- Email: [email protected]
Spectroscopic measurements for atmospheric nitrogen and helium arcs
J. Quanr.
Spmmsc.
Radiar.
Trans/er.
Vol.
12, pp. 1369-1377.
Pergamon
Press 1972. Printed in Great
Britain
SPECTROSCOPIC MEASUREMENTS FOR ATMOSPHERIC NITROGEN AND HELIUM ARCS F. P. INCROPERA and E. S. MURRER School of Mechanical Engineering, Purdue University, Lafayette, Indiana 47907, U.S.A. (Received 11 February 1972)
Abstract-Thermal conditions in the asymptotic region of atmospheric nitrogen and helium arcs are determined spectroscopically and calculated using an equilibrium flow model. Tbe equilibrium model is shown to be ill-suited for both gases. The helium arc is characterized by a high degree of thermochemical nonequilibrium, and significant thermochemical and excitation nonequilibrium effects characterize the nitrogen arc.
1. INTRODUCTION ALTHOUGH constricted arc plasmas have been studied for two decades, it is only in recent years that serious consideration has been given to their thermodynamic state. Because the assumption of local thermodynamic equilibrium (LTE) greatly simplifies the use of quantitative optical diagnostics and the performance of radiative and flow calculations, this assumption has frequently been made. However, recent studies have shown that, to varying degree, departures from thermal, chemical, and excitation equilibrium may characterize arc behavior. The principal thermal effect is one of nonequipartition of translational energy between electrons and heavy particles, and the chemical and excitation nonequilibrium conditions are due to the failure of the Saha and Boltzmann equations, respectively, to provide accurate species concentrations and populations. To date the most detailed studies of arc nonequilibrium effects have been performed for argon plasmas. Through a combination of spectroscopic diagnostics and equilibrium and nonequilibrium flow calculations,“-4’ considerable understanding of the nature, cause and degree of nonequilibrium condition has been derived. On the basis of this work it is known that significant thermochemical nonequilibrium and some excitation nonequilibrium exist in the peripheral regions of the argon arc. Hence, although prediction methods based upon the assumption of LTE suffice for the description of arc behavior in the core region, such methods are inadequate for use in the outer plasma layers. The degree of nonequilibrium becomes more pronounced and its spatial extent increases with decreasing arc current and pressure. The effects are promoted primarily by the combination of a large ambipolar diffusion velocity and insufficient inelastic collision rates. The purpose of this study is to obtain an improved understanding of the nature and degree of the nonequilibrium effects in atmospheric nitrogen and helium arcs. The methodology parallels that used previously for argon”’ and involves the comparison of temperature profiles computed from a rigorous equilibrium flow model with profiles 1369
1370
F. P. INCROPERA and E. S. MURRER
inferred from the spectroscopic measurement of absolute line and continuum intensities. At minimum, such comparisons determine the extent to which the oft used assumption of equilibrium is valid and are useful to those concerned with application of the arc for radiative and transport property measurements. In addition, when combined with multi-fluid arc analyses, the comparisons do much to suggest the detailed nature and underlying causes of the nonequilibrium condition. Previous spectroscopic studies have suggested the existence of nonequilibrium conditions in both nitrogen and helium arcs. For nitrogen,@-‘) measurements reveal the existence of excitation nonequilibrium and, for helium,‘8-*0’ results suggest the presence of a severe thermochemical nonequilibrium condition. In this study an improved understanding of these nonequilibrium effects is obtained through comparison of measured results with those obtained from an equilibrium flow model. 2. THEORETICAL AND EXPERIMENTAL METHODS To determine the importance of arc nonequilibrium effects, it is useful to have, as a reference, the thermal conditions which would exist were LTE (defined to include thermal, chemical, and ionization equilibrium) valid throughout. Accordingly, the conservation equations (mass, momentum, and energy), together with Ohm’s law and the caloric and thermal equations of state, are solved for laminar, axisymmetric flow in the arc. The flow model assumes the existence of LTE and depends upon knowledge of the transport and thermophysical properties for a solution. For nitrogen appropriate property values have been obtained from AHTYE(“) and Yos,(‘~) and for helium the property values have been obtained from LICK and EMMONS(‘~) and DEVOTOand LI.(‘~’ For this study, the most important result of the solution is the equilibrium thermodynamic temperature profiles computed for the asymptotic region of the arc. Additional details concerning the flow model are provided by GIANNARISand INCROPERA.‘~) For comparison with the predicted temperature profiles, experimental temperatures have been obtained using the cascade arc plasma generator, optical system, and procedures previously described. (2)Measurements were made with the optical access slit located 5.14 cm downstream from the cathode tip. This was sufficient to insure the existence of an asymptotic condition for both the nitrogen and helium arcs, which were operated at the laminar flow rates of 0.30 and 0.075 g/set, respectively. Results were obtained for nitrogen arcs operated at 75, 125 and 200 A ; however, due to limitations in the power supply, helium arc results could only be obtained at a current of 65 A. Excitation and electron temperatures were inferred from absolute line and continuum intensity measurements, respectively. Although such determinations are weakened by the necessity of assuming equilibrium relations, they remain valuable for the detection of departures from equilibrium. In regions of the arc for which LTE exists, the experimental temperatures will agree with the computed equilibrium temperature. In regions characterized by nonequilibrium effects, the experimental and theoretical temperatures will differ. Although such differences do not provide the precise degree of nonequilibrium, they remain useful for inferring the nature of the nonequilibrium condition. The spectral lines selected for use in this study are the 4935 (32P-42S), 6008 (32S-42P) and 7468 (34P-34S) lines for nitrogen and the 4713 (23P-43S) and 5876 (23P-330) lines for helium. Each line is sufficiently isolated from other lines of the spectrum and may be
Spectroscopic measurements for atmospheric nitrogen and helium arcs
1371
assumed to be optically thin. All transition property values were taken from the NBS tables.“” Due to the low electron concentrations characteristic of the helium plasmas of this study, the continuum radiation is extremely weak. Hence, helium continuum intensity measurements were not made. For nitrogen, absolute continuum intensity measurements (16)both the neutral atom and ionic were made at 4955 A, and, as suggested by MORRIS, contributions to the continuum were considered in the subsequent determination of the electron kinetic temperature. The continuum rate coefficients required for this determination were obtained from MORRIS.(’7, 3. RESULTS
The comparison between experimental and theoretical results for the atmospheric nitrogen arc are shown in Figs. l-3. Results are presented in the form of radial temperature distributions for the asymptotic region of the arc. On each figure, the predicted equilibrium profile is presented along with spectroscopic temperature profiles inferred from the electron continuum and the NI 4935 A, NI 6008 A and NI 7468 A spectral lines. These lines correspond to transitions for which the upper energy levels, E,, are 13.20,13.66 and 11.99 eV, respectively. For each current, the experimental results are generally lower than the theoretical distribution by several thousand degrees in the arc core. In the periphery the trend is reversed, with the theoretical distribution underpredicting the data by a considerable degree. These results are clearly suggestive of a thermochemical nonequilibrium condition, in which the electron temperature and concentration exceed the values which might
ARC
CURRENT
rh m 0.30
- 75
amp
gm/rcc
p = I atm
-
a
4935
ii (E” = 13.20
x
6006
i
kn=
13.66
ev)
0
7466
i
cc,=
11.99
ev)
+
CONTINUUM EQUlLl6RlUM
WI
SOLUTION
RADIAL
POSITION
, (mm.)
FIG. 1. Radial temperature profiles for the 75 A nitrogen arc.
F. P.
1372 14
and E. S. MURRER
INCROPERA
I
I
I
I
ARC
CURRENT
rh = 0.30
= 125
amp
gm/sec
0
D
4935
A
(6” = 13 20
ev)
X
6006
%
(~"-13.66
ev)
0
7466
i
(E,=11.99
ev)
+
CONTINUUM
-
EQUILIBRIUM
o0
SOLUTION
1.0
2.0 RADIAL
FIG.2. Radial
3.0 POSITION
temperature
4.0
, (mm.)
profiles for the 125 A nitrogen
arc.
+
E -I
ARC ti
p *
-
CURRENT
= 0.3
i
= 200
amp
otm
q
4935
i
(E”=
13.20
ev)
x
6006
i
(en=
13.66
ev)
0 +
7466 8 (En= CONTINUUM
II.99
ev)
EOUILIBRIUM
SOLUTION
1.0
3.0
2.0 RADIAL
FIG.3. Radial
I
I
I
'0
\
gm/stc
temperature
POSITION
I
4.0
, (mm.)
profiles for the 200 A nitrogen
arc.
Spectroscopic measurements for atmospheric nitrogen and helium arcs
1373
be expected under equilibrium conditions in the arc periphery but fall considerably below the equilibrium values in the arc core. A possible explanation of this behavior is provided by consideration of the mass and thermal diffusion processes. In the absence of sufficient ionization-recombination reactions and elastic electron-heavy particle collisions, ambipolar and neutral atom diffusion, combined with thermal conduction, will promote an underpopulation of charged species and lower temperatures in the arc core. Similarly, these processes will promote an overpopulation of the charged species and high temperatures in the outer regions of the arc. The significance of the mass and thermal diffusion processes is confirmed in a qualitative sense by the “flatness” of the experimental profiles. Although this explanation of the observed nonequilibrium effects is plausible, final verification must await the performance of a detailed multifluid analysis for the nitrogen arc. The disparity between the predicted and experimental results clearly implies that use of an equilibrium model is only appropriate for gross estimates of the thermal condition in a nitrogen arc. This is contrary to observations made for the Ar arc, where good agreement between equilibrium and spectroscopic results was found to exist in the arc core over a wide range of currents.‘2’ Figures 1-3 also reveal a significant difference between the electron continuum and excitation temperatures. Except for the 75 A arc (for which the measurements are somewhat erratic), the electron temperature exceeds the excitation temperatures by as much as 2000°K in the arc core. At 75 A the continuum temperature is close to the excitation temperatures characteristic of the lower values of E,. These results indicate that the bound electronic states are not in equilibrium with the electronic continuum and that, for the most part, the bound states are underpopulated. Moreover, there is no tendency for the continuum and excitation temperatures to coalesce with increasing current. These results are contrary to those observed for the Ar plasma, where good agreement between excitation and continuum temperatures existed in the arc core over a wide current range. Further observation of Figs. 1-3 reveals considerable disparity between the various excitation temperatures. For each current, the transition corresponding to the largest upper energy level (6008 A) provides the lowest temperature. However, for the higher currents, the transition associated with the intermediate energy level (4935 A) provides the highest temperature, whereas at 75 A the highest temperature corresponds to transitions from the smallest upper energy level (7468 A). Again, there is no discernible trend for the temperatures to merge with increasing current. The erratic behavior which exists in the arc periphery for each current is possibly due to the influence ofmolecular dissociationrecombination processes which are most significant at 7000°K. The experimental temperature profiles are clearly symptomatic of an excitation nonequilibrium condition. Similar observations have been made by BERTRAND,‘@ who suggested that the nonequilibrium effects are in part due to the metastable 2P and 2D levels which lie from 2 to 3 eV above the NI ground level. Due to the large difference between the energies of the metastable levels and that of the next highest excited level, electrons tend to become trapped in the metastable levels causing the higher levels to be underpopulated. However, this argument remains somewhat speculative, and any satisfactory explanation of the experimental trends should come from a complete solution for the level populations using the BKM method.“*’ The comparisons between experimental and theoretical results for the atmospheric 65 and 100 A helium arcs are shown in Figs. 4 and 5. The spectroscopic temperature profiles
F. P.
1374
INCROPERA
and E. S. MURRER
18
16
8
6
-
EQUILIBRIUM
SOLUTION
RADIAL POSITION , (mm.) FIG. 4. Radial temperature profiles for the 65 A helium arc.
of this study were inferred from the He1 4713 A (E, = 23.59 eV) and He1 5876 (E, = 23.07 eV) spectral lines, and those obtained by BOTT@) were from the He1 4027 A (E, = 24.04 eV) and He1 5876 A lines. The disparity which exists between the excitation temperatures and the theoretical equilibrium temperature is striking. Again, the theoretical results exceed the data by a considerable amount in the arc core and greatly underpredict the data in the arc periphery. Although the effect is similar in form to that which characterizes the nitrogen arc, it occurs to a far greater degree. For He, however, the different excitation temperatures are virtually identical, and the profile forms are nearly horizontal. Although the experimental results, when considered alone, suggest the existence of excitation equilibrium, their comparison with the theoretical results implies the existence of a severe thermochemical nonequilibrium condition throughout the arc. The most likely sources of this condition are the concurrent ambipolar and neutral atom diffusion processes and thermal conduction. The occurrence of these processes in the absence of large ionization-recombination and elastic electron-heavy particle reaction rates will promote both chemical nonequilibrium and nonequipartition of species translational energies. These processes are particularly dominant in a He plasma, for which the diffusion and thermal conduction coefficients are comparatively large. The importance of these transport processes (particularly ambipolar diffusion) in promoting thermochemical nonequilibrium
Spectroscopic measurements for atmospheric nitrogen and
heliumarcs
1375
I6
ARCCURRENT - 100amp rir = 0.02
gm/scc
16
‘:-
12
9 Y e
IO
iii 2 2
6
p” I c”
6
-
EQUILIBRIUM 5876
0
0
1.0
SOLUTION (Ret.
6)
2.0 RADIAL
FIG.
5.
3.0 POSITION ,
4.0 (mm.)
Radial temperature profiles for the 100 A helium arc.
has been verified by the multi-fluid calculations of KRUGER(~)and UHLJZNBUSCH.~“) The significance of these processes is also demonstrated by the “flatness” of the measured profiles. The severity of the nonequilibrium condition for He becomes more apparent when the results of LIJ~~NS(~~)are considered. For the low current arcs of interest in this study, Lukens was able to infer a mean heavy particle temperature of approximately 1000°K for the asymptotic region. This was done by calorimetrically measuring the mean enthalpy of the plasma and assuming that virtually all of the gas energy resides in the heavy particles (an assumption which is an excellent approximation for the low degree of ionization characteristic of the He arcs of interest). Although excitation equilibrium exists over most of the arc, there is a small but discernable departure from this form of equilibrium at the arc periphery. The trend is toward a relative overpopulation of the lower excited states which becomes progressively larger with increasing radius. Moreover, the results of this study indicate a significant overpopulation of the ground state relative to the excited states. A reasonable estimate of the actual ground state population may be obtained by evaluating the thermal equation of state at p = 1 atm and T = 1000°K and assuming that the plasma is comprised predominantly of ground state He atoms. This gives a ground state population of approximately 7 x lo’* cmm3. In contrast, using the Boltzmann distribution under the assumption
1376
F. P. INCROPERAand E. S. MURRER
of LTE at an experimental excitation temperature of 12,OOO”K,a ground state population of approximately 6 x 10” cm- 3 is obtained. This result is consistent with the observations of BOTT@) and UHLENBUSCH.(‘~) 4. CONCLUSIONS
On the basis of the comparisons of this study, for low current, atmospheric helium and nitrogen arcs the following conclusions are derived. (i) Flow models based upon the assumption of LTE are grossly inadequate for describing the thermal state of helium arcs and are suitable only as a first approximation for the description of nitrogen arcs. This result has particular bearing on the use of quantitative spectroscopic diagnostics with an equilibrium flow model to infer high temperature gas transport properties. (ii) The helium arc is characterized by a significant thermochemical nonequilibrium condition in which excitation and electron temperatures are in the neighborhood of 104”K while the heavy particle temperature is approximately 103”K. On the basis of multi-fluid flow calculations, the ambipolar diffusion of charged species is known to be the major mechanism for promoting the nonequilibrium effect. (iii) Excitation equilibrium among the upper bound levels of the He1 atom exists in the core of the helium arc, but in the periphery the excited levels become progressively overpopulated with decreasing energy. The He1 ground level is overpopulated with respect to the excited levels. (iv) The nitrogen arc is characterized by both thermochemical and excitation nonequilibrium conditions. Although plausible explanations may be offered for the cause of the nonequilibrium conditions, strict confirmation of any interpretation may only come from detailed multi-fluid calculations combined with determination of the nonequilibrium level populations using standard methods.(“) Acknowledgements-One of us (E.S.M.) is grateful for support under the NSF-URP program during the early stages of the study. We are grateful to Doctor VELVINWATSONof the NASA-Ames Research Center for his assistance with the nitrogen equilibrium flow calculations.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
14.
J. F. BOTT,Phys. Fluids 9, 1540 (1966). R. J. GIANNAI&and F. P. INCROP&, JQSRT 11,291 (1971). C. H. KRUGER.Phvs. Fluids 13. 1737 (1970). K. J. CLARKand F. P. INCROP& AiAA i 10, 17 (1972). W. H. VENAEILE and J. B. SHUMAKFX, JQSRT9, 1215 (1969). W. T. BERTRAND, Arnold Engineering Development Center, AEDC-TR-68 (1968). L. KLEIN,NASA-CR-73656 (1968). J. F. Bar-r, JQSRT6, 807 (1966). A. T. HATTENBURG and H. J. KOSTKOWSKI,Temperature-Its Measurement and Control in Science and Industry, Vol. 3, Pt. 1, p. 587. Reinhold, New York (1962). V. Y. ALEKSANDROV, D. B. GUREVICHand I. V. PODMOGHENSKII. ht. Suectrosc. 25. 18 (1969). W. F. AHTYEand T. C. PENG,NASA TN D-1303 (1962). J. M. Yos, Avco Corn. Reo. RAD TM 63-7 (1963). ’ W. J. Lrck and H. W. E~UONS, Thermodynknic’Properties of Helium to 50,OOO”K.Harvard Univ. Press (1962). R. S. DEVOTOand C. P. LI, J. Plasma Phys. 2,17 (1968).
Spectroscopic measurements for atmospheric nitrogen and helium arcs 15. 16. 17. 18. 19. 20.
W. L. WIESE,M. W. SMITHand B. M. GLENNON,NSRDS-NBS 4 (1966). J. C. MORRIS,Avco RAD Corp., Private communication (1970). J. C. MORRIS,R. V. KREY and R. L. GARRISON,ARL 68-0103 (1968). D. R. BATE$ A. E. KINGSTONand R. W. P. MCWHIRTER,Proc. R. Sot. A267,297 (1962). J. UHLENBUSCH, E. FISCHERand J. HACKMANN,2. Phys. 238,404 (1970). L. A. LUKENS,Ph.D. Thesis, School of Mech. Eng., Purdue Univ. (1971).
1377
Spmmsc.
Radiar.
Trans/er.
Vol.
12, pp. 1369-1377.
Pergamon
Press 1972. Printed in Great
Britain
SPECTROSCOPIC MEASUREMENTS FOR ATMOSPHERIC NITROGEN AND HELIUM ARCS F. P. INCROPERA and E. S. MURRER School of Mechanical Engineering, Purdue University, Lafayette, Indiana 47907, U.S.A. (Received 11 February 1972)
Abstract-Thermal conditions in the asymptotic region of atmospheric nitrogen and helium arcs are determined spectroscopically and calculated using an equilibrium flow model. Tbe equilibrium model is shown to be ill-suited for both gases. The helium arc is characterized by a high degree of thermochemical nonequilibrium, and significant thermochemical and excitation nonequilibrium effects characterize the nitrogen arc.
1. INTRODUCTION ALTHOUGH constricted arc plasmas have been studied for two decades, it is only in recent years that serious consideration has been given to their thermodynamic state. Because the assumption of local thermodynamic equilibrium (LTE) greatly simplifies the use of quantitative optical diagnostics and the performance of radiative and flow calculations, this assumption has frequently been made. However, recent studies have shown that, to varying degree, departures from thermal, chemical, and excitation equilibrium may characterize arc behavior. The principal thermal effect is one of nonequipartition of translational energy between electrons and heavy particles, and the chemical and excitation nonequilibrium conditions are due to the failure of the Saha and Boltzmann equations, respectively, to provide accurate species concentrations and populations. To date the most detailed studies of arc nonequilibrium effects have been performed for argon plasmas. Through a combination of spectroscopic diagnostics and equilibrium and nonequilibrium flow calculations,“-4’ considerable understanding of the nature, cause and degree of nonequilibrium condition has been derived. On the basis of this work it is known that significant thermochemical nonequilibrium and some excitation nonequilibrium exist in the peripheral regions of the argon arc. Hence, although prediction methods based upon the assumption of LTE suffice for the description of arc behavior in the core region, such methods are inadequate for use in the outer plasma layers. The degree of nonequilibrium becomes more pronounced and its spatial extent increases with decreasing arc current and pressure. The effects are promoted primarily by the combination of a large ambipolar diffusion velocity and insufficient inelastic collision rates. The purpose of this study is to obtain an improved understanding of the nature and degree of the nonequilibrium effects in atmospheric nitrogen and helium arcs. The methodology parallels that used previously for argon”’ and involves the comparison of temperature profiles computed from a rigorous equilibrium flow model with profiles 1369
1370
F. P. INCROPERA and E. S. MURRER
inferred from the spectroscopic measurement of absolute line and continuum intensities. At minimum, such comparisons determine the extent to which the oft used assumption of equilibrium is valid and are useful to those concerned with application of the arc for radiative and transport property measurements. In addition, when combined with multi-fluid arc analyses, the comparisons do much to suggest the detailed nature and underlying causes of the nonequilibrium condition. Previous spectroscopic studies have suggested the existence of nonequilibrium conditions in both nitrogen and helium arcs. For nitrogen,@-‘) measurements reveal the existence of excitation nonequilibrium and, for helium,‘8-*0’ results suggest the presence of a severe thermochemical nonequilibrium condition. In this study an improved understanding of these nonequilibrium effects is obtained through comparison of measured results with those obtained from an equilibrium flow model. 2. THEORETICAL AND EXPERIMENTAL METHODS To determine the importance of arc nonequilibrium effects, it is useful to have, as a reference, the thermal conditions which would exist were LTE (defined to include thermal, chemical, and ionization equilibrium) valid throughout. Accordingly, the conservation equations (mass, momentum, and energy), together with Ohm’s law and the caloric and thermal equations of state, are solved for laminar, axisymmetric flow in the arc. The flow model assumes the existence of LTE and depends upon knowledge of the transport and thermophysical properties for a solution. For nitrogen appropriate property values have been obtained from AHTYE(“) and Yos,(‘~) and for helium the property values have been obtained from LICK and EMMONS(‘~) and DEVOTOand LI.(‘~’ For this study, the most important result of the solution is the equilibrium thermodynamic temperature profiles computed for the asymptotic region of the arc. Additional details concerning the flow model are provided by GIANNARISand INCROPERA.‘~) For comparison with the predicted temperature profiles, experimental temperatures have been obtained using the cascade arc plasma generator, optical system, and procedures previously described. (2)Measurements were made with the optical access slit located 5.14 cm downstream from the cathode tip. This was sufficient to insure the existence of an asymptotic condition for both the nitrogen and helium arcs, which were operated at the laminar flow rates of 0.30 and 0.075 g/set, respectively. Results were obtained for nitrogen arcs operated at 75, 125 and 200 A ; however, due to limitations in the power supply, helium arc results could only be obtained at a current of 65 A. Excitation and electron temperatures were inferred from absolute line and continuum intensity measurements, respectively. Although such determinations are weakened by the necessity of assuming equilibrium relations, they remain valuable for the detection of departures from equilibrium. In regions of the arc for which LTE exists, the experimental temperatures will agree with the computed equilibrium temperature. In regions characterized by nonequilibrium effects, the experimental and theoretical temperatures will differ. Although such differences do not provide the precise degree of nonequilibrium, they remain useful for inferring the nature of the nonequilibrium condition. The spectral lines selected for use in this study are the 4935 (32P-42S), 6008 (32S-42P) and 7468 (34P-34S) lines for nitrogen and the 4713 (23P-43S) and 5876 (23P-330) lines for helium. Each line is sufficiently isolated from other lines of the spectrum and may be
Spectroscopic measurements for atmospheric nitrogen and helium arcs
1371
assumed to be optically thin. All transition property values were taken from the NBS tables.“” Due to the low electron concentrations characteristic of the helium plasmas of this study, the continuum radiation is extremely weak. Hence, helium continuum intensity measurements were not made. For nitrogen, absolute continuum intensity measurements (16)both the neutral atom and ionic were made at 4955 A, and, as suggested by MORRIS, contributions to the continuum were considered in the subsequent determination of the electron kinetic temperature. The continuum rate coefficients required for this determination were obtained from MORRIS.(’7, 3. RESULTS
The comparison between experimental and theoretical results for the atmospheric nitrogen arc are shown in Figs. l-3. Results are presented in the form of radial temperature distributions for the asymptotic region of the arc. On each figure, the predicted equilibrium profile is presented along with spectroscopic temperature profiles inferred from the electron continuum and the NI 4935 A, NI 6008 A and NI 7468 A spectral lines. These lines correspond to transitions for which the upper energy levels, E,, are 13.20,13.66 and 11.99 eV, respectively. For each current, the experimental results are generally lower than the theoretical distribution by several thousand degrees in the arc core. In the periphery the trend is reversed, with the theoretical distribution underpredicting the data by a considerable degree. These results are clearly suggestive of a thermochemical nonequilibrium condition, in which the electron temperature and concentration exceed the values which might
ARC
CURRENT
rh m 0.30
- 75
amp
gm/rcc
p = I atm
-
a
4935
ii (E” = 13.20
x
6006
i
kn=
13.66
ev)
0
7466
i
cc,=
11.99
ev)
+
CONTINUUM EQUlLl6RlUM
WI
SOLUTION
RADIAL
POSITION
, (mm.)
FIG. 1. Radial temperature profiles for the 75 A nitrogen arc.
F. P.
1372 14
and E. S. MURRER
INCROPERA
I
I
I
I
ARC
CURRENT
rh = 0.30
= 125
amp
gm/sec
0
D
4935
A
(6” = 13 20
ev)
X
6006
%
(~"-13.66
ev)
0
7466
i
(E,=11.99
ev)
+
CONTINUUM
-
EQUILIBRIUM
o0
SOLUTION
1.0
2.0 RADIAL
FIG.2. Radial
3.0 POSITION
temperature
4.0
, (mm.)
profiles for the 125 A nitrogen
arc.
+
E -I
ARC ti
p *
-
CURRENT
= 0.3
i
= 200
amp
otm
q
4935
i
(E”=
13.20
ev)
x
6006
i
(en=
13.66
ev)
0 +
7466 8 (En= CONTINUUM
II.99
ev)
EOUILIBRIUM
SOLUTION
1.0
3.0
2.0 RADIAL
FIG.3. Radial
I
I
I
'0
\
gm/stc
temperature
POSITION
I
4.0
, (mm.)
profiles for the 200 A nitrogen
arc.
Spectroscopic measurements for atmospheric nitrogen and helium arcs
1373
be expected under equilibrium conditions in the arc periphery but fall considerably below the equilibrium values in the arc core. A possible explanation of this behavior is provided by consideration of the mass and thermal diffusion processes. In the absence of sufficient ionization-recombination reactions and elastic electron-heavy particle collisions, ambipolar and neutral atom diffusion, combined with thermal conduction, will promote an underpopulation of charged species and lower temperatures in the arc core. Similarly, these processes will promote an overpopulation of the charged species and high temperatures in the outer regions of the arc. The significance of the mass and thermal diffusion processes is confirmed in a qualitative sense by the “flatness” of the experimental profiles. Although this explanation of the observed nonequilibrium effects is plausible, final verification must await the performance of a detailed multifluid analysis for the nitrogen arc. The disparity between the predicted and experimental results clearly implies that use of an equilibrium model is only appropriate for gross estimates of the thermal condition in a nitrogen arc. This is contrary to observations made for the Ar arc, where good agreement between equilibrium and spectroscopic results was found to exist in the arc core over a wide range of currents.‘2’ Figures 1-3 also reveal a significant difference between the electron continuum and excitation temperatures. Except for the 75 A arc (for which the measurements are somewhat erratic), the electron temperature exceeds the excitation temperatures by as much as 2000°K in the arc core. At 75 A the continuum temperature is close to the excitation temperatures characteristic of the lower values of E,. These results indicate that the bound electronic states are not in equilibrium with the electronic continuum and that, for the most part, the bound states are underpopulated. Moreover, there is no tendency for the continuum and excitation temperatures to coalesce with increasing current. These results are contrary to those observed for the Ar plasma, where good agreement between excitation and continuum temperatures existed in the arc core over a wide current range. Further observation of Figs. 1-3 reveals considerable disparity between the various excitation temperatures. For each current, the transition corresponding to the largest upper energy level (6008 A) provides the lowest temperature. However, for the higher currents, the transition associated with the intermediate energy level (4935 A) provides the highest temperature, whereas at 75 A the highest temperature corresponds to transitions from the smallest upper energy level (7468 A). Again, there is no discernible trend for the temperatures to merge with increasing current. The erratic behavior which exists in the arc periphery for each current is possibly due to the influence ofmolecular dissociationrecombination processes which are most significant at 7000°K. The experimental temperature profiles are clearly symptomatic of an excitation nonequilibrium condition. Similar observations have been made by BERTRAND,‘@ who suggested that the nonequilibrium effects are in part due to the metastable 2P and 2D levels which lie from 2 to 3 eV above the NI ground level. Due to the large difference between the energies of the metastable levels and that of the next highest excited level, electrons tend to become trapped in the metastable levels causing the higher levels to be underpopulated. However, this argument remains somewhat speculative, and any satisfactory explanation of the experimental trends should come from a complete solution for the level populations using the BKM method.“*’ The comparisons between experimental and theoretical results for the atmospheric 65 and 100 A helium arcs are shown in Figs. 4 and 5. The spectroscopic temperature profiles
F. P.
1374
INCROPERA
and E. S. MURRER
18
16
8
6
-
EQUILIBRIUM
SOLUTION
RADIAL POSITION , (mm.) FIG. 4. Radial temperature profiles for the 65 A helium arc.
of this study were inferred from the He1 4713 A (E, = 23.59 eV) and He1 5876 (E, = 23.07 eV) spectral lines, and those obtained by BOTT@) were from the He1 4027 A (E, = 24.04 eV) and He1 5876 A lines. The disparity which exists between the excitation temperatures and the theoretical equilibrium temperature is striking. Again, the theoretical results exceed the data by a considerable amount in the arc core and greatly underpredict the data in the arc periphery. Although the effect is similar in form to that which characterizes the nitrogen arc, it occurs to a far greater degree. For He, however, the different excitation temperatures are virtually identical, and the profile forms are nearly horizontal. Although the experimental results, when considered alone, suggest the existence of excitation equilibrium, their comparison with the theoretical results implies the existence of a severe thermochemical nonequilibrium condition throughout the arc. The most likely sources of this condition are the concurrent ambipolar and neutral atom diffusion processes and thermal conduction. The occurrence of these processes in the absence of large ionization-recombination and elastic electron-heavy particle reaction rates will promote both chemical nonequilibrium and nonequipartition of species translational energies. These processes are particularly dominant in a He plasma, for which the diffusion and thermal conduction coefficients are comparatively large. The importance of these transport processes (particularly ambipolar diffusion) in promoting thermochemical nonequilibrium
Spectroscopic measurements for atmospheric nitrogen and
heliumarcs
1375
I6
ARCCURRENT - 100amp rir = 0.02
gm/scc
16
‘:-
12
9 Y e
IO
iii 2 2
6
p” I c”
6
-
EQUILIBRIUM 5876
0
0
1.0
SOLUTION (Ret.
6)
2.0 RADIAL
FIG.
5.
3.0 POSITION ,
4.0 (mm.)
Radial temperature profiles for the 100 A helium arc.
has been verified by the multi-fluid calculations of KRUGER(~)and UHLJZNBUSCH.~“) The significance of these processes is also demonstrated by the “flatness” of the measured profiles. The severity of the nonequilibrium condition for He becomes more apparent when the results of LIJ~~NS(~~)are considered. For the low current arcs of interest in this study, Lukens was able to infer a mean heavy particle temperature of approximately 1000°K for the asymptotic region. This was done by calorimetrically measuring the mean enthalpy of the plasma and assuming that virtually all of the gas energy resides in the heavy particles (an assumption which is an excellent approximation for the low degree of ionization characteristic of the He arcs of interest). Although excitation equilibrium exists over most of the arc, there is a small but discernable departure from this form of equilibrium at the arc periphery. The trend is toward a relative overpopulation of the lower excited states which becomes progressively larger with increasing radius. Moreover, the results of this study indicate a significant overpopulation of the ground state relative to the excited states. A reasonable estimate of the actual ground state population may be obtained by evaluating the thermal equation of state at p = 1 atm and T = 1000°K and assuming that the plasma is comprised predominantly of ground state He atoms. This gives a ground state population of approximately 7 x lo’* cmm3. In contrast, using the Boltzmann distribution under the assumption
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F. P. INCROPERAand E. S. MURRER
of LTE at an experimental excitation temperature of 12,OOO”K,a ground state population of approximately 6 x 10” cm- 3 is obtained. This result is consistent with the observations of BOTT@) and UHLENBUSCH.(‘~) 4. CONCLUSIONS
On the basis of the comparisons of this study, for low current, atmospheric helium and nitrogen arcs the following conclusions are derived. (i) Flow models based upon the assumption of LTE are grossly inadequate for describing the thermal state of helium arcs and are suitable only as a first approximation for the description of nitrogen arcs. This result has particular bearing on the use of quantitative spectroscopic diagnostics with an equilibrium flow model to infer high temperature gas transport properties. (ii) The helium arc is characterized by a significant thermochemical nonequilibrium condition in which excitation and electron temperatures are in the neighborhood of 104”K while the heavy particle temperature is approximately 103”K. On the basis of multi-fluid flow calculations, the ambipolar diffusion of charged species is known to be the major mechanism for promoting the nonequilibrium effect. (iii) Excitation equilibrium among the upper bound levels of the He1 atom exists in the core of the helium arc, but in the periphery the excited levels become progressively overpopulated with decreasing energy. The He1 ground level is overpopulated with respect to the excited levels. (iv) The nitrogen arc is characterized by both thermochemical and excitation nonequilibrium conditions. Although plausible explanations may be offered for the cause of the nonequilibrium conditions, strict confirmation of any interpretation may only come from detailed multi-fluid calculations combined with determination of the nonequilibrium level populations using standard methods.(“) Acknowledgements-One of us (E.S.M.) is grateful for support under the NSF-URP program during the early stages of the study. We are grateful to Doctor VELVINWATSONof the NASA-Ames Research Center for his assistance with the nitrogen equilibrium flow calculations.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
14.
J. F. BOTT,Phys. Fluids 9, 1540 (1966). R. J. GIANNAI&and F. P. INCROP&, JQSRT 11,291 (1971). C. H. KRUGER.Phvs. Fluids 13. 1737 (1970). K. J. CLARKand F. P. INCROP& AiAA i 10, 17 (1972). W. H. VENAEILE and J. B. SHUMAKFX, JQSRT9, 1215 (1969). W. T. BERTRAND, Arnold Engineering Development Center, AEDC-TR-68 (1968). L. KLEIN,NASA-CR-73656 (1968). J. F. Bar-r, JQSRT6, 807 (1966). A. T. HATTENBURG and H. J. KOSTKOWSKI,Temperature-Its Measurement and Control in Science and Industry, Vol. 3, Pt. 1, p. 587. Reinhold, New York (1962). V. Y. ALEKSANDROV, D. B. GUREVICHand I. V. PODMOGHENSKII. ht. Suectrosc. 25. 18 (1969). W. F. AHTYEand T. C. PENG,NASA TN D-1303 (1962). J. M. Yos, Avco Corn. Reo. RAD TM 63-7 (1963). ’ W. J. Lrck and H. W. E~UONS, Thermodynknic’Properties of Helium to 50,OOO”K.Harvard Univ. Press (1962). R. S. DEVOTOand C. P. LI, J. Plasma Phys. 2,17 (1968).
Spectroscopic measurements for atmospheric nitrogen and helium arcs 15. 16. 17. 18. 19. 20.
W. L. WIESE,M. W. SMITHand B. M. GLENNON,NSRDS-NBS 4 (1966). J. C. MORRIS,Avco RAD Corp., Private communication (1970). J. C. MORRIS,R. V. KREY and R. L. GARRISON,ARL 68-0103 (1968). D. R. BATE$ A. E. KINGSTONand R. W. P. MCWHIRTER,Proc. R. Sot. A267,297 (1962). J. UHLENBUSCH, E. FISCHERand J. HACKMANN,2. Phys. 238,404 (1970). L. A. LUKENS,Ph.D. Thesis, School of Mech. Eng., Purdue Univ. (1971).
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