- Email: [email protected]
Three-dimensional flow and heat transfer in thermal plasma systems
Surface and Coatings Technology 171 (2003) 124–133
Three-dimensional flow and heat transfer in thermal plasma systems Xi Chen*, He-Ping Li1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Abstract Three-dimensional (3-D) modeling of thermal plasma systems is still a challenging problem. Modeling results recently obtained in our group are briefly presented in this paper concerning the 3-D flow and heat transfer characteristics of the thermal plasma reactor, plasma jet and non-transferred arc plasma torch. A well-validated non-commercial computer code is employed in the study. It is shown that when particulate-matter and its carrier-gas are injected into a plasma reactor through a single port at the side-wall of reactor, appreciable 3-D flow and heat transfer effects will appear and cannot be well modeled by any twodimensional models. The 3-D effects influence the particle motion and heating within the reactor. For a plasma jet with lateral injection of carrier-gas and particles, the 3-D effects are also shown to be non-negligible. Marked 3-D special features of the flow and heat transfer within DC non-transferred arc plasma torches have been demonstrated even for the torch with completely axisymmetrical geometrical configuration, working gas admission and electrical current connection. The predicted results are well consistent with experimental observation. Further research requirement is also discussed in this paper. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Thermal plasma reactor; Plasma jet; Arc plasma torch; 3-D simulation
1. Introduction Thermal plasmas have found extensive applications in materials processing, such as plasma spraying, cutting, welding, ultra-fine particle synthesis, etc. w1,2x. Numerous experimental and modeling studies have been conducted in recent decades in order to clarify the basic processes related to thermal plasma material processing. In the past decades, two-dimensional (2-D) models have been widely employed to simulate the flow and heat transfer within thermal plasma reactors, plasma torches or particle-laden plasma jets (e.g. w3–6x and references cited therein). 2-D modeling can significantly simplify the problems under study, reveal some basic physical phenomena and reduce the numerical efforts. However, it cannot study any three-dimensional (3-D) processes occurring in thermal plasma systems while 3-D effects may be critical for many cases to determine the flow and heat transfer characteristics. For example, although being not completely reasonable, the 2-D model with injection of raw-material particles and their carrier-gas through an annular slot is often employed even for a *Corresponding author. Fax: q86-10-6278-1824. E-mail address: [email protected] (Xi Chen). 1 Present address: Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
plasma reactor with only one or few separate injection ports at the reactor side-wall w7–9x. In 2-D modeling of particle-loaded plasma jets, the 3-D effects caused by the lateral injection of carrier-gas are completely ignored w5x. In the 2-D model of DC non-transferred arc plasma torches, the arc is assumed to be attached on the anode surface in a circumferentially uniform form. As a result, all the working gas admitted into the torch must be heated directly by the arc. And thus axi-symmetrical flow and temperature fields, unrealistic arc-root location at the anode-nozzle surface and exaggerated arc voltage are often predicted w6x. It has been recognized that it is necessary to study the 3-D flow and heat transfer characteristics of plasma systems w1,2x. Now the 3-D modeling study is possible due to the advance in computer software and hardware. 3-D modeling results have been presented in a few recent papers w9–14x. Most of them were performed by using commercial software. Sometimes different modeling results were obtained using different commercial software or even using the same software for the same problem by different authors w13,14x. 3-D modeling of thermal plasma systems is still a challenging problem. This paper briefly presents some modeling results recently obtained in our group concerning the 3-D flow and heat transfer characteristics of thermal plasma systems with
0257-8972/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0257-8972(03)00252-4
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
125
Fig. 1. Schematic of the plasma reactor under study and the computational domain.
thermal plasma materials processing as the research background. 2. Modeling of the plasma reactor with lateral particulate-matter and carrier-gas injection For the plasma reactor (8 mm diameter and 80 mm length) schematically shown in Fig. 1, only one port is placed at the reactor side-wall for particulate-matter and its carrier-gas injection, and thus appreciable 3-D effects are expected to appear in the reactor. The 2-D model employed in previous studies w7,8x assumes that the lateral injection of particulate-matter and its carrier-gas can be simplified to be through an annular slot instead of the port. This simplification is acceptable when the injection port number is large (e.g. for eight or more injection ports w9x), but it is not good if only one or few separate ports are employed. In this section, 3-D modeling is used to predict the laminar flow and heat transfer in the reactor shown in Fig. 1, and the modeling results are compared with those obtained by using several different 2-D modeling schemes. Both the working gas and carrier-gas are taken to be argon. The modeling work can be divided into two steps for the case with low particle-loading rate. Namely, the first
step is the computation of the temperature and velocity fields within the reactor with lateral carrier-gas injection, whereas the second step is the calculation of the particle trajectory and heating history in the reactor. Main assumptions used in the study include steady and laminar flow, optically thin and local thermodynamic equilibrium plasma. The continuity, momentum and energy equations employed in the present 3-D modeling are as follows. 1 ≠ 1 ≠ ≠ Žrrvr.q Žrvu.q Žrvz.s0 r ≠r r ≠u ≠z ≠vr vu ≠vr ≠vr E F q qvz D ≠r r ≠u ≠z G ≠p ≠ B ≠vr E 1 ≠ Fq sy q C2m ≠r ≠r D ≠r G r ≠u w B 1 ≠vr ≠vu vu Ez ≠ =xmC q y F|q ≠r r G~ ≠z y D r ≠u w B z ≠vr ≠vz E 2m F|q =xmC q ≠r G~ r y D ≠z B ≠v 1 ≠vu vr E v2u r =C y y Fqr D ≠r r ≠u rG r
(1)
B
rCvr
Fig. 2. The computed isotherms on the injection plane of the plasma reactor. Vinsy5 mys. Isotherm interval is 1000 K.
(2)
126
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133 B
≠vz vu ≠vz ≠vz E F q qvz D ≠r r ≠u ≠z G ≠p 1 ≠ w B ≠vz ≠vr Ez 1 ≠ sy q xmrC q F|q ≠z r ≠r y D ≠r ≠z G~ r ≠u w B z 1 ≠vz ≠vu E ≠ B ≠v E F|q C2m z F =xmC q ≠z G~ ≠z D ≠z G y D r ≠u
rCvr
≠T vu ≠T ≠T E 1 ≠ B ≠T E Crk F q qvz Fs D ≠r r ≠u ≠z G r ≠r D ≠r G 1 ≠ B ≠T E ≠ B ≠T E q 2 Ck Fq Ck FySR r ≠u D ≠u G ≠z D ≠z G
(4)
B
rcpCvr
Fig. 3. The computed isotherms (a) and velocity vector field (b) on the cross-section through the axis of the injection port and perpendicular to the reactor axis.
≠vu vu ≠vu ≠vu E F q qvz D ≠r r ≠u ≠z G 1 ≠p ≠ w B ≠vu vu 1 ≠vr Ez 1 ≠ F|q sy q xmC y q r ≠u ≠r y D ≠r r r ≠u G~ r ≠u w B 1 ≠v vr Ez ≠ w B ≠vu 1 ≠vz Ez u F| =x2mC q F|q xmC q D r ≠u r G~ ≠z y D ≠z r ≠u G~ y 2m B 1 ≠vr ≠vu vu E vrvu q C q y Fyr r D r ≠u ≠r rG r
(5)
Here r, m, k and cp are temperature-dependent plasma density, viscosity, thermal conductivity and specific heat at constant pressure, and the argon plasma property database given in Ref. w15x has been employed in this study. vr, vu and vz are the radial (r), azimuthal (u) and axial (z) velocity components; T and p plasma temperature and pressure; and SR is the radiation power per unit volume of plasma. The calculation domain is denoted by ABCDEFA in Fig. 1. The inner diameter of the injection port is 0.8 mm. Boundary conditions are as follows: At the reactor inlet section the circumferentially averaged temperature and velocity profiles obtained from the 3-D modeling of a laminar non-transferred arc plasma torch (as described later on in this paper) are used. One-way conditions (≠y≠zs0) are used at the exit section, whereas room temperature and zero velocity components are used at tube wall. The averaged values of temperature and velocity components over the grid points on the small circle nearest to the tube axis are taken to be their values at the reactor axis. A well-validated non-commercial computer code, which represents a variableproperty version of FAST-3D w16x, is employed for the numerical solution. The computed isotherms on the injection plane (containing the reactor axis and injection port axis) for the case with the injection velocity Vinsy5 mys are shown in Fig. 2. It can be seen that the effect of carrier-gas injection on computed isotherms is obvious near the injection port. This 3-D effect is also clearly seen in Fig. 3 for the isotherms and velocity vector field on the
B
rCvr
Table 1 Comparison of calculated results by use of the 3 different 2-D simplified models (Cases 1–3) and the present 3-D modeling (Case 4) concerning the particle temperature, axial-velocity, diameter and radial position at the exit section of the plasma reactor
(3)
Case
Tp (K)
up (mys)
Dp (mm)
rp (mm)
1 2 3 4
2487.6 2955.4 2946.3 1314.4
38.7 27.6 27.1 9.0
9.66 9.32 9.32 9.58
y2.70 y0.62 y0.52 y3.44
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
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Fig. 4. Computed isotherms on the injection plane with different 2-D simplified models (Cases 1, 2, 3). Isotherm interval is 1000 K.
cross-section through the injection port axis. It is shown that the 3-D effect increases with increasing injection velocity w17x. Several different simplified 2-D models are also examined in the study, and their predicted results are compared with those obtained by the present 3-D modeling. All the simplified 2-D models are based on the assumption that the carrier-gas is injected through an annular slot instead of the single port w7,8x. Those 2-D models include: Case 1: It is assumed that the width of the annular slot (win) equals the inner diameter of the actual injection port (i.e. winsdins0.8 mm), and the carrier-gas
velocity is the same as the 3-D case (i.e. Vinsy5 my s). For this 2-D case, there is a 40-fold increase in the carrier-gas mass flow rate in comparison with the actual 3-D case. Case 2: It is assumed that the mass flow rate and injection velocity of the carrier-gas are identical to those for the actual 3-D case. For this case, there is a 40-fold decrease in the annual slot width compared with the port diameter, i.e. winsdin y40s0.02 mm. Case 3: It is assumed that the width of the annual slot equals the inner diameter of the port (i.e. wins dins0.8 mm), and the carrier-gas mass flow rate remains the same as the actual 3-D case. For this 2-D case, there
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Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
is a 40-fold decrease in the carrier-gas injection velocity, i.e. Vinsy0.125 mys, in comparison with the actual 3D case. The computed isotherms within the reactor corresponding to the 2-D Cases 1, 2 and 3 are shown in Fig. 4a–c, respectively. It is seen that there is almost no difference between Case 2 and Case 3 in their predicted isotherms, and almost no isotherm distortion near the injection slot can be seen for both Case 2 and Case 3 due to too narrow slot width (Case 2) or too low injection velocity (Case 3). Significant distortion in isotherms is seen near the injection slot for Case 1 since the same slotyport size and injection velocity as the actual 3-D case are involved, but the predicted isotherm distortion for Case 1 is axi-symmetrical, which is different from the actual 3-D case (Fig. 2). Employing different simplified 2-D models not only leads to different gas temperature and flow fields within the reactor, but also affects the calculated results of the moving trajectories and heating histories of the particles injected into the reactor. Typical calculated results using the foregoing three 2-D models are presented in Table 1, in which the results obtained using the present 3-D modeling are also included as Case 4 for comparison. The calculated values of the surface temperature (Tp), axial-velocity component (up), particle diameter (Dp) and radial position (rp) for injected nickel particles (initial diameter Dp.0s10 mm, injection velocity Vins y5 mys) at the exit section of the reactor have been listed in Table 1. Examination of the calculated results in Table 1 shows that no one among the foregoing 2-D simplified models can give good predicted results for the particle trajectories and heating histories. 3. Modeling of 3-D flow and heat transfer in the plasma jet and DC non-transferred arc plasma torch Since some of our 3-D modeling results concerning the particle-loaded plasma jet and non-transferred arc plasma torch have been published else w18–21x, only brief description concerning this subject is given in the present paper. For the 3-D modeling of laminar plasma jets, Eqs. (1)–(5) can still be used. On the other hand, for the modeling of turbulent plasma jet with lateral carrier-gas injection, Eqs. (1)–(5) must be modified as follows: All the physical quantities are taken to be their timeaveraged values and the transport coefficients are substituted by their combined molecular and turbulent components. Two-equation turbulence model is employed to calculate the turbulent kinetic energy and its dissipation rate as well as the turbulent viscosity w17–19,21x. The computational domain is denoted as ABCDEFA in Fig. 5, and 0–2p is taken in the circumferential direction. The effect of lateral injection of carrier-gas
Fig. 5. Schematic of the plasma jet under study and the computational domain.
(argon) on the temperature and velocity fields in the turbulent argon plasma jets has been studied in some detail w17,21x. It is found that the lateral carrier-gas injection may cause appreciable deflection of jet from its geometrical axis on the injection plane and the local distortion of isotherms and stream lines near the injection tube is also appreciable. This 3-D effect is shown to be dependent not only on the carrier-gas injection velocity (or the mass velocity ratio of carrier-gas to main plasma stream w9x), but also on the distance (D) between the injection tube tip and the plasma jet edge. Using the computed 3-D jet temperature and velocity fields, the moving trajectories and heating histories of injected particles are calculated w17,19,21x and the predicted results are shown to be appreciably different from those obtained by corresponding 2-D modeling in which the carrier-gas injection effects are ignored. Up to 10 000 particles are used to study the particle dispersion caused by the turbulent fluctuation, and three independent random numbers are used to calculate turbulent fluctuating velocity components along the particle trajectories w17,21x. Some typical modeling results are presented here for a turbulent plasma jet with lateral injection of particulate-matter and carrier-gas. The axial-velocity and temperature profiles at the jet inlet are given in parabolic forms and the maximum values of temperature and axial-velocity on the torch axis are 13 000 K and 500 mys, respectively. The carrier-gasyplasma mass flow rate ratio is taken to be 0.06 or 0.12 (for carrier-gas injection velocity of 10 or 20 mys) w17,21x. Fig. 6 shows the computed isotherms on the injection plane for the turbulent argon plasma jet with two different carrier-gas injection velocity (Vin sy10, y20 mys) and two different injection tube distance (Ds0, 1 mm). The jet deflection on the injection plane can be clearly seen, and the 3-D effect caused by the lateral carrier-gas injection increases with the increase of injection velocity
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
129
Fig. 6. Computed isotherms on the injection plane of the turbulent plasma jet. (a) Carrier-gas injection velocity Vin sy10 mys and injection tube distance Ds0 mm; (b) Vinsy20 and Ds0 mm; (c) Vinsy20 mys and Ds1 mm.
but decreases with the increase of the injection tube distance (D). Fig. 7 plots the calculated particle trajectories for nickel particles injected into the plasma jet with the same initial conditions (diameter of 20 mm, injection velocity of Vinsy10 mys and injection tube distance of Ds0 mm). Turbulent dispersion in particle trajectories can be clearly seen, and the dispersion in particle trajectories also leads to the dispersion in particle heating histories as described in Refs. w17,21x. For the DC non-transferred arc plasma torch shown in Fig. 8, it has been shown that the flow and heat transfer are always of 3-D special features even for the case with completely axi-symmetrical geometrical con-
figuration, working gas admission and electrical current connection w17,18,20x. For conducting the 3-D modeling of such a non-transferred arc plasma torch, Lorentz force components are added in the momentum Eqs. (2)–(4), whereas Joule heating rate and electron enthalpy transport terms are added in the energy Eq. (5). For the solution of the electromagnetic fields, additional equations concerning the electrical potential and the magnetic vector potential are also employed w17,18,20x. It is found that the key for a successful 3-D modeling of the non-transferred arc plasma torch is that the computational domain (the region formed by the revolution of ABCDEFGHA about the torch axis shown in
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Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
Fig. 7. Computed trajectories of the nickel particles on the injection plane (Vinsy10 mys, Ds0 mm; Dp0s20 mm).
Fig. 8) should include the anode-nozzle wall w17,18,20x. For this case, zero velocity components, room temperature and zero electrical potential conditions can be adopted along the outer surface of the water-cooled anode-nozzle wall, and thus reasonable temperature distribution and arc attachment on the inner surface of the anode wall can be predicted. The 3-D modeling results concerning the isotherms in two planes perpendicular to each other (0–p plane and py2–3py2 plane) inside the plasma torch are shown in Fig. 9a and b for the laminar case with Is 200 A, Qs0.35 STP m3 yh. Corresponding 2-D modeling results are also shown there as Fig. 9c for comparison. It is seen from Fig. 9a and b that different from the prediction of 2-D model, the 3-D modeling shows that the isotherms within the plasma torch are not axi-symmetrical and of appreciable 3-D features. The computed distribution of the radial current density component on the inner surface of the anode-nozzle is plotted in Fig. 10. It is clearly seen in Fig. 10 that the arc-root does not distribute circumferentially uniformly
on the inner surface of the anode. This predicted result about local arc attachment is consistent with our experimental observation. Fig. 11 shows a photograph of the incrustation pattern at the outer surface of the torch anode-nozzle after the plasma torch has been operated for tens of hours. Incrustation layer is always formed slowly at the high wall temperature region of the outer surface of water-cooled copper anode during the torch operation. When the thickness of incrustation layer is great enough, the incrustation layer may even break away from the anode surface. The higher wall temperature region at the outer surface of water-cooled anode should correspond to the location of arc attachment at the inner surface of the anode. Fig. 11 clearly demonstrates that the arc attachment at the anode surface is indeed local and circumferentially non-uniform, and the axial location of the arc attachment is near the intersection of the conical part and the cylindrical part of the anode as predicted by the 3-D modeling. Similar modeling results are also obtained for the turbulent nontransferred arc plasma torch (Is200 A, Qs2.1 STP
Fig. 8. Schematic of the non-transferred DC arc plasma torch under study and the computational domain.
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
131
Fig. 9. Computed isotherms within the laminar non-transferred arc plasma torch (Is200 A, Qs0.35 STP m3 yh). (a) 3-D modeling results on 0–p plane; (b) 3-D modeling results on py2–3py2 plane; (c) 2-D modeling results.
m3 yh) w17,18x, but are not presented here due to paper space limit. Although some progress in the 3-D modeling of thermal plasma systems has been achieved in recent years w9–14,17–21x to reveal the 3-D flow and heat
transfer characteristics, many complicated factors are not included in the modeling studies. The non-stationary phenomena within plasma torches, the large-scale engulfment of the environmental gas into the plasma jet and the non-equilibrium effects (including kinetic andy
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Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
Fig. 10. Computed distribution of the radial component of current density on the inner surface of the anode (Is200 A, Qs0.35 STP m3yh).
or chemical non-equilibrium effects) in plasma flows are only a few among the complicated factors. They will constitute the subjects of subsequent studies. 4. Conclusions Main conclusions obtained from the present 3-D modeling study concerning the plasma flow and heat transfer in thermal plasma systems are as follows. (1) Lateral injection of carrier-gas into a plasma reactor from a port at the side-wall appreciably affects the temperature and velocity fields within the reactor. Available 2-D modeling approaches cannot give satisfactory predicted results for this case. (2) Lateral injection of carrier-gas into a plasma jet may lead to the appreciable deflection of the plasma jet from its geometrical axis on the injection plane. This 3-D effect will affect the moving trajectories and heating histories of particles injected into the plasma jet. The 3-D effect increases with increasing injection velocity and decreasing distance between the injection tube tip and the jet edge.
Fig. 11. Photograph of the arc anode-nozzle after the torch has been operated for tens of hours, showing the incrustation pattern on the outer surface of the anode-nozzle.
(3) Appreciable 3-D flow and heat transfer features exist in the DC non-transferred arc plasma torch, even for the case with completely axi-symmetrical geometrical configuration, working gas admission and the electrical current collection. The 3-D modeling can predict the local arc attachment, which is consistent with the experimental observation. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 50176024, 59836220). References w1x E. Pfender, Plasma Chem. Plasma Process. 19 (1999) 1. w2x P. Fauchais, A. Vardelle, Plasma Phys. Control. Fusion 42 (2000) B365. w3x Xi Chen, Heat Transfer and Fluid Flow under Thermal Plasma Conditions, Science Press, Beijing, 1993, in Chinese. w4x R. Westhoff, J. Szekely, J. Appl. Phys. 70 (1991) 3455. w5x Y.P. Chyou, E. Pfender, Plasma Chem. Plasma Process. 9 (1989) 45. w6x Peng Han, Numerical and Experimental Studies on the Characteristics of DC Arc Plasma Torches and Jets, Ph. D. Thesis, Department of Engineering Mechanics, Tsinghua University, 1999 (in Chinese). w7x Y.C. Lee, K.C. Hsu, E. Pfender, Proceedings of the 5th International Symposium Plasma Chemistry, Edinburgh, 1981, vol. 2, 795. w8x Xi Chen, Y.C. Lee, E. Pfender, Proceedings of the 6th International Symposium Plasma Chemistry, Montreal, 1983, vol. 1, 51. w9x Z. Njah, J. Mostaghimi, M. Boulos, Int. J. Heat Mass Transfer 36 (1993) 3909. w10x M. Leylavergne, B. Dussoubs, A. Vardelle, N. Goubot, J. Therm. Spray Technol. 7 (1998) 527. w11x A. Vardelle, P. Fauchais, B. Dussoubs, N.J. Themelis, Plasma Chem. Plasma Process. 18 (1998) 551. w12x P. Freton, J.J. Gonzalez, A. Gleizes, J. Phys. D: Appl. Phys. 33 (2000) 2442. w13x I. Ahmed, T.L. Bergman, ASME J. Heat Transfer 123 (2001) 188.
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133 w14x A. Boussagol, G. Mariaux, E. Legros, A. Vardelle, P. Nylen, Proceedings of the 15th Symposium Plasma Chemistry, Orleans, 2001, Vol. 3, 1015. w15x M.I. Boulos, P. Fauchais, E. Pfender, Thermal Plasmas: Fundamentals and Applications, vol. 1, Plenum, New York, 1994, pp. 388–392, Appendix A3. w16x J. Zhu, An Introduction and Guide to the Computer Program FAST-3D, Report No. 691, Institute for Hydromechanics, University of Karlsruhe, 1992.
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w17x He-Ping Li, Studies of Heat Transfer and Fluid Flow in a DC Arc Plasma Torch and Plasma Jet, Ph. D. Thesis, Department of Engineering Mechanics, Tsinghua University, 2001 (in Chinese). w18x He-Ping Li, Xi Chen, J. Phys. D: Appl. Phys. 34 (2001) L99. w19x He-Ping Li, Xi Chen, Thin Solid Films 390 (2001) 175. w20x He-Ping Li, Xi Chen, Chinese Phys. 11 (2002) 44. w21x He-Ping Li, Xi Chen, Plasma Chem. Plasma Process. 22 (2002) 27.
Three-dimensional flow and heat transfer in thermal plasma systems Xi Chen*, He-Ping Li1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Abstract Three-dimensional (3-D) modeling of thermal plasma systems is still a challenging problem. Modeling results recently obtained in our group are briefly presented in this paper concerning the 3-D flow and heat transfer characteristics of the thermal plasma reactor, plasma jet and non-transferred arc plasma torch. A well-validated non-commercial computer code is employed in the study. It is shown that when particulate-matter and its carrier-gas are injected into a plasma reactor through a single port at the side-wall of reactor, appreciable 3-D flow and heat transfer effects will appear and cannot be well modeled by any twodimensional models. The 3-D effects influence the particle motion and heating within the reactor. For a plasma jet with lateral injection of carrier-gas and particles, the 3-D effects are also shown to be non-negligible. Marked 3-D special features of the flow and heat transfer within DC non-transferred arc plasma torches have been demonstrated even for the torch with completely axisymmetrical geometrical configuration, working gas admission and electrical current connection. The predicted results are well consistent with experimental observation. Further research requirement is also discussed in this paper. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Thermal plasma reactor; Plasma jet; Arc plasma torch; 3-D simulation
1. Introduction Thermal plasmas have found extensive applications in materials processing, such as plasma spraying, cutting, welding, ultra-fine particle synthesis, etc. w1,2x. Numerous experimental and modeling studies have been conducted in recent decades in order to clarify the basic processes related to thermal plasma material processing. In the past decades, two-dimensional (2-D) models have been widely employed to simulate the flow and heat transfer within thermal plasma reactors, plasma torches or particle-laden plasma jets (e.g. w3–6x and references cited therein). 2-D modeling can significantly simplify the problems under study, reveal some basic physical phenomena and reduce the numerical efforts. However, it cannot study any three-dimensional (3-D) processes occurring in thermal plasma systems while 3-D effects may be critical for many cases to determine the flow and heat transfer characteristics. For example, although being not completely reasonable, the 2-D model with injection of raw-material particles and their carrier-gas through an annular slot is often employed even for a *Corresponding author. Fax: q86-10-6278-1824. E-mail address: [email protected] (Xi Chen). 1 Present address: Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
plasma reactor with only one or few separate injection ports at the reactor side-wall w7–9x. In 2-D modeling of particle-loaded plasma jets, the 3-D effects caused by the lateral injection of carrier-gas are completely ignored w5x. In the 2-D model of DC non-transferred arc plasma torches, the arc is assumed to be attached on the anode surface in a circumferentially uniform form. As a result, all the working gas admitted into the torch must be heated directly by the arc. And thus axi-symmetrical flow and temperature fields, unrealistic arc-root location at the anode-nozzle surface and exaggerated arc voltage are often predicted w6x. It has been recognized that it is necessary to study the 3-D flow and heat transfer characteristics of plasma systems w1,2x. Now the 3-D modeling study is possible due to the advance in computer software and hardware. 3-D modeling results have been presented in a few recent papers w9–14x. Most of them were performed by using commercial software. Sometimes different modeling results were obtained using different commercial software or even using the same software for the same problem by different authors w13,14x. 3-D modeling of thermal plasma systems is still a challenging problem. This paper briefly presents some modeling results recently obtained in our group concerning the 3-D flow and heat transfer characteristics of thermal plasma systems with
0257-8972/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0257-8972(03)00252-4
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133
125
Fig. 1. Schematic of the plasma reactor under study and the computational domain.
thermal plasma materials processing as the research background. 2. Modeling of the plasma reactor with lateral particulate-matter and carrier-gas injection For the plasma reactor (8 mm diameter and 80 mm length) schematically shown in Fig. 1, only one port is placed at the reactor side-wall for particulate-matter and its carrier-gas injection, and thus appreciable 3-D effects are expected to appear in the reactor. The 2-D model employed in previous studies w7,8x assumes that the lateral injection of particulate-matter and its carrier-gas can be simplified to be through an annular slot instead of the port. This simplification is acceptable when the injection port number is large (e.g. for eight or more injection ports w9x), but it is not good if only one or few separate ports are employed. In this section, 3-D modeling is used to predict the laminar flow and heat transfer in the reactor shown in Fig. 1, and the modeling results are compared with those obtained by using several different 2-D modeling schemes. Both the working gas and carrier-gas are taken to be argon. The modeling work can be divided into two steps for the case with low particle-loading rate. Namely, the first
step is the computation of the temperature and velocity fields within the reactor with lateral carrier-gas injection, whereas the second step is the calculation of the particle trajectory and heating history in the reactor. Main assumptions used in the study include steady and laminar flow, optically thin and local thermodynamic equilibrium plasma. The continuity, momentum and energy equations employed in the present 3-D modeling are as follows. 1 ≠ 1 ≠ ≠ Žrrvr.q Žrvu.q Žrvz.s0 r ≠r r ≠u ≠z ≠vr vu ≠vr ≠vr E F q qvz D ≠r r ≠u ≠z G ≠p ≠ B ≠vr E 1 ≠ Fq sy q C2m ≠r ≠r D ≠r G r ≠u w B 1 ≠vr ≠vu vu Ez ≠ =xmC q y F|q ≠r r G~ ≠z y D r ≠u w B z ≠vr ≠vz E 2m F|q =xmC q ≠r G~ r y D ≠z B ≠v 1 ≠vu vr E v2u r =C y y Fqr D ≠r r ≠u rG r
(1)
B
rCvr
Fig. 2. The computed isotherms on the injection plane of the plasma reactor. Vinsy5 mys. Isotherm interval is 1000 K.
(2)
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Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133 B
≠vz vu ≠vz ≠vz E F q qvz D ≠r r ≠u ≠z G ≠p 1 ≠ w B ≠vz ≠vr Ez 1 ≠ sy q xmrC q F|q ≠z r ≠r y D ≠r ≠z G~ r ≠u w B z 1 ≠vz ≠vu E ≠ B ≠v E F|q C2m z F =xmC q ≠z G~ ≠z D ≠z G y D r ≠u
rCvr
≠T vu ≠T ≠T E 1 ≠ B ≠T E Crk F q qvz Fs D ≠r r ≠u ≠z G r ≠r D ≠r G 1 ≠ B ≠T E ≠ B ≠T E q 2 Ck Fq Ck FySR r ≠u D ≠u G ≠z D ≠z G
(4)
B
rcpCvr
Fig. 3. The computed isotherms (a) and velocity vector field (b) on the cross-section through the axis of the injection port and perpendicular to the reactor axis.
≠vu vu ≠vu ≠vu E F q qvz D ≠r r ≠u ≠z G 1 ≠p ≠ w B ≠vu vu 1 ≠vr Ez 1 ≠ F|q sy q xmC y q r ≠u ≠r y D ≠r r r ≠u G~ r ≠u w B 1 ≠v vr Ez ≠ w B ≠vu 1 ≠vz Ez u F| =x2mC q F|q xmC q D r ≠u r G~ ≠z y D ≠z r ≠u G~ y 2m B 1 ≠vr ≠vu vu E vrvu q C q y Fyr r D r ≠u ≠r rG r
(5)
Here r, m, k and cp are temperature-dependent plasma density, viscosity, thermal conductivity and specific heat at constant pressure, and the argon plasma property database given in Ref. w15x has been employed in this study. vr, vu and vz are the radial (r), azimuthal (u) and axial (z) velocity components; T and p plasma temperature and pressure; and SR is the radiation power per unit volume of plasma. The calculation domain is denoted by ABCDEFA in Fig. 1. The inner diameter of the injection port is 0.8 mm. Boundary conditions are as follows: At the reactor inlet section the circumferentially averaged temperature and velocity profiles obtained from the 3-D modeling of a laminar non-transferred arc plasma torch (as described later on in this paper) are used. One-way conditions (≠y≠zs0) are used at the exit section, whereas room temperature and zero velocity components are used at tube wall. The averaged values of temperature and velocity components over the grid points on the small circle nearest to the tube axis are taken to be their values at the reactor axis. A well-validated non-commercial computer code, which represents a variableproperty version of FAST-3D w16x, is employed for the numerical solution. The computed isotherms on the injection plane (containing the reactor axis and injection port axis) for the case with the injection velocity Vinsy5 mys are shown in Fig. 2. It can be seen that the effect of carrier-gas injection on computed isotherms is obvious near the injection port. This 3-D effect is also clearly seen in Fig. 3 for the isotherms and velocity vector field on the
B
rCvr
Table 1 Comparison of calculated results by use of the 3 different 2-D simplified models (Cases 1–3) and the present 3-D modeling (Case 4) concerning the particle temperature, axial-velocity, diameter and radial position at the exit section of the plasma reactor
(3)
Case
Tp (K)
up (mys)
Dp (mm)
rp (mm)
1 2 3 4
2487.6 2955.4 2946.3 1314.4
38.7 27.6 27.1 9.0
9.66 9.32 9.32 9.58
y2.70 y0.62 y0.52 y3.44
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Fig. 4. Computed isotherms on the injection plane with different 2-D simplified models (Cases 1, 2, 3). Isotherm interval is 1000 K.
cross-section through the injection port axis. It is shown that the 3-D effect increases with increasing injection velocity w17x. Several different simplified 2-D models are also examined in the study, and their predicted results are compared with those obtained by the present 3-D modeling. All the simplified 2-D models are based on the assumption that the carrier-gas is injected through an annular slot instead of the single port w7,8x. Those 2-D models include: Case 1: It is assumed that the width of the annular slot (win) equals the inner diameter of the actual injection port (i.e. winsdins0.8 mm), and the carrier-gas
velocity is the same as the 3-D case (i.e. Vinsy5 my s). For this 2-D case, there is a 40-fold increase in the carrier-gas mass flow rate in comparison with the actual 3-D case. Case 2: It is assumed that the mass flow rate and injection velocity of the carrier-gas are identical to those for the actual 3-D case. For this case, there is a 40-fold decrease in the annual slot width compared with the port diameter, i.e. winsdin y40s0.02 mm. Case 3: It is assumed that the width of the annual slot equals the inner diameter of the port (i.e. wins dins0.8 mm), and the carrier-gas mass flow rate remains the same as the actual 3-D case. For this 2-D case, there
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is a 40-fold decrease in the carrier-gas injection velocity, i.e. Vinsy0.125 mys, in comparison with the actual 3D case. The computed isotherms within the reactor corresponding to the 2-D Cases 1, 2 and 3 are shown in Fig. 4a–c, respectively. It is seen that there is almost no difference between Case 2 and Case 3 in their predicted isotherms, and almost no isotherm distortion near the injection slot can be seen for both Case 2 and Case 3 due to too narrow slot width (Case 2) or too low injection velocity (Case 3). Significant distortion in isotherms is seen near the injection slot for Case 1 since the same slotyport size and injection velocity as the actual 3-D case are involved, but the predicted isotherm distortion for Case 1 is axi-symmetrical, which is different from the actual 3-D case (Fig. 2). Employing different simplified 2-D models not only leads to different gas temperature and flow fields within the reactor, but also affects the calculated results of the moving trajectories and heating histories of the particles injected into the reactor. Typical calculated results using the foregoing three 2-D models are presented in Table 1, in which the results obtained using the present 3-D modeling are also included as Case 4 for comparison. The calculated values of the surface temperature (Tp), axial-velocity component (up), particle diameter (Dp) and radial position (rp) for injected nickel particles (initial diameter Dp.0s10 mm, injection velocity Vins y5 mys) at the exit section of the reactor have been listed in Table 1. Examination of the calculated results in Table 1 shows that no one among the foregoing 2-D simplified models can give good predicted results for the particle trajectories and heating histories. 3. Modeling of 3-D flow and heat transfer in the plasma jet and DC non-transferred arc plasma torch Since some of our 3-D modeling results concerning the particle-loaded plasma jet and non-transferred arc plasma torch have been published else w18–21x, only brief description concerning this subject is given in the present paper. For the 3-D modeling of laminar plasma jets, Eqs. (1)–(5) can still be used. On the other hand, for the modeling of turbulent plasma jet with lateral carrier-gas injection, Eqs. (1)–(5) must be modified as follows: All the physical quantities are taken to be their timeaveraged values and the transport coefficients are substituted by their combined molecular and turbulent components. Two-equation turbulence model is employed to calculate the turbulent kinetic energy and its dissipation rate as well as the turbulent viscosity w17–19,21x. The computational domain is denoted as ABCDEFA in Fig. 5, and 0–2p is taken in the circumferential direction. The effect of lateral injection of carrier-gas
Fig. 5. Schematic of the plasma jet under study and the computational domain.
(argon) on the temperature and velocity fields in the turbulent argon plasma jets has been studied in some detail w17,21x. It is found that the lateral carrier-gas injection may cause appreciable deflection of jet from its geometrical axis on the injection plane and the local distortion of isotherms and stream lines near the injection tube is also appreciable. This 3-D effect is shown to be dependent not only on the carrier-gas injection velocity (or the mass velocity ratio of carrier-gas to main plasma stream w9x), but also on the distance (D) between the injection tube tip and the plasma jet edge. Using the computed 3-D jet temperature and velocity fields, the moving trajectories and heating histories of injected particles are calculated w17,19,21x and the predicted results are shown to be appreciably different from those obtained by corresponding 2-D modeling in which the carrier-gas injection effects are ignored. Up to 10 000 particles are used to study the particle dispersion caused by the turbulent fluctuation, and three independent random numbers are used to calculate turbulent fluctuating velocity components along the particle trajectories w17,21x. Some typical modeling results are presented here for a turbulent plasma jet with lateral injection of particulate-matter and carrier-gas. The axial-velocity and temperature profiles at the jet inlet are given in parabolic forms and the maximum values of temperature and axial-velocity on the torch axis are 13 000 K and 500 mys, respectively. The carrier-gasyplasma mass flow rate ratio is taken to be 0.06 or 0.12 (for carrier-gas injection velocity of 10 or 20 mys) w17,21x. Fig. 6 shows the computed isotherms on the injection plane for the turbulent argon plasma jet with two different carrier-gas injection velocity (Vin sy10, y20 mys) and two different injection tube distance (Ds0, 1 mm). The jet deflection on the injection plane can be clearly seen, and the 3-D effect caused by the lateral carrier-gas injection increases with the increase of injection velocity
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Fig. 6. Computed isotherms on the injection plane of the turbulent plasma jet. (a) Carrier-gas injection velocity Vin sy10 mys and injection tube distance Ds0 mm; (b) Vinsy20 and Ds0 mm; (c) Vinsy20 mys and Ds1 mm.
but decreases with the increase of the injection tube distance (D). Fig. 7 plots the calculated particle trajectories for nickel particles injected into the plasma jet with the same initial conditions (diameter of 20 mm, injection velocity of Vinsy10 mys and injection tube distance of Ds0 mm). Turbulent dispersion in particle trajectories can be clearly seen, and the dispersion in particle trajectories also leads to the dispersion in particle heating histories as described in Refs. w17,21x. For the DC non-transferred arc plasma torch shown in Fig. 8, it has been shown that the flow and heat transfer are always of 3-D special features even for the case with completely axi-symmetrical geometrical con-
figuration, working gas admission and electrical current connection w17,18,20x. For conducting the 3-D modeling of such a non-transferred arc plasma torch, Lorentz force components are added in the momentum Eqs. (2)–(4), whereas Joule heating rate and electron enthalpy transport terms are added in the energy Eq. (5). For the solution of the electromagnetic fields, additional equations concerning the electrical potential and the magnetic vector potential are also employed w17,18,20x. It is found that the key for a successful 3-D modeling of the non-transferred arc plasma torch is that the computational domain (the region formed by the revolution of ABCDEFGHA about the torch axis shown in
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Fig. 7. Computed trajectories of the nickel particles on the injection plane (Vinsy10 mys, Ds0 mm; Dp0s20 mm).
Fig. 8) should include the anode-nozzle wall w17,18,20x. For this case, zero velocity components, room temperature and zero electrical potential conditions can be adopted along the outer surface of the water-cooled anode-nozzle wall, and thus reasonable temperature distribution and arc attachment on the inner surface of the anode wall can be predicted. The 3-D modeling results concerning the isotherms in two planes perpendicular to each other (0–p plane and py2–3py2 plane) inside the plasma torch are shown in Fig. 9a and b for the laminar case with Is 200 A, Qs0.35 STP m3 yh. Corresponding 2-D modeling results are also shown there as Fig. 9c for comparison. It is seen from Fig. 9a and b that different from the prediction of 2-D model, the 3-D modeling shows that the isotherms within the plasma torch are not axi-symmetrical and of appreciable 3-D features. The computed distribution of the radial current density component on the inner surface of the anode-nozzle is plotted in Fig. 10. It is clearly seen in Fig. 10 that the arc-root does not distribute circumferentially uniformly
on the inner surface of the anode. This predicted result about local arc attachment is consistent with our experimental observation. Fig. 11 shows a photograph of the incrustation pattern at the outer surface of the torch anode-nozzle after the plasma torch has been operated for tens of hours. Incrustation layer is always formed slowly at the high wall temperature region of the outer surface of water-cooled copper anode during the torch operation. When the thickness of incrustation layer is great enough, the incrustation layer may even break away from the anode surface. The higher wall temperature region at the outer surface of water-cooled anode should correspond to the location of arc attachment at the inner surface of the anode. Fig. 11 clearly demonstrates that the arc attachment at the anode surface is indeed local and circumferentially non-uniform, and the axial location of the arc attachment is near the intersection of the conical part and the cylindrical part of the anode as predicted by the 3-D modeling. Similar modeling results are also obtained for the turbulent nontransferred arc plasma torch (Is200 A, Qs2.1 STP
Fig. 8. Schematic of the non-transferred DC arc plasma torch under study and the computational domain.
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Fig. 9. Computed isotherms within the laminar non-transferred arc plasma torch (Is200 A, Qs0.35 STP m3 yh). (a) 3-D modeling results on 0–p plane; (b) 3-D modeling results on py2–3py2 plane; (c) 2-D modeling results.
m3 yh) w17,18x, but are not presented here due to paper space limit. Although some progress in the 3-D modeling of thermal plasma systems has been achieved in recent years w9–14,17–21x to reveal the 3-D flow and heat
transfer characteristics, many complicated factors are not included in the modeling studies. The non-stationary phenomena within plasma torches, the large-scale engulfment of the environmental gas into the plasma jet and the non-equilibrium effects (including kinetic andy
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Fig. 10. Computed distribution of the radial component of current density on the inner surface of the anode (Is200 A, Qs0.35 STP m3yh).
or chemical non-equilibrium effects) in plasma flows are only a few among the complicated factors. They will constitute the subjects of subsequent studies. 4. Conclusions Main conclusions obtained from the present 3-D modeling study concerning the plasma flow and heat transfer in thermal plasma systems are as follows. (1) Lateral injection of carrier-gas into a plasma reactor from a port at the side-wall appreciably affects the temperature and velocity fields within the reactor. Available 2-D modeling approaches cannot give satisfactory predicted results for this case. (2) Lateral injection of carrier-gas into a plasma jet may lead to the appreciable deflection of the plasma jet from its geometrical axis on the injection plane. This 3-D effect will affect the moving trajectories and heating histories of particles injected into the plasma jet. The 3-D effect increases with increasing injection velocity and decreasing distance between the injection tube tip and the jet edge.
Fig. 11. Photograph of the arc anode-nozzle after the torch has been operated for tens of hours, showing the incrustation pattern on the outer surface of the anode-nozzle.
(3) Appreciable 3-D flow and heat transfer features exist in the DC non-transferred arc plasma torch, even for the case with completely axi-symmetrical geometrical configuration, working gas admission and the electrical current collection. The 3-D modeling can predict the local arc attachment, which is consistent with the experimental observation. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 50176024, 59836220). References w1x E. Pfender, Plasma Chem. Plasma Process. 19 (1999) 1. w2x P. Fauchais, A. Vardelle, Plasma Phys. Control. Fusion 42 (2000) B365. w3x Xi Chen, Heat Transfer and Fluid Flow under Thermal Plasma Conditions, Science Press, Beijing, 1993, in Chinese. w4x R. Westhoff, J. Szekely, J. Appl. Phys. 70 (1991) 3455. w5x Y.P. Chyou, E. Pfender, Plasma Chem. Plasma Process. 9 (1989) 45. w6x Peng Han, Numerical and Experimental Studies on the Characteristics of DC Arc Plasma Torches and Jets, Ph. D. Thesis, Department of Engineering Mechanics, Tsinghua University, 1999 (in Chinese). w7x Y.C. Lee, K.C. Hsu, E. Pfender, Proceedings of the 5th International Symposium Plasma Chemistry, Edinburgh, 1981, vol. 2, 795. w8x Xi Chen, Y.C. Lee, E. Pfender, Proceedings of the 6th International Symposium Plasma Chemistry, Montreal, 1983, vol. 1, 51. w9x Z. Njah, J. Mostaghimi, M. Boulos, Int. J. Heat Mass Transfer 36 (1993) 3909. w10x M. Leylavergne, B. Dussoubs, A. Vardelle, N. Goubot, J. Therm. Spray Technol. 7 (1998) 527. w11x A. Vardelle, P. Fauchais, B. Dussoubs, N.J. Themelis, Plasma Chem. Plasma Process. 18 (1998) 551. w12x P. Freton, J.J. Gonzalez, A. Gleizes, J. Phys. D: Appl. Phys. 33 (2000) 2442. w13x I. Ahmed, T.L. Bergman, ASME J. Heat Transfer 123 (2001) 188.
Xi Chen, H.-P. Li / Surface and Coatings Technology 171 (2003) 124–133 w14x A. Boussagol, G. Mariaux, E. Legros, A. Vardelle, P. Nylen, Proceedings of the 15th Symposium Plasma Chemistry, Orleans, 2001, Vol. 3, 1015. w15x M.I. Boulos, P. Fauchais, E. Pfender, Thermal Plasmas: Fundamentals and Applications, vol. 1, Plenum, New York, 1994, pp. 388–392, Appendix A3. w16x J. Zhu, An Introduction and Guide to the Computer Program FAST-3D, Report No. 691, Institute for Hydromechanics, University of Karlsruhe, 1992.
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w17x He-Ping Li, Studies of Heat Transfer and Fluid Flow in a DC Arc Plasma Torch and Plasma Jet, Ph. D. Thesis, Department of Engineering Mechanics, Tsinghua University, 2001 (in Chinese). w18x He-Ping Li, Xi Chen, J. Phys. D: Appl. Phys. 34 (2001) L99. w19x He-Ping Li, Xi Chen, Thin Solid Films 390 (2001) 175. w20x He-Ping Li, Xi Chen, Chinese Phys. 11 (2002) 44. w21x He-Ping Li, Xi Chen, Plasma Chem. Plasma Process. 22 (2002) 27.