), fall below the predicted values based on 2 percent of stagnation-pointtheory. In general, the measurements were less than or equal to 1 percent of thestagnation-point theory during the first pulse. The turbulent theory of equation (1) ade-

quately describes the heating rates that exceed the laminar theory. The flat-platetheory of equation (2) adjusted to account for separated flow was found to be conserva-tive. The theoretical assessment of the leeward conical heating is illustrated in fig-ure 20, which shows representative data from both spacecraft as a function of local

Reynolds number. A transition Reynolds number criterion is not immediately discern-ible from figure 20. However, examination of the data for discrete locations revealsthat transition could occur at local Reynolds numbers as low as 20 000 and as high as

52 000. The scatter in the data shown in figure 20 may be due to the use of the wetted-length Reynolds number when the separated-flow pattern obviously does not follow thespacecraft surface. Thus, such a Reynolds number length may be inappropriate.

Effects of reaction control system on heating.- The heating-rate spikes that canbe observed in the leeward measurements on spacecraft 011 were found to correspondto the times of the reaction control subsystem (RCS) firings. During entry, the RCSperformed several roll maneuvers to control and guide the spacecraft to a predeter-mined landing target. The momentary response of the asymptotic calorimeters on

spacecraft 011 showedheating rates as high as 5 times that measuredbetweenfirings.The momentary increase amountedto only a 10-percent increase in the heat load. Thecont,'ol firings performed on spacecraft 009during the heatingportion of the entry werenegligible.

CONCLUSIONS

Local pressure and heat-transfer measurements were obtained on the Apollocommand module during entry from orbital velocities. Comparisons of the flight meas-urements with theoretical predictions and with wind-tunnel measurements yield the fol-lowing conclusions.

1. Flight data verify that wind-tunnel measurements provide a good descriptionof the pressure variations on the aft and conical section of the command module duringentry.

2. Heating rates measured with asymptotic calorimeters on the conical section

agreed with wind-tunnel measurements extrapolated on the basis of laminar theory.

3. Interpretation of heating rates measured in the charred regions of the ablatorrequires consideration of local blowing or mass injection.

4. The turbulent heating rates are described adequately by the flat-plate theoryfor the windward conical section and by Van Driest's theory for the leeward conicalsection.

5. The data suggest that the transition Reynolds number may be appreciablylower in attached-flow regions than the preflight predictions of 150 000.

6. The firings of the reaction control rocket engines located on the entry vehiclewere found to raise the heating rates momentarily to as much as 5 times the no-firingcondition; however, because the total firing times are short, tile heat load was in-creased by only 10 percent.

Manned Spacecraft CenterNational Aeronautics and Space Administration

Houston, Texas, July 3, 1970914-11-20-10-72

10

REFERENCES

.

.

.

.

.

.

.

.

,

10.

11.

12.

13.

Bertin, John J." Wind-Tunnel Heating Rates for the Apollo Spacecraft.NASA TMX-1033, 1965.

Bertin, John J. : The Effect of Protuberances, Cavities, and Angle of Attack onthe Wind-Tunnel Pressure and Heat-Transfer Distribution for the Apollo Com-mand Module. NASA TM X-1243, 1966.

Jones, Jim J. ; and Moore, John A. : Shock-Tunnel Heat-Transfer Investigation onthe Afterbody of an Apollo-Type Configuration at Angles of Attack up to 45 ° (U).NASA TMX-1042, 1964.

Jones, Robert A. : Experimental Investigation of the Overall Pressure Distribu-tion, Flow Field, and Afterbody Heat-Transfer Distribution of an Apollo ReentryConfiguration at a Mach Number of 8 (U). NASA TM X-813, 1963.

Jones, Robert A." Measured Heat-Transfer and Pressure Distributions on theApollo Face at a Mach Number of 8 and Estimates for Flight Conditions.NASA TMX-919, 1964.

Marvin, Joseph G. ; and Kussoy, Marvin: Experimental Investigation of the FlowField and Heat Transfer Over the Apollo-Capsule Afterbody at a Mach Number of

20 (U). NASA TMX-1032, 1965.

Grimaud, John E. ; and Tillian, Donald J. : Heat Transfer Rate MeasurementTechniques In Arc-Heated Facilities. Paper presented to ASME 88th WinterAnnual Meeting and 2nd Energy Systems Exposition, Pittsburgh, Pa.,

Nov. 12-17, 1967.

Yanswitz, Herbert; and Beckman, Paul: A Heat-Flux Gage for Use on RecessiveSurfaces. ISA Transactions, vol. 6, no. 3, July 1967, pp. 188-193.

Hillje, Ernest R. : Entry Flight Aerodynamics From Apollo Mission AS-202.NASA TN D-4185, 1967.

Detra, R. W. ; Kemp, N. H. ; and Riddell, F. R." Addendum to "Heat Transferto Satellite Vehicles Re-entering the Atmosphere. " Jet Propulsion, vol. 27,

no. 12, Dec. 1957, pp. 1256-1257.

Van Driest, E. R." On Skin Friction and Heat Transfer Near the Stagnation Point.NAA Rep., AL-2267, Mar. 1, 1956.

Curry, Donald M. : An Analysis of a Charring Ablation Thermal Protection System.NASA TND-3150, 1965.

Hearne, L. F.; Chin, J. H. ; and Woodruff, L. W. : Study of AerothermodynamicPhenomena Associated With Reentry of Manned Spacecraft. NASA CR-65368,

May 1966.

11

14. Woodruff, L. W.; Hearne, L. F. ; and Keliher, T. J. : Interpretation of Asymp-totic Calorimeter Measurements. AIAA, vol. 5, no. 4, Apr. 1967,pp. 795-797.

12

TABLE I.- LOCATIONSAND RANGESOF PRESSURESENSORS

AND CALORIMETERS

(a) Aft compartment

Yc'

in.

0

2.25

2.25

71.8

0

0

-2.1

0

34.3

-36.7

6.0

42.4

Z ,

C ¸¸

in,

75

-71.8

70.5

-.8

58.4

54.4

35.2

-35.0

-2.1

-3.8

-2.5

45.9

Pressure sensor Calorimeter

Range, psia

Spacecraft 009

0to 10

0to 10

0to 17.5

0to 15

0to 17.5

0to 17.5

0to 17.5

0to 15

0to 15

0to 15

0to 15

0to 10

Spacecraft

0to 5

0to3

0to 5

0to 3

0to5

0to 5

0to 5

0to 3

0to 5

0to 5

0to 5

0to 5

011

Y ,

C

in.

,

4.

4.

71.

4.

-2.

4.

-2.

39.

-38.

41.

Z o

C ¸

in.

3 74. 7

75 -71.

0 71.

8 -3.

75 58.

0 56.

0 33.

7 -35.

0 4.

6 -5.

2

1 44.

Range,

Btu_t2-sec

300

8 200

8 300

25 200

4 300

3 200

3 250

0 200

6 200

7 200

6 250

4 300

13

TABLE I.- LOCATIONSANDRANGESOF PRESSURESENSORS

AND CALORIMETERS- Concluded

(b) Conical section - Concluded

Pressure sensor Calorimeter

X , _, Range, X , _z, Range,c deg psia c deg /_in. in. Btu t2-sec

26.5

45.5

62.3

78.9

110.0

25.3

19.4

82.6

19.4

25.3

78.9

37.5

78.9

114.0

45.5

59.0

35.0

57.4

70.5

133.0

58.0

27.1

32.6

32.6

91.8

88. 1

93.4

118.2

95.8

136. 1

271.6

219.8

177.0

223.5

187.9

215.3

263.9

275.0

226.0

142.8

176.5

177.6

271.9

Apex

232.0

253.0

253.0

253.0

Oto 3.0

Oto 3.0

Oto3.0

Oto 3.0

Oto 3.0

Oto 3.0

Oto3.0

Oto 3.0

Oto3.0

Oto3.0

Oto 3.0

Oto 3.0

Oto3.0

Oto3.0

Oto 3.0

Oto3.0

Oto3.0

Oto 3.0

Oto 3.0

Oto3.0

Oto3.0

Oto 7.0

0to 7.0

0to 7.0

26.5

45.5

64.8

78.9

114.0

25.3

19.4

88.0

19.4

25.3

78.9

40.0

78.9

114.0

51.7

61.5

35. O

60.0

70.5

133.0

58.0

27.1

32.6

93.7

85.3

92.0

115.0

83.4

138.0

270.0

182.9

178.5

225.5

191.3

215.3

267.8

265.0

229.8

142.8

178.6

177.5

276.4

Apex

234.0

253.0

253.0

100

50

50

50

50

50

10

25

25

10

25

10

25

25

10

25

25

25

25

25

25

25

5O

14

Forward compartment

engine

hatch

"Y'rTLaunch escape system

tower leg

Crew compartment

mbilical

Yaw engine

Aft compartment

(a)

Steam vent

_ine Scimitar antenna

Leeward view of the command module configuration.

Figure 1.- Apollo entry vehicle.

Pitch engine

15

+ZC

90o

X = -112 in.¢

X : -81 in. XC C

Scimitar

[]

135:well

\-Yc 'c

180_ 0_

Rendezvous wind ation window

0 Pressure

[] Calorimeter

Scimilar antenna __ Umbilical housingz_

C

270 _

(b) Sketch of forward and crew compartments showing instrumentation location.

Figure 1.- Continued.

16

O0

x

Uo

N 0

4- e-

ll

0

COI

o

(1)t_

c_

©

o

o

©

o

0

z"

-S

4.-I

©r.)

I

b_

17

o

C

4.0

o

N

o

,-,.i

_N

© m,--i

%

©

m

m

%

m

m

0

-S

"do

(.)

I

18

c

c

Sc

<..

.... "" V>>_PYL-_

_'JJJJJJ_"

_"JJJJJJl

v_

v^

Z _ >'/,,_/// />< .....

©

o

o

o

©

!

19

t.---

o

..Q

-_ ©

_ cj

2O

0

oo

o

oO

o ©

,-,--, _ ©

%

_ M

_ M.r,.l

g

x

3as/].J ' °°A0

x I I I 1 I

N N N o o

)4 'apm,!].IV

21

i × 10-2

-3i×i0

1 x 10-4

i x 10-5

i × 10 -6

1 × 10-7

i x 10.8

1 x 10-9

1560 1600 1640 1680

t,sec

1720 1760 1800

(b) Free-stream density.


22

32

a_

14

12

10

%8

6

4

0

1560 1600 1640 1680 1720 1760 1800 1840

t, sec

(c) Total pressure and free-stream Mach number.

Figure 3.- Concluded.

23

J

400 x lO 3

35o

3OO

25o

200

15o

lOO

5o

28 x 103_

26

24

22

20

18

16

14

12

10

8

6

4

24300 4400 4500 4600 4700 4800 4900

Entry t, sec

(a) Altitude and relative free-streanl velocity.

5000 5100

C3

8

(b)

4xlO 6

2 8

I

o

4O

30

20

io

o

4300 4400 4500 4600 4700 4800 4900 5000 5100

Entry t, sec

Free-stream Mach number and Reynolds number based on body diameter.

Figure 4.- Entry conditions of spacecraft 011.

24

o_

I x 10 -2

-3IxlO

ixlO -4

IxlO "5

I x 10 -64400

L-J_I

F:

Z-

F

Arcasonde data and statistical extrapolation

! r -

++

• +.+ !

_q "r

I 1

I'

:i

/I £=_

4500 4600 4700 4800 4900

t, sec

L

!_

5000 5100

(c) Free-stream density.


25

Figure 5.- Photographshowing streak patterns onaft heat shieldof spacecraft 009.

26

(a) +Yc' 0 = 0 °.

(b) o ---45 ° .

Figure 6.- Photograph of conical section showingchar demarcation.

27

(c) 0 = 135 °.

(d) -Yc' 0 = 180°"


28

+Z c, 90'Windward

Umbilical housing

-Z c. 270 ;°Leeward

Figure 7.- Illustrationof char pattern on conical section.

_Yc'

0 o

29

1.2

1.0

.8

,4

.2

0 .4 .8 1.2 1.6

S/R

Ca) a = 18 °.

1.0

.6

0 .4 .8

SIR

(b) a = 20 °.

Figure 9.- Wind-tunnel distributions oflocal-to-total pressure ratio.

2.8

31

10

.m

on.

in..

4-_

itr

1620

(a) Y = 0, Z = 75.C C

::1::::ZE....... t....

.... '" :t::::

L_A_

i i......

ll_ 111111 ....HI ....

lit il ....444_. -i----H_

i

1640 1660

6 ::

_i!!i

ill

1560

ii[i

iili_

iiii__rr

!i ......._ii !i!i!!!i!ii_ii !!!i!!!

•:: _ !!iiii

1570 1580

_ _i :I: _ :i_iii...........

/

i: ! : 11' _! STIr

iii................... ii:::.I!]:2 :!i': :i :i i _ iii_

_ ,t '_ ,".-? .:h

15qO 1500 1610

t, sec

!!ii iii!

i!ii

ii!i !!_i

i!i!

1620

(b) Y = 2.25, Z = -71.8.C C

Figure 10.- Time histories of pressures measured on spacecraft 009.

32

1630

_i!Jil

, !.....!

I i

! ;

ii!4

ililt1650

!/i

:ii

zn

=Q

1660

(c) Y : 2.25, Z = 70.5, S/R : 0.94.C C

1o

6

4

1570

_ _ +Zc

I:l_',;ti d:itl:l

1600 1510

t, sec

16_

-r-y-T"Y[-'*-_ S!l

,l::q

1550 1660

(d) Y : 71.8, Z = -0.8.C C


33

[66O

=0, Z =58 4.(e) Yc c "

; :: ff;;Zil[! !i[i _!l_!_tliu

1620 1630

_G!?!!!?!_ti}ii!!

_!!!itli!i?il

tilili!i !1640

= O, Z = 54.4.(f) Yc c


34

i-I

÷+++++,_

,>+÷++÷+

::_tt_tP

i!:-!m_

tHt_t!F,++,

ttFFIFftttt:t_

_tttFE

+++. ....t_;l:::iftfft?Tt _

ttfl¢:_Y

H+, ....

.... _::(.... ,

"tHtftH_;_H4H

HH

_. + +H

trtl

r! !t kt+_+Jt

_ttttt:.-

!}TTF,+++, ....

;_TTTT.... _+_,_,++.ttH÷t t t-t_ _fff+

ftttt-t_+fiSH: :A_tt;F;_T

t t ftl._-_?

,±ttm:ftttlt:tt

lfftt::::_+*+t ....tttt!_'T"'HH_'+-IH;t;:t:,ttttttt*

o

+.++_

trot1

++**_t_tH

ttIH

*,HH+++_ttH!,+++_++,H

iiiii.+++_

ttt i-]

*tt_

i!ttt

:::;i

iiAi

?:7,;:):_:

:HL

!!!-rff+t

_qt_tttT:l;t;

:TF4

;: HH}H4fF_-_Ft :;: iFTT

P.:!: U: _U-

:i:_!l!tlI!{!1i _: ....i{ m:--z7{ ::::,. m ;:::{i:ii:F _ :!Hi!T:

v. -._*VF H:,::F...,_, T!: i_'"

-rt := :'tI_ !'H;

.7_:_I_'HH!F[TITTI ! A!T

i! ';1_* q_*"t ;;: iHi

CO ,,0

g!sd 'd

Httt_

÷++tH

titHt

t

EIT

TH

÷++

_H

_H

o

0

o0 o

oo

II o

b_v

35

6

4

1570

• Flight--Wind tunnel

_qT

i:i

1580 15gO

!iil

:if! i!!i

F_

+Z c

E!!

m:

1600 1610

t,sec

1620 16_ 1640 1650 1660

(h) Y = 34.3, Z = -2.1.C C

12

1o

1560 1570 1610

t, sec

+z ii ::,i::!

......... I:....

ihii::',!!iii_, ii:::.!!ii

i! d!_ _i!ii!ii iii " ii_ ::il i!i_

!i i1,i ':!ii _!! !U

11il _-fi m

iill i_!] ii_!!::!i !!iii:!!

._i!iil iiiliiii _iilii_i1620 1630

_ .... iili _ii gii!figi::::iiiiii

::_! _ _i _ii_

::1ii!ii }::ii::iii Ii::ii_ii::!!iii_ ii} ili:

li_i ',_ i:i: r_i!ill! ....

i;i; i_ ill !!_ !!i!!iiiIi!i !iti iiii

ii_iii i!if :z_.I 'm

!ii i!!ii!_ii_iiii iii_ilili fli !!f

ii:,ii:,ii:iiliiii:i:_j',iliiiii'_i_ii_1640 1650 1660

(i) Y = -36.7, Z = -3.8.C C


36

c£

-2

1560 1570 1580 1590 1600 1610

t, sec

!iii_

1620 1630 1640 1650 1660

(j) Y = 6.0, Z = -2.5.c c

-.21560 1570 1580 1590 1600 1610

t, sec1640

(k) X : 45.5, _ = 88 ° , S/R : 1.44.c


1650 1660

37

1.0Flight _!I!

-- -- Windtunnel _!_

-1.0

1.0

LO

0

1.0

01560 1580 15_ 1600 1610 1620 1630

t, sec1640 1650 1660

(1) Toroid-conical tangency point.

o

(m) Conical section.


1640 16.50 1660

38

Figure 11.- Photograph ot 1tow pattern around windward scimitar antenna.

39

(a) Pitch plane, -Z c to +Zc.

1.2

1.0__ --Wind tunnel, = =20", M =10.__ _ --Wind tunnel,= :25 °, N1°10

I Flight data, M - 21.9 to 11.5

4a

.4 *_

T

0 _-2.0 -1.6 -1.2 -.8 -.4 0 .4 .8 1.2 1.6 2.0

SIR

(b) Yaw plane, -Y to +Y .C C

Figure 12.- Comparison of spacecraft 009 pressure distributionwith wind-tunnel results.

4O

r--I

00

000

000'_'RI"

00O0

,L)

.be.-

i.a.i

0o

oo

oo

oo

o,::I-

o

c_o.,

o

o

g

I

g

41

0.

.2

T

(a) Pitch plane, _ = 90 ° and 270 °.

FigTare 14.- Comparison of spacecraft 011 pressure distribution withwind-tunnel results.

42

1.4

1.2

1.0

.8

e_

.6

.4

.2

0

-I .2 -.8

(b)

-.4

Yaw plane,

0 .4

S/R

= 0 ° and 180 °.


.8 1.2

43

o

O

÷L ._HI _I I'.I:] 111_:I :::I IIIj

:i_t: !t; :.......

_o Hi_iit:r_ i_

iiii|iiii'i:ii _i

.2

iiiiii[i!!!!!!!!!!_HI H_HWWI+_+!

IIIitl!_]_IIIHiIII,l;,Ii!!,

+

;Ji_ H;i ::: ::: ::::tq!_I_UI_H_L+!;|!iF

90 °

270 °

.. _ . . _ --..__ 1,,_i.i!iiIt _ _ _ _ _ _ _ i _ _

l Z .... _ _ _ _ _ _ " _ ]

_ _ _ ___ '_ __:l l ]

;-'_; ":_ _ 4 _: I,H ::L: :_ "" _!

[[[[ _;; ; t+HH _H _ _-, e,_ 17'-t_ ..................................... Ill[ li[iillii[l

ZIH_

i_ _ i _ _

i!_!_!:ii!i:liil_

]7]] l

':{{{

0 .4 .8 1.2 1.6 2.0 2.4 2.8

S/R

(a) _ : 18 :' .

Fig_re 15.- Wind-tunnel distribution of local heating rate divided by zero angle-of-attack stagnation-poh_t heating rate.

44

._--

1.6

1.4

1.2

1.0

.8

.6

.4

.2

e = o0_18o o

0 .4 .8 1.2 1.6 2.0 2.4 2.8

S/R

(b) c_ = 20".


45

x.

,Y

mi

%

rn

,_r

24

20

16

12

o1560

iiii_iii_i:li!

_II__ I_I

ii::IIii::

1620

,:_..,ilIi!lil!lb."

!Hli!:illlHim_l!_

i!i! ,, .......F;111 i i :

;111

_i!f!]i_:.,==

I!;:_i_ii.i.:..i!;iti!_I:fi_

t;_,_' _ .......I_:H ,

1630 1640

WE_,..

...., !fi!

_'!a,,.iw

1650 1660

(a) X = 45.5, p = 85.3 °, S/R = 1. 475.C

Figure 16.- Histories of local Reynolds number and heating rates on conical sec-tion of spacecraft 009.

46

6.2 X 10 , . . .

!t7:

Flight mea'surement

A Corrected measurement

24

2O

u_I

12

o156o 1570 1580 1610

t, sec

t_T+Lilli_l_it

f_f_l:Lcl!

_, t-+lt+;tllt

v++++ tI_ _i4t,+HIi

li_Hililtl

1: !,_!!.!T.tl

:} qi:

ii_ii_iiiii:pf':::=:: _]

...._ _t;

1620

,,_ H_:

mt_.

7ti:TI

_7

:illit!_t!,if:.:!iitFi

._i1:#:!7itiiil1630

:;:;7!H_i!f4::7r..i!r! i_i!mm_

CrT .

__

mN-'H L_-

1650

ii4i

W:N++.f ,

!';1

Co) x = 64.8, e =92 °, S/R = 1.775.C


47

.3 x lO 6

i_ ::i!i_i::ili_ii_i_ti_+,+;_ii_:!t:-!::::li+i!ii:: I i iil:: ,+,, " *" :;ii:_....'"" _i " ....+'_:.2 m!_iii!{_!i_=,.,m_t_ii:,iiiitiiii i !i !i i ilitt!!_!_HI*':.ii!i!_::i::ti _,I!t_F +_

Tn; "_:W ........ ""

_!ai_;........... _ !!i;, _IH Itli!ill=:i!i!iii7:_:::;':;_: ..........

0

i!Z: ii ii::

N

o1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660

t,sec

(c) x = 78.9, _ = 115 °, S/R = 1.99.C


48

x

cz:

.4 X 10 6

ii!i ii_i!

.2ilil !i!4

::_:!!!i

0

24

::It ;H: !!:_ ::il _U:i::lhb!:J::!l:H : ,:

!i!]i:i _: l!ii Hil ' iH_:!:ililliiiii iili iil_i!!ii!ii! _

!iil fill _:'_=_i:I:H :!:: ::ii :H:hiH

:_I: F:_ 1111

2O

16

uli

i2

01560 1570 1580 1590 1600 1610 1620 1630

t z sec

1640 1650 1660

(d) XC

= 114, _ = 83.4 °, S/R : 2.5.


49

oNN1560

• Flightmeasure,neot/I _ t___

gi; ; t:+t+ ::+e+!i++i+++q:t+;:+.++d+:. + ' " " +._{ =++++_ l.IJ!, h & ,.++.h+.,t.,.+l+,,+lJ__ +._+++[_,_;,++ + _ + _ _+ .+. , ; a;

1570 1580 1590 1600 1610

t, sec

{,+ I

)E

+fl

+++++

1620

++:

I+....... . :+..

_ 11+_q-H _+4_44tad +4 '.H I '.H I I U ',',: ',t ',',: H H :

1630 1640 1650 1660

(e) Apex.


5O

mi

.o-

.12 X 106 _L/f_LF/ISrj£

_I_

o____

2O

I0

oiiiilii1560

I:L7:H: _-'v :_!: -t

........... _ _ i!ilii?:t!717}_i!{7

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1570 1580 1590 1600

ill'_t+ ,._

H:qi!li f;i:

H:t: ,'-

it Niti_ht_[Hti_!::_:;_:,::_::ii_:.,.,_:__;_:. n__:._:_::_:::_:=::_,_:_:_::_'_:__t_i K;_ .A. iI+_;

' _f::i i:14_t:: ]Tti'ii:7'{:i_:r.:; m:ilri 7iii_!i _

1610 1620 1630 1640

t, sec

!I!!!!_!!i_i_li!!il

777_ii_ii4ri-

i650 1660

(_) xc

= 25.3, e = 138 ° , S/R = 1.16.


51

4o i

30 :!

¢N I

2o i

._r

10

1560 1570 1580 1590 1600 "1610 1620 1630 1640

t, SeC

1650 1660

(g) X = 19.4, _ = 178. 5 ° , S/R = 1.071.C


52

.4 X 10 6

×

.2

o

40

°11560 157o 1580 159o 16oo 161o 162o 1630 164o 165o 166o

t, sec

(h) X = 19.4, @ = 270 °, S/IR = I.071.c


53

.2 X 106

X_

W-_n

lO ._

!b

_t!++'+r:_1liz[....IB_

N_

t_t

1560

x

,.*,..

I

%

1:4 b+:tUt]I ,

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Laminar prediction

Turbulent predk tio

.u ;[:[_i_iiii!:iu;i::iilii i![ii_IF}i:*_'!F_

....._;" F

1570

ti.:tiiii!i,, !_i"'__"+_'iti!':"!i_i_}

i!l:_!ii!_'_ ....

1580 1590

'I"/

Hii iU

:H: H:;tii !1:

ii

iiii

_ __i@_i ........!!!! !!iii! ......... , ........

f'_!ii',!ii_. _I _ti_t

1',iJF'_fi_ fit!_If:Bei!_4 , ;

I71',

1600 1610

t _ sec

!UT

._t_tI_t!ii__ _+f__

1620 1630 1640

@!

¢ U II"_'i 1_.,,

1650 1660

(i) XC

= 88, ,_ = 182.9 ° , S/R = 2. 135.


54

N I

.16_:,:.o,6__._,__ ___i_:__: _;;III_H:_:____tt:H:t_

x _ .............._ ................... _ _ _- ........ _

[I[I]I',",ll]HII]IHI'A]II ',...... _....... H ;H[IIIHI;I I;;HIIIH[ ....... HIHI[II[HI]_ I _ E_, - _ * _ _ +_- ,++, + _

, Flight measurement _ ............... : i _ _: _" : _ '_i ' . '. , -_' ' i

1560 1570 1580 1590 1600 1610 1620 1630 1640 1650t, sec

!ii

1660

(j) X = 78.9, _ = 191.3 °, S/R= 1.97.c


55

.16xlO61_ikqii?"_ .'i......

|!!_ti: !_llfi_lt: hl_,h+ff::

0 |;" : ;_ t ;"_1:t_;| l_t: |: _';:t_:

r_

i;!

_ _i_q_;_l- i!iI_ili!iiii:iTii!i!!i,i:,iliiiil!i

0156o

iv:: il[i

it$i_!!_-i::iii::!_Iiiii! !!¢!

gt:=i_Ii::Ii!g!:,_:::!i::t!i!i!1111610 1620t, sec

• measurement II _l_i!!i-- -- L_,,n,arp_edi_Uo,-4-+---------e-_.

.... Turbulent predicUon \1"/ _

1570 1580 1590 1600

.... _ !!!_i_i_t._t_:.ttii_i!i_l_!Ilil_l

1630 1640 1650 1660

(k) X 40, _ = 215.3 ° , /= S.R = 1.39.C


56

i i :_':Ei !_{![!II!I_ii!i[::][_!!il!i!li!iliiil!{{!il!i

/!i :ii_]:._i!_: _':ii_,iI _: :]ii iili ..........

5 [!it!i!iil::ii!i:::.i_i:_:<: i....isi!iiiii!5!',i;;.....;.;::i,,.._..,i!!i!::,il:_,

:!]!

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..:. .i" ii _ [ii _+_ i'!i,i'_ i ._i

:", ;v.: ::: :!<:,:: :I: .:::_: .: :',: _t]i h_ iii: _!I! _o_ _ _=_ S=_ _1560 1570 1580 1590 1600 1610

[, sec

_ii!!t!!_iiiiift!_t!ii

_i_ _ii!l,........... ill;!_itl],iits!!_li!ii!iililil_*_ _;:i_ .... Iii

,f_!it

1620 1630 1640 1650

_=;it!:ii I

i i i!;

;]:ii:l...

i_!!!!!i!!i!

1660

(I) X : 25.3, _ = 225.5 °, S/R-- 1.16.e


57

x

I

%

(:a

.16

.12

.08

.04

xlO6.,_____+++_i_+_T__+_ )iiiiii::ii}iiiiii::ii::ii::ii::i::iiiiiii::iiiiiii'_"i_T_r_ _ +_H_ff_H_:IU,_,;NI ',N_II [[I_I!!H_HIHr,_I+H+H+I_;GGII :''_H''H_';H_''''_I_U'_I'_1U';:T._''[IN::U'T:.J_[.':..U'::[_U'':.'.''/'./'N:)U` ',

_I__ _.............................................................."_.....................)++_,__:,?_i_

_: R " _i iiiiii;:;i_::_;;:'""_::"_'_':i::::;::_;"_+iiii{iiiii{i+iiii{iii!!!{!!!!!!!!!!!!!!!!!!!!!!!!!!_":"::::::;::::;:::;:::::r-:;:::_:+_

........... + + " + _ _': ........ :'r'i '"''!_I........................ r_iii[iiii!!!!!![!!!![v[!!!!! !!!!{!!!!!!{!!!!!!(!!!!!{!!!!!!![!!!!_;";m";:::::::;:;:;;;::::::[;_'_'_+_..........................................

_ _+e [IIZF: V,',',',: ',_ :NUJFI I:]',N _ _+_[',]',:[:]U,',','r_]]_;IN_IINU,:[:t_:',::I:U,:_U= ........ _'t_d'_ +; +_ dFF_ER_I_i ] I _ i i: i i ii,,,: ........... _ ........................................................... ! {!!!!!! !!!{!!!!!!!!!]!!!!{!:!!{{ {!!!![?_!!!

_ ÷ ............................ :Hz,r:H.,, ............... : ...... _ ............. , .......................................................................

']'''_ .......... ::]_ N ::]][ ,_[_ ; ......................... : ', ', : : : I [ ', '. [ ', [ ',: ', ', : ',: : ',+__

_:, ,,N_ ,:H :: ,N u,;,_: N_+Fy.H ;U,_ :;]; N ::,U,_N N,:,I ::[,HI]H HNIHU HIH ;;:;, ,;:;]i_;; U,;:,,,U,:;;_:::::::::,:::::::_:::::_::IH{ ; .............................................

_}_Lt_l_H_+r++l+++_,_+(;+];ll _i illl N] I[[ [1 N [] [i N 1N ,j _: [11) ;_ )lIT1=1 [ N 11[[11 : I[:1111[[1, N , N [1:1: :]::I[IIT_ ,=,_,,:.=1 ,_= N f :: ,.: N,I .............................................

_+_{II_[[_T_ H. _ _!! ,_, I:I N )I 1 _H_ ,;_I;i_[[ H ] H [] N 1U N : ,_[ U. U;i[II N ,, : _:, 1 ,, ,,: N :Uj [ .: U, ,...[ [ ,,, ..: N l[,j,_ ,,I

_. .... _; _+i ',:?,tli_:,:_;_ ::iiii_iiiii_b_-_;i+_iiiiiiii iiiiiii_iiii_iiii_iiiii[iii_iii',_',iilY,!!!!!!!!!!!iiiiii[]

+ o +-k_+_l+:-+++,++F.++++H+ _;;;N_;+:+I:+++,+II+N4F_+I:++_+H+{.+,-_ ._+,._+ic+m_+'_ ' I+H-_-_-_ fi++ 4-t++H-_

++_1+t_++.....................................................................................................++_++J+++++_u+++++_++i+++++_+4_+__++ + + ++ + _'+_++++++P+++++++++++++%++++TTT++_Tl.+_+_++_._++#++f+[P+P+I_P++++++P_ +'++rt++'+Tl_FT+t'+F_ _++T+!. :':'N: ...... I_IllilHIHN:/,t:+_:/: t , ! .. C _:N_ +_:+_:]++_; ] -: .......................

4 ........................................................... t,,, ,+,r ], I r _LIIIIIIllll ifl llilltlllillll++_ ;+;++_+;+;, +]++;+;]+;:+_ ;_++: :::+;;:3;;::3;;+:++_ [:;+3 3:_+;::;_++:;, +_:+;;;_;3;;:;;+;

:r_ ++.[...............];[ ::T]][:] [; J:1111+++11..'11:1]!!]['1+?]11_]+;: [;:]]::::: :+: : ::::: :+:::tt+:::]ii+++++i!!+ j++ +!+!++ ++++++++++Ji+++++++i+++++i+++++ +++++++[+++++i+[+i++i_+++++[i++++++[+3t +t+i++i+)++++[:++++ _ _:::":::'::

Lr_-_:l t I / h Ilil IH I++llil U :::: ::::;::T',::_ [:: :! ?'_,_: _,, ,":_, : N_::: U: ;:;] :: ::[:: ..................... ! +H'H+I2 _ .... Turbulent. prediction _1 "/ _'_+i_i_i+i_r_r+_;_r_`_]_u_'';;_;;_;_;_;_;_'_T;_'_;_i_

XL,/ ++t=i]=i=+Hiir_!_::!:::!]_+_'_r--'!::!::!!!::]E!::::::!!::!!_ _!::!!!!!_:__--T=--:!:'!:;:+!!::_

o _+_+_+:, ............ __+++_T_++;J])+]+]+++]))+++])+i;_)i))+)]))+))+)+)+)+)+3++_1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660

t, sec

(m) X : 51.7, _ : 229.8 °, S/R : 1.57.C


58

Flight measurement

_ _ Laminar prediction --1_1-.-- TM

°N_ .... Turbulent prediction

o_ ___!i_,!_ TM1560 1570 1580 1590 1600

, z}] : Lti:;_ :if: - ; ; i, ; :i. : _H_i _ : :_

1610 1620 1630 1640 1650 1660

t, sec

(n) X = 58, e = 234 ° , S/R= I.67.C


59

2 X 106• , :E:,:_: : _ : _'?t!!l_li!!iliil_ll_!!!ili_i!li_il:,_!_J_i_i,__;l_i_i_!J_ii_l!_iii_:,i:l!i_i_t!_!_i,!_il !ill_illiii_:!

_I" ':,i;" -_'i; i';i ;': ; lu;q-_ I-_: l;-:_I _.. U iq-_- !.q _lii _ _ iqi

0

_ " Flight measurement /I _ _! !::i!i]i::

!i::::!!fiit_iiit;i:;t;!_ilii:iti:tit !:iti:iii!i:if: _ili:.: t:i_il[ii:. :;i!ti_iil!ii!ii_i!lhi:.::i}i_;iit

r i_:]::u::"!ii! !:!!!)!!!!!_:i...........'........': ':_ '1: " :i" !_iiu:_! i il]i _

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• _. ......................... I ....... I' 1 ..... _ ............ _ ..... _,

1 :.iii!ii!::t!:iii::i!i_::i::iliii::_ili?.ii:..:_i::i,::ii::}:._i}il_!1_:_.,...!_i!,,"iii;..,,H!i''_,;,,:![:i

::::::::::::::::::::::::::::::::::::::::::::: :: ;i;_.!i ,:.

1560 1570 1580 1590 1600 1610

[, sec

!ill !iiiiii[i!i[i_iiiiiiiiiii_!iiiiii!i_vi!!!_t_i

u:,_iiiii!i!_i_ iIiil

.n . .h:H I!!.,.

ih', :li: !:!if:!:; ::_! ":I :H!:!!! r_T_[;ii'iii_ ii:i i;il i!il iii! _.!:[ : '.i'.

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:m; ".; ":: il!i .........

.... ':: iii ,}iliii=:_;i:*'l!,i:-iJ',," .....!ii_151i_ , ,,._iii_ii_ii_

":iit! !i!-" _li

.._ _!._

1620 1630 1640 1650

f_?ii!i_ii_ii_i-i-iii

i_ liiii[;i}iii_}!fi

!il! Hii'!i[!I:!!!

,, ,--

!iii_i_iiill[;ii

1660

(o) X c = 70.5, _ = 276.4 ° , S/R = 1.865.


60

.3

mi

N

• or 4

o1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660

t, sec

(p) X c = 114, _ = 265 °, S/'R = 2.5.

Figmre 16.- Concluded.

61

.5 x 10 6

.2

X

1.0

2.5

2

04 D

1.5rn

.5

0

4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300

Elapsed t, sec

(a) X = 45.5, 0 = 85.3 °, S/R = 1.475.c

Figure 17. - Histories of local Reynolds number and heating rates on conical sectionof spacecraft 011.

62

.3 I06 1 1 1 1 1 1 1 1 1 1 i i i i i i i i i i i

.2

><

.i

3o

2.5

2

If)I

1.5rn

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0

4300

Laminar prediction ._ \Turbulent. prediction -9

/FI ighL measurement

I Ii I

! °

! •!

Iti

.fL

ki

_ ,:T '.

- :r,. t_ _

_ . .

.2'

-\, 1 k

/,/

i

,!1 ,7.zI-t..,i.

I

I

ii

i

I

i

! ,

i

4600 4700 4800 4900 5000 5100 5200 5300

Elapsed t, sec

(b) X = 64.8, _ =92 °, S/R = 1.775.c


63

06.oxl

.2

)<

rv _

.i

0

3

2.5

2

LZ_i

1.5

1

.5

04300 4400 45O0 4600 4700 4800 4900 5000

Elapsed t, sec

5100 5200 53OO

(c) xc

= 78.9, _: = 115 °, S/R= 1.99.

Figu,'e 17.- Continued.

64

X

rv

o_I

CxJ

4d

r'n

.3 x 10 6

.2 :

I i

0 : :

i

3 :

2.5 iIII

2 III

!

1.5 JIIII

1 I

1I

I.5 I

II

o .--44300

,IIi t: !

I_

I

: il i

I' I

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I

i _L

f

i

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jr

w_

Laminar prediction _\Turbulent predicLion - -

FI icjllt measurement /

I '.Z_ ."

: r,j ,,.,

. jE.:

I

._-:_:. _c' K. i

5 \L ;.I

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1 " jJi\ :, :

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i ii

I

i

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, ._.'t_.

4400 4500 4600 4700 4800 4900 5000

IAii/!I/I I#11IIIIIIIIIIIIIIIIllI I I

i

i

i

i

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i

,,.4_

5100

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i!

]

5200 53OO

(d) X = 114, _ --83.4 ° , S/R= 2.5.c


65

6.4xl

x°2

3.5

3

2.5

2I

Oq

1.5

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04300 4400 4500 4600 4700 4800

Elapsed t, sec

4900 5OOO 5100 5200 530O

(e) Apex.


66

X

rw

I

'4

r_

.15 x 106i:ii

I :

.10 , ,,i i; !. J

.o5 I!

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0 '-'-'-

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II

21"1

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O k4300 4400

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4500 4600

I

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I IIIIIIIII IIIIIIIII IIIIIIIII IIIIII N

lilill Hi IIIIIII 'I IIIII IIIII III Ii IIIII II /

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I

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5100 5200

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IIIIIIIII II

lilllIIIII

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Fi6ure 17.- Continued.

67

.15 x 106

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x

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1.5

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.75

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0

4300 44O0 450O 4600 4700 4800 4900 5000

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5100 52OO 5300

(g) xc

= 61.5, _ = 142.8 ° , S/R= 1.723.


68

12

11

10

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4;26

.g5

04300 4400 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 5200 5300

(h) xc

= 19.4, _ = 178 5 ° S/R = 1 071


69

.15 x 106

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X

ty"

.05

5

4

_ni

C_

3n_

,c3-

04300 4400 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 520O 53OO

(i) X = 19.4, _ = 270 _, S/R = 1.071.c

Fixture 17.- Continued.

7O

I_4

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1.25_

1:

.75:

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04300 4400 4500 4600

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4700 4800 4900 5000 5].00 5200 5300

Elapsed t, sec

(j) x = 35, _ = 178 6 ° S/R = 1 31c


71

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X

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m__ Laminar prediction

Flight measurement

Elapsed t, sec

4900 5000 5100 5200 5300

(k) X = 60, _ = 177.5 °, S/R = I. 696.C


72

.15 x 106

.10X

cY

.05

3

2.5

2

II#illI

1.5

rn

.5

0

4300 44O0 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 520O 5300

(1) X = 88, _ = 182.9 °, S/R = 2. 135.c


73

.15 x 106

.lO

x

r_

.05

0

1.5

1.25

1

_n!

.75

.G

.5

.25

0

4300 4400 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 520O 5300

(m) X = 40, _ = 21 5.3 °, S/R = 1.39.c


74

15 × 106

.i0

X

.c_f

.05

2.5

2

_n!

C'4

_1.5

Q3

.5

0

4300

-- -- Laminar prediction

FIight measurement

..L

,'::"_

4400 4500 4600

JJ

5

-r

A':.-

4700 4800 4900

Elapsed t, sec

I

//

/

i"

!'.°

!

5000 5100

I

7-

!

i

i

5200 5300

(n) xc

= 25.3, _ = 225.5 ° , S/R = 1.16.


75

.15 x 10 6

1.25

04300 44O0 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 5200 53O0

(o) X = 51.7, _ = 229.8 ° , S/R= 1.57.c


76

x

Oj m

.25 x 1

.2O

.15

.10

.O5

1.5

.5

04300 4600

Laminar prediction

4700 4800 4900

Elapsed l, sec

5OOO 5100 5200

"qi

II

I

I!

II5300

(_) xc

= 58, _ = 234 °, S/R = 1.67.


77

.20 x 106

.15

.10

X

(_,i I

.G

.O5

1.25

.75

.5

.25

0

4300 4400

j!! t tlt,i;:: I III_I

::: I III I., ; ;

" Ilia;;: : lll/l.... III/I

lil/l::: i III'I::: i flat_;: i II/II.... II/II::: : li'll;:: i I/III;:: : VIII;:: AIII.... / IIII !..J .llll :I].-1 IIIII :

_r!! ,llll :::: IIIII :

IIII" : : ! : ! II II :ii: iiiilll; ; ; •::_J :_i IIII:.:: ,, III i, :

:2_ _Laminar prediction _"

• Flight measurement _,,,/,_ 7

B

ii!i.i i iiiiii i :!!::-;.5 III!ll i Ji

: :., .,.!:,: • I I I I I I

i ilL'i," ': t till t i i' I1:111- I II

i VII" _-, t ' .i I : ! !

/ I I-1." "'_,'" • I I_1 I:: I : ! !

' I _._!;-' _.,'!'1 I I I_il :_: l I ' : :!;_'i! _-I',_-:r'. t ". :._;'1 I

:L I'1

,qll

!!!

i i i

! ! I

iiiIlY

"!!!I ! !| i .i

; ": :._'1, "J.'.'4-.

4700

:i,I II II Ii L I 1 I P_.. ::[ II I I I I I_-_,r-:.l

4900 5000 51004500 4600 4800 5200

Elapsed t, sec

(q) X =70.5, _ =276.4 °, S/R=1.865.c

Fig_ure 17.- Continued.

78

.25 x

.2O

.15

X

.lO

.O5

.75!

0,1

CO.5

.25

04300 4400 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 5200 5300

(r) X = 78.9, _ = 267.8 ° , S/'R = 1.99.c


79

2.5

2.25

1.75

1.5

¢.)

_nI

1.25

1

.75

.5

.25

04300 4400 4500 4600 4700 4800 4900 5000

Elapsed t, sec

5100 5200 5300

(s) xc

= 114, _ = 265 ° , S/R= 2.5.


80

O

IIO

2

._:_"

!Attached flow

0 10 20 30

a,, deg

I .772

Fly, are 18.- Wind-tunnel heating rate measurements on wind-ward conical section (_ = 90 ° ) at Mach numbers from7.42 to 10.18.

81

6_p '_ i_lO.L

82

1.00

.17

.16

.15

.14

.13

.12

.i0

.08

.060

" .04

..2

.02

.010

.008

.006

.004

.002

.001

103 104 I05 106

R_tX

Figure 20. - Leeward heating as a function of local Reynolds number.

NASA-Langley, 1970 -- 33 S-159 83

nasa technical note nasa tn d-6028

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