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Modelling of a microwave postdischarge nitriding reactor
Surface and Coatings Technology, 59 (1993) 59—66
59
Modelling of a microwave postdischarge nitriding reactor H. Malvosa,b A. Ricardc, J. SzekeIy~’,H. Michela, M. Gantoisa and D. Ablitzer” aLaboratoire de Science et Genie des Surfaces, URA CNRS 1402, and bLaboratoire de Science et Genie des Matériaux Metalliques, URA CNRS 159, Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex (France) cLaboratoire de Physique des Gaz et des Plasmas, URA CNRS, Bt 212, Université Paris-Sud, 91405 Orsay (France) dMJT Department ofMaterials Science and Engineering, Cambridge, MA 02139 (USA)
Abstract In a postdischarge nitriding reactor, reactive species, which have a short lifetime, are created by means of a plasma and then sent by convection towards the sample which is to be treated. The aim of the model presented here is to optimize the gas flow characteristics (composition, flow rate, pressure etc.) in order to obtain a maximum reactivity around the sample. The experimental reactor used has a very simple geometry and works with low power (less than 200 W) microwave discharges (2450 MHz) in Ar—N 2 mixtures for a pressure in the 10—1000 hPa range. This reactor allowed us to point out the complexity of the different operating parameters, justifying the development of a predictive model. Such a model was developed with the code PHOENICS. It allowed us to determine the effect of the operating parameters on the velocity field, the temperature field and the atomic nitrogen (the nitriding species) mass fraction map. The standard operating conditions used for the treatment of iron samples were chosen as reference conditions. Then several sets of operating conditions were tested, pointing out the extremely important effect ofpressure and gas velocity in the reactor on the atomic nitrogen mass fraction.
1. Introduction Postdischarge nitriding treatments have been performed recently. In such treatments, nitrogen active species are produced in flowing postdischarges and work-pieces are placed downstream inside a separate heating device [1]. The first metallurgic results obtained show that there is a strong correlation between the superficial nitrogen composition of the treated iron samples and the atomic nitrogen density of the flowing gas inside the nitriding reactor [2, 3]. Experimental studies allowed us to show the effect of the main operating parameters on this density [4, 5] and to propose an interpretation from simple kinetic models [5, 6]. The complexity of the interactions between these parameters justifies the development of a predictive model, which is presented now. 2. Postdischarge reactor 2.1. Experimental set-up The reactor we modelled uses a microwave discharge. The experimental set-up is shown in Fig. 1. The power generator (1200 W) sends microwaves (2450 MHz) along a waveguide. The plasma is created in a quartz tube and remains in this position. The neutral excited species are transported by the gas flow towards the sample. Using an external heater, this sample is maintained at the correct temperature to activate the
0257—8972/93/$6.00
diffusion mechanisms. Thus, the gas velocity must be high enough so that the active species do not become de-excited before they reach the sample. We notice here that the higher the pressure is, the more frequent are the impacts between the particles and the shorter is the
Active sp.c:e! generation
I
I
Transport
i
of species 5 mm
I I
Nitriding reactor a 30 mm
L 0.7 m
L 1.2
I I
I I
I
I
I I I Vacuum pump
I _j_j[~amPl~~
jj
—__________________
I
___ __________________
Plasma sourca
surfaguide
Heating devic.
2450 MHz
Optic fiber
Ar-NO
Pressure spectroscopic
gauge
L~UiPment Fig. I. Experimental reactor.
©
1993
—
Elsevier Sequoia. All rights reserved
60
H. Malvos et al.
/
Modelling of a microwave postdischarge nitriding reactor
lifetime of the active species. None the less, from an industrial point of view, it is interesting to work close to atmospheric pressure, because this allows convective heating of the reactor and, thus, natural homogenization in the temperature of the samples to be treated. The model presented represents the flowing postdischarge only. Therefore, the electromagnetic problems related to the discharge itself are not involved and we consider only the cylindrical reactor and the external heater whose dimensions are reported in Fig. 2.
can easily pass through the activation gap, thus forming in solution in the metal sample. Therefore, the only reactive species that will be considered here is atomic nitrogen: the dissociation, at the surface of the sample, of molecular nitrogen vibrationally excited only represents a small percentage of the atomic nitrogen which forms in solution in the metal sample. Moreover, as the densities of the excited species in the postdischarge are very low in comparison with the density of the molecules in their fundamental state, we will take the physical properties of the molecular nitrogen (or of the Ar—N mixture used) in its fundamental state (viscosity, thermal diffusivity, specific heat) for the study of the plasma flow in the reactor.
2.2. Reactive species in the plasma Our model takes into account all the transport phenomena in order to draw maps of reactive species densities in the reactor. Therefore, we will first recall here what are the main species responsible for the nitriding. The plasma is generated in a small volume by an electrical field which creates ion—electron pairs. The electrons are then accelerated by the electrical field and their collisions with the gas molecules create three different kinds of transfer: transfer of momentum; transfer of kinetic energy~ transfer from kinetic energy of the electron to potential energy of the molecule. The first two transfers are negligible for the gas molecules, because of the low mass of the electron compared with the mass of the nitrogen molecule. However, the third type of transfer can lead to an excitation (electronic, vibrational and rotational) of the nitrogen molecule, to an ionization or to a split into atomic nitrogen, Different experiments, carried out at the Laboratoire de Physique des Gaz et des Plasmas, Orsay, showed that the species mainly responsible for the nitriding is the atomic nitrogen [7]. Indeed, because of its high potential energy (around 9.6 eV), the atomic nitrogen
3. Transport of the reactive species 3.1. Study of the mass balance 3.1.1. Mass conservation equation The mass balance for the atomic nitrogen is given by V (P Ct) V convection
1
30
380
iron Sample
300
Fig. 2. Geometry of the flowing postdischarge reactor.
300
2t) --
..
D p V CD) diffusion
=
S net
creation
where p represents the density of the plasma, co the mass fraction of the species N, V the barycentric velocity, D the diffusion coefficient and S the source term of the species N (creation minus destruction). Here we are in a steady state hypothesis. This means that we do not consider the problems inherent to the starting of the treatment. In fact, we should call this a ‘quasi-steady state’, because, during the process, the sample surface is made up of the phases Fe(ot), Fe(y’) and Fe(s), one after another. However, each of these phases remains at the surface long enough to apply the quasi-steady state hypothesis.
Exierii,ti I lealci
-
—
200
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
61
-
-~
p
50 rn/s.
(a)
330
(b) 2. E-3
__
Velocity
350
~
330
4~gj\\71io 601)
700 Temperature tK )
., ~
300 600
1.
1¼O~ ~
~
2.SE.3
N
2.~3
I (c)
Atomic Nitrogen Mass Fraction
Fig. 3. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 0.53 kg s
3.1.2. Source term S The increase in volume of the atomic nitrogen occurs entirely in the discharge, In the postdischarge, the atomic nitrogen only recombines itself by the mechanism
2 of N
m
2.
Unfortunately, this mechanism is not quantified at this time. However, Yamashita [9] proposed the following mechanisms for the destruction of atomic nitrogen on Pyrex walls:
N+N+N2—+N~+N2 N+wall—~N~+wall as shown by Partridge et a!. [8] and Yamashita [9]. Moreover, the variation of k with temperature was determined experimentally [10]. 3.1.3. Boundary condition The atomic nitrogen concentration at the entrance of the reactor is known. It is determined by the NO titration method [3]. On the surface of the sample, the atomic nitrogen disappears as it goes into solution in the metal sample.
k
N + N + wall
—*
N~+ wall
k
In fact, Yamashita showed that only the first mechanism is significant. 3.2. Study ofthe momentum balance 3.2.1. Nature oftheflow To determine the nature of the flow, we calculate the Reynolds number:
62
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
I
--
--
50 rn/s. (a)
Velocity
841)
350 ~400
(b)
10‘700
\
8o0~”~/ \ ‘400 700\5o0 600
Temperature (K.)
1.4 E-3 I.2E-3
1.6E-3 I.8E~3
l.E.3\\t/~
~ if!
~
I’
3\~
1.6 E-3
.4
E-3
.2 E-3
~LE.
3. E-3 (c)
Atomic Nitrogen Mass Fraction 2 of Ar—20%N
Fig. 4. Computed results obtained for the following parameters: pressure, iO~Pa; mass flux, 0.70 kg s
Vd Re_p
2.
3.2.3. Momentum conservation equation (pVV)V=—VT—VP+pg
—
—
where d represents the diameter of the reactor (3 cm), V the mean velocity (around s~)and kinematic 2 s~5atm 380 K, 5.8v xthe iO~ Pa for a viscosityof(4 Ar—li x l0~ m mixture %N 2). The Reynolds number is around 400, which means that the flow can be considered as being laminar (Re.cz 2100). 3.2.2. Fluid continuity equation Since we are in a steady state, the continuity equation is: V (p V)=0
m
where t represents the stress tensor, VP the pressure gradient and g the gravity acceleration. We have a newtonian fluid, so and the the stress tensor is a simple expression of the viscosity velocity. 3.2.4. Boundary conditions At the entrance to the reactor, the radial velocity value is zero. On the walls, the velocity value is zero. At the exit from the reactor, the mean velocity is calculated from the mass flow conservation. 3.3. Study of the heat balance 3.3.1. Energy conservation equation V (p C~TV—k V T) =
H. Malvos et a!.
—~
:
/
Modelling of a microwave postdischarge nitriding reactor
63
50 rn/s. Velocity
(a)
330
\
____________________________
8 1)
(b) 1.E-5
KtX)~/
Temperature tK.)
/
7(X)
5.E-5
I_ ____ (c)
350
3.E.4~
___
\ 2.E.4
Atomic Nitrogen Mass Fraction
Fig. 5. Computed results obtained for the following parameters: pressure, 5.8 x l0~Pa; mass flux, 4.62 kg s -
m
2
of Ar— 11 %N
2.
TABLE 1. Experimental data used as boundary conditions for the model
Mass flow rate (kg s - m 2) Gas mixture composition Pressure (Pa) Temperature of the external heater (K) Temperature of the gas at the entrance to the reactor (K) Atomic nitrogen mass fraction at the entrance to the reactor
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
0.53 N2 I0~ 843 450
0.70 Ar—20%N2 l0~ 843 350
4.62 Ar—ll%N2 5.8 x l0~ 900 400
4.62 Ar—11%N2 l0~ 900 400
7.97 Ar—ll%N2 l0~ 900 400
5.0 x l0~
3.0 x iO~
1.3 x I0~
1.3 x I0~~
1.3 x l0~
where T represents the gas temperature, C~,the specific heat at constant pressure, k the thermal diffusion coefficient and ST the source term. In the case of low pressures, photons are not absorbed
by gas molecules and immediately reach the reactor walls. In this case, radiation does not participate in the heating of the gas. For higher pressures, experiments have showed that the temperature variation is also
64
H. Malvos et a!.
-*
/
Modelling of a microwave postdischarge nitriding reactor
50 mIs.
(a)
Velocity 330\~
__
1140 (b)
Temperature tK.)
5. E.6
8tX///’ 7(X)
LE.5
l.E-3
5. E.4
(c)
2!E.4 Atomic Nitrogen Mass Fraction
Fig. 6. Effect of pressure with a constant mass flow rate. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 1 m2 of Ar—1l%N 4.62 kg s 2.
negligible. In the same way, the contribution of the ‘vibration—translation’ collisions between the gas molecules is negligible. Finally, the value of the source term ST is considered to be zero and the energy conservation equation is written V ( C TV k V T) = 0 p —
3.3.2. Boundary conditions The gas temperature at the entrance to the reactor is measured by spectroscopic analysis. The heat flow at the reactor and sample walls is estimated by the calculation of the corresponding heat transfer coefficients. With this aim, we had to consider the radiative exchanges
between the sample and the external heater to determine the equilibrium temperature of the sample. 3.4. Physical properties of the gas Density. Since the pressure is quite low (less than atmospheric pressure), we use the perfect gas law. Diffusion coefficient of atomic nitrogen in argon or in molecular nitrogen. We use the empirical relationship developed by Cussler [11] and Fuller et al. [12]. This relationship takes account of the effect of temperature and pressure. Heat capacity. Since the heat capacity of argon or nitrogen shows little sensitivity to pressure or temperature in our experimental range, we use a constant value [13].
H. Malvos et al.
/
Modelling of a microwave postdischarge nitriding reactor
-
65
_________
—~
:
5(1 m/s.
(a)
Velocity
\
330 ____________________
350
8(X) (b) 5.E-6
~
‘IX)
Temperature (K.) l.E.5
~
2.5 E.4
I. E.4
5. E.4
(c)
Atomic Nitrogen Mass Fraction
Fig. 7. Effect of with a constant volume flow rate. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 2 pressure of Ar—ll%N 7.97 kg s-~m 2.
Thermal conductivity. Since the thermal conductivity is pressure independent in our experimental range [14], we simply have to take account of the temperature effect
[15]. Dynamic viscosity. Since the dynamic viscosity is also pressure independent in our experimental range [16], we only consider the temperature effect [17]. The properties we have just considered correspond to pure gases; for gas mixtures, we used several combination relationships proposed in refs. 18, 19, 14 and 20 respectively, 4. Computed results The linked hydrodynamic equations were solved with the PHOENICS code, which embodies a variant of the
algorithm of Patankar and Spalding [21]. The grid used here is uniform (56 x 250). To make the figures easier to read, we use a scale factor of 25 in the y direction. Moreover, since the problem is symmetrical, we represent half a cross-section passing through the z axis. In each set of figures, we represent (a) the velocity of the gas in the reactor, (b) the temperature map and (c) the mass fraction map of atomic nitrogen. Figure 3 corresponds to a pressure 2 of N of iO~Pa and a mass flow rate of 0.53 kg s~m 2 Fig. 4 represents a pressure of Pa and a mass flow rate of 0.70 kg s~ 2 of an Ar—20%N m 2 gas mixture, and Fig. 5 corresponds to a pressure of 5.8 x l0~Pa and a mass flow rate of 4.62 kg ~ m -2 of an Ar—11 %N2 gas mixture. For these three sets of conditions, the gas temperature and SIMPLE
io~
66
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
the atomic nitrogen density at the entrance to the reactor were determined experimentally by spectroscopic analysis and NO titration respectively. These parameters, and the temperature of the external heater required to maintam the iron sample at around 843 K, are reproduced in Table 1. Figure 5 corresponds to the experimental conditions chosen to perform the nitriding of cylindrical iron samples. From these last experimental conditions, we tried to increase the pressure to l0~Pa to study the effect of this on the atomic nitrogen density in the reactor. For this treatment, we kept constant all the experimental values used previously (especially the gas temperature and the atomic nitrogen density at the entrance to the reactor), except the mass flow rate and, of course, the pressure (see Table 1). Then, Fig. 6 represents a pressure of 1 Pa with the same mass flow rate (4.62 kg s~’m 2) of the Ar—1l%N2 mixture. This means that the mean velocity
o~
at the entrance to the reactor is nearly half of that in the preceding case. In contrast, in Fig. 7, we kept the same mean velocity and, thus, the 2. pressure is 1 0~Pa and the mass flow rate 7.97 kg s’ m 5. Conclusions The results we presented show the extremely important effect of pressure and gas velocity in the reactor on the atomic nitrogen density. Indeed, the atomic nitrogen mass fraction around the sample decreases from 4 X l0~ to 1.5 x iO~ when we increase the pressure from 5.8 x io~to l0~Pa, keeping the same mass flow rate (Figs. 5 and 6). Since the mean velocity is smaller in the second case, we can assume that this is in part responsible for the decrease in the atomic nitrogen concentration. Moreover, the comparison of Fig. 5 with Fig. 7 (where we kept the same mean velocity) points out the marked effect of pressure itself on the atomic nitrogen concentration, since the atomic nitrogen mass fraction around the sample decreases from 4 x l0~ to 2.5 x i0~ when pressure increases from 5.8 x to iO~Pa. This result was expected, since the atomic nitrogen recombination is a three-body mechanism. The model used here for a two-dimension geometry could be developed to describe three-dimensional flows encountered in laboratory experiments or in an industrial set-up.
io~
Acknowledgment We are grateful to the Ministère de la Recherche et de la Technologie and Electricité de France for the support of this work.
References 1 A. Ricard, A. Pilorget, H. Michel and M. Gantois, Fr. Patent App!., 87 10698 (1987); Eur. Patent App!., 88 4019 506 (1988). 2 A. Ricard, J. E. Oseguera-Pena, H. Michel and M. Gantois, Proc. 1st mt. Conf on Plasma Surface Engineering, GarmishPartenkirchen, September 1988, Vol. 1, Deutsche Gesellschaft für Metallkunde Informations Gesellschaft, Oberursel, 1989, p. 83. 3 A. Ricard, J. E. Oseguera-Pena, L. Falk, H. Michel and M. Gantois, IEEE Trans. Plasma Sci., 18 (1990) 940. 4 A. Ricard, J. Deschamps, J. L. Godard, L. Falk and H. Michel, Mater. Sci. Eng., A139 (1991) 9—14. 5 L. Falk, J. E. Oseguera-Pena, A. Ricard, H. Michel and M. Gantois, Mater. Sci. Eng., A139 (1991) 132—36. 6 C. C. Boisse-Laporte, Sci.Chave, Eng., A140 (1991) 494—98. J. Marec and Ph. Leprince, Mater. 7 A. Ricard, Topical Invited Lecture, XVII ICPIG, Budapest, 1985. 8 H. Partridge, S. R. Langhoff, C. W. Bauschlicher and D. W. Schwenke, J. Chem. Phys., 88 (5) (1988) 3 180—83. 9 T. Yamashita, J. Chem. Phys., 70 (9) (1979) 4248—53. 10 J. E. Oseguera-Pena, Dip!ôme de These, INPL, Nancy, 1990, p. 99. 11 E. L. Cussler, Diffusion, Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, 1984, pp. 112—13. 12 E. N. Fuller, P. D. Schettler and J. C. Giddings, md. Eng. Chem., 58 (1966) 19. 13 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, pp.2—90. 14 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3—225, 3—226. 15 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, Table 35, pp. 2-82—2-85. 16 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, pp. 1-5. 17 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, Table 31, pp. 2-72, 2-73. 18 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., Chap. 14, p. 13. 19 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3-220. 20 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3-230. 21 S. V. Patankar and D. B. Spalding, Ire. J. Heat Mass Transfer, 15 (1972) 1787—1806.
59
Modelling of a microwave postdischarge nitriding reactor H. Malvosa,b A. Ricardc, J. SzekeIy~’,H. Michela, M. Gantoisa and D. Ablitzer” aLaboratoire de Science et Genie des Surfaces, URA CNRS 1402, and bLaboratoire de Science et Genie des Matériaux Metalliques, URA CNRS 159, Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex (France) cLaboratoire de Physique des Gaz et des Plasmas, URA CNRS, Bt 212, Université Paris-Sud, 91405 Orsay (France) dMJT Department ofMaterials Science and Engineering, Cambridge, MA 02139 (USA)
Abstract In a postdischarge nitriding reactor, reactive species, which have a short lifetime, are created by means of a plasma and then sent by convection towards the sample which is to be treated. The aim of the model presented here is to optimize the gas flow characteristics (composition, flow rate, pressure etc.) in order to obtain a maximum reactivity around the sample. The experimental reactor used has a very simple geometry and works with low power (less than 200 W) microwave discharges (2450 MHz) in Ar—N 2 mixtures for a pressure in the 10—1000 hPa range. This reactor allowed us to point out the complexity of the different operating parameters, justifying the development of a predictive model. Such a model was developed with the code PHOENICS. It allowed us to determine the effect of the operating parameters on the velocity field, the temperature field and the atomic nitrogen (the nitriding species) mass fraction map. The standard operating conditions used for the treatment of iron samples were chosen as reference conditions. Then several sets of operating conditions were tested, pointing out the extremely important effect ofpressure and gas velocity in the reactor on the atomic nitrogen mass fraction.
1. Introduction Postdischarge nitriding treatments have been performed recently. In such treatments, nitrogen active species are produced in flowing postdischarges and work-pieces are placed downstream inside a separate heating device [1]. The first metallurgic results obtained show that there is a strong correlation between the superficial nitrogen composition of the treated iron samples and the atomic nitrogen density of the flowing gas inside the nitriding reactor [2, 3]. Experimental studies allowed us to show the effect of the main operating parameters on this density [4, 5] and to propose an interpretation from simple kinetic models [5, 6]. The complexity of the interactions between these parameters justifies the development of a predictive model, which is presented now. 2. Postdischarge reactor 2.1. Experimental set-up The reactor we modelled uses a microwave discharge. The experimental set-up is shown in Fig. 1. The power generator (1200 W) sends microwaves (2450 MHz) along a waveguide. The plasma is created in a quartz tube and remains in this position. The neutral excited species are transported by the gas flow towards the sample. Using an external heater, this sample is maintained at the correct temperature to activate the
0257—8972/93/$6.00
diffusion mechanisms. Thus, the gas velocity must be high enough so that the active species do not become de-excited before they reach the sample. We notice here that the higher the pressure is, the more frequent are the impacts between the particles and the shorter is the
Active sp.c:e! generation
I
I
Transport
i
of species 5 mm
I I
Nitriding reactor a 30 mm
L 0.7 m
L 1.2
I I
I I
I
I
I I I Vacuum pump
I _j_j[~amPl~~
jj
—__________________
I
___ __________________
Plasma sourca
surfaguide
Heating devic.
2450 MHz
Optic fiber
Ar-NO
Pressure spectroscopic
gauge
L~UiPment Fig. I. Experimental reactor.
©
1993
—
Elsevier Sequoia. All rights reserved
60
H. Malvos et al.
/
Modelling of a microwave postdischarge nitriding reactor
lifetime of the active species. None the less, from an industrial point of view, it is interesting to work close to atmospheric pressure, because this allows convective heating of the reactor and, thus, natural homogenization in the temperature of the samples to be treated. The model presented represents the flowing postdischarge only. Therefore, the electromagnetic problems related to the discharge itself are not involved and we consider only the cylindrical reactor and the external heater whose dimensions are reported in Fig. 2.
can easily pass through the activation gap, thus forming in solution in the metal sample. Therefore, the only reactive species that will be considered here is atomic nitrogen: the dissociation, at the surface of the sample, of molecular nitrogen vibrationally excited only represents a small percentage of the atomic nitrogen which forms in solution in the metal sample. Moreover, as the densities of the excited species in the postdischarge are very low in comparison with the density of the molecules in their fundamental state, we will take the physical properties of the molecular nitrogen (or of the Ar—N mixture used) in its fundamental state (viscosity, thermal diffusivity, specific heat) for the study of the plasma flow in the reactor.
2.2. Reactive species in the plasma Our model takes into account all the transport phenomena in order to draw maps of reactive species densities in the reactor. Therefore, we will first recall here what are the main species responsible for the nitriding. The plasma is generated in a small volume by an electrical field which creates ion—electron pairs. The electrons are then accelerated by the electrical field and their collisions with the gas molecules create three different kinds of transfer: transfer of momentum; transfer of kinetic energy~ transfer from kinetic energy of the electron to potential energy of the molecule. The first two transfers are negligible for the gas molecules, because of the low mass of the electron compared with the mass of the nitrogen molecule. However, the third type of transfer can lead to an excitation (electronic, vibrational and rotational) of the nitrogen molecule, to an ionization or to a split into atomic nitrogen, Different experiments, carried out at the Laboratoire de Physique des Gaz et des Plasmas, Orsay, showed that the species mainly responsible for the nitriding is the atomic nitrogen [7]. Indeed, because of its high potential energy (around 9.6 eV), the atomic nitrogen
3. Transport of the reactive species 3.1. Study of the mass balance 3.1.1. Mass conservation equation The mass balance for the atomic nitrogen is given by V (P Ct) V convection
1
30
380
iron Sample
300
Fig. 2. Geometry of the flowing postdischarge reactor.
300
2t) --
..
D p V CD) diffusion
=
S net
creation
where p represents the density of the plasma, co the mass fraction of the species N, V the barycentric velocity, D the diffusion coefficient and S the source term of the species N (creation minus destruction). Here we are in a steady state hypothesis. This means that we do not consider the problems inherent to the starting of the treatment. In fact, we should call this a ‘quasi-steady state’, because, during the process, the sample surface is made up of the phases Fe(ot), Fe(y’) and Fe(s), one after another. However, each of these phases remains at the surface long enough to apply the quasi-steady state hypothesis.
Exierii,ti I lealci
-
—
200
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
61
-
-~
p
50 rn/s.
(a)
330
(b) 2. E-3
__
Velocity
350
~
330
4~gj\\71io 601)
700 Temperature tK )
., ~
300 600
1.
1¼O~ ~
~
2.SE.3
N
2.~3
I (c)
Atomic Nitrogen Mass Fraction
Fig. 3. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 0.53 kg s
3.1.2. Source term S The increase in volume of the atomic nitrogen occurs entirely in the discharge, In the postdischarge, the atomic nitrogen only recombines itself by the mechanism
2 of N
m
2.
Unfortunately, this mechanism is not quantified at this time. However, Yamashita [9] proposed the following mechanisms for the destruction of atomic nitrogen on Pyrex walls:
N+N+N2—+N~+N2 N+wall—~N~+wall as shown by Partridge et a!. [8] and Yamashita [9]. Moreover, the variation of k with temperature was determined experimentally [10]. 3.1.3. Boundary condition The atomic nitrogen concentration at the entrance of the reactor is known. It is determined by the NO titration method [3]. On the surface of the sample, the atomic nitrogen disappears as it goes into solution in the metal sample.
k
N + N + wall
—*
N~+ wall
k
In fact, Yamashita showed that only the first mechanism is significant. 3.2. Study ofthe momentum balance 3.2.1. Nature oftheflow To determine the nature of the flow, we calculate the Reynolds number:
62
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
I
--
--
50 rn/s. (a)
Velocity
841)
350 ~400
(b)
10‘700
\
8o0~”~/ \ ‘400 700\5o0 600
Temperature (K.)
1.4 E-3 I.2E-3
1.6E-3 I.8E~3
l.E.3\\t/~
~ if!
~
I’
3\~
1.6 E-3
.4
E-3
.2 E-3
~LE.
3. E-3 (c)
Atomic Nitrogen Mass Fraction 2 of Ar—20%N
Fig. 4. Computed results obtained for the following parameters: pressure, iO~Pa; mass flux, 0.70 kg s
Vd Re_p
2.
3.2.3. Momentum conservation equation (pVV)V=—VT—VP+pg
—
—
where d represents the diameter of the reactor (3 cm), V the mean velocity (around s~)and kinematic 2 s~5atm 380 K, 5.8v xthe iO~ Pa for a viscosityof(4 Ar—li x l0~ m mixture %N 2). The Reynolds number is around 400, which means that the flow can be considered as being laminar (Re.cz 2100). 3.2.2. Fluid continuity equation Since we are in a steady state, the continuity equation is: V (p V)=0
m
where t represents the stress tensor, VP the pressure gradient and g the gravity acceleration. We have a newtonian fluid, so and the the stress tensor is a simple expression of the viscosity velocity. 3.2.4. Boundary conditions At the entrance to the reactor, the radial velocity value is zero. On the walls, the velocity value is zero. At the exit from the reactor, the mean velocity is calculated from the mass flow conservation. 3.3. Study of the heat balance 3.3.1. Energy conservation equation V (p C~TV—k V T) =
H. Malvos et a!.
—~
:
/
Modelling of a microwave postdischarge nitriding reactor
63
50 rn/s. Velocity
(a)
330
\
____________________________
8 1)
(b) 1.E-5
KtX)~/
Temperature tK.)
/
7(X)
5.E-5
I_ ____ (c)
350
3.E.4~
___
\ 2.E.4
Atomic Nitrogen Mass Fraction
Fig. 5. Computed results obtained for the following parameters: pressure, 5.8 x l0~Pa; mass flux, 4.62 kg s -
m
2
of Ar— 11 %N
2.
TABLE 1. Experimental data used as boundary conditions for the model
Mass flow rate (kg s - m 2) Gas mixture composition Pressure (Pa) Temperature of the external heater (K) Temperature of the gas at the entrance to the reactor (K) Atomic nitrogen mass fraction at the entrance to the reactor
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
0.53 N2 I0~ 843 450
0.70 Ar—20%N2 l0~ 843 350
4.62 Ar—ll%N2 5.8 x l0~ 900 400
4.62 Ar—11%N2 l0~ 900 400
7.97 Ar—ll%N2 l0~ 900 400
5.0 x l0~
3.0 x iO~
1.3 x I0~
1.3 x I0~~
1.3 x l0~
where T represents the gas temperature, C~,the specific heat at constant pressure, k the thermal diffusion coefficient and ST the source term. In the case of low pressures, photons are not absorbed
by gas molecules and immediately reach the reactor walls. In this case, radiation does not participate in the heating of the gas. For higher pressures, experiments have showed that the temperature variation is also
64
H. Malvos et a!.
-*
/
Modelling of a microwave postdischarge nitriding reactor
50 mIs.
(a)
Velocity 330\~
__
1140 (b)
Temperature tK.)
5. E.6
8tX///’ 7(X)
LE.5
l.E-3
5. E.4
(c)
2!E.4 Atomic Nitrogen Mass Fraction
Fig. 6. Effect of pressure with a constant mass flow rate. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 1 m2 of Ar—1l%N 4.62 kg s 2.
negligible. In the same way, the contribution of the ‘vibration—translation’ collisions between the gas molecules is negligible. Finally, the value of the source term ST is considered to be zero and the energy conservation equation is written V ( C TV k V T) = 0 p —
3.3.2. Boundary conditions The gas temperature at the entrance to the reactor is measured by spectroscopic analysis. The heat flow at the reactor and sample walls is estimated by the calculation of the corresponding heat transfer coefficients. With this aim, we had to consider the radiative exchanges
between the sample and the external heater to determine the equilibrium temperature of the sample. 3.4. Physical properties of the gas Density. Since the pressure is quite low (less than atmospheric pressure), we use the perfect gas law. Diffusion coefficient of atomic nitrogen in argon or in molecular nitrogen. We use the empirical relationship developed by Cussler [11] and Fuller et al. [12]. This relationship takes account of the effect of temperature and pressure. Heat capacity. Since the heat capacity of argon or nitrogen shows little sensitivity to pressure or temperature in our experimental range, we use a constant value [13].
H. Malvos et al.
/
Modelling of a microwave postdischarge nitriding reactor
-
65
_________
—~
:
5(1 m/s.
(a)
Velocity
\
330 ____________________
350
8(X) (b) 5.E-6
~
‘IX)
Temperature (K.) l.E.5
~
2.5 E.4
I. E.4
5. E.4
(c)
Atomic Nitrogen Mass Fraction
Fig. 7. Effect of with a constant volume flow rate. Computed results obtained for the following parameters: pressure, l0~Pa; mass flux, 2 pressure of Ar—ll%N 7.97 kg s-~m 2.
Thermal conductivity. Since the thermal conductivity is pressure independent in our experimental range [14], we simply have to take account of the temperature effect
[15]. Dynamic viscosity. Since the dynamic viscosity is also pressure independent in our experimental range [16], we only consider the temperature effect [17]. The properties we have just considered correspond to pure gases; for gas mixtures, we used several combination relationships proposed in refs. 18, 19, 14 and 20 respectively, 4. Computed results The linked hydrodynamic equations were solved with the PHOENICS code, which embodies a variant of the
algorithm of Patankar and Spalding [21]. The grid used here is uniform (56 x 250). To make the figures easier to read, we use a scale factor of 25 in the y direction. Moreover, since the problem is symmetrical, we represent half a cross-section passing through the z axis. In each set of figures, we represent (a) the velocity of the gas in the reactor, (b) the temperature map and (c) the mass fraction map of atomic nitrogen. Figure 3 corresponds to a pressure 2 of N of iO~Pa and a mass flow rate of 0.53 kg s~m 2 Fig. 4 represents a pressure of Pa and a mass flow rate of 0.70 kg s~ 2 of an Ar—20%N m 2 gas mixture, and Fig. 5 corresponds to a pressure of 5.8 x l0~Pa and a mass flow rate of 4.62 kg ~ m -2 of an Ar—11 %N2 gas mixture. For these three sets of conditions, the gas temperature and SIMPLE
io~
66
H. Malvos et a!.
/
Modelling of a microwave postdischarge nitriding reactor
the atomic nitrogen density at the entrance to the reactor were determined experimentally by spectroscopic analysis and NO titration respectively. These parameters, and the temperature of the external heater required to maintam the iron sample at around 843 K, are reproduced in Table 1. Figure 5 corresponds to the experimental conditions chosen to perform the nitriding of cylindrical iron samples. From these last experimental conditions, we tried to increase the pressure to l0~Pa to study the effect of this on the atomic nitrogen density in the reactor. For this treatment, we kept constant all the experimental values used previously (especially the gas temperature and the atomic nitrogen density at the entrance to the reactor), except the mass flow rate and, of course, the pressure (see Table 1). Then, Fig. 6 represents a pressure of 1 Pa with the same mass flow rate (4.62 kg s~’m 2) of the Ar—1l%N2 mixture. This means that the mean velocity
o~
at the entrance to the reactor is nearly half of that in the preceding case. In contrast, in Fig. 7, we kept the same mean velocity and, thus, the 2. pressure is 1 0~Pa and the mass flow rate 7.97 kg s’ m 5. Conclusions The results we presented show the extremely important effect of pressure and gas velocity in the reactor on the atomic nitrogen density. Indeed, the atomic nitrogen mass fraction around the sample decreases from 4 X l0~ to 1.5 x iO~ when we increase the pressure from 5.8 x io~to l0~Pa, keeping the same mass flow rate (Figs. 5 and 6). Since the mean velocity is smaller in the second case, we can assume that this is in part responsible for the decrease in the atomic nitrogen concentration. Moreover, the comparison of Fig. 5 with Fig. 7 (where we kept the same mean velocity) points out the marked effect of pressure itself on the atomic nitrogen concentration, since the atomic nitrogen mass fraction around the sample decreases from 4 x l0~ to 2.5 x i0~ when pressure increases from 5.8 x to iO~Pa. This result was expected, since the atomic nitrogen recombination is a three-body mechanism. The model used here for a two-dimension geometry could be developed to describe three-dimensional flows encountered in laboratory experiments or in an industrial set-up.
io~
Acknowledgment We are grateful to the Ministère de la Recherche et de la Technologie and Electricité de France for the support of this work.
References 1 A. Ricard, A. Pilorget, H. Michel and M. Gantois, Fr. Patent App!., 87 10698 (1987); Eur. Patent App!., 88 4019 506 (1988). 2 A. Ricard, J. E. Oseguera-Pena, H. Michel and M. Gantois, Proc. 1st mt. Conf on Plasma Surface Engineering, GarmishPartenkirchen, September 1988, Vol. 1, Deutsche Gesellschaft für Metallkunde Informations Gesellschaft, Oberursel, 1989, p. 83. 3 A. Ricard, J. E. Oseguera-Pena, L. Falk, H. Michel and M. Gantois, IEEE Trans. Plasma Sci., 18 (1990) 940. 4 A. Ricard, J. Deschamps, J. L. Godard, L. Falk and H. Michel, Mater. Sci. Eng., A139 (1991) 9—14. 5 L. Falk, J. E. Oseguera-Pena, A. Ricard, H. Michel and M. Gantois, Mater. Sci. Eng., A139 (1991) 132—36. 6 C. C. Boisse-Laporte, Sci.Chave, Eng., A140 (1991) 494—98. J. Marec and Ph. Leprince, Mater. 7 A. Ricard, Topical Invited Lecture, XVII ICPIG, Budapest, 1985. 8 H. Partridge, S. R. Langhoff, C. W. Bauschlicher and D. W. Schwenke, J. Chem. Phys., 88 (5) (1988) 3 180—83. 9 T. Yamashita, J. Chem. Phys., 70 (9) (1979) 4248—53. 10 J. E. Oseguera-Pena, Dip!ôme de These, INPL, Nancy, 1990, p. 99. 11 E. L. Cussler, Diffusion, Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, 1984, pp. 112—13. 12 E. N. Fuller, P. D. Schettler and J. C. Giddings, md. Eng. Chem., 58 (1966) 19. 13 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, pp.2—90. 14 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3—225, 3—226. 15 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, Table 35, pp. 2-82—2-85. 16 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, pp. 1-5. 17 W. M. Rohsenow and J. P. Hartnett, Handbook of Heat Transfer, McGraw-Hill, New York, Table 31, pp. 2-72, 2-73. 18 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., Chap. 14, p. 13. 19 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3-220. 20 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New York, 4th edn., pp. 3-230. 21 S. V. Patankar and D. B. Spalding, Ire. J. Heat Mass Transfer, 15 (1972) 1787—1806.