120 3 6 A LABORATORY STAR ?

In document A study of radiating argon flows at high opacities (Page 142-160)

95 results obtained during this period, are analysed, and a picture of what

120 3 6 A LABORATORY STAR ?

As a s i m i l a r s o l u t i o n h o l d s f o r t h e n o z z l e f l o w a s f o r t h e s t e l l a r a t m o s p h e r e , t h e n p e r h a p s t h e n o z z l e f l o w c a n b e u s e d t o p r o v i d e a r a d i a t i o n f i e l d s i m i l a r t o t h a t e x i s t i n g i n t h e o u t e r l a y e r s o f a s t a r . Even t h o u g h t h e two s i t u a t i o n s a r e o p t i c a l l y t h i c k , t h e i r o p t i c a l t h i c k n e s s comes a b o u t f r o m two d i f f e r e n t c a u s e s . W i t h a s t a r , t h e g a s i s o f r e l a t i v e l y l o w d e n s i t y , and t h e l a r g e o p t i c a l d e p t h i s p r o d u c e d by t h e l a r g e d i s t a n c e s i n v o l v e d , w h e r e a s w i t h t h e n o z z l e f l o w t h e o p t i c a l d e p t h i s p r o d u c e d by t h e l a r g e d e n s i t i e s ( e s p e c i a l l y t h e e l e c t r o n d e n s i t y ) . I f o n e l o o k s a t t h e t r a n s f e r e q u a t i o n f o r c o n t i n u u m r a d i a t i o n v i z . ~ = - I + J {T(t) } dx v v o n e c a n s e e f r o m t h i s e q u a t i o n , t h e a c t u a l d i s t a n c e d o e s n o t e n t e r b u t r a t h e r t h e o p t i c a l d e p t h . He n c e i f o n e c a n m a t c h t h e d e p e n d e n c e o f T on T f o r a s t e l l a r a t m o s p h e r e and a n o z z l e f l o w , t h e c o n t i n u u m r a d i a t i o n f rom b o t h s h o u l d b e q u a l i t a t i v e l y s i m i l a r . The n e x t p r o b l e m i s t h e s i m u l a t i o n o f t h e r a d i a t i v e p r o p e r t i e s o f t h e g a s . F o r a p a r t i c u l a r f r e q u e n c y , t h i s i s n o t r e q u i r e d f o r a p a r t f r o m m a t c h i n g t h e T- x r e l a t i o n s h i p t h e o n l y o t h e r p a r a m e t e r i s t h e s o u r c e f u n c t i o n , J ^ ( T ) . W i t h l o c a l t h e r m a l e q u i l i b r i u m h o l d i n g f o r t h e c o n t i n u u m r a d i a t i o n , t h e s o u r c e f u n c t i o n w i l l become P l a n c k ’ s b l a c k body r a d i a t i o n f u n c t i o n B ^ ( T ) , w h i c h w i l l b e i n d e p e n d e n t o f t h e g a s p r e s e n t . He n ce i n p r i n c i p l e t h e r e i s no n e e d t o m a t c h t h e two g a s e s . However d i f f i c u l t i e s w i l l a r i s e i n m a t c h i n g t h e T-x r e l a t i o n s a t a l l f r e q u e n c i e s , i f t h e g a s e s a r e n o t s i m i l a r , f o r t h e o p t i c a l d e p t h ’s d e p e n d e n c e on f r e q u e n c y w i l l b e a

s

KVT)t^

c h a r a c t e r i s t i c o f t h e g a s . (N.B. x = pk x and ok = 7—B ( T ) ^ --- ,---B (T) v v v 4tt v v w h e r e £ ^ ( T ) i s t h e o n l y p a r a m e t e r d e p e n d e n t on t h e g a s s p e c i e s ; t h e v a r i a t i o n o f £ ^ ( T ) w i t h v i s shown i n F i g u r e 8 . 1 3 f o r v a r i o u s g a s e s ( f r o m B i b e r m a n e t a l ( 1 9 6 3 ) ) . From t h e d e r i v a t i o n , e a'N N. , o n e woul d e x p e c t

KN B (T) , v e 1

t h e m i x t u r e r u l e pk = — ---Z£1 (T)N. , . , .

v / m h . v i w h e r e m t h i s c a s e £ (T)

121

is the Schlüter type value with the cut off frequency included in it.) For the line radiation, the line shape is important and this is controlled by the electron density (as well as other parameters for a star). For exact duplication one would require an N^-x and a T-x match which would need a full scale model.

Simulation of both continuum and line radiation has been studied in a little more detail in a paper on simulation (Logan and Stalker

(1971)). However, it would appear that whilst qualitative simulation of some effects may be possible, accurate duplication of the line radiation is not feasible. Nevertheless it seems that duplication of the characteristics of the continuum radiation may be possible.

So far only the modelling of hot stars has been discussed. In hot stars, absorption is primarily due to bound-free and free-free

transitions as in the nozzle. However Logan and Stalker (1971) discuss the case of cooler stars, like the sun, in which absorption is due to the presence of negative hydrogen ions. In both cases the same general analysis should hold.

Thus to analyse the continuum radiation, one would design the nozzle shape such that the T-x relationship was either completely simulated by using the same gas (normally a mixture of hydrogen and helium) or simulated in a spectral region of interest to the study. A gas mixture which could simulate the T-x of a star in both the visible and the ultraviolet would provide interesting results, in which the visible can be compared with that observed for the star in question and

then the ultraviolet which cannot be readily observed due to its absorption in the earth's atmosphere could be analysed. Furthermore by subjecting the radiation fields to atmospheric disturbances (e.g. magnetic fields or shock waves) it is anticipated that simulation of some astrophysical phenomena can be obtained under well established laboratory conditions.

3.7 CONCLUSIONS

This chapter has been an aside to the major theme of the thesis. It has only been a preliminary study because of the available equipment. The main experimental problem was due to the limited intensity of

radiation emitted from the nozzle. Although the poor wavelength resolution of the spectrometer was an associated problem.

The chapter looked at the mechanism by which absorption lines were formed and subsequently a theory was developed for an equilibrium flow. This theory was modified for the nonequilibrium flows which are encountered in the two nozzles used in this investigation.

In the theory four parameters were varied to study their effect on the absorption line profile; the nozzle shape, the reservoir slug conditions, the impurity concentration and the gas conditions downstream of the throat. Because of the thermodynamics of the nozzle flow, varying the nozzle shape and the reservoir slug conditions made little difference to the shape of the line profile. However altering the gas conditions downstream of the throat by using the thermodynamic conditions for an equilibrium nozzle flow, does appreciably change the line profile.

Reasonable agreement was found between the theoretical and experimental profiles, though this could not be interpreted as a unique confirmation of the conditions down the nozzle for the reasons mentioned above.

The similarity between the radiation field in the nozzle and in a stellar atmosphere was noted. However a fuller discussion of this is given in the paper on possible laboratory simulation of stellar phenomena

CHAPTER 9 CONCLUSIONS

The basic aims and motivations for this thesis were discussed at length in the Introduction (Chapter 1). Only the major points of that discussion need be reiterated here. Because of the nature of studies on reentry from interplanetry missions, one needs to produce a gas flow with as high a velocity as possible. One technique used to obtain high

velocities is the free piston reflected shock tunnel.

In a reflected shock tunnel, the driver gas pushes a shock into the test gas and collects the shock heated test gas as it propagates down the shock tube. This shock reflects off the end wall of the shock tube and passes through the already shock heated test gas increasing its temperature and density and brings it to rest.

This stationary slug of high temperature, high density gas is used as a reservoir for a hypersonic nozzle flow. The gas is fed through a small orifice and then down a nozzle with a large area ratio. The nozzle converts the energy that is in the gas as randomised motion

measured as temperature in the reservoir region into the directed motion of the gas at the nozzle’s exit.

This technique has been used at lower enthalpies and it was found to give the expected theoretical results. However as one strives for higher velocities at the nozzle exit additional problems arise. This thesis looked at these problems and offers an explanation of the real behaviour of a high performance reflected shock tunnel. Of major interest, to this investigation was the effect of radiative energy loss from the test gas, however subsidiary effects had also to be examined.

The thermodynamic conditions of the gas immediately behind the incident shock are in agreement with those calculated from the measured shock velocity and the initial shock tube pressure. At high incident shock speeds and large initial pressures (greater than 25.4 torr) the shock velocity attenuated as it travelled down the shock tube and hence the velocity used in the calculations needs to be measured at the point

124 in question.

The reason for this attenuation was not completely understood however calculations showed qualitative agreement could be reached by a theory that accounted for energy loss through the boundary layer.

Alternatively, attenuation could be due to expansion waves generated in the driver section catching up to the contact surface.

The energy loss through radiation from the shock heated test gas was substantial under the thermodynamic conditions of this study. This resulted in a gradient of thermodynamic conditions in the test gas. Korn had developed a model that could account for the radiative energy loss from argon at lower electron densities than the present study. His model was modified for this investigation by accounting for the optical depth of the continuum radiation. Furthermore additional neutral argon electronic transitions were included as well as the lower electronic

transitions of ionized argon. The observed decay of the electron density was in agreement with that obtained from calculations using this altered model.

The oblique shock on a wedge in the shock tube was studied, in part because the gas behind the oblique shock gave higher electron

densities and temperatures than the incident shock, whilst avoiding the problems with impurity contamination which characterized the gas behind the reflected shock. However the most important feature of the oblique shock was that the thermodynamic conditions were almost independent of time. Whereas behind the incident shock the fast changing electron density made time resolved measurements quite difficult to interpret. Because of these characteristics the oblique shock provided a suitable light source for calibrating photographic emulsions.

With the reflected shock, the behaviour of the shock heated region is not fully understood quantitatively, even at low incident shock speeds. At the high enthalpies encountered in this investigation, the

Situation is still more complex with additional problems arising due to the large optical depth of the test gas sample. This made spectroscopic diagnoses of the reservoir region virtually impossible.

Due to the limited experimental results for the reservoir region and the thermodynamic conditions down the nozzle, these two regions and the test section flows are discussed together.

For the reflected shock there are three important interactions, the interactions with the test gas, boundary layer and contact surface. The interaction with the contact surface is described in detail in the

literature as is the boundary layer interaction. Both of these

interactions are described briefly in the text of the thesis. The boundary layer interaction leads to the contamination of the test gas in the

reservoir region and the mechanism proposed in the text for the

contamination of the nozzle flew follows from the reflected shock boundary layer interaction.

The reflected shock - test gas interaction is quite important for this present study for the reflected shock propagates in a test gas with varying thermodynamic conditions because of the radiation loss behind the

incident shock. This slug of gas is stratified to simplify the

theoretical analysis and the thermodynamic conditions in each stratum behind the reflected shock are changed isentropically so that the measured

pressure is obtained. The resulting test gas in the reservoir slug

quickly looses energy due to radiation. However the radiative energy loss is greatly restricted by the fact that the gas is optically opaque to all visible and near visible radiation. In fact about 95% of the radiation

emitted from the gas is reabsorbed. Nevertheless, the energy loss due to radiation is still considerable and strongly influences the nozzle exit conditions. The radiative energy loss changes the enthalpy of the gas in the reservoir slug by 45% in 50ysec.

126 nonequilibrium flow is established in the nozzle. This flow is reasonably well behaved until the helium driver, which flows down the side walls,

reaches the throat of the nozzle and starts to contaminate the nozzle flow. As the gas in the reservoir region is optically opaque and it becomes optically thin as it goes down the nozzle, the radiation field observed looking up the centre of the nozzle towards the throat is similar to that of a stellar atmosphere. The mechanism by which the absorption spectrum from the impurity atoms is formed was investigated. The aim was to determine whether the spectrum could be used as a diagnostic technique to study the flow in the nozzle. Theoretical analyses showed it was not

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