Sodium line reversal temperature measurements in shock-tube flows

SODIUM LINE REVERSAL TEMPERATURE MEASUREMENTS MAY, 1963 IN SHOCK-TUBE FLOWS by W. H. Mak

rrCHNISCHf HOGESCHOOL

VLIEGTUIGBOUW/(UNDE Bl~iiOn![EK

1

NOV. 1963

•

SODIUM LINE REVERSAL TEMPERATURE MEASUREMENTS IN SHOCK-TUBE FLOWS

by W. H. Mak

,

ACKNOWLEDGEMENTS

I should like to thank Dr. G. N. Patterson for his interest in the present work. The research was suggested and supervised by Dr. 1. 1. Glass. His guidance, discussions and critical reading of the final manuscript are acknowledged with thanks. The valuable discussions held with Dr.LR. Hurle of the Cornell Aeronautical Laboratories are sin-cerely appreciated.

I wish to express my indebtedness to Dr. D. R. Lovejoy for the calibration of the tungsten filament strip lam p. The assistance of Mr. J. Leffers and Mr. R. H. Chappell in building the apparatus and the typing of the final manuscript by Mrs. J. Dublack are also gratefully acknow ledged.

The research was supported by the U. S. Office of Naval Research, and the National Research Council and the Defence Research Board of Canada.

\t

SUMMARY

The sodium line reversal method was applied to study the elec~ronic excitation (vibrational) temperature profiles behind moving norrnal shock waves in nitrogen and air in a 3 in. x 3 in. shock tube. The ternperature range was approximately between 23000_{K and 2600}0_{K at shock} Mach numbers between 6.5 and 6. 9 and initial gas pressures of 3 and 4 mrn. Hg. The effects of the finite light source and the cool boundary layer have been considered. Satisfactory agreement between observed and theo-retical values of the temperature was obtained for shock waves in nitrogen. The results in air in general gave temperatures higher than the calculated values. The recording apparatus had a rise time of 3~s and the precision of rneasurement was limited by the photomultiplier noise level to the order of 2%. The effect of the bound'ary layer was found significant in comparison with the error of the measurement. Greater precision could have been achieved by using a phototubeoflower noise level, but it would still be limited by the fluctuations in the sodium population in the hot flow.

1. 2. 3. 4. TABLE OF CONTENTS NOTATION INTRODUCTION

PRINCIPLE OF SPECTRUM LINE REVERSAL METHOD

2. 1 Analysis for "Point" Light Source 2. 2 Analysis for "Finite" 'Light Source 2.3 Correction Due to Cool Boundary Layer 2.4 Modificatïon ofthe Méthod

2. 4.1 Two-Lens Arrangement 2.4. 2 Three-Lens Arrangement

2. 5 Accuracy of the Method

EXPERIMENT AL ARRANGEMENT

3. 1 3 in. x 3 in. Wave Interaction Tube 3.2 Reference Tungsten Strip Lamp 3.3 Optical System

3. 4 Photomultiplier System

3. 5 Introduction of Sodium Chloride

EXPERIMENTAL RESULTS AND DISCUSSIONS

4. 1 Calibration Constants

BiûU011-lEEK

Page vi 1 2 4 6 6 10 11 11 12 14 14 16 17 17 19 19 19

4.1.1 Spectral Transmission Factors 't l' 't"2 and 1:'w 20

4. 1. 2 Solid Angle Ratio ks 20

4. 1. 3 Photomultiplier Sensitivity Ratio km 21

4. 2 Excitation of Sodium Atoms 4.3 Shape of the Light Pulse 4. 4 Emissivity-Time Histories 4.5 Temperature-Time Histories

4. 5. 1 Results in Nitrogen 4. 5. 2 Results in Air

4. 5.3 Vibrational Relaxation Phenomenon

23 24 26 27 27 29 30

4.6 Comparison of Accuracy Between Present (Parallel- 32 Beam) Method and Cross-Beam Method

4.7 Extension to Higher Temperatures 32

'

.

5. CONCLUDING REMARKS 34

REFÉRENCES 35

APPENDIX A - Brightness Temperature of Light Source 38

APPENDIX B - Calibration of Tungsten Strip Lam p 40

APPENDIX C - Determination of Spectral Transm ission 42 Factors

APPENDIX D - Solid Angle Ratio ks for "Point" and "Finite" 43 Light Sources

APPENDIX E - Accuracy of the Method: Cross-Beam 45

A a e

o.O.

P .R T NOTATION area

absorption signal (Appendix E) coefficient defined in Eq. 17 coefficient defined in Eq. 19. integration constant (Eq. 16b)

first radiation constant (= 4. 992 x 10- 15 erg. cm.) second radiation constant (= 1. 439 cmoK

diameter

.aperture diameter

electronic charge (coul.). emission signal (Appendix E) frequency (c. p. s. )

Planck's constant current (amp. )

radiation intensity at wavelength

1\

Boltzmann's constant

photom ultiplier sensitivity ratio solid angle ratio

optical path length Mach number

shock Mach number

secondary multiple emission constant optical dens ity

pressure

resistance (ohms) temperature

Ta TB, T o TE TG TGM TGMmin TG, t Tt T w T't" t u u~ v ~v W w x,y Xl' X 2

aLp

o(~

'6>.

/;

apparent temperature brightness temperature

electronic excitation temperature gas tem pera ture

mean gas temperature

minimum gas temperature (Eq. 31) true gas tem perature

true temperature·

wan tem perature

temperature defined in Eq. (44) time (sec. )

object distance (cm)

radiation density per unit wavelength

image distance, voltage, velocity in stationary shock reference system

voltage defined in Eq. (11)

defined in Eq. (34) shock wave speed

distance (cm. )

integrals defined in Eq. (28) and (29)

pyrometric absorption (10-6 oK-I)

spectral absorptivity

spectral sensitivity (watts /lumen) boundary layer thickness

p

...n

_B

Sla

laminar boundary layer thickness turbulent boundary layer thickness spectral emissivity

radiation flux at wavelength 'i'\

,.,.

l'Ol"'~-1/

ui .. , . 111:1:h

radiation flux from background light source (Eq. 8)

radiation flux from luminous gas (Eq. 7)

total radiation flux (Eq. 6)

defined in Eq. (22)

o

wavelength (A ,

j( )

density

vibrational relaxation time (sec) spectral transm ission

kinematic viscosity (cm2/sec), frequency

solid angle (rad. )

solid angle from image source solid angle from gas

1. INTRODUCTION

The study of a high temperature gas using pyrometric tech-niques has become increasingly important in the fundamental research of gas-dynamics, chemical kinetics and combustion. Bundy and Strong (Ref. 1) pre-sented an excellent review of the spectrum line reversal method and the apparatus developed for the measurement of flame temperatures. Buchele (Ref. 2) constru-cted a self-balancing line reversal pyrometer which gave di-rect temperature readings for working gases in the rocket engine and

Tsuchiya (Ref. 3) developed an automatic recording pyrometer to include the non-balancing method. More recently Burrows et al (Ref. 4) worked with the emission-absorption bands of water vapour and carbon dioxide and devised an infrared pyrometer for measuring unburnt end gas temperatures in an engine.

In non-stationary processes, Clouston, Gaydon and Glass (Ref. 5) first adapted the sodium-line reversal method for time-resolved studies of temperature behind shock waves, but it only gave information whether a particular shock was hotter or cooler than the brightness tem-perature of the background source. A later modification of the method to use two beams (Ref. 6) enabled an actual determination to be made of the temperature course behind a single shock wave. This modified method was then applied by Gaydon and Hurle (Ref. 7) to investigate the relaxation

phenomenon at the luminous front in shocked gases. Independently in Russia, Fatzulloy and his coworkers (Ref. 8) also adapted the sodium line reversal method to measure the temperature distribution behind shock waves. The difference between these two modified methods is in the arrangement of the two optical beams (see Fig. 1), one being a cross-beam and the other being a parallel beam arrangement.

While the sodium D-lines are most commonly used in spectrum line reversal studies other spectrum lines such as the lithium red line, the indium blue line and lines from the iron spectrum have been employed in flame temperature measurements (Ref. 9). Bauer et al (Ref. 10) studied the emission intensities of chromium lines from shocked gases up to tempera-tures of 55000_{K and Gaydon and Hurle (Ref. 11) used the chromium blue}

triplets to measure the temperatures in detonation mixtures. Faizullov et al also reported using the resonance line of ionized barium, Ba II 4554

if

successfully behind incident shock waves (Ref. 8) and reflected shock waves (Ref. 12).

At U. T. 1. A. it is planned to investigate in the 4 in. x 7 in. hypervelocity shock tube the Prandtl-Meyer flows in oxygen and argon in order to obtain information about the temperature variation and the chemical processes through an expansion wave. The pyrometric technique to be used is the spectrum line reversal method modified by Faizullov et al (Ref. 8). In the previous papers it has been assumed that the two beams traverse two conical volumes in the luminous gaseous body of identical emission-absorption

properties and sodium concentration. However, it is the purpose of this investigation to study critically the accuracy of the method and to take into account the finite size of the reference light s.ource and the absorption in the cool boundary layer. This is a preliminary work on the excitation of the resonance lines in sodium. introduced in trace amounts as sodium chloride. in nitrogen and air. The experimental gas is shocked to temperatures from 23000K to 26000K at shock Mach numbers of 6.50 to 6.86 and initia 1 pressures of 3 and 4 mm Hg. in the 3 in. x 3 in. wave interaction tube (Ref. 13).

2. PRINCIPLE OF SPECTRUM LINE REVERSAL METHOD

The radiation density in energy per cu. cm. of a black body at temperature TOK having wavelengths between À. and )..

+

dÀ can be

formulated from the statistical point of view by Planck's radiation law (Ref. 14):

-5

8rrhcÀ

- - - - : - - - d,\

exp~

- I

kT

\-s-C. I À

exp~

_I ÀT (1)

where cl and c~ are the first and second radiation constants having the value of 4. 992 x 10-1 erg. cm. and 1. 439 cm. oK respectively. The corresponding relation for the radiation intensity I À in ergs. per sec. (or watts) per unit solid angle norm al to the surface of the black body of area A is

I,À

=

2AC.À-S-eXb~-1

f À I

(2) Instead of Planck's equation, Wien's equation is a very good approximation for c2/

>--

T

>

5 in the visible range of the spectrum, so that Eq. (2) becomes

\ -s

C )

I).. =-

2 A

c,

A eX

p (- '"

~

d

À

(3)

The radiation flux over asolid angle 12 is then

(4)

For a non-black body with aspectral emissivity é À the radiation flux is reduced to

(4a)

In the spectrum line reversal method, one beam of light from the reference background light source at a brightness temperature TB (see Appendix A) passes through a gaseous body at a temperature TG' The radiation flux having wavelengths between À. -

cf

À and

À.

+

JA

is isolated by a spectrograph (or interference filter) and received by a photo-multiplier. The total radiation flux measured is then the sum of the spectral emission and transmission of the gas:

(5 )

By assuming thermal equilibrium and applying Kirchhoff's law where ~À

=-

~,

and

1:'",

= (1 - ~), Eq. · (5) becomes

<PTV T

=

ct>

G ( À ,TG ) -t- (\ - é)..)

q;

8 ( >---I

TB)

(6 )

When TG is greater than TB'

cp

TOT is larger than

f>

Band the spectrum

line appears brighter than the background intensity. Similarly when Ta is

less than TB'

<P

TOT is smaller than

q::>

Band the spectrum line appears

darker than the background intensity. The reversal condition is that when

the total radiation flux is unchanged in the presence of the gaseous body.

When this happens, from Eq. (6), TG

=

TB' i. e. the temperature of the gas

and the brightness temperature of the reference light source are the same.

This is the null method used in self-balancing pyrometers.

In shock-tube flows of high-temperature gases, it is almost

impossible to achieve experimentally this null condition. The temperature

difference between the hot shocked gas and the reference source will vary

from shock to shock. In order to determine the actual temperature of the

gas, a double beam arrangement is used. Figure 1b shows the optical paths

of the two beams in this investigation. With the two beam arrangement

three quantities are measured and they are necessary and sufficient to

de-termine the temperature of the gas. These quantities are: .

(1)

cp

G

(2)

<:\'

B

(3)

<?

TOT

=

radiation flux from the luminous hot gas alone at temperature

TG'

= radiation flux from the background light source at its image

position in the hot gas region, its effective brightness tem-perature being TB, and

=

total radiation flux from the hot gas and the background light

source.

The principal assumptions of temperature measurement using the spectrum line reversal method are as follows:

(1) (2)

(3)

The flow is one dimensional and planar.

The presence of small amounts of sodium chloride does not affect the properties of the test gas.

The electronic excitation of the sodium atoms follows the vibrational degrees of freedom of the gas.

Assumption (1) is necessary. With reference to Fig. lb, it is

ver-tical plane and there may be a mean temperature difference between these twö volumes. However, by making the two beams overlap more in the test section such that their separation is small compared with the height of the shock tube, and positioning them close to the axis of the tube (away from the cool boundary layer) an insignificant temperature difference may be assumed.

The extent to which the concentration of sodium vapour, chlorine vapour and sodium chloride crystallites affect the shock relations

cannot be estimated. A high concentration of light emitters will introduce

self-absorption in the cool boundary la~er and as aresult will change the

magnitude of the quantities

cp

G and qJ TOT' The correction due to this

self-absorption will be considered in Section 2.3. Bauer et al (Ref. 10) were able to work with a controlled concentration of their light emitter and main-tain the same experimental condition. In the case of sodium chloride this

control has not been possible because of its very low vapour pressure. It is

not known what the maximum quantity of light emitter is that can be introduced without affecting the properties of the test gas appreciably.

As for assumption (3) Gaydon and Wolfhard (Ref. 9) have shown strong arguments for this mechanism of excitation of the sodium atoms. In Ref. 7 the results of studying the relaxation times at shock fronts for various gases and their close agreement with theoretical predictions gave further support for this view too. However, anomalies have been found in flame

temperature measurements (see Ref. 9) and the observed reversal

tempera-tures are much higher than theoretical, especially in the reaction zone,

where the temperature tends to increase for resonance lines of shorter wave length,greatly exceeding the theoretical flame temperature for lines in the ultraviolet.

2. 1 Analysis for "Point" Light Source

By a "point" light source it is meant that (hl d) is much less

than unity, where h is the effective size of the light source or its image

as seen by the photomultiplier and d is the diameter of the cone of light

em ergent from h as it fills the lens. Figure 2 shows the details of the two

beam arrangement. M1 and M2 are the mirrors which reflect the beams into

the photomultipliers. The two identical apertures on S3 ensures the two beams

having the same effective emitting areas AB(h) and AG(h), and S2 ensures

their having the same solid angle, .J7... e

=

Sè..G::I , if (hl d) ~c::.. 1. It is not

necessary to keep a one-to-one magnification of the .light .. source at any

image position. Any magnification or reduction of .the light source as aresult

of the arrangement of the lens will not affect the te,mperature measured

pro-vided that the inequality (

nl

d

c::..<

1) is true for every image of the s~urce.

The three quantities

4>

G J ~B and

.q:>

TOT are expressed

~6

2

E,À C I \ - 5"

e )(

F (-

~

),TG

) A6

çz~

JA

(7 )

CPB

Zei ,.-\ - s"e-x

p ( -

,AC';:"B)

AsRs

JA

(8)

<?TO'T

=

CP<s

+

(I -

é).. )

~

B

(9)

Since AG

=

AB and

S2..

_G

=

RB and af ter some manipulation of Eq. (7), (8)

and (9), the temperature TG of the gas may be expressed in terms of the flux quantities as

(10)

The temperature TB of the light source can be found by calibration against

a standard pyrometer at the wavelength

À

and then correcting for the loss

of light at the test section window

xt\i

and at the lenses between Wl and the

light source. The flux quantities are measured from the output signals of

the two photomultipliers. The arrangement of the two beams is such that

one will respond to ~ G and the other to

ct>

TOT. Since the zero level of

the second beam corresponds to

c?

=

4>

B' then the deflection will be a

measure of ( ~ TOT - ~ B). The currents generated by these radiation

fluxes flow through two identical resistors R, and the voltages developed across them indicate the magnitude of the flux quantities if the spectral

sensitivity

&

/.

of each photomultiplier is known. Let these voltages be

Ll v and vG respectively such that

6 V

=-

?f

>-- I (

cp

TOT -

cp

8)

R

'( \' ".,h

R

V6

=

À ~c;

(11)

(12)

When Eq. (11) and (12) are substituted in Eq. (10), one finally obtains the

temperature TG as

\1

....L

== _\ +

L \

h ( \ _

'6

À •

~

)

\ 6 T B (.2..

't)....'

V6 (13)

.../ \\ \

The ratio ( 0 À / t).. ) is the spectral sensitivity ratio km of the

2.2 Analysis for "Finite" Light Source*

When (hl d) is approximately greater than O. 02 the finite size

of the light source will have to be taken into consideration. This is due to the fact that the photom ultipliers will collect radiation from the luminous

gaseous body over asolid angle which is larger than the light source. The

ray diagram in Fig. 3 makes this point clear.

The reference light source 11 forms an image 12 in the hot gas region and it is focussed again at image 13 to fill the whole of the

aperture S3 to the photomultiplier. It is seen that the area of the aperture

S3 receives radiation from the image source 12 over asolid angle f2.._{B ,}

while it receives radiation from the hot gas over asolid angle

..n.

_{G , which}

is larger than St- B' The values of AG and AB are still equal by virtue of

identical aperture sizes on S3' Therefore if the solid angle terms in Eq. (7)

and (8) are retained, the temperature of the gas is then given by

=-

_\-TB

(14)

The ratio

(SZ

GI

QB) is the solid angle ks of the optical system. When

the areas of the two apertures on S3 are not the same, an additional area

ratio correction term will have to be applied to ( ~ v lVG) to correlate the

signal output of the two beams. This term, however, is taken care of .

automatically in the calibration of km. The physical significance of th'e

factor ks is apparently to increase the temperature of the gas. For example,

in a typical case for the present optical system, ks

=

1. 20, TB

=

23530_K

(1 - km Àv )

=

O. 5, the calculated temperature assuming a "point" sóurce

vG

is 25210_{K, while thetrue temperature is 2474}0_{K, which gives a differenc.e}

of

+

470_{K. The reversal temperature at which the reference light source}

has to be operated is then increased accordingly in order to compensate

for the added flux from the hot gas arising from the larger solid angle .J2 G'

2. 3 Correction Due to Cool Boundary Layer

In an actual flow in a simple shock tube of constant

cross-section there is a boundary layer growth along the walls'. It starts growing

at the shock front and increases in thickness until it reaches a maximum

at the contact region. Any sodium vapour trapped in this cool layer will

absorb energy from the radiation in the main body of the hot gas, so that

* The author is grateful to Dr. 1. R. Hurle of Cornell Aeronautical

Labora-tories, who pointed out the finite size effect in a discussion. It may be

corrected by using a larger lens L1 and an aperture (Fig. 3). See also

~ TOT and

cp

G measured will be mean quantities. along the optical path

length in the test section. The temperature thus calculated from

c?

TOT

and

c?

G is then a mean value TG, M which is less than the true freestream

value TG t

_,

· TG _, M will dep end on the boundary conditions and thermal

gradients present in the cool boundary layer.

In order to study the effect of a thermal gradient across the

boundary layer on the measured gas temperature TG M, a simplified analysis

of the diffusion of radiation through a non-isothermal emitting region is pre

-sented in the following:

Consider an elemental

volume

Jv

in the emitting region,

the monochromatic radiation flux inci

-dent on the surface A(x} is

4'>-

(y.)

and the radiation flux emergent from the surface A(x +

8"

x} is ~>- (x +

d

x).

Hence the change in the radiation flux on passing through this volume is, neglecting 2nd and higher order terms)

d~À

S

X.

óX

by

The amount of incident radiation transmitted is al ~À (x)

J

x and the

amount emitted is a2

q>

/

\

g

(x)

cS

x, al and a2 being functions to be evaluated

from the boundary conditions. (Note that

4>"9

C)'..) is the black-body value}.

Thereforethe net increase in the radiation flux is (q\

~À

(l"-)cl

X-;-C!2..<f/

\

Slx

)

]d.x

This must be equal to ~

S

X

'

so that

<::1><

::=. ct \

cp"

+

Cl l -

<f

>-

<j-or

-

_-

₍₁₅₎

It is now necessary to determine al and a2 in terms of the physical quantities

of the emitting gas. Assume th at the gas is non-emitting, i. e.

<V

>-.

9

=

0,

then Eq. (15) is reduced to

and the solution for

q:>.À

is, for a path length of L,

L...

C

I

e

jo

q\d

X

(16)

o ~.x~L (16a)

If L

=

0 is identified with the edge of the region, then at L

=

0,

Cl

=

~À (o), where ~ A (o) is the radiation flux from a source outside the

The exponential term may now be identified with the coefficient of trans-mission -C-~ of the region over a path length L. Since ~::: \ -o<.~ the value of al is given by \ \'î

L,\ -

\

n

(I

-O<A)

For al

=

constant

Cl,

=

(16b) (17a) (17b) and al is the logarithmic decrement of the transmission coefficient over the path length L. It should be noted here that the quantities 'l"A, 0<.>.. and ~)\ are not constant values, but will vary with the density and temperature of the emitters.

To determine a2' consider the case when the radiation flux remains unchanged on passing through the volume. From Eq. (15)

Physically, this is achieved when the intensity of the incident radiation matches that of the emitting gas, i. e. ~~ ( ü)

=

4t.>..

3-

so that

(18)

(19)

Substituting Eq.

obtains the general solution as

l-(19) in Eq. (15) and solving for ~i-

(L..).

one

j

<::1,oX

~>-lL..)

==

~,>.

(0)

~

0

J~

Ci,d)(

j

l.. ril. -

J:

c:rtcb(

é

0

Q")'5

e

dx

(20) For al

=

constant, (21) where l... _ Ot. 1 'J.

~

(l...) ';:.

jo

4'

>--

s

e

d X

(22)

When the temperature variation along L is given,

c:\?

>-9

may be ca1culated and Eq. (22) can be evaluated numerically.

We may identify the terms in Eq. (21) with the flux quantities obtained in Section 2. 1:

1'TOT ::::.

CPr

CL.)

(23)

4>B

-

-

cP>-

(0) (24)

~~

Q1l- (25)

-Cl,

e

~

CL-)

-It has been shown that the measurement of

cP

TOT'

q,

Band

cp

G only gives the mean temperature TGM of the gas. In order to find the true free-strearn temperature TG, t, Eq. (2.5) will have to be solved by trial and error. al is known from 0<). (= €),) calculated from E.q. (9). 'l'he tem-perature profile through a laminar (or turbulent) boundary layer is either plotted or expressed in closed form, and the boundary layer growth behind the moving shock wave is also given explicitly in terms of the flow variables

(Ref. 16). A value of TG, t is then assumed and ~ (L) is evaluated numeri

-cally. This is repeated until that value of Tq, t is found which matches the right hand side of Eq. (25) to the measured

C1'

G. Burrows et aI (R,ef. 4) used the null rnethod in their measurement of unburnt gas temperatures in an engine by an infrared pyrometer. They applied this correction due to the cool boundary layer and assumed a linear temperature profile across the layer.

However, Eq. (25) may be solved in an other way. The flux

cp

G may be expressed in terms of TG M as

1'~

==

2

Cl )..- S

(I -€

~Il..)

e

'i<f (-

>.~;

M)

AG

RG

Ó),

Substitute this in Eq. (25) and simplify.

obtained as:

The mean gas temperature TG is

(26)

Let the boundary layer thickness be band the temperature profile along the path length

L

be as follows:

Tg

=

T(x) ~ ~ ,x~ ~

Tg

=

TG, t

S

~ >< S:- L-Ó

T _g

=

T(L-x) L~~~ )(.S:: L Then, Eq. (26) may be simplified to

_ \ :=.

--L -

À

\r,

T6M T~t- c.'l..

where Xl and X2 are the integrals:

j

f

_

[

~

(..l-

-

+- )

1-

q, I )<

J

.x::;

e

À T !~t

d

x

\ 0 (28) r

[..!:=..I

\

.J.-)

Cl

J

X

~

=

j

b o

é

- /\

I I -

TG

c - , 'j

dl

(29)

(Note in Eq. (29) the substitution of y

=

L-x has been used here). The

mini-mum value of TG, M is obtained when the integral terms are neglected:

>-.

_o\\~

-

~\

C. L.-J) }

-..!-

Infe

- e

TE,;t, CL

l

I -

e

-~I~

--

(30)

when al

cS

is small, Eq. (30) may be reduced to

.

-L

-2..

In

( èÓ)

1

-T~d~

Cl.

L..

(31)

Tc

",

M I IV' ,'"

The actual measured temperature therefore lies somewhere between TG, t

and TG M min. For the shock Mach, number range and initial conditions

used in' the present experirnents, the growth of the laminar boundary layer

win be very slow behind the moving normal shock wave, so that (TG, t -TG, M min) is of the order of 2% of -TG, t. Therefore, the temperature mea-sured by the spectrum line Feversal method is a very good approximation to the true temperature of the hot gas(See Sec. 4.5.1).

2.4 Modification of the Method

It has been shown in Section 2. 2 th at the finite size of the

light source win introduce significant error in the measured gas tempera-ture and that the correction factor ks has to be included in the analysis in

order to give the true temperature. The value of ks can be determined from

the dimensions of the optical system. This is done in Appendix D and the

. results are summarized here:

For a two-lens arrangement,

k:~

- ( , -t

h

~

;-d I

l

~I

~

+-

I )

J

2.. (32)

For a three-lens arrangement,

[ \ -+

n

1-

-

l~

..

+

IJJ

'

~

r

1-+

h

3

~::6::.

+

I

)J~

1,\...-\:.4\

L

h

)

~ d.~ '-'\.~

(33)

From these relations it is seen that the ratio (hl d) determines the ratio of

Even though the light from the background source fills the aperture S~ (Fig. 3), this does not ensure that the same cone of light from the gas is received by the measuring system. Two values of ks (= 1. 20 and 1. 57) have been used in the present investigation and their effect on the photom ultiplier ratio km wiU be discussed in Section 4. 1. 3.

2.4. 1 Two-Lens Arrangement* (Fig. 4a)

Most optical systems in the past using the spectrum line re-versal method to measure temperatures were composed of a two-lens arrangement. With reference to Fig. 4a, the first lens focussed the light from the reference source into the middle of the luminous region a:n,d the second lens collects all the light into the spectrogr~ph (or interference filter)-photom ultiplier unit. Since the image of the light source usually overfills the aperture S3' it is then required tha,.t the aperture S2 only passes that cone of light which goes through S3. _{The diameter da of the aperture is} deter-mined by closing S2 (adjustable) until the d. c. level from the photomultiplier output begins to fall. ks can now be found from Eq. (32).

~

2 .. 4.2 Three-Lens Arrangement (Fig. 4b)

This optical arrangement was used in the present experiments.

The reference light source was a tungsten strip lamp with aJong vertica{ fila-ment. In order that the image formed on S3 did not fall on the entrance

a,perture to the other photomultiplier, it was found necessary to form a small effective light source Sl with an extra-lens. As a result of this, more light loss would be incurred due to the extra lens. The advantage. however, is that a region on the filament with a_ uniform temperature cam be selected and there is more freedom in controlling the image size.

The value of ks for a three-lens arrangement is in general

larger than that for a two-lens arrangement. lts appearance in the logarithmic term in Eq. (14) can significantly influence the value of that term when

(1 - km 6. V ) is small or large. This occurs when

~

km

~

v

~

vG' i. e. vG

when the gas temperature TG is appreciably higher or lower than the back-ground temperature TB and any error in ~ v will.showup as a large error in TG' For example in run No. HN-74A, ~ v

=

.17, vG

=

.29, km

=

1. 20, ks

=

1. 57 and this gives (1 - km 6\1 )

=

.296 and a temperature TG

=

25470_K.

vG

If l:l v

=

.

18, this will give (1 - km ~

v )

=

.

255 and a temperature TG

=

2581 oK, a difference of 340K already.

vG

This difference will be sm~!ler if ks is near unity.

* This arrangement is recommended by Dr, 1. R. Hurle, Cornell Aeronautical Laboratories, Buffalo, N. Y.

2. 5 Accuracy of the Method

The temperature TG measured is the mean value along the pa th

length of the be am in the hot gas region. To estimate the probable error

_b

TG in TG, consider the general relation in Eq. (14):

J=-

~ ..L ₊

l

_{ltl \/ti}

'c:; Î(\ ? L (14) where

kMÓV)

W

-

k.s

(1-\l~

(34)

In finite difference form

~

~-r;,

':. t; where

~

~ VII

-L

"l0-

e

~

:s

~Tg

') ~W cl..

'iJ

(35)

k~L1V/1 [bk~

of.

~v)_ ~l

1_ k",.ó.

v

\I,

~

.

M

V~

_J

₍₃₆₎

Since, TG Is made up of the algebraic sum of two independent quantities TB and W, each subject to errors of measurement, the combined probable error

_tT

G· in TG is the weighted sum of the errors

bTB

and

bw,

and from

Eqs. (35) and (36), it _{may be approximated by the relation:}

r-i''i

~ ~ /(;~r

_($'8)

1-

(21-

T~ )~

(t;)"

₍₃₇₎ where

The main contribution to

è

_{TG are the errors}

_tT

B , '?;ks'

2>k

m ,

S(

A v) and bvG. _{Each of these errors wiU be considered below:}

(1)

"ST

B This term is mainly the probable error of the calibration

of the brightness temperature of the reference light source

(see Appendix A). It _{is the random error in brightness}

match-ing when the standard pyrometer lamp filament is matched

against the tungsten strip filament. In the range of

tempera-tures from 20000

K to 3000oK, errors can vary from

i"

50K to

~ _{20oK, depending on the type of light source and the method}

of calibration used. In this case as noted, the error was about

O. 4%.

This is _{the probable error in determining the value of ks, which}

is a constant for a fixed geometry of the lenses and aperture

sizes. _{Ideally ks can be determined as accurately as it}

(3)

~k"",

desired. However a limitation is imposed. by the accuracy of the imag.e positions, distances and sizes. In this work the error was about 3%. In Ref. 15 where ks is made equal to unity by using. the correct aperture size for the lens

J...1

in the two-lens arrangement, there wiU be an uncertainty

in

deter-mining this aperture size and therefore a probable error in matching JG G

=

52.

B. This error may be assumed to be of the order of 3% too.

This error is not introduced by the photom ultipliers but by the non-uniformity of the flow behind the shock wave. Even though the spectral sensitivities of the two photomultipliers can safely be assumed constant, the difference in temperature and pop-ulation of the excited sodium atoms between the two conical volumes traced out. by the beams wiU induce fluctuations in the level of radiation flux, and therefore fluctuations in the value of km as a function of flow time. This is the reason why a static calibration of the sensitivity ratio of the phototubes is not sufficient and a dynamic calibration is required to give the true flow picture. The results of this calibration are presented in Section 4. 1. 3.

This error in the signal is mainly due to the noise generated by the photom ultiplier when the steady light from the background source is shining on it. This noise arises from the fact that photoemission is a statistical process. Thus for a fixed amount of incident light, the average photoelectric current wiU be fixed, but the instantaneous current wiU fluctuate around the average. This fluctuation shows up as noise in the signal and H is

entirely similar to "shot noise" in a thermionic tube. The photoelectric current I in terms of the flux is

(39)

Also the mean square value of this photoelectric "shot noise" current is given by (Ref. 17)

(40)

where n is the secondary multiple ernission factor, e is the electronic charge and A F is the frequency band width of the recording system. Combining Eqs. (39) and (40) gives

2lr

L

_ Z V'1

e

r'À

~~

Ll

'F-and the mean square root voltage fluctuation is

-(5)

b

VG

Now, the change in the voltage level is caused by a change

in the incident radiation flux, i. e.

K

v =

K..

fA ~~;'\.

There-fore the signal-to-noise ratio is

~V

_ ;:

a)

or-~À

(42)

J

rIJ)..

cp/-

'

2.

neDr

Equation (42) shows that a high spectral sensitivity

lS"A

and

large 64,A are necessary to give a l~rge ratio. The results

of Clouston, Gaydon and Hurle (Ref. 0) show a very good

signal-to-noise ratio by using the E .rl·r.6095 and 6097

photo-tubes, while in Stollery's work (Ref. 18) the signal-to-noise

ratio seems to be less favourable.

T~ error i~G due to noise is usually small compared with

ó(b. 'I) and 8 km and it may be neglected. This is justified by

the results of the experiments.

Equation (37) also shows that the probable error

óre,

is

tempera-ture dependent. Since (TG/TB)4 seldom exceeds two for the normal working

range ~as temperatures the first term contribution is only considerable

when ~\B is large. Usually the second term is predominant and will limit

the accuracy of the method at high temperatures unless an ef.fort is made to

reduce(

t5 WW)

.

An examination of Eq. (38) shows that (

JVi/W)

is

mini-mum when ó v is zero. However when ~ v is small it will be difficult to

distinguish the signal from the noise and a compromise has to be made

be-t~n accuracy and goog signal-to-noise ratio. In run No. HN78A at t

=

601"'5,

bT6 =

±

lOoK, d K ... =

i'

. 04 , ~ =

't .

05 ) J(ÓV)

I

~ V = • 120. These yield

'è 16

=

±

460_{K at TG}

=

₂₄₆₃0_{K, an error of about 2%.}

Figure 5 is a plot of TG vs 'W (Eq. 14) at TB

=

23530K and

2427 oK. The two brightness temperatures correspond to the tungsten strip

lamp currents of 18.00 and 19. 00 amp. respectively in the present

experi-ments. Figure 6 is a plot of the probable error ~T<S7 vs the gas temperature

TG' There is on~ little increase in

6 T

q with temperature TG at the

same value of (

r

W/W).

The difference between values for TB

=

23530_{K and}

Ta..-:: 24270K is ~mall. However, th~ror ~Tq increases rapidly with

(

~

W /W)

and doubling the value of ( JW

/W)

just doubles the error, showing

that the second term in Eq. (37) is predominant.

3. EXPERIMENT AL ARRANGEMENT

3. 1 3 in. x 3 in. Wave Interaction Tube

The present investigation was done in the 3 in. x 3 in. (7. 62 cm

x 7. 62 cm) wave interaction tube (Ref. 13). The schematic arrangement of

the shock tube and the optical and electronic components is shown in Fig. 7 and an overall view of the apparatus is shown in Fig. 8.

The driver section was 91. 4 cm. long, the driver gas being hydrogen supplied from high pressure commercial cylinders. The use of helium as a driver gas was attempted, but it failed to generate shock waves of high enough temperatures and sufficient sodium resonance radiation to give areasonabie pulse deflection on the oscilloscope. The limitation is due to the low maximum operating driver pressure, about 90 psi, and the low density behind the shock wave. The channel section had a length of 411. 5 cm. The experimental gases chosen were nitrogen and air, and they were intro-duced through a sharing chamber into the channel. The sharing chamber was a short (30.5 cm. ) channel section, but was later replaced by a large glass cylinder because of leakage problems.

Initial runs were made with red-zip cellophane diaphragms, but the wrinkling of the diaphragms on pressurizing the driver section intro-duced much leakage at the diaphragm station. Finally a cellulose acetate dia-phragm of O. 25 mmo thickness was found to be satisfactory. It ruptured into fine shreds which were carried down the length of the shock tube. These shreds were blown away by a jet of compressed air after each run. The dia-phragm was held between rubber gaskets bonded on to the tube sections by contact cement and clamped in position by four pairs of vise-grip pliers.

A solenoid-operated mechanical plunger supplied by a 6-volt car battery broke the diaphragm to initiate the flow.

The station for optical observation was 34.3 cm. from the end plate. The glass windows being 46 cm x 8 cm high installed in a special 61 cm. section of the shock tube. These windows were set flush with the inside surface of the tube. A white cloud of fine NaCl crystals covered the inside surfaces of the windows af ter each run and a thorough cleansing of these surfaces was do ne each time to ensure no additional loss of light from the reference tungsten strip lamp because of the opacity of this cloud.

The vacuum system consisted of a Kinney CVD-556 compound high vacuum pump and Wallace and Tiernan absolute pressure gauges. The leakage of the tube was found to be 0. 13 mm Hg per minute, pressure rise, at PI = 0,.25 mm Hg. This was believed to be through the lead seals in the

individual sections and this leakage rate gave rise to an impurity of 1% oxygen in nitrogen at a channel pressure of PI

=

4 mm Hg. The effect of this amount of impurity on the thermodynamic properties of the shocked gas has been neglected, although it would slightly affect the vibrational relaxa-tion time of the nitrogen molecules. The leakage presented no problems in the case of air as the experimental gas.

The shock wave velocity was determined by measuring the time interval for the shock to travel over two temperature sensitive platinum films 76.2 cm. apart. These films were made of Hanovia colloidal platinum paint fired on to the surfaces of two small thin pieces of ordinary glass. The piece of glass was then bonded on to a wall plug and made flush with the inside surface of the wall. The output signals from theseplatinum resistance film gauges were led to a dual channel pulse amplifier and a Potter 8 megacycle

chronograph. The response time of the system was about ~

JAS

and the time interval was read to the nearest microsecond. The accuracy of the shock wave velocity is estimated to be 10/0, which corresponds to an error of

!

500_{K in T2 at 2500}0_K.

The radiation from the luminous hot gas was received by two photomultipliers and the output signals were displaced on a dual beam cathode rayoscilloscope, Tektronix type 555, which was triggered through a time

delay unit by the output pulse from the first platinum resistance film gauge. The sweep of the oscilloscope was calibrated by a 200 kc / s audio oscillator. 3.2 Reference Tungsten Strip Lamp

The reference background light source was a gas-filled tung-sten strip lamp manufactured by the General Electric Co. Ltd. of Wembley, England. It was chosen for two reasons:

(1)

(2)

According to the data of Barber (Ref. 19), this particular lamp "provides a source of substantial area reproducible in brightness to a high degree of precision. " Since the

emissivity characteristics of tungsten are well known, e. g. Larabbee's data (Ref. 20). it is then most suitable for a temperature substandard.

The sighting position in the lamp is defined by a small notch clipped in the edge of the filament half way along its length. This provides for a fixed point of reference both for calibra-tion and for comparison as a light source.

The lamp had a cylindrical glass bulb 19. 0 cm. long and

6.3 cm. in diameter. and a strip filament 1. 3 mmo wide and 0. 07 mm. thick. The strip had right-angle bends to the supports at about 5 mm. from the ends to allow for expansion. The total length of the filament was 45 mm. The lamp was calibrated to its maximum operating current of 19 amperes corres-ponding to a brightness temperature of about 25000_{K at an effective} wave-length of À

=

0.655

r

.

The calibration of the brightness temperature of this lamp. UTIA # 259A. as a function of lamp current is described in Appendix B. An area of approximately 1. 0 mm diameter at 5.0 mm. above the notch was

selected by.the optical system as the reference light source. At this position of the filament. the temperature was found to be uniform to

:!"

50K for a

length of

t

2. 5 mm. The accuracy of the brightness temperature was esti -mated to be ~ 50_K.

The current to the lamp was supplied by the d. C. generator in the laboratory through a series of 1 kw rheostats of resistances 1. 3. 5 and 25 ohms respectively. The

a.

C. ripple was very small and negligible. The

lamp current was determined by measuring the voltage_drop across a

Reichsanstalt standard resistor of 0.01 absolute ohms with a Pye universal

precision potentiometer. The value of the current was controlled to

!

.02 amp.

3.3 Optical System

The optical system was a three-lens arrangement described

in Sec. 2.4.2. Light from the reference lamp was focussed on to the aperture

Sl (Fig. 4b). The filament was magnified three times by the lens L1 and an

effective source of 3.0 mmo diameter was selected from the filament image. The emergent cone of light was collected by lens L2 and focussed into the

middle of the test section. The light then filled the aperture S2 before the

lens L3 and formed a sharp image on the aperture S3'

The two-beam arrangement is illustratedschematically in Fig. 2. S3 consisted of two identical holes of 1. 68 mmo diameter on a smal!

sheet of shim metal. The bottom hole was filled by the image of the

refer-ence lamp and the top hole collected the light emitted by the body of luminous gas only. The centers were spaced 5.6 mmo apart, so that they looked at

two effective areas 3.0 mmo apart in the test section. Two first surface

mirrors M1 and M2 reflected the beams into the left and right photomultipliers respectively. An interference filter placed behind S3 isolated a narrow band

of the continuous spectrum of radiation. It replaced the spectrograph

normally used in spectrum line reversal work. Two such filters, supplied

by Aird Atomic Ltd., were used. oThey weÓe centered at 5893

~

on the sodium

D -lines and had a 'band width of 85A and 15 A respectively at half-peak

trans-mission. The final results were taken using the filter with the narrower band width, and it was found necessary to introduce two neutral density gelatin

filters of a total optical density of 1. 03 behind S3 to reduce the light intensity from the lamp so that the photomultipliers would not be overloaded. Two sets of aperture sizes were used to vary the solid angle ratio ks in order to check this effect.

Since the absorption and reflection losses at the lenses L1,

L2 and the test section window W1 effectively reduced the brightness tempera

-ture of the lamp, their spectral transmission was separately determined.

This is described in Appendix C and the results are presented in Sec. 4. 1. 1.

The dimensions of the lenses and distances of the optical system are given in Sec. 4.1.2.

3. 4 Photom ultiplier System

It has been shown in Sec. 2.5 that to obtain a high

signal-to-noise ratio, it is best to choose photomultipliers with the highest spectral

sensitivity (f" This can be done as follows:

(1) Match as closely as possible the wavelength of the spectrum

( 2)

( 3)

Select a tube with the highest photocathode sensitivity, i. e. the highest nurnber of electrons emitted per ,incident quanta. Keep the collection efficiency of the,first dynode for

photo-electrons as high as possible. The Gollection efficiency is, the percentàge of electrons emi'tted from the cathode which

actually enter the multiplier structure to give rise to the !;lignal at the anode.

Since there are no commel'cially available photomultipliers with a spectral response of peak sensitivity at the sodium D-lines, a com-promise had 'to be made between (1) q.nd (2) in the choice of ~hatotubes. The collection efficiency depends on the electrode designs and literature supplied by manufacturers usually claims almost 100% efficiency. Two ReA 1P2'~ were chosen. They have a S-:4 spectral response, obtained with a cesium-antimony surface. The 1P21 'has nine dynodes with a sensitlvity at 5890A estimated at 8 rnilliamperes per watt and the l(j)~est dark current among the ReA tubes. However, the "shot noise" was fO\.ihd to be exceedingly large, cot>responding to n of the order of 10 6 at a supply voltage of 960 volts, ari anode current of 70.A amps and a bleeder current to photocurrent ratio of 14 (!3ee Fig. 12). The reason for the high value of n is not fully known and '

it cannat be explained by statistical considerations. These ~ubes were later replaced by two Dumont type,k1290 ten stage photot'llbes. TheU" p'erformance was satisfaètory and acceptable at an anode curremt.of 300A dmp and a ~leeder current to photocurrent ratio of 8. The value of

n

is still of the order of

106, but the signal-to-noise ratio increased to 30.

The circuit for the photomultiplier tube is shown schematically in Fig. 9. The tubes were driven at 1500 volts by the same reguI'ated high voltage d. c. power supply. Model N401 manufactured by Hamer Electronics Co. Inc., Princeton, N. J. The regulation was 2 1/2 parts .per 'million· per milliampere. The unit was housed in a ,black box and shiel;ded optically from the indoor fluorescent lighting. These lights in~roduced a'noisy 120-cyc1e ripple which limited the us'eable gain on the cathode ray oscilloscope. It was also found necessary to use shielded coaxial cable~ for all electrical con-nections to eliminate picking up electrical noi~es from the laboratory. The values of the jacket capacitances of these cables were included in estimating the response times of the recording apparatus.

The Dumont k1290 design utilizes the end-on window, trans-parent type of ph0toemissive surface. The size of the ph0to'cathode is 2. 5 cm. in diameter and large enough not to ~mpose any lfmitati~n on the solid angle of the two cones of light aftel' lens L3' These two cprles of light were checked against overlapping at the mirrors by a test lamp in the test section. The results of the dynamic calibration of the s:en~i~ivity ratio of the two photo-multipliers are presented in Sec. 4. 1. 3., This ratio was aiso calibrated statically using the reference tungsten strip lamp.

3.5 Introduction of Sodium Chloride

The procedure to introduce sodium into the flow system was

similar to that used in Ref. 5. Pure sodium chloride crystals were first

heated almost to boiling inside a Cl,uartz tube by a propane flame and the experimental gas was passed over this pool of molten salt into the channel of the shock tube prior to breaking the diaphragm. The operating channel pressure P 1 was controlled by the high pressure Ps in the sharing chamber, and the rate of decrease in Ps determined the flow time over the salt.

However, the quartz tube cracked quite easily despite careful heating. This might be due to nascent Na attacking the quartz. In later runs it was replaced by a Pyrex tube with an electrically heated platinum spiral. The platinum spiral was mounted onto the tube by a side tube. Salt was

coated onto the platinum by heating the latter to red hot and melting the salt

on it. Heating the salt in this way produced fine streams of dense white smoke.

The experimental gas passed over the spiral as it entered the channel. No difference was found in the shape of the light pulse between the two different methods of heating. The position of introducing the salt was also varied, viz at 23, 65 and 140 cm respectively from the end plate, and no significant

change in the pulse shape was observed. The length of the waiting time

be-fore breaking the diaphragm affected the strength of the radiation because

the NaCI cloud would settle to the bottom surface of the channel. In general,

the waiting time between the complete introduction of the salt and the rupture of the diaphragm varied between 15 to 30 seconds from run to run.

4. EXPERIMENTAL RESULTS AND DISCUSSIONS

4. 1 Calibration Constants

The calibration constants which are to be determined

separate-ly are as follows:

(1)

(2)

(3 )

the spectral transmission of lens Ll'

"t

1, lens L2' ~2;

and the test section wind ow W 1; 'Lw;

the solid angle ratios ks for various image and aperture sizes, and,

the photomultiplier sensitivity ratio km.

The quantities in (1) are required in order to reduce the brightness

tempera-ture of the lamp to its correct value in the test section. The solid angle ratio ks is the correction to the finite size of the light source. The photo-multiplier sensitivity ratio km is needed to correlate and interpret the

4.1.1 Spectral Transmission Factors ·_{1'1. 't2 and 't"w}

These spectral transmission factors were determined by the method outlined in Appendix C. The lenses are achromats ; L1 is coated and L2 is not. W1 is ordinary plate glass.

Lens L1 oi.

_r

I

=

2. 7 mireds (l0-60K-1);

Lens L 2 ~f1. = 4.8 mireds; window w1 ~

vi

= 6.4 mireds;

te' 1 = O. 94

't_{2 = 0.89}

'tw = 0.86

The error of the total pyrom etric absorption (= 0< PI

+

0< P2

+

0<. w) was estimated at t 1 mired. i. e. approximately!

70/0.

4. 1. 2 Solid Angle Ratio ks

The dimensions of the optical system are given as follows (units in centimeters): uI = 23.8 vI = 88.1 u2 = 52.5 v2 = 17.3 u3 = 10.0 v3 = 18.6 Lens L1 Dl = 4.4 • f1 = 18.9 Lens L2 Dl = 3.8 • f 2 = 13.0 Lens L3 Dl = 3.4 • f3 = 6.5

Two sets of aperture sizes were used in order to show the dependence of the measured temperature on ks. Their values are listed below:

Set A Set B dl = 4. 24 d 2 = 2. 92 d_a

=

1. 78 Sl= 0.305 S3 = O. 169 (upper) O. 167 (lower) O. D.

=

1. 03 dl = 4. 24 d 2 = 2.62 d_a = 1.45 S1 = O. 152 S3 = O. 082 (upper) O. 079 (lower) O. D.

=

.43 ksA = 1. 57

! .

05 k sB = 1. 20 ! . 05

In Set B. no attempt was made to match the sizes of the upper and lower apertures in S3

4. 1. 3 Photomultiplier Sensitivity Ratio km

It was believed necessary because of assumption (1) in Sec.

2 that the sensitivity ratio of the photomultipliers should be calibrated both statically by using the reference tungsten strip lamp and dynamically by using the chemiluminesence of the hot gas as the calibration signa!. The

reasons for these are two-fold:

(1)

(2)

The photomultipliers look at two volumes (overlapping) in the hot gas which may have a difference between them both in the m ean temperature and sodium atom concentration.

the dynam ic calibration will also show how uniform the flow

is in the hot gas region.

Runs were made in nitrogen and air at P1

=

3, 4 or 5 mm.

Hg. The introduction of NaCI was done in the same way throughout and the

inside surfaces of the windows were cleansed af ter each run. Figure 10

shows two oscillograph records of the radiation pulse. The deflection of

the traces were measured to 0.005 in. (1 cm deflection

=

.355 in. ) to

cal-culate the sensitivity ratio as a function of flow time. The results for ni-trogen and air are plotted in Fig. 11.

In Fig. l1(a) and (b), it is seen that when an individual run

is considered, the ratio km is nearly constant. The waviness of the curve may be partly due to the limiting accuracy of measuring the deflections and only very rarely will a curve show large fluctuation like that for run No.

HN68 (Fig. 11a). The scatter in the value of kmfrom run to run, however,

conclusively shows that the flow was not the same from run to run and that

using a static calibration factor would be in error. Nevertheless, it is still

possible to draw a mean calibration curve through all the points and take

into account the scatter in the error analysis. The points beyond t

=

130p5

are disregarded because they lie in the region of the burning interface (for

air) or turbulent mixing (for nitrogen) at the contact front. The scatter for

these points is quite appreciable. For t <:: 130/,",s the values of km are

taken to be N₂::If AIR:';'" km

=

1. 20 ~ O. 04; km

=

1. 21

t

O. 04; ksA

=

1. 57, ksA

=

1.57, 25 ~ t .. 130 10 ~ t ~ 130

These ratios are practicallY the same for the two gases within the error of measurement. There is a slight tendency for the ratio to increase as t increases, but this is not statistically significant.

It is of interest to estimate the difference in temperature or

sodium atom population which would give rise to the scatter in the value of

km. If the scatter is due to a mean temperature difference alone between

è

TG that corresponds to a scatter

b

km is given by

~1;

=

-ç'- '.\

k ...

A"/~ (~)

(35a)

..., -, c~ I _ K~à\lJ,

""'"

Flor example, from Fig. '17(b). att

=

70/"s km 6v/vG

=

.676, km

=

1.20,

Ok_m

=

0.04, TG

=

25l70_K,

Ó

_TG

=

_l80_{K for two volumes 3.0 mm apart.} This value is equivalent to a temperature gradient of 600_{K per cm or l52}0_K per inch, which is very significant if one considers that the measured tempera-ture agrees with the expected value (T2) to 300_K.

On the other hand, the scatter can be due to the difference in the concentration of sodium atoms between the two conical volumes of the beams. This effect will appear in the flux terms in Eq. (10) if we assume that the effective emitting area A is directly proportional to the number den-sity of the excited sodium atoms. The numerator (<PTOT - <PB) is propor-tional to the effective emitting area AL of the lower beam and the denominator

cp

G' which is obtained from Eq. (9) and not from Eq. (7). is also propor-tional to AL. However, in the experiment the value of

f/J

G used is that

corresponding to the effective area AU of the upper beam so that a correction factor AU/AL is required. This factor is implicitly included in km as a re-sult of the dynamic calibration process. Therefore, the fluctuation in km is a direct measure of the fluctuation of the density ratio of the excited sodium atoms in the two conical volumes. From Fig. ll(a) and (b), the peak-to-peak fluctuation is seen to be of the order of

±

O. 06/1. 20 or

!

5%. This is areasonabIe and acceptable value, i. e. an error of l80_{K in 25l7}0_K, if one considers the change of the radiation intensity with flow time, the un-certainty of the spatial distribution of the sodium atoms and the thickness of the cool boundary layer.

Figure ll(c) is a similar plot of km for air at ksA = 1. 57.

The difference from Fig. ll(b) is the shape of the radiation pulses from which the value of km is calculated (compare Fig. l5(a) with Fig. 15(b». In Fig.

l1(c), all the six runs have very sharp and strong signals at the burning interface. An apparent effect on km has been noticed, the value usually de-creasing from 1. 15 to 1. 10 at the combustion region. In the data evaluation of the temperature runs in air, the shape of the radiation pulse, i. e. the

<PG -trace, will determine the value of km to be used according as it resembles those from which Fig. 11(b) or l1(c) is plotted.

Calibration runs were also made for Set B of the aperture sizes. The value of ksB is 1. 20 and the results for km in nitrogen and air are plotted together in Fig. 11(d). The curves fluctuate considerably for t "7' 75,P4 s. km for nitrogen shows a relaxation time of about 40~s to reach a steady value and remains fairly constant around 1. 40 up to t

=

130 ~ s. For air, however, the shape of the pulses begins to differ at t = 60

""M

s and for larger t, the value of km gradually rises and the scatter becomes un-acceptable beyond 100

rs

.

The calibration constant is taken to be:

N_{2 km}

₌

1. 15, t

=

20

p-S

1. 23, t

=

25 /"".5 1. 31, t

_""

30

r-

s

1. 38, t

=

35

!-'-S

1. 40, 40

_r

<; $ t ~ 130,S Air _km

₌

1. 40 15 f's, t ~ 60 jv'v:' 1. 40

+

.

0025 (t - 60) 60

rs<

t

t::

100

jAs.

.

The uncertainty is

!

O. 05 for these ranges of flow tim e.

When the values of km are compared for the two values of ks, it ean be safely concluded that there is a noticeable dependence on the solid angle ratio and the density ratio of excited sodium atoms in the two beam

volumes. The value of km from astatic calibration is 1. 10. It is obtained

by sighting eaeh photomultiplier at the referenee tungsten strip lamp at the same value of lamp current and measuring the voltage developed across the

resistance R. The value of km may be taken to eorrespond to that for a

uni-form and isothermal hot flow region. Since the km 's are all greater than

1. 10 and km

==

vlower eone/vupper cone, it shows that the population of the

sodium atoms is greater nearer the bottom surface of the shock tube, i. e.

the NaCI vapour would tend to sink. The accuraey of this method of

tempera-ture measurement using tracer emitters might be limited by this factor. 4. 2 Excitation of Sodium Atoms

At room temperature and low pressure in the channel

(P1

-7

4 mm Hg.) the NaClvapour will condense as a cloud of very fine

crystals along the channel. When the shock wave passes over this cloud, the high temperature will vaporize the crystallites and dissociate them into

sodium and chlorine atoms. It will be desirabIe to show analytically that

the time to reaeh, 0. 9 saypftheequilibrium coneentration of sodium is much

less than the response time of the reeording system, so that the intensity of

the radiation is indeed a measure of the temperature of the gas. In order

todo this, it is necessary to know the rate processes for the vaporization of the NaCI crystallites and the simultaneous dissociation into their atomie

elements. These, however, are not accurately knoWI\. Bauer et al (Ref. 10)

worked with a known vapour pressure of chromium carbonyl and were able to give an estimate of the time required for the eoncentration of chromium

atoms to reaeh O. 90fits end value at 10000K, hence showing that the change

of radiation intensity with time in the shock front was an aetual indication of the rates of excitation of the chromium atoms.

Although it is not possible to make a similar estimate for sodium chloride, it is of interest to determine experimentally the time lag between the arrival of the shock wave and the rise of the radiation pulse.