Cross-hatching: A comparison between behaviour of liquifying and subliming ablation materials

18 SEP. 1973

Kluyverweg 1 - C:LFT

van

KARMAN

INSTITUTE

FOR FL UlD DYNAMlCS

TECHNICAL BOTE

85

CROSS - HATCHING

A COMPARISON BETWEEN THE BEHAVIOUR OF

LIQUEFYING AND SUBLIMING ABLATION MATERlALS

H.W. STOCK and M. GODARD

APRIL 1973

AA~

-~O~-

RHODE SAINT GENESE BELGIUM

~VW

TECHNICAL NOTE

85

CROSS - HATCHING

A COMPARISON BETWEEN THE BEHAVIOUR OF

LIQUEFYING AND SUBLIMING ABLATION MATERIALS

1 Research Assistant 2 Research Student H.W. STOCK 1 and M. . GODARD 2 APRIL

1973

The authors gratefully acknowledge

the guidance of Professor

J.J.

Ginoux

who suggested this researah.

Muah credit is also due to

F. Thiry~

Tunnel

Engineer~

for his helpful

suggestions.

ABSTRACT

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.

LIST OF FIGURES • LIST OF SYMBOLS • 1. INTRODUCTION

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2. EXPERIMENTAL TECHNIQUE •

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2.1 Test faci1ity • • • 2.2 Mode1s • • _• 2.3 Ab1ation materials •

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3. TEST RESULTS AND DISCUSSION •

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3.1 Necessary conditions for the existence of cross-hatching • 3.1.1 Supersonic flow • • •

3.1.2 Transitiona1 or turbulent boundary 1ayer flow •

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3.2 Cross-hatching pattern parameters. 3.2.1 Cant ang1e ~ • • 3.2.2 Stream~ise spac~ng À

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3.3 Run time

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3.4 Comparison between wax and camphor

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test resu1ts •

3.5 Inf1uence of the viscosity of the solid ab1ation material on the streamwise

i ii 1 3 3 3 3

4

4

4

4

5

6

7

8

9 spac ing À . • • • • • 10 4. CONCLUSIONS • REFERENCES

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TABLES FIGURES APPENDICES • •

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A CAMPHOR MODEL MANUFACTURING PROCEDURE

B MEASUREMENTS OF THE RELAXATION TIME AND THE ELASTICITY MODULUS FOR CAMPHOR AND WAX AS A FUNCTION OF MATERlAL TEMPERATURE

14 15

C CALCULATION OF THE WALL TEMPERATURE OF SUBLIMING CAMPHOR IN HIGH SPEED

TURBULENT BOUNDARY LAYER FLOWS D STEADY STATE ABLATION CALCULATIONS

D.I Calculation of the turbulent heat transfer to cones

D.2 Calculation of the run time t a f ter which steady state ablation condi-tions are achieved

D.3 Temperature distribution in the melting solid for steady state ablation conditions

ABSTRACT

The cross-hatching phenomenon has been studied experimentally at a free stream Mach number of

5.3,

using two different low temperature ablation materiaIs, camphor and wax, which sublime and liquefy respectively under the test conditions.

The Burface pattern parameters (i.e., the cant angle and the streamwise spacing) have been compared for both ablation modes and correlated with flow field properties. The effect of exposure time under ablation conditions has been studied. It has been qualitatively shown that the viscosity of the solid ablation material inflaences the streamwise

-

~~

-LIST OF TABLES

1 Dimensions ofaxisymmetric models

2 Thermal and mechanical properties of the ablation materials 3 Data on self-blunted cones

LIST OF FIGURES

1 Ablation surface patterns or cones

2 Cross-hatching on recovered entry-vehicles 3 Typical test results on camphor models

4

Ablation surface patterns on lucite cones of var~ous angles

5

Local Reynolds number eveluated at the position of transition and of the start of the cross-hatched pattern versus Mach number

6

Shadowgraph of a wax cone (with steel nose) pr~or to

7

8

9

ablation

Influence of the local Mach number Me on the cant angle ~ Influence of the Mach number M on the cant angle ~

e

- M calculated for unblunted cones e

Influence of the Mach number M on the cant angle ~

e 'or self-blunted cones

10 Influence of the local statie pressure p on the e

streamwise spacing À

11 Influence of the local statie pressure p on the e

12

13

14

streamwise spacing À

Influence of the driving temperature ratio T -T /T _{r w w} on the streamwise spacing À

Influence of the driving temperature ratio T -T /T r w w on the streamwise spacing À

Run time required for a developed cross-hatched pattern as a function of the local statie pressure p

e

15 Run time required for a developed cross-hatched. pattern as a function of the driving temperature ratio

T -T /T r w w

16 Run time required for a developed cross-hatched pattern depending on the streamwise spacing À

17

Propagation speed of the cross-hatched pattern V versus s

the driving temperature ratio

18 Stress-strain dependenee for a constant strain rate at different material temperatures

19 Stress-variation with time for constant strain at different material temperatures

.

20 Variation of the elasticity modulus with material temperature

21 Heat flux into the solid ablation material qs versus the driving temperature ratio

22 Temperature distribution in the solid wax at different driving temperature ratios T -T _{r w w}

IT

23 Run time up to the melting temperature of wax versus the driving temperature ratio

24 Mass transfer rate mxH

Iq

on wax models as a function 1 w

of the run time t-tl/tl

25 qil film surface patterns on the wall ~n the expansion region of a Mach 3.5 nozzle

26 Camphor eintering apparatus 27 Sintered camphor models

28 Equilibrium phase diagram for camphor

29 Surface temperature of campher models depending on the statie pressure Pe and the total temperature TST-in the presence of a turbulent boundary layer

A B B Bt c c p c v E e p Pv

•

q Re St St 0 T T t t I t3 u

v

s x - ~v LIST OF SYMBOLS

Factor defined ~n eq. D3 Factor defined in eq. D3

Mass addition parameter eq. C2 Mass addition parameter equ.C3

Specific heat of asolid

Specific heat of a gas at constant pressure Mass fraction of injected gas in air

Elasticity modulus Strain

Shear modulus Heat of fusion

Heat of sublimation

Heat conductivity coefficient Mach number

Molecular weight Mass flux

Pressure

Partial pressure of injected gas Heat flux

Reynolds number Stanton number

Stanton number ~n the absence of gas injection Temperature

Relaxation time of the viscous solid Time

Run time up to liquefaction temperature of wax Run time required for a developed cross-hatched

pattern Gas velocity

Velocity of rooving pattern Coordinate in solid

a a

a

a

v p a w e i m r 5 ST w 00 Angle of attack

Factor defined in equ.D3 Factor defined ~n equ. D3 Factor defined in equ. c8

Total cone angle Total flare angle

Streamwise sp~cing of the cross-hatched pattern Viscosity

Poisson coefficient Densi ty

Normal stress

Initial normal stress

Tangential stress or shear stress

Cant angle of the cross-hatched pattern

Exponent in the viscosity-temperature law. equ. D3

Subscript s

Conditions at the outer edge of the boundary layer Conditions at the interface gas-liquid or gas-solid Melting conditions

Recovery conditions

Conàitions in the solid ablation material Stagnation conditions

Wall conditions

1. INTRODUCTION

The high enthalpy environment of re-entry vehicles at hypersonic speeds and the associated high heating rates re-quire the development of methods to prevent damage to the vehicle structure. Three possible types of techniques are the heat sink, forced mass transfer (transpiration cooling) and self-regulating mass transfer systerns (ablation) 1

Among these, ablation has proven to be an effective method of thermal protection for both short and long duration re-entry trajectories.

It has been observed on recovered re-entry vehicles, that the ablation mass transfer rates we re not uniform and that rather regular patterns were scorched into the surface. Similar phenomena were seen in the course of wind tunnel tests on low temperature ablation models. These surface patterns can be classified in th ree different types: streamwise grooves, tur-bulent wedges and cross-hatching, Fig. 1.

Streamwise grooves 2-5 are believed to be created by streamwise vortices situated in the boundary layer which

lo~ally increase heat and mass transfer rates. The vortices have been shown to exist in supersonic laminar, transitional and turbulent reattaching boundary layers 6, for instanee

downstream of backward facing steps and also on concave surfaces. In wind tunnel tests, ~ckward facing steps naturally develop by ablation just downstream of a non-ablating nose, Fig. 1, and concave surfaces are formed in the transition region due to increased mass transfer rates.

Turbulent wedges have been investigated in Refs.

7, 8, 9

and 10. In these experiments local areas of turbulent

boundary layer flow, in which turbulence is triggered by sur-face roughnesses, are imbedded into a laminar boundary layer. The lateral spreading of turbulence produces wedge-shaped

- 2

-regions. in which the mass transfer rates are increased.

The third type of surface pattern is cross-hatching. It consists of two families of nearly straight grooves of regu-lar spacing. running obliquely to the flow direction outside the boundary layer. producing a highly ordered pattern. Examples of cross-hatched patterns on recovered re-entry vehicles are shown in Fig. 2.

The important cross-hatching pattern parameters are: the cant angle .; the half angle between a left and right

running groove,

the streamwise spacing or wavelength À, equal to the streamwise length of a c e l l o f the pattern.

The interest ~n the study of surface patterns, and especially in cross-hatching, is partly due to the fact that such ablation surface roughnesses may create a rolling moment and thus affect the stability of slender re-entry bodies. There-fore, the pro~lem of how to avoid thie ablation pattern has to be solved and consequently efforts we re made to understand the physical mechanism which creates cross-hatching.

2. EXPERIMENTAL TECHNIQUE

2.1 Test facility

The present tests were carried out in the hyper-sonic blowdown facility H-l at the von Karman Institute. The two-dimensional contoured nozzle provides a uniform flow at a Mach number of 5.3 in a test section of 14 cm x 14 cm. The tunnel stagnation conditions are :

T_ST

=

385 - 6000 K Kgf PST

=

12 - 33

cm 2

giving unit free-stream Reynolds numbers of

0.85 - 7.0 x 107 l/m

2.2 Models

Cones of 100 _{to 62}0 _{total vertex angle, and 10}0

cones with 120 _{to 40}0 _{total angle flares were tested at zero}

angle of attack. The dimensions of the models are g1ven in Table 1. In most of the tests, steel noses we re used to avoid apex deformation by ablation. In a few cases, cones entirely made of ablation material, weretested to study nose blunting effects on the cross-hatching phenomenon.

2.3 Ablation materials

Two ablation materials were tested, natural wax without seedings, which liquefied under the test conditions without vaporizing, and camphor, a purely subliming material. The apparatus and technique used to manufacture camphor models are described in Appendix A. The product ion of wax models is straight for~ard. The thermal and mechanical properties of the ablation materials are given in Table 2. The description of how

4

-the measurements of -the mechanical properties were done is given in Appendix B.

3.

TEST RESULTS AND DISCUSSION

The test programme on cross-hatching at the von Karman Institute consisted of two main parts. In the first part, wax models were tested to investigate the main para-meters influencing the development of cross-hatching 11, In the second part, camphor modeIs, Fig. 3, were studied under a few typical test conditions to compare with the wax results. The findings ar'e discussed in this technicéó.l note.

3.1

Necessary conditions for the existence of cross-hatching

It is now well accepted that the boundary layer flow must be supersonic to obtain cross-hatching. Larson and Mateer 2 stated this requirement for the first time. Figure

4

demonstrates this condition very clearly. Cones of different apex angles have been tested in a Mach

7.4

flow and it can be seen that cross-hatching was formed only as long as the cone Mach number was greater than one.

Although no sy.tematic experimental evidence was available, it has been stated in the literature 2,3 that cross-hatching has never been observed in regions where the boundary layer was laminar. This condition was carefully tested and analyzed in the present study.

In Figure

5,

the Reynolds n~mber Rex' where x is the distance rrom the apex or cones to the loc at ion at which the cross-hatched pattern started, has been plotted against the Mach number at the outer edge or the boundary layer. Figure

5

also shows the transition Reynolds number ror smooth

cones. The latter was selected rrom the literature ror wall to recovery temperature ratios similar to those in the present study. Furthermore, the unit rree stream Reynolds numbers Re

e and the wind tunnel test section sizes, ror which the transi-tion data we re obtained, are such that comparison can be made, taking into a~count that the transition Reynolds number in-creases with Re and decreases with the test section size 12

e

Figure

5

demonstrates that the boundary layer is at least transitional in the reg10n where the cross-hatched pattern starts ~b develop.

An additional result which relates the onset or cross-hatching with boundary layer transition is given in Fig.

6

which is a shadowgraph of the flow on a cone which has a steel nose and an ablative arterbody. The photograph was taken pr10r to ablation. The arrows in Fig.

6

indicate the location at which the cross-hatched pattern started later during that run. It can be seen that transition occurs close to this location.

Another example is g1ven in Fig. 1. The photograph _

in the middle shows turbulent wedges on a self-blunting cone. Cross-hatching appears only inside the turbulent wedges and not outside where the boundary layer is still laminar.

3.2 Cross-hatching pattern parameters

From experimental observations. correlations have been established between the pattern parameters, i.e., the

streamwise spacing À and the cant angle ~. and rlow rield con-ditions. The qualitative dependence or À on ablation material properties is shown. The cant angle and the streamwise spacing have been measured on photographs or the models taken arter the runs.

6

-The cant angle , is plotted versus the local Mach number M in Fig.

7

and compared with the Mach angle (solid

e

line). Available wind tunnel data and free flight data 3 are shown for comparison. As seen, the present .results follow the Mach angle trend in the Mach number range 2.5-5.0 for both types of ablation materials. On the other hand, the flight data of Ref. 3 do not correlate with the Mach angle law. An explanation has been suggested on Ref.

16

that the cone Mach number at the location, where the cant angle ~ was measured, was rather indeterminate due to nose blunting occuring in free flight tests. This is demonstrated in Fig. 8 which shows the cant angle , measured on self-blunting cones plotted against the Mach number M calculated for sharp nose cones and compared

e

with present data from Fig. 7 and free flight data 3. (Details of the blunted cone data are given in Table

3).

An approximate method 17 has been used to calQulate the Mach number distribution on self-blunting cones. Figure

9

shows the cant angle ~ plotted versus the Mach number Me calcu-lated either for sharp nose cones or with the method of Ref.

17.

As may be seen, the data for wax and camphor based on the true local Mach number lie below the Mach angle lin~solid curve) instead of above as in Fig.

7.

This difference may be due to the two following facts. First, the method of Ref.

17

is valid for laminar boundary layers whilst the measurements are made in a reg ion where the boundary layer flow is turbulent - see Chapter

3.1.2.

Secondly, which is of larger importance, M is

e astrong function of the radius R of the nose 17(M decreases

e

with R). The nose radius increases with the run time 50 that its value is not exactly known at the very moment when cross-hatching is formed. ThUs M is underestimated, since the calculations are

e

based on a nose radius which was measured af ter a run time t 3 , when the pattern is fully developed. Figure

9

also shows that the camphor test results differ even more from the Mach angle law than the wax data, which may be explained by the fact that

the R-run time dependenee is different for each ablation material.

The cant angle , is seen to depend uniquely on the local Mach number. It was found that unit free stream Reynolds number, Re~, the Reynolds number based on conditions at the outer edge of the boundary layer, Re , the statie pressure. p ,

e e

the driving temperature ratio, (T -T )/T ~ the run time, the r w w

ablation mode1 and the material properties had no influence. The recovery temperature T was calculated by assuming a

tur-r

bulent recovery factor of 0.895. The influence on the recovery temperature of the liquid film which exists in the tests with wax and the effect of mass injection due to sublimation in the camphor tests was neglected. The wall temperature, T_w

=

337°K, is the temperature at which wax liquefies independently of Pee For the camphor tests T_w is dependent on Pet the heat transfer rate and thereby the ma6S transfer. In Appendix C. a method is described to calculate T for subliming materials in the presence

w

of a turbulent boundary layer. The results were used to corre-late the camphor test data.

The effect of the surface pressure Pe on À ~s shown in Fig. 10. The results agree quite weIl with those of Williams 4 • extending the range to lower statie pressures and greater values of À. The surface pressure p waS varied both by changing the

e

cone or flare angle and by occasionnaly altering the tunnel stagnation preS6ure. Figure 11 demonstrates that nose blunting has no influence on À contrary to its effect on the cant angle

~. The statie pressure p approaches rapidly (close to the

e

junction sphere-cone) the sharp cone value as opposed to the slow trend of the Mach number M •

e

The effect of the driving temperature ratio

(T -T )/T on the streamwise spacing is shown in Fig. 12 for r w w

constant values of p • À is strongly dependent on (T -T )/T

e r w w

8

-with the driving temperature. An obvious physical explanation for the different behaviour of wax and camphor is given in chapter 3.4. Figure 13 shows photographs of camphor models tested at d~fferent values of (T -T )/T • _{r w w}

Re , and e

The Mach number, M , the Reynol_e ds numbers, Re and

~

the run time did not appear to have any influence on ~, when the statie pressure pand the d~iving temperature ratio

e

were held constant. No influence of nose blunting on ~ could be observed. The body size does not seem to be a sealing factor for ~. Indeed, Williams 4 used camphor models which we re three times larger than those tested at VKI and no difference in ~ ~ould be seen, Fig. 10.

3.3 Run time

During a run on an ablating model, several distinct time intervals can be defined corresponding to different stages in the development of the cross-hatched pattern:

lst time interval: to ~ _{t l}

From tunnel start until the model surface reaches the liquefac-tion or sublimaliquefac-tion temperature and starts to ablate.

2nd time interval: tl ~ t ₂

From the onset of ablation until cross-hatching starts to appear. 3rd time interval: t ₂ ~ t ₃

From the first visible evidence of cross-hatching until the surface pattern is fu~ly developed, showing the maximum height difference between the bottom of the grooves a~d the enclosed hills.

4th time interval: t _{3 ~}

Af ter being fully developed, the pattern starts to desintegrate showing a regmaglypt pattern resembling those on meteorites shown in Ref. 2.

It was found that the run time t3 for both camphor and wax models was dependent on the local statie pressure p ,

e Fig. 14. t3 decreased with increasing statie pressure Pe and was roughly twice as long for camphor than for wax models for the same p • In Figure 15, t3 is shown as a function of the

e

driving temperature ratio (T -T )/T _{for constant p • t 3}

in-r w w e

creases nearly linearly with (T -T )/T for wax, whilst for r w w

camphor t3 remains constant.

Figure 16 is a cross-plot of Figs. 10, 12, 14, 15 showing the streamwise spacing À as a function of t3 for both camphor and wax tests. As may be seen, t3 increases nearly proportionally to À at a rate which depends upon the type of material. Included are wax results obtained for constant p a n d

e

different driving temperature ratios and those obtained at a low constant driving temperature ratio and varying Pet Fig. 10. Thus, t 3 is a unique function of the streamwise spacing À. in-dependent of Re • Re and M •

00 e e

Further results obtained on bi-conic models tested at different local statie pressures p a n d consequently with

e

variable run time t3. Fig. 14, are reported in Refs. 11 and 18.

In the course of a few runs with wax and camphor cones of same apex angles. tested at the same statie pressure Pe but at different driving temperature ratios, a c~ne film was taken during the complete testing periode This showed that

the whole cross-hatched pattern moved very slowly downstream. Furthermore, i t was verified that the velocity of propagation was a function of the driving temperature. The result is shown

in Fig. 17 which indicates that this velocity decreases nearly linearly with (T -T ) /T •

r w w

3.4 Comparison between wax and camphor test results

The same value of the cant angle • was observed on wax and camphor models, depending uniquely on the local Mach

number M •

e

10

-The streamwise spacing À for both materials is

in-versely proportional to the statie pressure p • The data for _e

wax and camphor tests can be superposed if the driving tempe-rature for runs on wax models is chosen to be

T -T

r

w

T _w

The run time t3 varies in ~nverse proportion to

the statie pressure Pe for both materiaIs. The fact that for

camphor tests t 3 is about twice as large 1S probably due to

differences in material properties which in turn affect the

cross-hatching formation process. t 3 increases linearly with

(T -T )/T for wax models and stays constant for camphor.

r w w

For both materiaIs, t3 is a unique function of the streamwise

spacing À, increasing proportionally with À.

The results obtained for wax and camphor models were similar in every respect but one. It was found that in the wax tests, at a constant cone pressure, the streamwise

spacing À was strongly influenced by the driving temperature

ratio, contrary to the results on camphor modeIs. It was there-fore decided to investigate the possible effect of the different material properties on the physical mechanism which produced

this phenomenon.

3.5

Influence of the viscosity of the solid

ablation m&tè~ial on the streamwise spacing À

On wax modeIs, keeping all conditions constant, it

was shown that À increased fr om 5-20 mm for only small changes

in the stagnation temperature (600_{K), Figure 12. On the other}

hand, a change in stagnation temperature of 1200_{K for the}

~ The cross-hatching phenomenon resu1ts from an interaction between the boundary 1ayer and the solid ab1ation material. It is reasonab1e to assume that the boundary layer is not significantly modified by the small changes in the stag-nation temperature. Consequently, it was deduced that there must be a difference in the behaviour of some material property

sensitive to amall changes in heat transfer rate, i.e., tempe-rature. The physical property of wax which is very sensitive to a small temperature change is the viscosity of the solid wax

E

~

=

G.T

=

~ T

It is shown in Appendix B that both materials, wax and camphor, are visco-elastic solids. The determination of the elasticity modulus E and the relaxation time T for both wax and camphor, are described in Appendix B, the results are given in Figs. 18, 19 and 20. Figure 20 shows that E decreases drastically from

wax

150 to 2 Kg_f /cm2 _{during a temperature rise of 295 to 323°K,} which corresponds to the expected temperature variation of the

solid wax during a test (293°K is the initial temperature before the test and 337°K is the liquefaction temperature of wax). In the same range of material temperature, E h changes only

camp or

slightly (293°K initial temperature, 344°K maximum wall tempe-rature).

On the other hand, it ~s shown in Fig. 19 that the relaxation time T decreases considerably with temperature for wax but not for camphor, hence the viscosity of the wax ohly,

see equ. B7, is a highly dependent function of the temperature.

It has to be demonstrated now that the streamwise

spac~ng À varies with the viscosity of the solid wax, based on the informatiQn of Figs. 12, 19 and 20. To do so, it is suffi-cient to proove that the temperature of the ablation material underneath the liquid-so1id interface, changes with the heat transfer rate. In Appendix D,a method ia given to ca1culate the heat flux to, and the temperature distribution in the solid

- 12

-material for the steady state ablation case. (Steady state ablation is defined for a constant beat flux if the ablation mass transfer is constant, thus prodqcing a recession of the surface at constant speed. In this case, tbe temperature pro-file inside the solid stays constant with respect to the

receding surface). The results for the actual tests are shown

~n Figs. 21 and 22. As may be seen from Fig. 21, the heat flux to the solid rises linearly with the driving temperature for both materials. Figure 22 shows the temperature distribution in tbe solid wax; the liquid/solid interface is at x

=

O. As the material close to the interface gets colder for increasing

(T -T )/T , the viscosity of the solid wax increases rapidly. r w w

Figs. 19 and 20. For the lowest abd highest value of (T -T )/T _{r w w} of the actual tests, there is a temperature difference of 15°K in a depth of only .5 mmo

In Appendix D i t is shown that steady state ablation conditions exist when the pattern starts to be formed. Figure 23 shows the time tI. which is necessary to reach the liquefac-tion temperature of wax, plotted against the driving tempera-ture ratio of the actual tests. tI has a maximum value of about 0.3 secon~s. Figure 24 shows the mass transfer rate for wax as a function of the run time. It can be seen that for run times larger than 10 tI the mass transfer stays constant and the

steady ablation condition is achieved. It can be concluded that for wax the cross-hatched pattern was formed under steady state conditions, as the maximum t} ~s 0.3 seconds and the minimum run time t ₃ ~s about 10 seconds.

It is thus experimentally shown that the streamwise spacing À decreases if the viscosity of the affected layer of

the solid material gets smaller.

Knowing this i t ~s easy to understand the results of

Fig~l!,wbich shows a decrease ofthe,'doVnstream propagation speed of the cross-hatched pattern when the driving temperature ratio

transmitted from the gas V1a a constant velocity gradient liquid film, does not change significantly with (T -T )/T • Hence, the _{r w w} difference in the propagation velocity V comes from the change

s

in the viscosity of the solid. It was shown that E and Tand thereby ~ increase with increasing driving temperature ratio, thus V should decrease as shown in Fig. 17.

s

Probstein and Gold 19 proposed a model for the triggering mechanism for cross-hatc4ing which is based on an interaction between the shear stress fluctuations in a turbulent boundary layer at the wall and a viscous deformable body. The behaviour of a viscous solid is described by its relaxation time and shear orelasticity modulus. The experiment al findings thus support the hypothesis used in the calculations of Refs. 19, 20 and 21. Furthermore, no ablative mass transfer is

neces-sary in this model for the formation of cross-hatching. This is supported by some experimental results which are shown in Fig. 25. In this case, the cross-hatched pattern is produced

on the surface of an oil film containing magnes1um oxide spreading out under the effect of friction on a glass-window in the

expansion part of a supersonic nozzle. The vapour pressure of the highly viseous oil was weIl below the statie pressure level in the tunnel, and therefore there was no ablation mass trans-fer. A close inspection of the pattern shows all the features of conventionally obtained cross-hatching. The streamwise

spaeing À inereases and the cant angle ~ decreases in the flow direetion as the statie pressure falls and the Mach number rises.

14

-4.

CONCLUSIONS

1. It is shown that a necessary condition for the existence of cross-hatching is that the boundary layer should be transitional or turbulent.

2. The cant angle ~ 1S a unique function of the local Mach

number outside the boundary layer and is nearly equal to the local Mach angle even on self-blunting cones for both sUbliming and liquefying ablation materials.

3.

The streamwise spacing À is inversely proportional to the local static pressure p for both materials. À increases with

e

the driving temperature ratio (T -T )/T _{r w w} for wax and stays nearly constant for camphor.

4.

The streamwise spacing À increases as the viscosity of the solid ablation material increases.

5.

The run time necessary to form the cross-hatching pattern t3 is inversely proportional to the local static pressure Pe for wax and camphor but in proportion to (T -T )/T _{r w w} for wax only.

6.

The time t3 depends uniquely on the streamwise spac1ng À for both materials and t3 increases with À.

7.

The cross-hatched pattern propagates slowly 1n the down-stream direct ion at a speed which increases as the viscosity

REFERENCES

1. SCALA, S.M.: The therma1 protection of a re-entry sate11ite. ARS J. Vol. 29, No 9, Sept. 1959, p. 670.

2. LARSON, H.K. and MATEER, G.G.: Cross-hatchi~g - A coup1ing of gas dynamics with the ablation process.

AIAA Paper No 68-170.

3. LAGANELLI, A.L. and NESTLER, D.E.: Surface ab1ation patterns: a phenomenology study.

AIAA Paper No 68-671.

4. WILLIAMS, E.P.: Experimenta1 studies of ablation surface patterns and resu1ting ro11 torques.

AIAA Paper No 69-180.

5. McDEVITT, J.B. and MELLENTHIN, J.A.: Upwash patterns on

ab1ating and non-ab1ating cones at hypersonic speeds. NASA TN D 5346, 1969.

6. GINOUX, J.J.: The existence of three-dimensiona1 perturba-tions in the reattachment of a two-dimensiona1 supersonic boundary 1ayer af ter separation. AGARD R 272, April 1960.

7. CANNING, T.N., TAUBER, M.E., WILKINS, M.E.: Order1y three-dimensiona1 processes in turbulent boundary 1ayers on ab1ating bodies.

AGARD CP 30 and supplement "Hypersonic boundary 1ayers and flow fie1ds", May 1968.

8. CANNING, T.N., WILKINS, M.E., TAUBER, M.E.: Ab1ation patterns on cones having 1aminar and turbulent f10ws.

AIAA J. Vol. 6, No 1, Jan. 1968, pp 174-175.

9. McDEVITT, J.B.: An exp10ratory study of the ro11 behaviour of ab1ating cones.

J. Spacecraft and Rockets, Vol. 8, No 2, Feb. 1971, pp 161-169.

10. WILKINS, M.E.: Evidence of surface waves and spreading of tu~bu1ence on ab1ating mode1s.

AIAA

J.,

Vol.

3,

No 10, Oct. 1965, pp 1963-65. 11. STOCK, H.W. and GINOUX, J.J.: Hypersonic 10w temperature

ab1ation - an experiment al study of cross-hatched surface patterns.

VKI TN

64,

Ju1y 1971.

1l. PATE, S.R.: Measurements and corre1ations of transition Reyno1ds numbers on sharp slender cones at high speeds.

16

-13. VAN DRIEST, E.R. and BOISON, J.C.: Experiments on boundary layer transition at supersonic speeds.

J.A.S. Vol. 24, No 12, Dec. 1957, pp 885-899.

14. VAN DRIEST, E.R. and BOIS0N, J.C.: Boundary layer stabili-zaVion by surface cooling in supersonic flow.

J.A.S. Vol. 22, No 1, Jan. 1955, p. 7~ •

15. POTTER, J.L. and WHITFIELD, J.D.: Boundary layer transition under hypersonic conditions.

AEDC TR 65-99, May 1965.

16. STOCK, H.W. and GINOUX, J.J.: Experimental results on cross-hatched ablation patterns.

AIAA J. Vol. 9, No 5, May 1971, pp 971-973.

17. STOCK, H.W.: An approximate method to calculate the Mach number distribution on spherically capped cones at

zero angle of attack in supersonic flow. To be published.

18. STOCK, H.W. and GINOUX, J.J.: Further experimental studies of croas-hatching.

AIAA J. Vol. 10, No

4,

April 1972, p. 557.

19. PROBSTEIN, R.F. and GOLD, H.: Cross-hatching - a rnaterial response phenornena.

AIAA J. Vol. 8, No 2, Feb. 1970, p. 364.

20. GOLD, H., PROBSTEIN, R.F., SCULLEN, R.: Inelastic deforma-tion and cross-hatching.

AIAA Paper No 70-768.

21. STOCK, H.W.: Role of the anelastic behaviour of the abla-tion material on cross-hatching.

AIAA J. Vol. 10, No 11, Nov. 1972, p. 1528.

22. CHARWAT, A.F.: Exploratory studies on the sublimation of slender carnphor and naphtalene rnodels 1n a

supersonic wind tunnel.

Rand Corp. RM 5506-ARPA, July 1968.

23. FREUDENTHAL, A.M.: The inelastic behaviour of engineering materials and structures.

J. Wiley and Sons, Inc., New York, 1950. 24. LEES, L.: Ablation in hypersonic flows.

Proceedings of the 7th Anglo-American Aeronautical Conference, p. 344,

Institute of Aeronautical Sciences, New York, 1959. 25. ADAMS, Mac C.: Recent advances in ablation.

26. LEES, L.: Convective heat transfer with mass addition and chemical reactions.

3rd Combustion and Propulsion COlloquium, AGARD, Italy, 1958, p. 451.

Pergamon Press, 1958.

27. VAN DRIEST, E.R.: Turbulent boundary layer in compressible fluids.

J.A.S. Vol. 18, No

3,

March 1951, p. 145.

28. VAN DRIEST, E.R.: Turbulent boundary layer on a cone ~n

a supersonic flow at zero angle of attack. J.A.S. Vol. 19, No I, Jan. 1952, p. ~5.

29. LANDAU, H.G.: Heat conduction in a melting solid.

Quarterly of Applied Mathematics, Vol. 8, No I, 1950, p. 81.

CONE DIMENSIONS :

STEEL NOSE

ABLATION MATERlAL

_.

s

0

°SASE

S

0 °BASE

S

0 °BASE

deg

mme mm"

deg

mm" mme

deg

mms mme'

10

20,45

80

24

30

80

42

20

70

12

32

80

26

33

80

46

20

60

14

32

80

28

35

80

50

20

60

16

32

80

30

38

80

54

20

50

..

_----18

32

80

34

20

70

58

22

50

20

26

80

38

20

70

62

22

50

22

28

80

40

18

70

CONE - FLARE DI MEN SlONS :

s

-

-

- -

-

-

-

- - 0

-

-°BASE STEEL NOSE ABLATION MATERlAL S

=

100

o

=

45

mme

0BASE

=

80

m

m-Sx

=

12-40

0 IN STEPS OF

2

0

THERMAL PROPERTIES OF THE ABLATION MATERlALS

WAX:

Melt ing temperature T

₌

337 oK

Latent heat of fusion _H,q,

₌

35.0 kcal/kg m Specific heat (solid) c

₌

0.7 kcal/kg oK

m Heat conductivity (solid) k

₌

5.78xlO-S kcal/msoK Thermal diffusivity ( solid) a

₌

8.99xlO-8 _m2_/s

Density ( solid) p

=

0.919xl03 kg /m_m 3

CAMPHOR:

Molecular weight M

₌

152.2 kg /kmol m Lat ent heat of sublimaiion H

₌

58.5 kcal/kgm

s

Specific heat (solid) c

₌

0.445 kcal/ksmoK Heat conductivity ( solid) k

₌

9.6xlO-S kcal/msoK Thermal diffusivity (solid) a

₌

2.18xlO-7 _m2_/s

Density (solid) p = 0.99xl03 kg / m3 m

Specific heat (liquid) c

=

0.44 kcal/kg oK m Specific heat (gas) c

=

0.283 kcal/kg oK

p m

MECHANICAL PROPERTIES OF THE ABLATION MATERlALS AND MEASUREMENT DETAILS

Compression apparatus

Constant compression speed for all measurements

Height of the cylindrical test piece Radius of the cylindrical test p~ece

Material temperature

Maximum compression force Elasticity modulus Instron -TT-CM V

=

0.1 cm/min h (cm) R _(cm) T (OK) F _(kgf) E (kg_f /cm2 )

TABLE 2 (cont'd) WAX T h R F E 395. 5.5 3.5 14.4 145. 403. 2.2 3.5 12.0 35. 413. 2.2 3.5 6.0 15. 423. 3.7 3.3 1.6 2. CAMPHOR T h R F E 395. 20.8 4.0 14.4 156. 403. 5.1 4.0 10.0 145. 413. 5.1 4.0 11.2 135. 423. 5.2 4.0 10.0 131.

SELF - BlUNTED CONES:

DIMENSIONS AND CROSS- HATCHING DATA

ABLATION MATERlAL

Me : MAC H- NUMBER AT THE OUTER EDGE OF THE BOUNDARY LAYER CALCULATED FOR POINTED NOSE CONES

e

Me ~ R L D_BASE deg

_-

deg

mm

mm

mm~ 20 4.5 19.5 3.8 180 80 -- -- -_ ...

_-

- . - . -.. , -26 4.2 20.5 4.0 150 80 WAX . - - f--- -.. 32 3.9 20.5,21.5 3.3 120 70 - -38 3.6 21.5 ,22.0 2.5 85 70 --- -_._ - -46 3.2 23D 2.5 60 60 26 4.2 19.5 5.0 90 80

-30 4.0 21.0 5.0 130 80 -- -CAMP HOR 32 3.9 21.0 5.3

~

70

-_.-38

3.6

21.5 5.0 80 70 --- --_._--- - - - --~--_. 44 3.3 223,23.5 4.0 50 i 60

CAMPHOR {WITH STEEL NOSE} CAMPHOR (WITHOUT STEEL NOSE) WAX (WITH STEEL NOSE) M(X) = 5.3

Lm

Mw = 5.3

Lcm

Mw = 5.3 1S1

=

493 oK i_S1

=

417 oK . TST

=

405 oK

Ilcm

PST = 30.0 kg_f

/cm

2 PST

=

30.0 k9_f

/cm

2 PST

=

291 k9f

/cm

2

t

=

35

sec

t = 29

sec

t =15

sec

IX

=

_0° (ANGLEOF ATTACK) IX

=

0° (ANGLE OF ATTACK) IX

=

·0° (ANGLE Of ATTACK)

e

=

26° (TOTAL CONE ANGLE)

e

=

38° (TOT AL CONE ANGLE)

e

=

26° (TOTAL CONE ANGLE)

-FLOW DIRECTION

PHENOLIC REFRASIL (FROM REF.3)

fIG.2.

CROSS- HATCHJNG ON RECQVEREO ENTRY

VEHICLES

TST

=

523 PST:: 33.1) t- :: 32 oe :: 00

e ::

10°

ex

=

240

I

tcm sec (ANGLE OF ATTACK) (TOTAL CONE ANGLE)

nOTAL .FLARE ANGLE)

T

_{ST :: 406} PST

=

30.0 t .. 20 a::

=

0°

e ::

34° sec (ANGLE OF ATTACK) (TOTAL CONE ANGLE)

e ::

100° (TOTAL CONE ANGLE) Me :: 1.3 (CONE MACH NUMBt:R.)

Ma) :: 7.4 TST :: 1100 PST:: 109

ex:

::

0°

FIG.4.

OK

k9_f/cm 2 (ANGLE OF A TT ACK)

ABLATION

SURFACE

OF VARIOUS ANGLES

e :::

110° (TOTAL CONE ANGLE)

Me :: Q9 (CONE MACH NUMBER)

PATTERNS ON LUCITE CONES

(FROM

REF. 2)

•

•

Re e-1O-7

(l/m)

1.97 - 2.64

3

.

6

lOri

_Tw/T

r

1.0

1.0

TUNNEL SIZE(cm-cm) 30.5 - 30.5

8.9 - 8.9

•

5

.

3

0.86

30.5- 30.5

•

l06 - 1.77

lO

30.5- 30.5

•

2.16 - 2.74

1.0

_o

REF

13

14

15

12

100. - 100.

12

I

I

0

8

I

o·A

~

I

o

A

IJl

~~~-+---I

I ---'L---(;)

Rex

_-6

_•

_~

______

~

-10 6

I

•

(>

~00

o·

o

IJl

•

o

VKI-WAX (CONE)

A

VKI-CAMPHOR (CONE)

Tw/Tr =0.89-0.97

Tw/Tr

=

0

.

86-0.94

Ree

=

4.67 - 7.15 - 107 (1

I

m )

2

I à

o

I

I

TUNNEL SlfE: l4.

aI4

.

lcmacml

2.5

3.0

3.5

4.0

4.5

5.0

Me

FIG.5

lOCAL REYNOLDS NUMBER EVALUATED AT THE POSITION OF TRANSITION AND OF THE

PST

=

30.0

a;

=

0°

e

=

26°

k9 f

/cm

2

(ANGLE OF ATTACK)

(TOTAL CONE ANGLE)

ARROW MARKS THE LOCATION WHERE THE

CROSS-HATCHED PATTERN STARTS

FIG.6.

SHADOWGRAPH OF A WAX CONE (WITH

STEEL NOSE) PRIOR TO ABLATION

50

Cf;

'rt'

u-

\

(dog) 0 0 I

40

I I'\.

30

1 ~ d

d'

AMES - CAMP HOR

\}

MALTA -CARBON PHENOLIC

V

MALTA-CARBON PHENOllC,cu = 6000 rpm

o

MALTA- PHENOLIC NYLON

d

MALTA- PHENOLIC

NYLON,CJ> = 2000 rpm

6

LANGLEY-WOOD (CONE)

6

LANGLEY -WOOD (WEDGE)

o

LANGLEY - TEFLON (CONE)

c:J

LANGLEY- TEFLON (WEDGE)

o

LANGLEY-LEXAN (WEDGE)

20

I

~

~-L-h

PRESENT DATA

:

o

VKI-WAX (CONE)

6.

VKI-WAX (CONE -FLARE,lO° FORECONE)

10

I

en

VKI-CAMPHOR (CO NE)

~---I----

-~--Moo

=

5

.

3

ex:

=

0° (ANGLE OF ATTACK)

SCATTER

!

2°

o '

!

lO

2.0

3.0

4.0

Me

5.0

91

(deg)

20

I ~ ... ' I " -...

10

FliGHT DATA REF

.

3

PRESENT DATA:

VKI-WAX (CONE)

o

POINTED STEEL NOSE

VKI-WAX ( CONE)

d

NOSE BLUNTING BY ABLATION

8. VKI- CAMPHOR ( CONE)

POINTE D STEEL NOSE

Á

VKI- CAMPHOR (CONE)

NOSE BLUNTING BY ABLATION

Mei)

=

5.3

a:

=

0° (ANGLE OF ATTACK)

8.

QO

0:

0

0

o '"

I I

2.0

3.0

4.0

5.0

SCATTER

±

2°

Me

FIG.8.

'

INFLUENCE OF THE MACH NUMBER Me ON THE CANT ANGLE

r/J

rIJ

(deg)

_--

6-6.

o

IJ::.

20

- I - - +

-IJ::.

it'd~

~

.

CD

~_

Ó

6- 6-

6.

Ä

VKI-WAX (CONE)

o

Me CALCULA1ED FOR UNBLUN1ED CONES

d

Me CALCULA1ED FOR BLUNl CONES (REF.1?)

10

H

VKI-CAMPHOR (CONE)

Cl Me CALCULA1ED FOR UNBLUNTED CONES

Á

Me CALCULA1ED FOR BLUNl CONES (REF.l?)

Mco

=

5.3

ex:

=

00

(ANGLE OF AllACK)

SCATTER ~ 20

E1

MA

0

' .

:

---- ""

.

0

I

.

I

~

. -1 1

I •

sm

Me

0~1'~========~==============~---~---~

4.0

Me

2D

3.0

FIG.9. INFLUENCE OF THE MACH NUMBER Me ON THE CANT ANGLE

0

FOR SELF-BLUNTED CONES

25

À

(mm)

20

15

10

5

00

00

FIG.l0.

Me~

Mro :: 6.0 TST :: 530 oK 0

I

ex;

=

00 (ANGLE OF ATTACK)

[1

PRESENT DATA: SCATTER !

lOOf.

I

I

cë _{0 VKI-WAX (CONE)}

B

_ó.

_{VKI-WAX (CONE -FLARE, 10}0 _FORECONE) 8. ₀

I

T51

=

393 -411 OK

-g_0

._-- - - - ---- _{lr -lwlTw}

=

_{0.0989 - 0.1278}

al

l

0

_I

T

w

=

337 OK

~ao

CD VKI-CAMPHOR (CONE)

I

I?

8. _T5T :: 397 -446 OK I _i

al

0 Tr - Tw/lw

=

0.0988- 0.2095 ~

Hl

B

MQ) :: 5.3

I

B 0 0 <:)

_ex:

:: 00 (ANGLE OF ATTACK)

C!l

'6.

I B eI] _eI] C!l

~

---

---r

·----I 1 I • CD B

0m

I

I

CD 0 C!:J i CD

a

I

I

I

0.1

0.2

0.3

0.4

0.5

0 6

Pe(k9f/cm

2) .

INFLUENCE OF THE LOCAL STATIC PRESSURE

Pe

ON THE

(;) 20J~ --- ----~---~ (mm)

A

I

d.

I

9

~

0

15

1 - 1 - - - -

-A

I

A 0

Mell

I

1]

---+---I

!

I

I

5

1 - - 1 -I

J

0.1

00

<c?t

A

ä

VKI-WAX (CONE)

r

-l

ct

NOSE BLUNTING BY ABLATION

--- -

---+--A

i

A

i

!

I

I

0.2

I

0

₀

_I

0

Á~é

IJ:Á

A

0

---

-

1

I I

0.3

P e

(k 9

f

Ic

m

2 )

À

(mm)

15

10

5

o

Men

0

e---[i

0

- . _. -.

I

I 0

I

A _A 0 i

_A

A

o

VKI- WAX (CONE)

A _T5T

₌

_{388 - 449}

oK

A

6

T

_w

=

337

oK

A VKI- CAMPHOR (CONE)

I TST

=

396 - 510

oK I I 0 !

_

.

__

._

... _--

...

+

....

__

..

__

._

.

__

.

.

_-

_Mco

₌

₅

_.

₃

Pe

=

0.134

k9f/cm 2 ,

a:

=

0°

(ANGlE OF ATTACK)

i

8

=

26°

OOTAl CONE ANGlE)

I

I

SCATTER !

10

°l.

o

0.1

0.2

0.3

0.4

lr - lw/lw

FIG.12.

INFLUENCE OF lHE DRIVING lEMPERAlURE RAllO

SIOE VIEW

Ac:o

PST tIC

e

t =41 sec TST " 396 OK " "

..

" 5.3 30.0 0° 26° k9_f/cm 2 (ANGLE OF 'ATTACK) (TOTAL CONE ANGLE)

= 38 sec TST " 448 oK t 40 sec TST = 460 oK

I

lcm CAMPHOR MODELS ~. -..o:'"'--"'<'?"" .

}'>~::':f:-FlG.13.

JN.F=L~ENCE

OF

lHE DRIVING

TEMPERAlURE RATIO

lr - lw/lw

ON

:

fHE

STREAMWISE SPACING )..

t = 36 sec

100

t3

(sec)

80

60

1.0

20

o

TST

=

393 -411 oK

8

I

lr - lw/lw

=

0.0989 - 0.1278 I

I

lw

=

337 oK i

f---

-

-

-- --

r

-

--

-

-

-

--

----

-

8

VKI- CAMPHOR (CO NE)

8

_I

₁₅₁

₌

_397-446 oK I i lr-lw/lw

=

0.0988- 0.2095 oK I

i

-- - _{- - - + --------} -Mco

=

5.3 I

I

_i

_ex:

=

0° (ANGLE OF ATTACK)

i

8

i I i

00

~_.-

---

-+

--

--8

i I I I

0

_I

I

I

O

l

₈

8

~

8

-

0

-

-I

c:Ib

0

;

i I

8

8

8

1

I

0

o

0

I

I

0

1

8

ti

1

8

T

o

0.1

0.2

0.3

0.4

0.5

Pe

(k9f/cm 2 )

FIG.14. RUN llME REQUIRED FOR A DEVELOPED CROSS-HAlCHED PAllERN AS A FUNCTION OF lHE LOC AL SlAllC PRESSURE

Pe

t3

(sec)

30

20

10

f---

-00

0

8

8

I

8

I

i

---

---

L

I

I

; I , ! I !

₀

0

0 0

I

o

l

----i

--

---- --- -- --- --

. "-- ---

-I

I

I I i j

0.1

0.2

8

8

----._- _--

-o

VKI-WAX (CONE)

151

=

388-449

oK

Tw =

337

oK

~

VKI- CAMPHOR (CONE)

151 =

396-510

oK

Moo

=

5.3

Pe

=

0.134

k9

_f

/cm

2

ex

=

00

_{(ANGLE OF ATTACK)}

e

=

260

(T01AL CONE ANGLE)

I i

i

0.3

0.4

Tr-Tw/Tw

FIG

.

15.

RUN TIME REQUIRED FOR A DEVELOPED CROSS- HA1CHED PATTERN AS A FUNCTION

~ (mm)

d

_{lr -lwlTw : 0.0564- 02240} VK 1- CAMPHOR (CONE) ~ lr -lw 1 lw: 0.0988-02095

~

lr-lw/lw: 0.1078- 0.3603 -_·_·_- c --- - -

---

(:)

0

_Pe

_{: Q0486-0.5025 kg} f/cm 2 .

25

I

MQ) : 5.3

0

_{ex; : 0° (ANGlE OF ATTACK)}

d

. SCATTER :!: 10

oIo

8.

20

d

0

0d~

8.

00

~.Á

8.

d

<:>

~ïS

0

8.

15

10

5

90

8.

8. 8.

Me~

0

~

~

[}

20

40

60

80

00

t

3

(seC> FIG.16. RUN TIME REQUIRED FOR A DEVELOPED CROSS-HATCHED PATTERN DEPENDING ON THE

SlREAMWISE SPACING

>.

I

V

_s

[~e~]

2.5

2

.

0

1.5

1.0

0.5

---o

0.05

0

--

-

-_.-0.10

-.

_"-I

I

0 0 0 -0

---I

I

0.15

TST T

_w

₌

337 oK

8.

VKI- CAMPHOR (CONE)

TST

=

432 oK

M Q)

=

53

PST

=

30.0 k9_f

/cm

2

ex:

=

0° (ANGlE OF ATTACK)

e

=

26° (TOTAl CONE ANGlE)

0

6

-0.20

T

_r

_-Tw/Tw

FIG.17.

PROPAGATION SPEED OF THE CROSS-HATCHED PATTERN V

_s

0.4

r '

/ T r ,

-cr

•

(kgf/enf)

WAX

0.3

rl --~--J.-.~

O. 2

I

,

---+-01

• 1 ' i

'

t

"

'Ç

Y

:I 4

4-00

₅

₁₀

₁₅

₂₀

(-10 3

0.4 ,...,

---r----~-~---G

( kg

f

/em2)

0.3

I

I

--

-

'--

-

r

0

.

2

I I I !

0.1

I J I / / I I J Y I

00

₁

₂

₃

₄

₅

₆

( -103

FIG.18.

STRESS- STRAIN DEPENDENCE FOR A CONSTANT STRAIN RATE

AT DIFFERENT MATERlAL TEMPERATURES

0.9

I

___

_

_

I

I

L

I

I

JL

-

T

~t-

0.9

---

-

-

-_

-L

_

~

~

WAX

!

cr

0.8

.

I

Uo

I

CAMPHOR

- f

----

r

-

-

0.8

0.7

I \

,,'X...

+

__

~

295 0 K

\

~

_

-t

---

_29S

--

0

303

o

K

.7

-

--

/

_{/ /""}

/

₃₁₃

323

I

0.6

l - \

0

.

6

- --

;

---

-

-

t

-

-I

I

I

I

i I

---

----

~

-

--

r

---

r-0.5

I I '\. - T

0.5

I

0.4

I ...

0.4

o

10

30

40

t

(sec)

30

_t

{seC>

40

20

50

o

10

20

50

FIG.19.

STRESS VARIATION WITH TIME FOR CONSTANT STRAIN AT

E

I

4AMPHOR

100~1---~----

+---[

~]

_cm2

501

!~<

0'

x

290

300

310

320

T(OK)

FIG.20. VARIATION OF THE ELASTICITY MODULUS W I TH

MATERlAL TEMPERATURE

TST

=

388-449 oK

0.4

_'""""

T

w

=

337

oK

ê

VKI-CAMPHOR (CONE)

qs

TST

=

396 -510

oK

₀

Mco

=

5

.

3

A

PST

=

30.0

kg

_f/cm

2

-

ex:

=

0

0

(ANGlE OF ATTACK)

e

=

26

0

tTOTAL CONE ANGLE)

₀

8

0.3

r

kcal]

lm2 sec

I

₀

8

I

0

8

0.2

I I i

0

I

I

A

I

I

.

-t

e

.. 1-

..

8

I

-~

I

-I I 1

8

I

I I

i

I

I

I

L

_

- --- - - . _.

0.1

00

_0.1

_0.2

lr -lw/lw

0.3

-VKI-WAX (CONE)

~

.

TSl = 388 - 449 oK

330

I

\\'\\.~

._0 _____ .• _ ••• __ lw = 337 oK T(OK)

_I

\

\ '\.

'"

~

I

I _{M = 5.3}

I

(X) PST = 30.0 k9_f/cm2

320

I

_\\

"'~

I

··--

~

oc

=

_0°

(ANGlE OF ATTACK)

e

=

_26°

(TOlAl CONE ANGlE)

310

I " '" I / ~ ... "'" -... + - - -- - - - ----p I I

300

lr-lwlTw= 0056

00920

0.1722 0.2240 ! ! , !

5

290

0

1

2

3

4

x

(mml

FIG.22.

TEMPERATURE OISTRIBUTION IN THE SOllO WAX AT DIFFERENT

0.3

t,

(sec)

0.2

0,1.

o

0.05

FIG.23

--I

i

_o

VKI-WAX (CONE)

r-I

TST

=

388 -L.L.9 oK : ; T

_w

₌

337

oK

Mco

=

5.3

PST

=

30.0

k9f

/cm

2

ex:

₌

0°

(ANGLE OF ATTACK)

e

=

26°

(TOT AL CONE ANGLE)

r-0

!

I

I

0 0 0 0

-0.10

015

0.20

lr -lw/lw

RUN TIME UP TO THE MELTING TEMPERATURE OF WAX

VERSUS lHE DRIVING TEMPERATURE RATIO

ril-Hl

qw

0.4

- - -

-WAX

0.3

---+-- -

I

i

0.2

---0.1

--- _{- - -- ---}

---+

. .--

_.-

·----·---

-

r

00

₅

₁₀

₁₅

₂₀

t-tl /t l

FIG.24.

MASS TRANSFER RATE ril-Ht/qwON WAX MODELS AS A FUNCTION

..

INCREASI NG MACH NUMBER

DECREASING STATIe PRESSURE

I

lcm

FIG.25.

Oll FilM SURFACE

PATTERNS ON THE WAll IN THE

PISTON TO VACUUM PUMP STING HIGH PRESSURE D I L -ADAPTER

r