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ROTATIONAL TEMPEBA!XRE MEASUREBENTS 300° K TO 1000° K

WITH ELEETRON BEAM PROBE

By William W. Hunter, Jr. I

NASA Langley Research Center Langley Stat ion, Hampton, Va.

Presented a t t he ISA Twenty-First Annual Conference and Exhibit .. ,..- .... ~.

I

New York, New York October 24-27, 1966

https://ntrs.nasa.gov/search.jsp?R=19680017944 2018-12-03T12:10:52+00:00Z

ROTATIONAL TEMF'EBATUFUZ MEASTJRFMBWS 300' K TO 1000° K WITH EZFCTRON BEAM PROBE

by W i l l i a m W. Hunter, Jr. Physicist

NASA Langley Research Center Langley Station, Hampton, Va.

ABSTRACT

Laboratory measurements of rotat ional temperatures were performed over a 300' K t o 1000° K range i n s t a t i c low-density air with an electron beam probe. t ional temperatures was found t o be a function of gas numbe? density and temperature. Inclusion of an experimentally determined correction for the gas number density effect enabled measurements t o be made with an accuracy tha t varied approximately from 0 percent t o -6 percent with increasing gas temperature.

The accuracy of the measured rota-

INTRODUCTION

The investigations described i n t h i s paper were undertaken as part of a continuing instru- ment development program at NASA's Langley Research Center. directed towards the verification of a technique f o r measuring free-stream temperatures of low- density m e r s o n i c Wind tunnels using air or

This par t icular e f for t was

N2.

The technique is t o pass a beam of high- energy electrons (10 t o 30 kV) through a low- density gas. coll isions with gas molecules which produce fluorescence. rescence provides a means f o r determining molecular gas rotat ional temperature.

The electrons have inelast ic

A spectral analysis of the fluo-

The i n i t i a l investigator, E. P. Muntz,' experimentally ver i f ied h i s theoret ical model f o r the electron beam probe technique f o r two temperatures, =300° K and 373O K. were conducted i n a low-velocity (0.5 m/sec) flow of nitrogen gas and the data were obtained from the 0-0 band of the nitrogen first negativ tem. Since the or iginal work, 0thers,~,3r$,5 have used the technique f o r diagnostic wind-tunnel measurements. Some have used the calculated tunnel parameters for comparison with the measured temperatures as a t e s t of the theory f o r temperatures below 300' K.4

These experiments

sys-

The purpose of the work reported here was t o experimentally ver i fy the theory for rotat ional temperature measurements over a 300° K f o 1000~ K range under controlled conditions i n the laboratory. These tests- were conducted i n a s t a t i c t e s t gas, air, and the rotat ional temperature

measurements were made from data obtained from the 0-0 band of nitrogen.

The procedure for t h i s investigation was t o pass high-energy electrons through the s t a t i c t e s t gas which was at a known temperature. The gas was contained in a test chamber which could be main- tained a t a desired temperature and pressure. With the t e s t gas under controlled conditions, measurements of the rotat ional temperature were performed and compared with a reference temperature. determining the applicabili ty of the theory over a range of temperatures.

Thhis comparison provided the basis f o r

The first portion of t h i s paper outlines the This is followed by a description of the theory.

experimental system, t e s t procedure, the experimental data, and resul ts .

THEORY

General *-

The t e s t gas used in th i s investigation was a i r and the primary sources of vis ible and near ul t raviolet radiation were the f i r s t negative and second posit ive systems of nitrogen. The excita- t ion and emission path for the first negative system is i l l u s t r a t e d by an energy level diagram i n Figure 1. A high-energy electron, designated as a primary electron, i s emitted by a source and has an inelast ic col l is ion with a ground s t a t e nitrogen molecule, NS~C;. The molecule i s excited t o the excited ionized s ta te , N>2G, from which it spontaneously radiates and drops in to the ground ionized energy s ta te , N$X2Zg. The intensi ty and spectral distribution of the spontaneous emitted radiation ref lects the rota- t iona l characterist ics of the molecules tha t were i n the N&,$ state .

Rotational temperature may be obtained from an application of the intensi ty of emission equation

Superior numbers refer t o similarly numbered references at the end of t h i s paper.

L-5121

where hcvm is the energy of the emitted radia- t i o n as a resu l t of the t ransi t ion between s ta tes n and m, vnm is the wave number of the emitted radiation, i s the t ransi t ion probability of emission, and Nn is the number density popula- t i o n of the i n i t i a l l eve l of t ransi t ion. An inspection of equation (1) shows tha t all terms are constants o r dependent only on the par t icular t ransi t ion involved except Nn. Application of equation (1) requires the determination of the population and its distribution i n the i n i t i a l l eve l , N$B~$.

it bY

Based on arguments presented i n reference 1, is assumed tha t N&2< i s populated primarily ionized and excited molecules from N2Xl.Z;.

Population contributions frou other possible ori- gins are neglected. Therefore, the population of the rotat ional energy s ta tes of mined by the excitation-transition process of N2X1Zi molecules.

is deter-

The excitation-transition process may be described through a Born-Oppenheimer approxima- t ion of the molecular wave function

where $e is the electronic wave function with the i t h electronic coordinate ?i referenced t o the molecular axis, qv is the vibrational wave function with nuclei separation FN? and $m the rotational wave function which is a function of the M e r angles (e ,X,@). The N e r angles re la te the molecular coordinate system t o the coordinate system of the fixed point of observation. Also, it i s assumed tha t the interaction of the primary electron with the orb i ta l electrons can be described by a coulombic potential . There- fore, the following m a t r i x element of t h i s interaction may be used t o describe the excitation:

In the above expression, the i n i t i a l and f i n a l wave functions of the primary electrons are repre- sented by ePtt and ep l , est the secondary

electron, XIZi and B2< represent the init ial and f i n a l electronic wave fimctions, vn and v ' the vibrational states, and J"A"M" and J'A'M'

the rotational s ta tes . O f course, 1 i

the coulombic interaction term where the quantity rli is the distance between the high-energy pr i - mary electron and the Lth orb i ta l electron.

i s e2

It should be noted tha t i n the notation t o be used, prime superscripts re fer t o s ta tes , double prime superscripts with a one (1) subscript refers t o N$'Z;

N?$2<

s ta tes , and double

prime superscripts with a two (2) subscript 'i.efer t o ~ 3 2 ~ ; s ta tes .

Since the particular t ransi t ion of interest resu l t s i n the removal of one orb i ta l electron

and for simplicity w i l l be replaced with k i - where the removed electron i s labeled with a r12 subscript 2. The removed orb i ta l electron is a uu2s

therefore, the electronic s t a t e may be expressed

as XIZ+ = p<uu2s] Equation ( 3 ) i s now

rewritten as

electron6 from N2X1Ci t o form N g 2 < ,

g

Note tha t K has been used i n place of JJ t h i s may be done from consideration of the applicable coupling scheme which is Hund's case (b)6 and by suppressing the spin angular momentum.

I n order t o evaluate t h i s matrix element f o r high-energy primary electrons, a plane wave approximation is made for the primary electron waye functions and the integration over the pr i - mary electron coordinates is performed. This integration gives7

where < is the momentum transfer and F2 is the position vector of the interacting orbi t electron.

A t t h i s point a ser ies expansion of e i s made

is. Q

To a first-order approximation the first two terms of the above expansion are retained. the contribution from the first term i n equa- t ion (6) i s zero because of the orthogonality of the i n i t i a l and f i n a l s ta tes of the molecule. Therefore, equation (4) is given by

But

(7 )

In order t o evaluate equation (7) further, the vector F2 is transformed t o the coorginates of the molecular axis through the dyadic D(e,X,$) which relates the molecular coordinate axis t o the fixed coordinate system of the point of observa- t ion. merefore, equation (7) is rewritten

i4ne25 is The absolute value squared of the term - contained i n the excitation function, Ce, and w i l l be suppressed i n the following equations.

q2

Evaluation of equation (8) shows tha t for the

Most significant point is; not only case A" = A ' = 0 only odd M t ransi t ions are allowed. LX = $1 t ransi t ions are permitted, as assumed i n reference 1, but AK = k3, a>, and etc. are also permitted. O f course the cross sections for t h e & = &3, 45, and etc . excitation-transitions w i l l determine t h e contribution t o the population of the excited state. This contribution is expected t o be small .

The square of t h e second matrix element i n equation (8) is defined as the band strength or the vibrational t ransi t ion probability and is designed Pv;rv*l. This band strength Pvrv*f m a ~ r be approxFmated by assuming- a mean value of the internuclear separation. The second matrix element of equation (8) may then be writ ten

The overlap integral of the vibrational wave func- t ions squared I(vt[v")12 is the well-known Franck-Condon factor, qvivll. Generally, equa- t i o n ( 9 ) i s then expressed as

In order t o take into account the variation of internuclear separation, a method of i: cen- troids8 is used where value of the internuclear separation, q, as determined by the vibrational wave functions. Now, the band strength is given by

is the expectation

The rotat ional l i n e strength is given by the first matrix element of eqmtion (8) squared, summed over M" and M f

This term is the well-known Hznl-London factor S$$, which is well tabulated.6 For the t ransi- t ion of interest , the re lat ive rotational l i n e strength may be obtained through the r a t i o of the l ine strength t o the sum of the l ine strengths, tha t is,

This equation is the relat ive l i n e strength f o r excitation-transition which i s indicated by the superscript a. The relat ive l i n e strength f o r emission is the same except the summation is over IC" and is designated PE.

The preceding work of t h i s section has been based on a plane wave approxLmtion f o r the high- energy incident primary electron. t o consider low-energy secondary electrons since these may contribute significantly t o the number of ionized nitrogen molecules. Several obsema- t ions may be made without making a detailed anal- ys i s of the excitation-transition process. should be noted tha t for electronic s ta tes of the homonuclear nitrogen molecule, rotat ional levels have symmetric and antisymmetric s ta tes under nuclear exchange. properties of X1X2 and B2< are the opposite with respect t o even and odd rotational quantum numbers. energy levels with the same symmetry are allowed. Therefore, the same selection rules with respect t o AK for high-energy electrons apply t o low- energy electrons. The only d i f f icu l ty would be i f the first-order approximation i s not suffi- ciently accurate such tha t = i3 or other transit ions would contribute appreciably i n order t o describe secondary electron-induced transit ions.

It is necessary

It

XIZi and B2G

The symmetry

And, only t ransi t ions between rotat ional

Rotational Temperature, !L'R

!Che rotat ional number density, %I of N22.& is a function of the excitation-transition process, depopulation rate, and number density, NK;I of NS1.X$. If it i s assumed tha t rotat ional s ta tes of a v: are i n thermal equilibrium, then N ~ ; is given by6

where % =I ( ~ 1 + 1 ) e -EKiikTR is the rota-

t ional par t i t ion function, %; = F(5)hc the

characterist ic energy of a rotational s ta te , F(K:) the rotat ional term, and !PR the rota- t ional temperature. temperature has been established through the Boltzmann factor based on the expl ic i t assumption that thermal equilibrium exis ts i n the ground electronic state of the neutral species of N2.

J s l

Notice tha t a relat ion t o a

In order t o interpret t h i s temperature dependence in the result ing intensi ty of radia- t ion, the selection rules f o r t ransi t ions between various rotat ional energy s ta tes are applied. As a first approximation t h e applicable selection rule f o r the excitation-transition process i s

taken t o be &S = 21. The LX = 31 selection rule predicts the f o m t i o n of a P branch and R branch i n the rotat ional f ine structure of a vibrational band i n excitation as well as emission. Shown i n Figure 2 are the R and p branches of the 0-0 band of I$.

With the formation of the P and R branches the steady-state population of i s given by*

where pm and F& are the relat ive rota- t iona l l i n e strengths of absorption, previously described, f o r the P and R branches.

With the determination of NKI, the intensi ty of emitted radiation may be calculated as a func- t ion of the rotat ional temperature, TR. Before the calculation may be accomplished, it is necessary t o s e t up an expression f o r the emission t ransi t ion probability, ~ I K I ,vs

where X is a constant, v is the waye number of the transit ion, and Pg is the relat ive rota- t iona l t ransi t ion probability f o r emission.

The intensi ty of emission f o r a par t icular R-branch t ransi t ion is given by

where

This equation is simplified by noting tha t the product

i s a constant, Z, fo r a par t icular v t - v" 2 transit ion. ventional form6 by noting that

Also, the equation may be put i n con- 2 ~ ' = K ' + K; + 1

f o r R-branch transit ions. Therefore,

(20) For the case of Tv <, 800' K, 99 percent of

the t o t a l population is i n the v: = 0 level. Equation (20) may now be writ ten

where Bo is the rotational constant related t o the vibrational leve l and

Dv;e-EOI w v

2QrIo Z' = (22)

and

Note tha t a reference intensi ty Io has been included t o permit the measurements of re la t ive intensi t ies . The term [G] involves TR and requires a solution of equation (21) through a process of i terat ion.

Analysis of equation (20) a lso reveals that only a small error &l percent w i l l be introduced by extending the appli$a&ianYsof equation (21) t o temperature of 1000° K. formed by calculating a Beff t o replace Bo i n equation (20).

This analysis was per-

For ease of application, equation (21) i s put i n the following form:

Bohc - K ~ ( K I + 1) + ztt WR

where vo is a reference wave number used t o normalize v. Following reference 1, vo value is chosen for K ' - K l = 3-2 transit ion. Also, Z" is jus t loglo Z', which is a constant.

Test G a s Temperature and Pressure Control System

The test gas temperature and pressure con- t r o l system, Figure 3, was designed t o provide

* The following derivation is similar t o that of reference 1 b y E. P. Muntz.

f l e x i b i l i t y i n temperature and vacuxm t e s t condi- t ions. Temperature and pressure operating ranges are approximately 300' K t o llOOo K and 6.7 t o 133.3 X 10-3 N/m2 (1 t o r r = 133.3 newton/meter2).

The major component of the system is the t e s t chamber which consists of three concentric cylinders. s t e e l water-cooled jacket and i s f i t t e d with vacuum-tight water-cooled top and bottom covers. Each cover is f i t t e d with large flanges, attached t o extensions, f o r mounting test hardware. Three 7.6-cm-diameter opt ical grade quartz windows are located i n the outer cylinder wal l . concentric cylinder consists of a hel ical ly wound nickel ribbon heating element and is attached t o ceramic supporting rods. Electr ical connections are made t o copper electrodes which extend through the outer cylinder. 20-cm-diameter 38-cm-long s ta inless-s teel electro- s t a t i c shield and is grounded together with the outer cylinder t o prevent charge buildup on the walls. Also, the inner cylinder provides a more uniform heating surface f o r the t e s t gas than would be provided by the ribbon heating element. The inner cylinder is equipped with end covers which have openings f o r passage of the electron beam. A 3.8-cm by 1.3-cm slit opening is provided i n the cylinder w a l l and is located i n l ine with one of the viewing windows of the outer cylinder.

The outer cylinder i s a stainless-

The next

The inner cylinder is a

Rectified heater current is supplied from a

Tempera- 440 Vac 3-phase system. Temperature control i s provided by coarse and f ine rheostats. tu re is regulated within 21 percent of the pre- set value by an on-off automatic pyrometer. An operating temperature of llOOo K i s obtained f o r a heating element voltage and current of 35 Vdc and 50 amperes.

A 35 p s i water cooling system is provided as

An inter- a heat sink for the outer chamber w a l l and covers, as well as cooling the diffusion pump. lock system prevents operation of the heating system and diffusion pump unless proper cooling flow is established.

A 5 CFM mechanical pump, 750 l i t e r / sec diffusion pump, cold t rap and necessary isolating valves comprise the vacuum pumping system. variable leak valve, with air dryer, i n combina- t i o n with the mechanical pump was used t o main- t a i n the t e s t chamber at the desired pressure. For a l l experiments the chamber pressure was measured with a McLeod gage.

A

Test Chamber Temperature Survey

A ser ies of t e s t s was conducted t o establish the test chamber gas temperature. The first test was a survey of the inner cylinder w a l l t o deter- &ne the uniformity of the heating surface. This survey was performed wlth 32 thermocouples attached t o the inner cylinder w a l l and located t o give reasonable coverage. The results

indicated t h a t a ?20° K variation existed at llOOo K. temperature. The second test was made t o determine the effects on the t e s t gas at the point of observation by the inner cylinder ends. This was necessary because the ends are not i n close prox- imity t o the heating element and therefore cooler than the side walls. on the bottom end p la te near the chamber center l ine. e s t temperature of t h e plate.

This variation decreased with decreasing

A thermocouple was located

The temperatme of t h i s polnt w a s the low-

These w a l l temperature measurements were used t o calculate the gas temperature on the cen- t e r l ine. The results of the calculations show t h a t the effects of the inner cylinder ends would lower the gas temperature at the midpoint of the cylinder no more than 4O K at llOOo K.

The f i n a l t e s t w a s an independent measurement of the test gas temperature at the point of observation. These measurements were made with a thermocouple whose leads were brought i n along the chiudber center l i n e and the junction located at the point of observation. Two thermocouple sizes, 0.1-mm and 0.5-mm diameters, were used t o determine i f there were significant heat losses at the point of observation due t o thermocouple conduction. The data shows tha t conduction losses were negligible. The resu l t s are indicated i n Figure 4. tu re at the point of observation i s lower than the mean w a l l temperature. This difference decreases with temperature and converges t o zero at an ambient value of temperature. This difference is at t r ibuted t o heat sinks provided by the observa- t i o n and pumping ports.

These data show that the gas tempera-

Electron Beam System

The electron beam system is i l lus t ra ted i n a block diagram, Figure 5 , and details of the elec- t ron gun are shown i n Figures 6 and 7. The elec- t ron gun is a conventional point cathode system which has a d i rec t ly heated hairpin tungsten fila- ment, independent negative grid bias f o r current control and cathode focusing. sage in to the d r i f t tube is magnetically focused and deflected. 1.0-mm-diaineter hole i n a 2r - em-long plug which

i s placed i n the end of the d r i f t tube. Because of the low gas conductance of t h i s passage through the plug the test chamber may be operated at pres- sures approaching 133 N/m2 while maintaining the gun within acceptable pressure range of 2.7 x loe2 N/m2 o r less .

The beam upon pas-

The focused beam passes through a

2

For the work reported here the beam system was operated a t potentials between 25 and 30 Kv with currents of 1.0 t o 1.5 ma. The beam poten- t i a l and currents were held constant withln ?l percent of the selected valves f o r a l l tes t s .

Optical and Electronic Detector System

The major component of the opt ical and electronic detector system is the 0.5-meter Fastie- Wer t mount scanning spectrometer. This instru- ment has 16.0 &m dispersion in the first order and a 0.2 B resolution. blind photomultiplier tube which has a S-13 spec- t ra l response characterist ic is mounted at the ex i t slit. The photomultiplier output i s fed into an electrometer amplifier which drives a s t r i p chart recorder. the system is approximately 1 second. the relat ively slow response of the system, a 5 B/min scanning speed was used.

A l3-stage venetian-

The overal l response of Based on

300' K t o 1000° K TR Experiments

Rotational temperature measurements were made i n air at approximately IOOO K intervals from 300' K t o 1000° K. formed f o r three s e t s of experiments. of experiments were performed with a constant gas number density of 1 x 1016/cm3 and the other with a constant number density of 5 x 1015/cm3. The rotat ional temperature measurements were made from the 0-0 band first negative system of nitrogen. Typical spectral traces are shown i n Figure 8.

This procedure was per- Two se ts

The procedure f o r the rotational temperature measurement i s t o measure the peak value of a rotat ional l i n e and enter t h i s value into equa- t ion (24) for 1 ~ 1 ~ 1 1 . It is necessary at t h i s

2 point t o make an estimate of the rotationaltem- perature by noting the rotat ional l ine at which maximum intensity is recorded. With the a i d of

t h i s estimate, a value f o r hGl(v/vo)y is determined from table 1. repeated f o r each rotat ional l ine . s tep is t o plot each point, f o r strong l ines , on a graph (e.g., Fig. g), then by leas t squares f i t determine the best s t ra ight l ine. From the slope of the curve a rotational temperature may be determined. the estimated value, the process i s repeated with another temperature estimate and t h i s process i s repeated u n t i l the estimated and calculated temperatures fall within the smallest temperature

division of the table of {[GI ( v/vo) '} values.

The ent i re procedure is repeated for the weak l i n e system of the band. The f i n a l measured rotat ional temperature is determined from a weighted mean average of the values obtained f r o m the strong and weak l i n e systems.

Th& procedur'e is The next

I f t h i s value does not agree with

Results of these t e s t s are given i n Figure 10 as a plot of the percent difference between weighted mean value of the rotationaltempera- tures and the reference temperature versus the gas

reference temperature. The gas reference tempera- tu re i s the mean value w a l l temperature of the chamber corrected i n accordance with Figure 4. There are two dis t inct groups of data, each corresponding t o measurements made at different gas number densit ies. Two other points should be noted also. The first is the general trend of the data indicating a change i n the percent difference between the measured value and reference temperatures with increasing gas temperature. The second is tha t the measured rotationaltem- perature is high at ambient temperature and the difference increased with an increase i n gas number density. This resul t indicated tha t the measured rotat ional temperature was dependent on gas number density.

TR G a s Number Density Dependence

In several cases investigators1J4 have pointed out tha t TR measurements made i n a s t a t i c gas were higher than the reference tempera- tu re and appeared t o be a function of gas number density. Because of these observations and resu l t s given above, t e s t s were conducted t o determine TR dependence on the gas number den- s i t y . perature which ranged from 2870 K t o 303O K with an average of 291' K. The measured TR w a s compared with the corresponding ambient temperature f o r tha t par t icular t e s t . The resul ts are shown i n Figure 11. An analysis of the resul ts provided the empirical equation

A l l t e s t s were conducted at ambient tem-

where aT is the increase i n gas temperature at the point of observation due t o the number den- s i ty , n, dependence and no i s the reference gas number density a rb i t ra r i ly selected as 3 x l0l4/cm3 since the resul ts appear t o converge t o t h i s value. The number density n is limited t o the range, 3 x 1Ol4/cd 6 n 5 3 x 1016/cd.

It is assumed, based on experimental observations, tha t t h i s increase i n temperature is a function of number density only and is independent of gas temperature. Therefore, as the gas temperature increases the change i n TR due t o number density would become relat ively small.

It is also assumed tha t equation (25) i s applicable only t o the physical conditions of the t e s t s reported here. That is, beam current, beam potential , and the distance of the observation point from the ex i t aperture of the electron gun. A l l observations were made at a point 30 cm from the gun exi t aperture, beam current of 1100 pa, and beam potential , 28.5 Kv. It is important t o note these conditions because of beam spreading. The greater the distance from the aperture the greater w i l l be beam spreading f o r a given gas

numbe,r density. dependent on the beam electron current density, then spreading wi l l be an important factor. It should be pointed out tha t changing the beam current by a factor of 2 did not change the measured TR within experimental accuracy. Also, the temperature of the gas at the point of observation w i l l be a function of a temperature gradient, therefore beam spreading again may be a factor since it could a l t e r the gradient. I n any case, u n t i l the exact molecular heating mechanism or process i s determined, t e s t s should be conducted for each test configuration. It is important t o determine the molecular heating mechanism t o determine conclusively the effects on temperature measurements i n a flowing gas.

If the gas heating should be

R e s u l t s

Corrections i n accordance with equation (25) were applied t o the measured rotat ional temperatures. The corrected resu l t s are shown in Fig- ure 12 which is a plot similar t o Figure 10. resultant sca t te r of data has been reduced from +10 percent t o -4 percent, i n Figure 10, t o +2 percent t o -6 percent, i n Figure 12. data are approximately grouped about a common curve. the data for the two different densit ies. This can be at t r ibuted t o the inaccuracy of equa- t i on (25) due t o experimental uncertainty associ- a ted with its derivation. The corrected resul ts s t i l l indicate a s l igh t ly increasing difference between gas temperature and the measured rota- t iona l temperature. An analysis of equation (24) does not reveal any apparent sources of t h i s difference. There are two possible causes. The f i r s t t o be considered is possible experimental error. But careful analyses have been made for a l l the experimental apparatus and reasonable confidence has been established. s ib le source i s in the formulation of the theory leading t o equation (24). t ransi t ion process is complex and no direct account has been made for the effects of secondary electron excitation. Also the expl ic i t assumption has been made tha t the rotat ional levels of the ground molecular s ta te , are i n thermal equilibrium. But, since a temperature difference does exis t between the reference gas temperature and the measured value, then there W i l l exis t a population distribution of the rotat ional levels at the point of observation which is at leas t s l i gh t ly non-Boltzmann.9 A s l ight deviation from a non-Boltzmann distribu- t ion would not be detected within the obtainable experimental precision, but would affect the measured rotat ional temperature value.

The

Also the

There still exis ts a slight difference in

The second pos-

The excitation-

NzX1$

Precision

A re lat ive precision of t5 percent was es t i - mated for these measurements. The factors affecting the re la t ive precision of the measurements were the uncertainties i n gas number

density, reference temperature, and the tempera- tu re values obtained from the graphic solutions. A value of *2 percent was calculated f o r the effects of density and reference temperature and +-3 percent was estimated for the uncertainty of the measured temperature based on standard e r ror values obtained from a large number of independent measurements.

CONCLUSIONS

Rotational temperature measurements per-

An empirical formed i n a s t a t i c gas were found t o be a fmc- t i on of the gas number density. equation relat ing the difference between the measured rotat ional temperature and a reference gas temperature t o the gas number density w a s developed from experimental data. The equation was assumed t o be applicable only t o the physical conditions of the experiments reported here. Also, it will be necessary t o determine the exact heating mechanism i n order t o evaluate th i s effect in a flowing gas environment such as a wind tunnel.

The resul ts of t h i s work indicated a minimum accuracy agreement with theory of +8 percent t o -4 percent for rotat ional temperature measurements i n a s t a t i c gas over the 300' K t o 1000° K range. Application of the corrections fo r the gas number density dependence of the measured temperatures resulted i n a minimum accuracy agreement of 0 percent t o -6 percent. the experiments that were conducted and reported here indicate tha t the theory developed by Muntz for the electron beam technique fo r measuring gas rotat ional temperatures is reasonably accurate over a 300' K t o 1000° K range.

Therefore,

NOMENCLATURE

defined by equation (18)

t ransi t ion probabili ty for emission between states n and m

t ransi t ion probabili ty f o r emission between vibrational energy s ta tes v' and v;

t ransi t ion probabili ty for emission between rotat ional energy states K' and Kz

vibrational level V;] = 0 rotat ional constant re la ted t o the

rotat ional constant re la ted t o the vibrational leve l vy

represents the electronic wave func- t ion for Q~C;

excitation function which describes the electron-molecular excitation process

e

J',J"

K'

Kf

k

M' ,MI'

Nn

NO

NK' r a t i o of the excitation function t o depopulation r a t e of @2< s t a t e

speed of l igh t

dyadic, function of Euler angles

characterist ic energy of KZ rota- t iona l energy leve l

characterist ic energy of v: vibra-

t iona l energy leve l

elt?ctron charge

primary electron

secondary electron

rotat ional term7

defined by equation (23)

vibrational term7

Planck's constant

intensity of emission for t ransi- t ions between n and m s ta tes

intensi ty of emission for transi- t ions between K' and K" rota- t iona l energy levels

reference intensity of emission

intensity of emission f o r t ransi- t ions between v r and v; vibra- t iona l energy levels

quantum number of the t o t a l angular momentum

quantum number of rotat ional energy level of ~32g

quantum number of rotat ional energy level of ~2x1~:

quantum number of rotat ional energy leve l of @+'x~

Boltzmannrs constant

quantum number of a component of t o t a l angular momentum

number density population of s t a t e n

steady-state number density popula- t i o n of NS'G

Nv I1

1

steady-state number density popua- t ion of a rotat ional energy leve l K' of N$ + 2 + &

steady-state number density popula- t ion of a rotational energy leve l X" of Ns1$

steady-state number density popula- t ion of a vibrational energy leve l v' of N p 2 g

steady-state number density popula- t i o n of a vibrational energy leve l VI1 of @2$ 1

neutral nitrogen

ionized nitrogen

gas number density

reference gas number density

excited ion s t a t e of

ground s t a t e of N 2

ground s t a t e of

re la t ive rotational l i n e strength f o r excitation

relat ive rotat ional l i n e strength f o r excitation, R branch and P branch, respectively

relat ive rotational l ine strength f o r emission

relat ive rotational l ine strength f o r emission, R branch and P branch, respectively

band strength

rotat ional par t i t ion f'unction

vibrational par t i t ion function

momentum transfer term

Franck-Condon factor

electronic t ransi t ion moment for electronic s ta tes i and j

position vector of i t h orbi ta l electron

'12

rli

f2

'/nul uu2s

nuclei separation

position vector of primary electron with respect t o point of observation

distance between primary md secondary electrons

distance between primary and i t h o r b i t a l electrons

posit ion vector o f secondary elec- t ron with respect t o point of observation

posit ion vector of secondary elec- t ron with respect t o molecular axis

bdnl-London factor

rotational temperature

vibrational temperature

vibrational energy s t a t e of N p

+ 2 + vibrational energy s ta tes of Np &

+ 2 +

vibrational energy s t a t e of NS~Y g

vibrational energy state of Q2Z+ g

a constant of & I K I , ~ F ;

represents the electronic wavefunc- t ion for N S ~ ;

constants defined i n the tex t

N e r angles

quantum number of the resultant electronic orb i ta l angular momentum

wave number of nm transi t ion

angular characterist ics of an orbi- t a l electron of NG~C;:

electronic s t a t e wave function

molecular wave function

rotat ional state wave function

'evJI1M

%JAM

vibrational s f a t e wave function *v

ACKNO-

The author would l ike t o express h is appre- ciation t o Stewart L. Oeheltree and Dr. George S. Ofelt for t h e i r helpful assistance i n the evaluation of the work reported here and i n the preparation of t h i s paper.

REFERFNCES

1. Muntz, E. P., "Static Temperatwe Measurements i n a Flowing Gas," The Physics of Fluids, 2, 80-90, 1962.

2. Sebacher, D. I.; and Duckett, R. J., "A Spec- trographic Analysis of a One-Foot Hy-personic- Arc-Tunnel A i r s t r e a m Using an Electron Beam Probe,'' NASA TR R-214, 1964.

3 . Petrie, S. L.; Pierce, G. A.; and Fishburne, E. S., "Analysis of the Thermochemical State of an Expanded Air Plasma," The Ohio State University Research Foundation, Technical Report Al?FDL-TR-64-191, 1965.

4, Robben, F. j and Talbot, L., 'IMeasurements of Rotational Temperatures i n a Low Density Wind Tunnel," The Physics of Fluids, 2, 644-652, 1966.

3 . Muntz, E. P.; and Abel, S. J., "The Direct Measurement of S t a t i c Temperatures i n Stock Tunnel Flows," Third Hy-personic Technique Symposium, 1964.

6 . Herzberg, G., Spectra of Diatomic Molecules, D. Van Nostrand and Co., Princeton, N.J. , 1950

7. Landau, L. D.; and Lifshitz, E. M., Quantum hec-ics: N- Addison-Wesley, Reading, Mass., 1958.

8. Fraser, P. A . , "A Method o f Determining the Electronic Transition Moment for Diatomic Molecules," Can. J. Pbys., 32, 515-521, 1954.

9. Kennard, E. H., Kinetic Theory of Gases, McGraw-Hill Book Co., Inc., New York, 1938.

P 0 cc 0 U

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a LO N m u VI u VI m ro or- u N u VI m * IC (u m 01 o N m m m ~ ~ ~ - o o c ~ - - ~ m ~ u m ~ r - m ~ o ~ m u C. 0 CI C' c1 0 ti u u 0 0 u 0 0 0 CI 0 u Ll -4 4

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N V I S N r - N h 3 m N F r - ~ m N ~ N N m P S m - t u u m m m ~ ~ 3 - t o o o - t ~ ~ u m ~ ~ m ~ 1 o - t ~ u 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 4 - t - 3 O O O O O O O O O O O O O D O O O O O O O O O O

m r - r - m ~ u m o m ~ ~ u ' ~ m V I ~ m m - Q ~ n ~ - m m 0 m N 3 o m n m 3 TU m P 3 m m VI \t oh- 10 o r- m N o * - - ~ ~ ~ ~ o ~ o o u o - - N T u ~ ~ ~ I ~ ~ L ~ I c ~ v I o 0 0 0 0 0 U 0 0 0 0 ~ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . r- I I I I I I O

h o h o 0 c? o n n n n o o o o n o n < > n n n o o 1 0 I I l I I 1

o n n n o n n < > n o 0 o n n o o o o o 1-1 c> no n

In Lo 0 o

0 I

m m u r r c u 0 0 0 0 0 0 . . . o o u I

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h

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0

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m ? ~ r n f f m u m ~ . n u u m m ~ ~ - + ~ 0 0 0 0 0 0 0 c, 0 0 c, 0 0 0 0 0 0 0

0 u o o o o o o o I I I I I I I I I

. . . . . . . . . -tor- 00.- 0 c3 0 n c , u . . . 0 c> c-

n u u u m w m u m a O O O O G 0 0 0 0 C ~ . . . . . o o o o c ~

or-VI

0 0 0 0 c, LJ 0 0 0

e m -

. . . * \ t m ~ r l ~ m m 4 3 4 3 . . . . o 0 0 c 7 0 0 0 0

~ Q O Q - C O u r - " V I ~ L o S Q r - ~ e , N m m N ~ N u u u m w ~ ~ - o n c - ~ m u m ~ ~ ~ o ~ m ~ ~

~ Q O I C ~ ' ~ N Q O G Q ~ ~ ~ - Q C P L ~ N N ~ - ~ I C N o <.> o o c, o o G o o o 0 n o o o 0 n P o - 3 3 3 3

I C L ~ ~ N ~ L ~ N N ~ ~ O ~ ~ ~ N - - - N ~ ^ ~ L ~ ~ - rn 0

0 U v G U 0 G u u 0 u 0 0 0 u 0 0 CI 0 0 0 0 0 o - - - ~ o ~ c o o - N N ~ ~ ~ L ~ ~ - ~ v I o - N ~ ~ o 0 0 < , 0 r, 0 C'O 0 c, 0 0 0 U 0 0 0 0 0 3 4 3 4 4 LO

0

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I l I 1 I I l I I I I I I I I I

u - r - ~ ~ ~ u r - ~ 0 ~ ~ 1 u - m ~ 0 m m m ~ 1 ~ m - ~ ~ m u u m m ~ - ~ o c ~ ~ m u m ~ r - ~ ~ o ~ m m r - ~ ~ o o n o o o o o o c u o o u rr o o n o c, o 0 o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I I I I O

m 3 m N N r- CI - \f a m 01 m c. m LO (r OD cx r- VI .or- N 0 m v u .o o N ~o Q r- 01 '9 c m o r- m u m u v in r- VI N * c, D o r) 0 c- C> C I o 0 o c1 o 3 3 .+ 3 .+ N N N N m m 0 o o 0 0 0 0 0 0 0 0 v 0 0 0 0 0 0 0 " 0 0 0 0

C G 0 0 0 0 0 0 U 0 0 0 0 c, 0 0 0 0 -4 3 3 3 3 4 0 . . . . . . . . . . . . . . . . . . . . . . . . ........................ ul

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0

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0 0 0 . . .

r-

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m u m m m t - V I 4 3 3 3 N u u o u . . . . 0 0 0 0

~ - ~ - u l m c ~ - - o ~ u m ~ r - u - 0 1 r - ~ r - 0 1 - v L ~ Q ~ ~ ~ V ~ ~ ~ N - O - N ~ ~ Q ~ O - ~ ~ ~ V I N V

IC ul k C N m m rn e N N N C> 3 0

0 0 U 0 0 C , 0 u 0 0 0 0 0 0 0 0 d 3 3 4 4 4 N N V Q N m r - v * V I r - c V I m f f l u - V I ~ ~ L o Q Q L o Q Q * 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C' 0 0 0 C, C, 0 LO u m 3 m \o VI m r- 3 9 0 Ln v u VI u u' v u' u 0 v 0

u o o u o CJ o 0 3 .+ N N m m v u u ul ul .c Q r- r- m VI ........................ . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 0 0 0 L, c10 0 0 c2 0 o 0 0 <J 0 u u 0 0 0 o u I I I I I I I I I

0 c> 0 c1 0 <, 0 0 0 c 0 u 0 c, 0 0 0 0 c, <> 0 0 0 0 I l l 1

Lo 9 4 -t v) -1 3 N \f m

M

- . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a SL . . . . . . . . . . . . . . . . . . . . . . . . LL Y ........................

o - ~ m u ~ ~ ~ ~ r n u ' o ~ ~ m u m ~ ~ r n ~ o ~ ~ m 4 3 3 4 3 4 3 3 3 3 N N N N

- ~ - ~ m u m ~ o ~ r n u ' o - ~ m ~ u l ~ ~ m p o ~ ~ ~ - c 4 - 4 4 3 4 + r 4 - # A ~ + N N N N c

0 0 0 0 0 c c> 0 c, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - -

I I

hcu z I I I

/

v1=2

V'=l

VI= 0 v;=2-- I J

I I

V i = ' I I

I i

v;=o K;

+ 2 + N2X c g

I

I I I I I

K'

+ 2 + N,B c,

\ I I L

~

v;=2 7 1 I

Vy=l - I I I

vy.0 K;'

N,Xk;

Figure 1. - Partial energy level diagram of nitrogen.

P BRANCH

R BRANCH

Figure 2.- Spectrometer trace N:O-O band rotational structure, =300° K.

Figure 3.- Test gas temperature and pressure control system.

5 - \Ln E 0- 0-

HIGH -VOLTAGE POWER SUPPLY

REGULATED POWER SUPPLY

I AC LINE VOLTAGE I I REGULATOR

. DEFL .

-CONTROL

ELECTRON GUN

C

I I DEFL.(

I I I - DEFL. - REGULATED

POWER SUPPLY CONTROLS ' I

I . ,

TO OUALPEN RECORDER

MICRO-

I ' I

I I I I I I

COLLECTOR 1

Figure 5.- Block diagram, electron beam system.

t

a 5

Figure 7.- Electron gun.

-DECREASING WAVELENGTH BAND ORIGIN, 3910 i4 Ng (0-0) BAND 1 TEMP., 800°K

INTENSITY

-DECREASING WAVELENGTH BAND ORIGIN, 3910 ~ , - ~

Figure 8.- Typical spectrum, N:(O-O) band R-branch.

0

01 -P

il

3 b a, a ffi

El

k 0 k -P

*rl /l B a,

k

M

0 0 n 0

8 (H

cd -P cd a a P 9 4

I

o\

bo

ic

>. I- cn 7 - W cnn E 0 \ X -

0 X -

- - -

0

L I I I

0 a, (o d- cu 0 d- 4 I - I i

0 0 0 -

0 0 a x

0 c

Li W CK

OI- 0 (o

m +J m a, c,

E55

w 0 0 0 r l

0 +J

w 0 0 rr\

li-l 0

m

0

0

5 m

2 I

0 4

$ hD ;=I

x a,- -

u) - 0

3 7

0 7 a: X w

- X ln

I (D (D

I d-

m

0

- I

X 0

- I

(D (0

I - I d-

o

0

0

I I I I I d- N 0

0 0 0 -

0 0 Q)x

0 c

Li W a

O F 0 (0

P V

k a, x

8

3 8 m

a k a,

El d z hD k 0 k a a, P 0 a, k k 0 0

m

a, -P

-$

ffi B

w 0 0 0 0 rl 0 P

w 0 0 Fc\

4-1 0 u1

0

5 m

8

2 I

cu rl

G

NASA-Langley, 1966

ROTATIONAL MEASUREBENTS 300° TO K - NASA · gpo prige $ cfsti price(s1 $ ff 653 july 65 -...

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Transcript of ROTATIONAL MEASUREBENTS 300° TO K - NASA · gpo prige $ cfsti price(s1 $ ff 653 july 65 -...