Hypersonic low temperature ablation: An experimental study of cross-hatched surface patterns

FOR FLUID DYNAMICS

TECHNICAL NOTE 64

:.

7

FE

B. 19

72

HYPERSONIC LOW TEMPERATURE ABLATION-AN EXPERIMENTAL STUDY OF _,

CROSS-HATCHED SURFACE PATTERNS

by Han& W. STOCK. and J.J • . GDIOUX RHODE-SAINT-GENESE, BELGIUM JULY 1971

x

TECHNICAL NOTE

64

HYPERSONIC LDW TEMPERATURE ABLATION-AN EXPERIMENTAL STUDY OF

CROSS-HATCHED SURFACE PATTERNS

by x Hans W. Stock arid J.J. Ginoux July 1971

This work was conducted by Hans W. Stock, Research Assistant at VKI, under the direct ion of Proressor Ginoux, and will constitute a part or his doctoral thesis.

ACKNOWLEDGEMENTS

Much credit is due to F. Thiry~ Tunnel Engineer, for his helpful suggestions and to J.C. Lobet, head of the photo-laboratory, for his patience and high quality work.

ABSTRACT

Cross-hatching has been studied experimentally at a free stream Mach number of

5.3,

using two different low temperature ablative materials, Camphor and wax, which respectively sublime and liquefy.

The surface pattern parameters (i.e. the cant angle ~ and the streamwise spacing ~) have been correlated with flow field properties, initial surface geometry and ablation material properties. The effect of the exposure time under ablation conditions has been studied intensively. The validity of some existing hypotheses on the origin of cross-hatching was examined experimentallY. The present results are compared with other available data.

A brief review of previous experimental and theoretical work on cross-hatching is included.

TABLE OF CONTENTS Acknowledgements Abstract Table of Contents List of Tables List of Figures List of Symbols 1. Introduction

1.1 Experimental work on cross-hatching

1.2 Theoretical work on cross-hatching

2. Experimental Technique 2.1 Test facility

2.2 Models

2.3 Ablation materials

3.

Results and Discussion

3.1 Flow field

3.2 Transitional or turbulent boundary layer at

the location of cross-hatching

3.3

Cross-hatching pattern parameters

3.31 Cant angle ~

3.32 Streamwise spacing À

3.4

Run time

3.5

Compression and expanS10n corners

3.6

Angle of attack

3.7

Initial surface perturbations

3.8

Some critical tests of cross-hatching

hypotheses

3.81

Perturbation visualization 3.82 Tobak's model

3.83

Hypothesis of Probstein and Gold

4.

Conclusions References Tables Figures i ii i i i iv iv vi

3

5

.. 8 8

8

8

9 9 9 10 1 1 12 13 1

4

1 5 16

18

18

18

19 20 22

LIST OF TABLES

2

Dimensions ofAxisymmetric models Data on self blunted-cones

LIST OF FIGURES 2 3

4

5

6

7 8 9 10 1 1 12 13 14

Hypersonic blow down facility H-l

Flow field properties on cones for M~

=

5.3

Dependenee on the Mach number M,' of the momentum e

thickness Reynolds number Reeevaluated at the

position of the start of the cross-hatched pattern:'

Typical test results on wax models

Influence of the local Mach number M,_e ~ on the cant angle ~

Influence of the Mach number M~ on the cant angle • -Me calculated for unblunted cones

Influence of the local statie pressure p~ _e on the streamwise spacing À

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

r W W

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

r W W

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

r W W

Influence of the run time on the cross-hatching development

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

Pe

Run time required for a developed cross-hatched pattern as a function of the driving temperature rat io T _{r W W} - T /T

Influence of flow compression on the cross-hatching formation

1 5 16 17 18 19 20 21 22 23

24

25

Influence of flow expans10n on the cross-hatching format ion

Influence of run time on the cross-hatching formation (flow expansion modeIs)

Influence of the angle of attack on the

cross-hatchi~g format ion

Comparison of the pattern inclination angle

~x

with the streamline inclination angle ~ of the

inviscid flow for cones at angle of attack on the

model side (~=900)

Influence of surface irregularities on the cross-hatching formation

Influence of a series of compression and expansion corners on ablation pattern formation

Schlieren-photos of the shock-Layer on an ablating cone

Visualisation of streamwise vortices by the sublimation technique

Influence of three-dimensional roughnesses on the cross-hatching formation

Influence of the backward facing step on the

cross-hatching format ion

Influence of the initial ablation material

LIST OF SYMBOLS d d h k L 1 1 M P Re T t a X 'Ir SUBSCRIPTS e r ST w IN CD Hole diameter Roughness diameter Step height Roughness height Length

Surface perturbation wavelength Spacing distance between holes Mach number Pressure Reynolds number Temperature Time Angle of attack

Spacing angle between roughness elements Boundary layer thickness

Compression or expansion angle

Streamwise spacing of the cross-hatched pattern Inviscid streamline inclination angle

Pattern inclination angle Total cone angle

Total fl4re. angle

Cant angl,~ __ of t he cro ss-ha t ched patt ern

Cone azimuthal angle, measured with respect to the most windward meridian

Conditions at the outer edge of the boundary layer Recovery condition

Stagnation condition Wall condition

Initial material condition Upstream infinity condition

re-entry or in rocket motors are such that effective thermal

protection techniques are required. Values of 100-10.000 BtU/ft 2

s

(0.113-11.3 KW/cm 2 ) are encountered in atmosphere re-entry

depending on trajectory and vehicle configuration1 •

Ablation has been found to be satisfactory for thermal protection in high heating conditions of fintte duration. The complex ablation phenomenon has been defined as "a self-regulating heat and mass transfer process in which incident thermal energy is expended by sacrificial loss of material"2.

Although the technological interest 1n ablation

phenomena is relatively new, the ablative aspect of meteorites and tektites has been studied for decades. In particular, surface

pattern s ·created by differential mass transfer rates during the ablation period of earth atmosphere penetration were investigated by Chapman and Larson 3 . They showed that ablation patterns

on tektites which exhibitedrin~wave flow ridges were simiiar to patterns observed in laboratory experiments on hypervelocity ablation. The regmaglypt pattern on some wind tunnel models resembIed the ablation surface structure on certain meteorites4.

The investigation on surface ablation patterns detected on recovered re-entry bodies of controlled initial shape and wind tunnel models is more recent. Three different kinds of patterns were distinguished, streamwise grooves, turbulent wedges and cross-hatching.

Streamwise grooves, which are believed to be created by streamwise vortices in the boundary layer leading to locally increased heat and mass transfer rates, have been treated in Refs.

4, 5. 6,

10. Streamwise vortices have been

shown to exist in supersonic laminar, transitional and turbulent reattaching boundary layers 11" for instance downstream of

backward facing steps and also on concave surfaces. In wind tunnel ablation tests, a backward facing step can be produced by ablatiQn behind a non-ablating nose, whilst the increased mass transfer at the location of transition creates a concave shaped surface .

Turbulent wedges have been investigated in

Re~s.

7-9,

12. Local areas of turbulent boundary layer flow, in which turbulence is triggered by surface roughnesses, are imbedded into a laminar boundary layer. The downstream

spreading of turbulence occurs within a wedge-shaped region, leading to increased mass transfer rates within this spatially limited flow ~iéld.

The third type of surface patterns is cross-hatching. It consists of nearly straight grooves of regular spacing, running obliquely to the external flow direct ion in both senses and crossing, thus producing a highly

ordered diamond shaped pattern.

The important cross-hatching pattern parameters are

1. The cant angle ~; the half angle between a left and right running groove;

2. The streamwise spacing or pattern wavelength À;

the streamwise length of a cellof the diamond shaped pattern;

3.

The height difference between the bottom of the grooves and the hills enclosed by the grooves.

The considerable interest in the study of surface patterns, and especiallY in cross-hatching, comes partly from the ~act that such ablation surface structures produce instabilities in the rolling moment of slender re-entry bodies. The vehicles start to oscillate or to spin up. Consequently, a part of the research activity is concentrated on the technological problem

of avoiding cross-hatching. Apart from this, the basic aspect of determining the physical mechanism which creates this

phenomenon has been studied experimentally and theoretically. Most of the experiments have been carried out with

non-realistie ablation materiaIs, so-called low-temperature ablators.

Canning et al13 gave perhaps the first insight into the cross-hatehed pattern phenomenon. They used 300 _half angle eones made of Delrin and Lexan in a ballistic range. Plexiglas models of a geometry which allowed a study of the effect of surface pressure gradients have been tested in a hypersonic facility by Canning et a1 7 . Larson and Mateer4 did a systematic experimental study of the development of cross-hatching using cones of various angles, thus producing locally subsonic or supersonic Mach numbers. The ablation materials tested were Lexan and Lucit~ Williams 6 measured the rOlling moment coefficient on ablating Camphor and Korotherm cones. Me Devitt 9 determined the oscillation and spirining frequency during ablation on Ammonium Chloride, Camphor and Korotherm cones in a hypersonic wind tunnel.

Experimental observations of cross-hatching formation

1.11 Cross-hatch1ng has been observed for

1. Different flight conditions a) Re-entry vehicles4,5 b) Ballistic range models 8,13 c) Wind-tunnel models4 - 7 ,9,lO,14-17

2. All ablation modes a) MeI tin g 1I - 8 , 1 5

] Hig~ _enVlronment enthalpy ]

I

Low. enthalpy

enVlronment

b) Melting and vaporizing13 c) SUbliming 5 ,6,9, 1 Q, 1 '1-17

Time integrated ablation process, flow parameters are time depen-dent.

d) Charforming S

3.

Different types of materials a) Acrylics 4 ,s,7,a,13 b) Phenolics S c) Teflon S ,14,16,17 d) Camphor 6 ,9,lO,lS e) WoodS f) Wax lS etc.

4.

Different types of model eonfiguration a) Two-dimensional models 4 ,S

b) Axisymmetrie mOdels 4 - 10 ,13,lS-17 c) Inside circular tubes 14

1.12 Requirements for the appearance of cross-hatching 1. Requirements for the gas flow

a) Supersonic boundary layer4

b) Transitional or turbulent boundary layer 4 ,13

c) The statie pressure and/or the heat transfer must exceed critical values 6

2. Requirements for the body material

a) For melters the Reynolds number of the liquid film U

1h/v (Ut being the liquid velocity at the liquid-gas

~t~rface,h the height and v the viscosity of the liquid film) must be below a certain value.17

b) Under ablation conditions the material must be sufficiently viscous (apparently for sublimers).17

3.

Requirements for the initial interface between the body and the boundary layer.

By grooving the initial surface perpendicular to the main

1. The pattern is~atially fixed on the model surface for

eharto~min~ ablato~s~

-2. The pattern moves slowly downstream on liquefying ablators. 1S

3. The spacing of the pattern ~ stays relatively constant in the streamwise direction on a given model, for either wedges or cones~

4.

The streamwise spacing ~ and the cant angle ~ are independent of the run time~

5.

Cross-hatching appears nearly simultaneously over much of the model surface~

6.

Longitudinal grooves frequently develop upstream of

cross-hatching~-10,13

Although many attempts have been made to explain the triggering mechanism of cross-hatched patterns, the

problem is not yet solved.

CroBs-hatching is commonly believed to result

from an interaction between the boundary layer and the ablation material.

Tobak 18 , Inger 19 ,20 and Mirels 21 have attempted to explain the phenomenon by treating perturbations in the gaseous boundary layer, and their consequent effects on mass transfer perturbations. Nachtsheim 22 and Probstein and Gold23 ,24 treat the cross-hatching phenomenon as an instability problem of the system of a gaseous boundary layer together with a liquid film or a deformable solid surface respectivelY.

Tobak 18 assumed a stationary array of counter-rotating, longitudinal, regularly spaeed vortices in the boundary layer, causing a sinusoidally shaped displacement

surface. Using linearized wing theory, he was able to calculate the resulting statie pressure distribution • It can be

described by overpressures, which are essentially sinusoidally distributed with amplitudes decaying in flow direction.

The pressure maxima occur at spaeed points which are connected by Mach lines. Hence, increased mass transfer will occur

along left and right running Mach lines leaving straight grooves in the surface, whose spacing depends on the initial arrange-ment of vortices.

Inger 18 analysed a turbulent boundary layer flow past a wavy wall in the transonic and slightly supersonic

flow regime. He calculated the amplitude and phase of pressure, temperature and shear fluctuations at the wall, depending on the sinusoidal surface perturbations and boundary layer

properties. Inger used these results in Ref.20 to predict mass transfer perturbations to the mean mass transfer on subliming materials. By assuming a concentration of the subliming

species of 100

%

at the wall, and streamwise heat condu6tion within the ablation material, he showed that a particular

value of a·~ exists at which the ablation rate is a maximum in the valleys of the sinusoidal wall, a being the wave number

of the surface perturbations and ~ the boundary layer thickness. Thus, a self-per~etuating interaction between the boundary layer and the surface perturbations of the ablation material may

exist.

Mirels21 _{assumed cross-hatching to be aresult}

of shock waves generated by small roughness elements interacting with a subliming ablation material. Such roughness elements

set up a weak, conical shock. Its intersection with the surface appears in the form of weak disturbances that are aligned in the localMach,line direction. Local overpressures

exist, resulting in grooves caused by increased mass-transfer. A non-linear interaction develops between the enhanced local surface blowing (sublimer) and the local shock strength.

This locally increased blowing sets up a trailing shock which intersects with the surface, and the process is thus repeated. As the resultant pattern is orderly spaced and the roughness

elements are randomly distributed, Mirels assumes that only

those grooves will survive which are of the "natural" spacing.

Nachtsheim 22 investigated the co~pling between a three-dimensional disturbance motion in a supersonic, uniform,

inviscid gas flow and the stability of an adjacent liquid

film. He showed that for very small liquid film Reynolds

numbers Ut-hiv (Ut being the liquid velocity at the liquid-gas

interface, h the height and v the viscosity of the liquid

film), an instability of the liquid layer can exist. Waves will be formed whose front inclination angle with respect to the gas flow direct ion is nearly equal to the local Mach angle. Hence, the mass transfer between the solid and

liquid ablation material will be influenced, producing a cross-hatched pattern in the solid.

In the analysis of Probstein and Gold 23 ,24,cross-hatching is believed to be a result of a differential

deformation of a viscous, inelastic, solid material due to pressure and shear stress fluctuations in a supersonic gas flow. In this model, it is not necessary for ablation to exist for the production of the surface pattern. In Ref.23,

the same authors treat the stability problem of a "" uniform,

inviscid, non heat conductive gas flow in~olving pressure

fluctuations and a viscous deformable solid. The pressure fluctuations are assumed to be proportional to the shear stress fluctuations at the wall. In Ref.24, Probstein and Gold modified the theory by now assuming a non-uniform, turbulent velocity profile, still making the assumption of an inviscid, non heat conductive boundary layer.

2. EXPERIMENTAL TECHNIQUE

The present tests were carried out in the hypersonic blow down facility H-1 at the von Karman Institute, shown

in Fig.1. The twe-dimensional contoured nozzle block provides a uniform flow at a Mach number of 5.3. The test section has the dimensions 14 cm % 14 cm. The tunnel stagnation conditions are

p

=

12 - 33 kg /cm2

ST f

giving unit free-stream Reynolds numbers of

0.85 - 5.1 x 10 7 /m

Cones of 10 to 620 _{total vertex angle, and 10}0 cones with 12 te 400 _{total angle flares were tested at zero} angle of attack. For one model configuration the influence of the angle of attack was examined. The dimensions of the models and the pointed steel noses are given in table 1.

These pointed steel noses were used to avoid apex deformation by ablation. Some cones consisting entirely of ablation

material were tested to study nose blunting effects. A few runs were made using flat plate models at various angles of attack.

Two ablation materials were tested, natural wax without seedings, which liquefi~~nder test conditions

~mphor models were manufactured by sintering the powdered

material in a vacuum under high compression (500 kgf/cm2) using the technique of Charwat 25 •

3. TEST RESULTS AND DISCUSSION

In Fig.2 the flow field properties on cones for an upstream Mach number of 5.3 are shown as a function of the total cone angle e. The local Mach number at the outer edge of the boundary layer Mand the local static

e

pressure p were calculated by the tangent cone method e

ignoring viscous interaction and surface deformation caused by ablation. The conical properties are also used for

cone-flare configurations. The effects of overcompression and overexpansion on the inviscid Mach number and statie preSBure distribution are small at this high Mach number. Because of the presence of the boundary layer, the actual Mach number and statie pressure distributions are even less different from the conical ones.

3.2 !~~~~!~!~~~!_~~_~~~~~!~~~_~~~~~~~~_!~~~~_~~

!~~_!~~~~!2~_2f_~~2~~:h~~~h!~g

Experiments were carried out to determine whether, as has been previously suggested4 ,13, a transitional or

turbulent boundary layer is a necessary requirement for the existence of cross-hatching. The momentum thickness Reynolds number Ree wás calculated at the position on cones where cross-hatching first starts to appear. Fig.3 shows Ree as a function of the local Mach number M • Values of the

e

momentum thickness Reynolds number Ree for the transition

range from laminar to turbulent boundary layer flow, which were measured on cones, are shown for comparison. For the present

ablation tests theReynolds numbers evaluated at the outer edge of the boundary layer Re varied from 4.66-7.06 x 107 1/m.

The ratio of wall temperature to free-stream total temperature Tw/T

ST was about 0.85, where Tw was ~upposed to be the liquefaction

temp~rature of the ablation material. The Reynolds numbe~Re

e·

for the transition tests were changed fr Om 1.5-4.5 x 10' 1/m, the temperature ratio Tw/T

ST varied from 0.40-0.895. As may may be seen, the valu~of Ree for the cross-hatching tests are considerable larger than those measured for transition on cones.

Furthermore Fig.3 shows that the values of Ree for the ablation tests increase with augmenting local Mach number M • Measurements for the onset of instability in a

e

laminar boundary layer, i.e. where perturbatiooofirst start to be amplitied, show that the boundary layer becomes more

stabIe tor increasing Mach number in the range of 2.227 - 5.828 • The theoretical predictions for the onset of instabilit y29

agree quite weIl with these experiments.

Hence, Fig.3 is believed to support the

experimental observation that a transitional or turbulent boundary layer flow is necessary for the existence of cross-hatching.

Typical test results are given in Fig.4 for axisymmetric and two-dimensional modeIs. From experimental observations, correlations have been attempted between pattern parameters, i.e. the streamwise spacing X and the cant angle ~,

and the flow field conditions, the ablation material properties or the initial geometry of the model surface. The cant angle ~ and the streamwise spacing X have been measured on photographs taken af ter the runs.

3.31 Cant angle ~

number M e

The cant angle ~ is shown versus the local Mach in Fig.5 and compared with the Mach angle (solid curve). Available wind tunnel data and free flight data from Ref.5 are shown for cornparison. As seen, the present results follow the Mach angle trend in the Mach number range 2.5 - 5.0 contrary to the flight data for which "freezing" was observed above a Mach number of 3. An explanation for the difference was suggested in Ref.15, that nose blunting occured in free

flight, whilst wind tunnel tests were made with models having pointed noses.

Fig.6 shows the cant angle ~ on self-blunting cones, consisting entirely of ablation material, versus the Mach nurnber M , where M _{e e ·} is calculated for unblunted cones. Data for cones with pointed steel noses and flight data are shown for comparison. As seen the blunted nOse data agree with those of the free flight models.

Zakkay et a130 and Rogers31 have shown theoretically and experimentally that the actual local Mach nurnber on

blunted cones is a highly dependent function of X/R, changing fr om subsonic conditions near the stagnation point to the supersonic conical value far downstream (X being the distance along a meridian and R the nose radius). Bearing this in mind, the actual local Mach number M on the sel~blunted cones at

e

the position where the cant angle was measured, see table 2, may be such that, using the true values of M , blunt cone

e data would agree with pointed nose data.

The cant angle ~ seems to depend uniquely on the local Mach number • The unit free stream Reynolds number, Re , and the Reynolds number based on conditions at the outer

_...

edge of the boundary layer,Re_e , the staticpressure Pet the driving temperature T - Tand the run time did not seem to

r w

have any influence. The recovery temperature T was

r

by assuming a turbulent recovery factor of o.895.T

w

is the temperature at which the ablation material liquefies, independent of p •

e

3.32 Streamwise spac~ng À

The effect of local surface pressure p on the

e

streamwise spacing À is shown in Fig.7 for a nearly constant

temperature ratio T _{r w w} - T /T

=

0.0989 - 0.1278 for wax modeIs. The results agree quite weIl with those of Williams 6 , extending the range to lower static pressuresand greater values of the streamwise spacing. The surface pressure p was varied both

e

by changing the co ne or flare angle and thereby the loc al Mach number, and by altering for some tests the tunnel stagnation pressure.

The effect of the driving temperature ratio

T - T /T on the streamwise spacing À measured on wax cones

r W w

~s shown in Figs.8 and 9 for constant values of Me and Pe' As seen, the streamwise spacing increases nearly linearly with the

driving temperature ratio.

Canning et a17 have made similar observations on conical plexiglas modeIs. The diagram on the left hand side of Fig.10 is taken from Ref.7. The streamwise spacing

À is shown versus the skin friction. Two distinct groups of data points are given for two different stagnation

temperatures. To compare these results with those in Fig.8, mean values of À were chosen as indicated by the arrows.

Taking plexiglas as a liquefying material, and the temperature where plexiglas starts to be sufficiently viscous as T

=

4400K,

w

the driving temperature ratio T - T /T can be calculated. T

r w w r

was computed with the turbulent recovery factor of 0.895 on 80° total angle cones in an air flow at a Mach number of 7. The diagram on the right hand side in Fig.10 shows À at these two stagnation temperature levels versus the driving temperature ratio. Here again a nearly linear dependence of À on

T T /T can be seen. r w w

The local Mach number M , the Reynolds numbers, Re _{e ...} and Re , _e and the run time did not appear to have any influence on the spacing ~, when the statie pressure p a n d the driving

e

temperature ratio were held constant. No influence of nose blunting on ~ could be seen, contrary to the effect on the cant angle ~. This may be due to the fact that the statie pressure approaches its conical value af ter a distance of a few nose radii, whereas the local Mach number reaches its conical value only for large distances from the nose. The body size does not seem to be a Bcàling factor for ~.

Williams 6 used models which were three times larger than those used at VKI, and for the Camphor test no difference in ~

could be seen, Fig.7.

Fig.11 shows photos of the cross-hatching development reproduced from a film taken during the test. During a run on a wax model, several distinct time intervals can be defined corresponding to different stages in the

pattern development

lst time interval : to + tI

From tunnel start until the model surface reaches the liquefaction temperature and starts to ablate. 2nd time interval : tI + t2

From the onset of ablation until the moment when cross-hatching starts to appear.

3rd time interval : t 2 + t 3

From the first appearance of cross-hatching until the surface pattern is fully developed, showing the maximum height difference between the bottom of the grooves and the enclosed hills

4th time interval : t3 + t 4

Af ter being fully developed, the pattern starts to des in-tegrate showing a regmaglypt pattern resembling those on

meteorites shown in Ref.4.

In the test shown in Fig.'1, eross-hatching started to

appear at t 2 = 7 seeonds and was fully developed at t3

=

13

to 16 seeonds. The long run time photos show the pattern

desintegration proeess. As may be seen, during the time period,

t2 until t3 the cant angle ~ and the streamwise spacing À

were independent of time.

It was found that the run time t 3 on wax models was dependent on the loeal statie pressure Pe and the driving

temperature ratio T - T /T • Fig.12 shows the run time t3

r w w

as a funetion of the statie pressure p , for a nearly constant e

temperature ratio T - T /T

=

0.0989 - 0.1278. Fig.13 shows

r w w

t ! for constant statie pressure p as a funetion of T - T /T •

e r w w

As may be seen, the test time inereases nearly linearly with the temperature ratio.

For a few tests with wax models (both axisymmetrie

and two-dimensional) a movie was taken during the complete

testing period. It showed a slow "creeping" motion of the whole cross-hatched pattern in the streamwise direction of the order of 1 streamwise spacing/10 sec.

Fig.14 shows the influenee of flow eompression on the eross-hatching formation. The models were eone-flare bOdies, of which a part of the fore-eone and all of the flare

eonsisted of ablation material. The total flare angle was

ehanged from 26° to 34° in steps of 2°. The tunnel was stopped when a marked pattern appeared on the flare, whieh resulted in a gradually decreasing run time as the flare angle, and hence the statie pressure on the flare, was inereased. The pattern

on the fore-cone became progressively less pronounced as the run time became insufficient to develop a marked cross-hatching.

A more striking result of the influence of run

time on the cross-hatching formation is shown on flow expansion models in Fig.15. The models were double-cones, of which a

part of the fore-cone and all of the after-cone eonsisted of ablation material. The total after-eone angle was changed from 26° to 18° in step of 2°. In this case, the tunnel was stopped af ter 14-15 seconds, when a developed pattern appeared on the fore-cone. As may be seen, the pattern on the af ter-body disappeared gradually beeause the after-cone angle, and hence the statie pressure on the after-eone, was decreased, resulting in a longer required run time t3.

Fig.16 shows observed patterns on the double-cone configuration (26° total fore-eone angle, 18° total after-cone angle) tested for two different times, 15 and 25 seconds,

these being the neeessary run tim~ t3 for the fore-cone and the af ter-body respectively. On the short run time model, cross-hatching appeared only on the fore-cone, the af ter-body being pattern free. The long run time model showed a desinte-grated pattern on the fore-cone, the aft er-part being eovered with cross-hatehing. This pattern is less elear than on a single cone of 18°, which is shown for comparison. The reason is that the boundary layer flow is highly perturbed by the surfaee irregularities on the fore-cone, when the pattern starts to develop on the af ter-body.

Fig.17 gives the test results on cones at angle of attack from 0° - 6° at 2° intervals. As the maximum pressure occurs on the windward side of the model, the tunnel was

stopped when a marked pattern was seen there. The run time decreased with increasing angle of attack, i.e. increasing

windward side statie pressure, leading to a gradually disappearanee of the pattern on the leeward side.

On the model sides,the pattern beeame progressi-vely inelined relative to the side-meridian, as the angle of attack was increased. (The pattern inclination or orientation is eharaeterized by a line whieh bisects the angle between

left and right running grooves~ This effect is caused by the

inclination of the streamlines of the inviscid flow around cones at angle of attack.

The inelination angle of the pattern was measured on the model sides and is plotted versus the angle of attack in Fig.18. The streamline inclination calculated

by a characteristics method for slender bodies lO is shown for comparison. As seen, the pattern orientation follows closely the streamline direction of the inviscid flow.

A similar observation of pattern orientation fOllowing the strèamiine direction is qualitatively

described in Ref.5. On ablating cones spinning at 2000 and 6000 rpm, the cross-hatched pattern was shifted in a direct ion consistent with the local cross flow.

Surface irregularities such as slots, holes, pins and a series of compression and expansion corners were machined into the ablation material.

In Ref.14, cracks perpendicular to the flow in the teflon heat shield inside a circular duct were observed, which forced the pattern to change its streamwise spacing or to disappear completely. An attempt to reproduce these

of widths 0.5 and 1.0 mm, was unsuccessful. The pattern did not disappear, but continued undisturbed downstream of the slots. The different behaviour may be attributed to the different modes of ablation. Teflon sublimes whereas wax liquefies, and in the latter case, liquid wax filled up the slots during the test, so that the surface was again essentially smooth.

Tests with pins of different height, diameter and spacingfixed in the ablation material, showed no detectable influence on the cross-hatching formation.

Fig.19 shows the results of tests in which a series of holes of different diameter and spacing was machined into the wax. The pattern dowstream of the holes was highly

disturbed, especially using the large diameter holes. The streamwise spacing À of the cross-hatched pattern,although

not always weIl defined, appeared to be increased, whereas the angle between left and right running grooves stayed nearly unchanged.

Nachtsheim and Larson 17 have investigated the idea that the formation of the cross-hatched pattern originates

from an interaction between the boundary layer and the ablation material (essentially at the surface), by trying to interfere with this interaction. Transverse grooves where machined in the Teflon surface such that conical shock waves form

that would interact with the formation of the pattern. The

grooves did prevent cross-hatching but, when ablation eliminated the grooves, the pattern appeared.

Fig.20 shows some results of the present test series using conical models on which a series of compression and expansion corners were machined into a part of the

ablation material surface. The surface perturbation wave-length I was chosen to be either equal to or twice the

exist on a smooth model. The photos show the cones af ter only a short run time, when a very narrow spaced striation pattern developed on the perturbated surface part, and af ter a long run time, when cross-hatching appeared on the smooth surface. Suppresàion of the cross-hatched pattern could not be observed. The model

(1

=

20 mm) tested for 14 seconds shows a disordered pattern, consisting of striations

in the valleys and a regmaglypt pattern on the convex surface part. The result on the model for 1

=

10 mm and a smaller

surface deviation angle E is more interesting. The surface perturbation wavelength 1 seems to be properly chosen, such that arrays of orderly arranged diamond shaped cells are

located in the valleys and on the convex surface parts, being in streamwise length equal to 1.

Some tests were done to verify or support hypotheses for the origin of cross-hatching.

3.81 Perturbation visualization

Fig.2l shows Schlieren-photos of the shock-layer on an ablating cone before and af ter cross-hatching appeared. The system of weak perturbation shocks is clearly seen which may be supposed to re sult in locally increased surface

pressures and ablation rates. A self-perpetuating interaction between the flow and the ablati~n surface disturbances may result, as supposed by Tobak18 , Inger19 and Mirels21

3.82 Tobak's model

In order to check Tobak's hypothesis18 that vortices are responsible for the origin of cross-hatching, streamwise vortices were artiticially introduced into the boundary layer by three-dimensional roughnesses and backward

facing steps.

Fig.22 shows streamwise vortices visualized by the sublimation technique on non-ablating modeIs. Fig.23 gives the test results o.n ablating cones, where three-dimensional roughnesses of different height, diameter and spacing, giving rise to different vortex intensities32 , triggered the

boundary layer. Although the tests were done over a considera-bIe range of roughness geometry parameters, the pattern

remained essentially unchanged. Fig.24 shows the results on ablating cones involving backward facing steps of different heights. Here again cross-hatching is unchanged.

Hence the following reasoning may be permitted. If the existence of streamwise vortices were necessary for the generation of cross-hatching, the resulting pattern should be coupled in some way to its creating mechanism. Weak perturbations have been observed on some models due to ablation-induced backward facing steps and surface concavities. Now, the perturbations artificially introduced by backward

facing steps of relatively large height and three-dimensional roughnesses create vortices of much larger strength. But, as mentioned above, they have no observed effect on the pattern formation. Hence, streamwise vortices are not believed to be necessary for cross-hatching to exist.

3.83 Hypothesis of Probstein and G6ld

In Fig. 25 are shown two cones of the same initial geometry, and tested under the same stagnation conditions. The initial ablation material temperatures were however different, 2900 _{and 332°K. The higher temperature model}

was preheated for 15 minutes at close to the liquefaction

temperature of wax. Only the af ter-part of the cone was heated, between 50 mm from the steel nose down to the base, in order to keep a smooth junction between the steel nose and the wax.

As may be seen, the streamwise spacing À is considerably larger on the preheated wax model.

To search for an explanation of this phenomenon,

the influence of the initial material temperature on 1. the

boundary layer flow, 2. the gas-liquid and liquid-solid

interfaces and 3. the ablation material have to be considered.

1. The boundary layer properties will not be changed, since -af ter

a few sedonds both models will have the same surface temperature, 2. The mass transfer rate at the liquid-solid interface is

certainly higher for the preheated model. In Ref.23, test

results are given for which no measurable ablation was observed,

nevertheless , showing cross-hatching. Hence, mass transfer may

not be an important parameter in the cross-hatching formation. 3. Body material properties such as density. specific heat and heat conductivity are supposed to be independent of temperature in the range from 290-332°K. The viscosity and shear modulus of wax however show considerable variations with temperature in this range, hence, leading to the conclusion that the ablation material properties viscosity and resistivity are important parameters in the cross-hatching formation.

This test result is believed to lend some support

to the hypothesis of Probstein and Gold23 ,24, in which

cross-hatching is supposed to be a result of a differential deformation of a viscous, inelastic solid.

4.

CONCLUSIONS

1. The necessity for the boundary layer to be transitional or turbulent in order that cross-hatching shall form is shown;

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

number outside the boundary layer and follows closely

3.

The pattern orientation follows closely the streamline direction of the inviscid flow;

4.

The streamwise spacing ~ varies in inverse proportion with the local static pressure pand in proportion with the _{e .} driving temperature ratio T - T /T ;

r w w

5.

The run time necessary to give cross-hatching is in

~nverse proportion with the local statie pressure pand

e

in proportion with the driving temperature ratio T

r - T /T . w w'

6.

Streamwise vortices do not appear to be necessary for existence of cross-hatching;

7.

Some evidence is given that cross-hatching may result from differential deformation of a viscous, inelastie solid.

1. M.L. MINGES

Ablation Phenomenology (A Review)

High Temperatures - High Pressures, 1969, Vol.1, p. 607-649 2. K.H. WILSON, F. KOUBEK

NOL TR 68- 1 2 6 , 1 69

3. D.R. CHAPMAN, H.K. LARSON, L.E. ANDERSON

Aerodynamic Evidence Pertaining to the Entty of Tektites into Earth's Atmosphere

NASA TR R-134, 1962

4. H.K. LARSON, G.G. MATEER

Cross-Hatching - A Coupling of Gas Dynamics with the Ablation Process

AIAA Paper No. 68-670

5. A.L. LAGANELLI, D.E. NESTLER

Surface Ablation Patterns : A Phenomenology Study AIAA Paper No. 68-671

6. E.P. WILLIAMS

Experimental Studies of Ablation Surface Patterns and Resulting Roll Torques

AIAA Paper No.69-180

7. T.N. CANNING, M.E. TAUBER, M.E. WILKINS

Orderly Three-Dimensional Processes in Turbulent Boundary Layer on Ablating Bodies

AGARD CP No.30 and Supplement

Hypersonic Boundary Layers and Flow Fields, May 1968 8. T.N. CANNING, M.E. WILKINS, M.E. TAUBER

Ablation Patterns on Cones having Laminar and Turbulent Flows

AIAA Journ. Vo1.6, No.1, Jan. 1968, p. 174-175 9. J. B. McDEVITT

An Exploratory Study of the Roll Behaviour of Ablating Cones J. Spacecraft, Vo1.8, No.2, Feb. 1971,

p.

161-169

10. J.B. McDEVITT, J.A. MELLENTHIN

Upwash Patterns on Ablating and non-Ablating Cones at Hypersonic Speeds

NASA TN D 5346, 1969 1,. J.J. GINOUX

The Existence of Three-Dimensional Perturbations in the Reattachment of A Two-Dimensional Supersonic Boundary Layer Separation

12. M.E. WILKINS

Evidence of Surface Waves and Spreading of Turbulence on Ablating Models

AIAA Journ. Vol.3 No.10~ Oct. 1965, p. 1963-65 13. T.N. CANNING~ M.E. WILKINS, M.E. TAUBER

Boundary Layer Phenomena observed on the Ablated Surfaces of Cones recovered af ter Flights at Speeds up to 7 km/sec. AGARD CP No.19, Vol.2

Fluid Physics of Hypersonic Wakes, May 1967

14. E.M. WINKLER, R.L. HUMPHREY~ M.T. MADDEN~ J.A. KOENIG Substructure Heating on Cracked Ablative Heat Shields AIAA Journ. Vol.8~ No.10~ Oct. 1970, p. 1895-1896 15. H.W. STOCK, J.J. GINOUX

Experimental Results on Cross-Hatched Ablation Patterns AIAA Journ. Vol.9, No.5, May 1971, p. 971-973

16. A.L. LAGANELLI~ R.E. ZEMPEL

Observations of Surface Ablation Patterns in Subliming Materials

AIAA Journ. Vol.8~ No.9, Sept. 1970, p. 1709-1711 17. P.R. NACHTSHEIM, H.K. LARSON

Cross-Hatched Ablation Patterns 1n Teflon AIAA Paper 70-769

18. M. TOBAK

Hypothesis for the Origin of Cross-Hatching AIAA Journ. Vol.8, No. 2~ Feb. 1970, p. 330-334 19. E.P. WILLIAMS, G.R. INGER

Investigations of Ablation Surface Cross-Hatching Mc Donnell Douglas SAMSO TR 70-246

20. G.R. INGER

Compressible Boundary Layer Flow Past a Swept Wavy Wall with Heat Transfer and Ablation

VKI TN 67, Dec. 1 970

21. H. MIRELS

Origin of Striations on Ablative Materials

AIAA Journ. Vol.7~ No.9, Sept. 1969, p. 1813-1814 22. P.R. NACHTSHEIM

Stability of Cross-Hatched Wave Patterns in Thin Liquid Films Adjacent to Supersonic Streams

23. R.F. PROBSTEIN, H. GOLD

Cr •• à·~&tching : A M~terial Response Pheno~ena

AIAA Journ. Vol.8 No.2, Feb.1970, p. 364-366 24. H. GOLD, R.F.PROBSTEIN, R. SCULLEN

Inelastic Deformation and Cross-Hatchin~

AIAA Paper Vo.70-768 25. A.F. WHARWAT

Exploratory Studies on the Sublimation of Slender

Camphor and Naphtalene Models in a Supersonic Wind Tunnel RM-5506-ARPA, July 1968, Rand Corporation

26. E.R. VAN DRIEST, J.C. BOISON

Boundary Layer Stabilisation by Surface Cooling in Supersonic Flow

J.A.S., Vol.22, No.1, Jan. 1955, p.70 27. J. LAUFER, T. VREBALOVICH

Stability and Transition of a Supersonic Laminar Boundary Layer on an Insulated Flat Plate

J. Fluid Mech., Vol.9, Part 2, Oct. 1960, p. 257-300 28. A. DEMETRIADES

An Experimental Investigation of the Stability of Hypersonic Laminar Boundary Layers

GALCIT Hypersonic Research Project, Memorandum No.43, May 1958; a1so J.A.S. Sept. 195 R, p.599-600

29. W. B. BR OWN

Stability of Compressible Boundary Layers

AIAA Journ. Vol.5, No.l0, Oct. 1967, p.1753-1759 30. V. ZAKKAY, E. KRAUSE

Boundary Conditions at the Outer Edge of the Boundary Layer on Blunted Conica1 Bodies

Polytechnic Institut of Brooklyn, ARL 62-386,

July 1962; a1so AIAA Journ. Vol.1, No.7, July 1963 p. 1671-72 3 1. H. ROG ER S

Boundary Layer Development in Supersonic Shear Flow AGARD Report No.269, April 1960

32. W.C. SCHNELL, J.J. GINOUX

Effect of Surface Roughness on Axisymmetric Laminar Separated F10ws at M

=

5.4

VKI TN 41, Jan. 1968

33. E.R. VAN DRIEST, J.C. FOISON

Experiments on Boundary-Layer Transition at Supersonic Speeds

Effect of Unit Reynolds Number, Nose Bluntness, Angle of Attack and Roughness on Transition on a

50 Half-Angle Cone at Mach 8

NASA TN D-4961, Jan. 1969 35. K.F. STETSON, G.H. RUSHTON

A Shock Tunnel Investigation of the Effects of Nose Bluntness, Angle of Attack and Boundary Layer

Cooling on Boundary Layer Transition at a Mach Number of 5.5.

STEEL NOSE

ABLATION MATERlAL

e

0

°SASE

e

0

°BASE

e

0

DB ASE

deg

mmo mmO

_deg

mmO mmS

deg

mmS mmlt

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 MENSIONS :

€f/2

e

.- -

'

-

'

-

'

-

0

-°BASE STEEL NOSE ABLATION MATERlAL

e

=

10°

o

=

45 mme

DSASE

=

80

m

m-ex

=

12 -40°

IN STEPS OF

2°

SELF - BLUNTED CONES:

DIMENSIONS AND CROSS- HATCHING DATA

ABLATION MATERlAL

Me: MACH- NUMBER AT THE OUTER EDGE OF THE BOUNDARY lAYER CALCULATED FOR POINTED NOSE CONES

e

Me ~ R L deg

-

deg

mm

mm

20

45

19.5

3.8

180

26

4.2

20.5

4.0

150

WAX

32

3.9

20.5,21.5

13

120

38

3.6

21.5

,22D

2S

85

46

32

23D

2.5

60

CAMPHOR

30

4.0

21.0

5.0

130

D_BASE

mm

ll

80

80

70

70

60

80

U Z

o

Cl)

n:::

UI

a..

>

:x:

'

-Pe

Pa>

"

'"

'.0

I

3

.

0

2D

I

, j

1.0

o

0

_{1 5}

15

10

5

o

0

₁₅

0 _ _ __

'"

~

30

30

"

~

45

60

e

(deg)

'5

60

e

(deg)

25

/

V

J

V

2.0

I

V

1.5

. /

15

30

45

60

9(deg)

1.6 , . . , . .

-1.,

I---+--I~-+----+-\- -1.3 1----lI---I----+---',....-+~

1.2

J---I-+---+---+--~___i 1.1

15

30

'5

60

e

(deg)

FIG.2. FLOW FIELD PROPERTIES ON CONES FOR Ma>= 5.3

Ree

-10-

2

TST

=

395-410

12

_Tw/TST

₌

_{0.822 -0.853}

k9

_f/cm

2

PST

=

30

.

0

0

a:

=

0°

(ANGlE OF ATTACK)

₀

Ree

=

4

.

66-7

.

06-107

11

m

_0-0

Ó

6

0

0 0 0

10

0

0

0

8

0

r

0

8

0

0

6

₀

1--0

i I

1

I

1

1

1

I

'r

J

t

REF

26

33

34

35

4

2

Ree

(Um)

3

.

6-107

2

.

4-107

4

.

5-107

1.5-107

0.895

0

.

895

0.40

0.58

o

2.0

3

.

0

Tw/TST

4.0

5

.

0

Me

6.0

FIG.3.

DEPENDENCE ON THE MACH NUMBER Me OF THE MOMENTUM THICKNESS REYNOlOS

NUMBER Ree EVAlUATED AT THE POSITION OF

HE

START OF THE CROSS - HATCHED

CONE- FLARE Lcm CONE

I

lcm FLAT PLATE II'cm

Ma> :: 5.3 Mco = '5.3 Ma> = 5.3

TST = '07 oK _T5T = 397 oK _TST = 399 OK PST s 32.0 kg_f/cm 2 _{PST = 30.'} k9f/cm 2 PST = 30.3 k9f/cm2

t : 13 sec t _{= 11} sec t = 12 sec

ex: :: 0° (ANGLE OF ATTACK) ex: = 0° (ANGLE OF ATT ACK) ex: :: 10° (ANGLE OF A TT ACK) e :: 10° (TOTAL CONE ANGLEI e :: 28° (TOTAL CONE ANGLE)

e" = 21.0 (TOTAL FLARE ANGLE)

sor~

'V

MALTA - CARBON PHENOLIC

(d~9)

V

MALTA-CARBON PHENOLlC,(.U

=

6000 rpm

y

0

MALTA- PHENOLIC NYLON

Ó

MALTA- PHENOLIC NYlON,CA)

=

2000 rpm

40

00

6

₆

LANGlEY-WOOD (CONE) _{lANGLEY -WOOD (WEDGE)}

0 LANGlEY-TEFlON (CONE)

Cs' I c LANGlEY- TEFLON (WEDGE)

0 lANGlEY-lEXAN (WEDGE) I ' - I ~ ~_

1./

V / / j i

30

20

I --- -

...

---.... / PRESENT DATA:

o

VKI-WAX (CONE)

10

I I I

ê

VKI- WAX (CONE -FLARE,lO° FORECONE)

Ma,

=

5

.

3

~----~---~~---ex:

=

0° (ANGlE OF ATTACK)

SCATTER :!: 2°

o

I

1:0

2'0

3'0

4D

Me

50

o

(deg)

20

I ----"'Cl:: I "'" -...

Fli

GHT DAT A RE

F.S

PRESENT DATA:

VKI-WAX (CONE)

o

POINTED STEEL NOSE

VKI-WAX (CONE)

ê.

NOSE BLUNTING BY ABlATION

10

H

VKI- CAMPHOR ( CONE)

B

NOSE BlUNTING BY ABLATION

MCl)

=

5.3

o

0 0 0

I

o

cc

=

QO(ANGLE OF ATTACKh

I I

SCATTER

~

2°

0'

! ! , ! •

2.0

3.0

4.0

5.0

FIG.6. INFLUENCE OF THE MACH

- Me CALCULATED

FOR

Me

NUMBER Me ON THE CANT ANGLE

rIJ

X

(mm)

1

00

I

M.

~

o

I

[ ]

I

~

20

I

6

I

D

I

6

0

_{' 0}

I

15

I

-&

,-

0 I

Aao

~

A

o

1 0

I

A

Hl

i

EI 0 0

I

I

_

I

5

1

I

I

_{86 0}

I

I

00

₀

_.

₁

₀

_.

₂

Moo

T5T

te

:: 530

:: 0°

OK

(ANGLE OF ATTACK)

PRESENT DATA

:

o

VKI-WAX (CONE)

II VKI-WAX (CONE -FLARE, 10° FORECONE)

1 oEl

0

.

3

T

_ST

::

393 -411

OK

T

_{r -}

T

_w

IT

_{w ::}

0

.

0989 - 0.1278

T

_w

::

337

OK

CD

VKI-CAMPHOR (CONE-FLARE.

10°

FORECONE)

T

_ST

::

523

OK

M

_m

::

5.3

ct ::

0°

(ANGLE OF ATTACK)

5CATTER

t

10

·1.

El 0

o

I

a

0.4

0.5

06

Pe

(kQ f/cm2) .

FIG.7.

INFLUENCE OF THE LOCAL STATIC PRESSURE Pe ON THE

(mm)

15

10

5

o

o

M·il

[]

0

I

0

0

I

0

ons

0.10

0

o

VKI-WAX (CONE)

M(D

=

5.3

2

PST

=

30.0

kgf/cm

Pe

=

0.134

kg f /cm

2

t

=

11.5 -22 sec

cr

=

0°

(ANGlE OF ATTACK)

e

=

26°

(TOTAl CONE ANGlE)

T

_w

=

337

oK

SCATTER

~

10

%

0.15

020

025

Tr-Tw/Tw

FIG.8. INFLUENCE OF THE DRIVING TEMPERATURE

_{RATiO Tr-Tw/Tw}

=

12 sec T_ST

=

388 oK t = 18 sec TST = 430 oK Mal :: 5.3 PST = 30.0 k9_f/cm2 a: :: 00 _{(ANGLE OF ATTACK) .}

e

= 260 _{(TOTAL CONE ANGLEl}

t = 11.5 sec T S1 = 401 oK t :: 22 sec T₅₁

=

449 oK WAX MODEL5

FIG.9.

INFLUENCE

OF THE DRIVING

TEMPERATURE

(mm)

10

5

2

1

0.5

••

-

..

,--Ó?>

8:JÖ)~

~

~Me

PLEXIGLAS

[3

0

T

ST

=

750

0

_K

•

TST

=

1070

0

K

10

3

₂

₅

₁₀

4

₂

₅

₁₀₅

SKIN FRICTION

(dynes/cm2 )

15

À (mm)

10

5

o

o

0

os

lO

0

PLEXIGLAS

T

_w

= 440 oK

t

Me

[3

1.5

Tr-Tw/Tw

FIG.l0. INFLUENCE OF

THE

DRIVING

TEMPERATURE

RATIO

_{Tr -Tw / Tw}

ON

THE

STREAMWISE

SPACING

À

(DATA FROM REF.7)

PST:; 33.0 kg_f/cm2

re ::: Cf' (ANGLE OF ATTACK}

e :::

10°

1

[TOTAL CONE ANGLE l

el< ;:

24° (TOTAL FLARE ANGLE)

I

WAX MODEL

FIG.11. INFLUENCE OF THE RUN TI ME ON THE

CROSS - HATCHI NG DEVELOPMEN T

t3

(sec)

30

20

10

o

-0

o

VKI-WAX (CONE)

Mco

=

5.3

I

PST

=

30.0

kQ f

/cm

2

TST =

393 -411

oK

0

Tr-Tw/Tw

=

00989-01278

T

_w

=

337

oK

a

a:

=

0° (ANGLE OF ATTACK)

0 0

0-0

0 0 --~. 0 0 0

Q

-o

0.1

0.2

Pe

(kQ f

/cm

2 )

0.3

FIG.12.

RUN TIME REQUIRED FOR A DEVELOPED CROSS-HATCHED PATTERN

(sec)

20

15

10

5

00

FIG.13.

c

0

0

0

0

0

_I

o

VKI -WAX (CONE)

Moo

=

5.3

k9_f

/cm

2

PST

=

30.0

Pe

=

0.134

k9_f

/cm

2

ex:

=

0°

(ANGLE OF ATIACK)

i

e

=

_26°

_{(TOTAL CONE ANGLE)}

! I

_T

w

=

337

oK

I

0.10

_0.15

_{_ T}

_I

_T

020

T

r

w

w

0.05

RUN

TIME REQUIRED FOR

A DEVELOPED CROSS-HATCHED

PATTERN

M;" S.3 PST 30.0 cc O' e 26° t = lS sec 15T= 404 oK t = 10 sec TST = 395 oK k!lf/cm2 IANGLE OF ATTACKJ I TOTAL CO NE ANGLEJ 1 ,14 sec T_ST' 401 oK t = 9 sac TST= 406 oK 1.12 SQC TST ' 398 oK WAX. MODElS L • 50 mm

SIDE VIEW

15 sec 14 sec t 15 sec t 14 sec

TST =. 404 oK _TST 395 oK _{TST 398 oK TST 401 OK}

M(I) = 5.3

PST' lnO k9f/cm2

a: 0° (ANGLE OF ATTACKl

e 26° ITOTAL CONE ANGLEl L = 50 mm

FIG.15. INFLUENCE OF FLOW EXPANSION ON THE CROSS-HATCHING FORMATION

I

lcm

WAX MODELS

t - -"-_ IS-.sec

SIDE VIEW t :: TST e Mro :: 5.3 PST :: 30.0 cc 0°

FIG.16.

15 sec 395 oK

26° (TOTAl CONE ANGlEl

kg/cm2

(ANGLE OF ATTACKI

t 2S sec

T_ST = 403 oK

11

cm

e

26° tTOTAl CONE ANGLEJ _---L-oO"I

---

~

WAX

!

L= 50 mmj

t = 25 sec

TST 404 oK

e

::

18° ITOTAl CONE ANGLEI

WAX MODELS

INFLUENCE

OF RUN- TIME

,

ON THE CROSS-

.

.

HATCHING

FOR MATI ON

,

2{M, ;",:,,~~._'~ '- ,'-' "~,"'"tc 'i'~ .

SIDE VIEW

I

1 cm

t = 15 sec t = 14 sec t = 12 sec t = 9.5 sec

MlD • 5.3 WAX MODELS

TST 404 oK PST 30._{0 kgf}/cm2

e • 26° (TOTAL CONE ANGLEI

~REF10

\

_1\

~Y"'~q)~

Men ~

,

~

'"

"'

!

~

_t----....

1T

1.4

a:xsin'"

1.2

1.0

0.8

0.6

0.4

Ma> = 5.3 FOR

e

= 26°:

lf

.

0

=0.9

t

cr- Sin

o~

00

₁₀

₂₀

₃₀

₄₀

₅₀

₆₀

e

(deg) '" I

Id!9)

51---J---=±:==~~~~~~~.-~.90.

lf-(deg)

4

3

I1 J

0

2

o

lf-:

VKI-CONE (WAX) Men: 5.3

1

I

V

I

_TST

=

404 oK PST: 3QO kg

_f

/cm

2

e :

26° (TOTAL CONE ANGLE)

t

=

9.5-14

sec

o

~-

1

2

3

4

5

6

OC(deg)

FIG.l8. COMPARISON OF THE PATTERN INCLINATION ANGLE

lT-

WITH THE STREAMLINE

INCL! NATION ANGLE

lf

OF THE tNVISCID FLOW FOR CONES AT ANGLE OF ATTACK

SIOE VIEW d • 1 mm# 1 • 2.5 mm d • 2 mmll I • 5 mm d ... I<.I) = 5.3 TST = 403 oK PST = 30D ks_f/cm2 t = 14 a: 9 = 0° = 26° .sec (ANGLE OF ATTACKl ITOTAL eONE ANGLE)

d • I mme' I = 5 mm

I

lcm d = 2 mm'" t = 10 mm -I.d -T

-

t

WAX

..

DEPTH OF THE HOLES 7min L .60mm

FIG.19. INFLUENCE OF SURFACE IRREGULARITIES ON THE CROSS - HATCHING' FORMATION

t 15 sec 3 sec 13 sec ₌ 4 sec TST = '0' oK _TST = '05 oK T 5T 398 oK T5T = '00 oK M(D 5.3 PST 30.0 k9f/cm2 a: 0° (ANGLE OF ATTACKI , '_ ~.ler·=~l· -L =45 mm WAX MOOELS WAX

e 26° (TOTAl CONE ANGLEI

FIG.20. INFLUENCE OF A SERIES OF COMPRESSION AND EXPANSION CORNERS ON ABLATION PATTERN FORMATION1 f$

M(D

=

S.3 WAX MODEL

TST

=

.412 OK PST = 30.0 kg_f/cm2

oe

₌

0° (ANSlE OF ATTACK)

e

₌

26° (TOTAl CONE ANSlE)