possible torch devitrification associated with running such systems at low argon flow rates. Keywords: RF plasma, LTE simulation, current induction disc, torchΒ ...
22nd International Symposium on Plasma Chemistry July 5-10, 2015; Antwerp, Belgium
Numerical simulation of heat transfer mechanisms in RF-ICP torches running at low argon flow rates A. Kashani1, J. Mostaghimi2, H. Badiei3 and K. Kahen3 1
2
Simulent Inc., Toronto, Ontario, Canada MIE Department, University of Toronto, Toronto, Ontario, Canada 3 PerkinElmer Inc., Woodbridge, Ontario, Canada
Abstract: While in most ICP systems the plasma field is generated by passing RF current through helical copper coils, we discuss the possibility of replacing coils with aluminium flat discs that have many advantages over the traditional systems. In this paper, we present new formulation, simulation and experimental results for the flat disc technology and study possible torch devitrification associated with running such systems at low argon flow rates. Keywords: RF plasma, LTE simulation, current induction disc, torch devitrification
1. Introduction In conventional ICP systems, the plasma is generated by a plasma gas flowing inside three concentric quartz or fused silica tubes and passing RF currents through coils wound around the torch (Fig. 1).
increase the devitrification process of quartz tubes and negate the advantage of the new design. To study the devitrification process and the new design of the induction coils, the mathematical formulation of the plasma must be revisited and the appropriate boundary conditions have to be developed for the quartz torch. 2. Mathematical Formulation The mathematical formulation of this work is based on the work of Mostaghimi and Boulos [1] where plasma flow assumed to be in LTE conditions, optically thin, laminar, steady state and with negligible viscous dissipation. The flow and energy equations in vector are given by: οΏ½β = 0 β. π οΏ½β. βπ οΏ½β = ββπ + β. πβπ οΏ½β + π½β Γ π΅ οΏ½β ππ οΏ½β. ββ = β. οΏ½π/ππ οΏ½ββ + π½β. πΈοΏ½β β π
Μ ππ
Fig. 1. Schematic diagram of the induction plasma torch. It is possible however to replace the copper coils with aluminium flat discs and achieve comparable analytical results. This replacement offers many advantages over helical coil configuration. For instance, the large surface area of flat discs is very efficient in dissipating heat without the need for external cooling and as a result requires considerably less maintenance. In addition, the new design generates perfectly symmetrical induction fields that are perpendicular to the flow minimizing the common upward lift caused by traditional helical coils. But perhaps the most interesting feature of the new technology is that it may operate at low argon flow rates (8-9 L.min-1) and reduces the operational costs dramatically. However, the reduced flow rates could
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(1) (2) (3)
These equations are coupled with electromagnetic equations through terms JΓB and J.E.As shown in [1], a vector potential formulation can be used to combine all the Maxwell equations into a single equation such that: β2 π΄π β ππ 0 πππ΄π = 0 πΈπ = βπππ΄π 1π (ππ΄π ) π ππ π π0 π»π = β (π΄π ) ππ π0 π»π§ =
(4) (5) (6) (7)
where A ΞΈ , E ΞΈ , H z , H r, Ο=2Οf , Ο are vector potential, electric and magnetic field intensities, frequency and electrical conductivity respectively. In Eqs. 4-7, A ΞΈ is a complex variable which requires to be expanded into its real and imaginary parts for numerical simulation.
1
π΄π = π΄π
+ ππ΄πΌ
(8)
Eq. (1) requires boundary conditions for 2D numerical domain. The boundary conditions are given by: π΄π = π΄πΌ = 0; ππ΄π
ππ΄πΌ = ; ππ ππ ππ΄π
ππ΄πΌ = ; ππ ππ
π=0
(9)
π§=0
(10)
π§ = πΏπ‘
(11)
However, at the torch walls where r=R 0 , the vector potential is determined by superposition of induction coil and current carrying regions of the plasma: π΄π = π΄πβπππππ + π΄πβππππππ ;
π = π
0
(12)
The vector potential of coils can be approximated from [2] by: π΄π (π
0 , π§) =
ππππ
π0 π
π πΌοΏ½ οΏ½ πΊ(ππ ) 2π π
0
(13)
π=1
where G(k) definition is given in [1]. Eq. (13) can be used to develop a new formulation for current carrying disc whose inner and outer radius is R c2 Assuming that the and R c1 respectively (Fig. 2). differential vector potential is generated by a differential current passing through the differential cross-section (dR c ΓΞ΄) where Ξ΄ is the skin depth we have: ππ΄π =
π0
2π
π
ππΌ οΏ½ π G(k) π
ππΌ = π½(π
π )πΏππ
π
(14) (15)
Assuming that a disc is made of current loops all connected to the same voltage difference then: π½β βπ = β οΏ½ . οΏ½οΏ½οΏ½β π = πππππ π π πΌ π½(π
π ) = π
π
π πΏ ln οΏ½ π2 οΏ½ π
π1
(16) (17)
By substituting Eq. [17] and [15] into Eq. (14) and integrating over the disc radius, the vector potential expression for a current carrying disc is given as: π΄π (π
0 , π§) =
π
π2 π
π0 π πΌ οΏ½ οΏ½ πΊ(π) 2π π
π1 π
0
ππ
π
π
π
π ln οΏ½ π2 οΏ½ π
π1
(18)
Large industrial torches are externally cooled in most applications, thus the assumption of constant wall temperature on the outer surface of such torches is valid. However, smaller torches especially those typically used in ICP-MS and ICP-OES are not externally cooled. This becomes critical especially at lower plasma gas flow rates (e.g., 4 mm). The gas velocity at its maximum reaches ~29 m.s-1 but the flow remains laminar due to high gas temperatures and lower gas density. Fig. 4 presents the electric and the axial magnetic field intensities inside the torch. The field intensities are the strongest in between the two disks and also closer to the torch walls. The field intensities, however, decrease as they near the torch centreline. 0.01
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the torch. Fig. 5 compares the effective ratio of the radiation to natural convection heat transfer coefficient along the torch outer surface. Based on the simulation results, the ratio is initially small at the inlet and decreases slightly up to z =20 mm, but then the ratio grows larger until it reaches a maximum at around z = 26 mm and decreases again beyond that point. Overall, the radiation heat transfer is on average an order of magnitude larger than the natural convection heat transfer. The effect of input power and plasma flow rates on the temperature of the inner and outer wall of the torch is shown in Fig. 6 for a plasma frequency of 40 MHz. As can be seen from the results, the difference between outer and inner torch temperatures grows larger by increasing the input power (red versus purple lines) and (blue versus. green lines) for the same flow rates. However this difference is more pronounced if the plasma flow rate is reduced from 15 to 9 L.min-1 (red versus blue lines) and (purple vs. green lines). In addition, for 15 L.min-1 flow rate, the devitrified length corresponding to temperatures above devitrification temperature (1423 K) is relatively small and negligible while this length reaches to 9-16 mm for input power of 1.0 and 1.5 kW respectively. Similarly, Fig. 7 compares the effect of plasma frequency on torch temperature profiles. While lowering the plasma flow rate increases the difference between inner and outer torch wall temperatures, changing the frequency has virtually now effect on this temperature difference. However, a temperature rise of approximately 100 K can be seen for inner and outer torch wall temperatures by increasing frequency from 27 to 40 MHz. Moreover, the change in plasma frequency has very little effect on the devitrification length shown in Fig. 7.
0.035
Z
Fig. 3. Temperature in [K] (up) and velocity magnitude in [m.s-1] (down) inside a torch running at P = 1.5 kW, f = 40 MHz and Qplasma = 9 L.min-1.
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20
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Fig. 4. Electric field intensity in [V/m] (up) and axial component of magnetic field intensity in [A/m] (down) for the same flow conditions as Fig. 3. In the absence of external cooling systems, the only heat dissipation mechanisms on the torch outer surface are radiation and natural convection heat transfer. However the two mechanisms are not equally efficient in cooling
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0.01
0.02
0.03
z [m]
Fig. 5. Ratio of radiation to natural convection heat transfer coefficient along the torch outer surface for f = 40 MHz, P = 1.5 kW and argon flow rate of Q plasma = 9 L.min-1.
3
5. Acknowledgement This work has been financially and technically supported by PerkinElmer Inc. The authors gratefully acknowledge this collaboration and support.
Ti, P=1.5 kW, Qaux=15 lpm To, P=1.5 kW, Qaux=15 lpm Ti, P=1.5 kW, Qaux=9 lpm To, P=1.5 kW, Qaux=9 lpm Ti, P=1.0 kW, Qaux=15 lpm To, P=1.0 kW, Qaux=15 lpm Ti, P=1.0 kW, Qaux=9 lpm To, P=1.0 kW, Qaux=9 lpm Devitrification Limit
2200 2000 1800
T [K]
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f=40 MHz
1000
Qinj = 0.7 lpm Qp = 0.2 lpm
Devitrified length
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References [1] J. Mostaghimi and M.I. Boulos. βTwo Dimensional Electromagnetic Field Effects in Induction Plasma Modelingβ. Plasma Chem. Plasma Phys., 9 (1989) [2] J.D. Jackson. Classical Electrodynamics. (New York: Wiley) (1962) / Part II (P.W.J.M. Boumans; Ed.) (New York: Wiley) (1987) [3] S.W. Churchill and H.H.S. Chu. βCorrelating Equations for Laminar and Turbulence Free Convection from a Horizontal Cylinderβ. Int. J. Heat Mass Transfer, 18 (1975)
0.035
z [m]
Fig. 6. Effect of input power and plasma flow rates on inner and outer surface temperatures of a torch running at f = 40 MHz.
2200
Ti, f=40 MHz, Qaux=15 lpm To, f=40 MHz, Qaux=15 lpm Ti, f=27 MHz, Qaux=15 lpm To, f=27 MHz, Qaux=15 lpm Ti, f=40 MHz, Qaux=9 lpm To, f=40 MHz, Qaux=9 lpm Ti, f=27 MHz, Qaux=9 lpm To, f=40 MHz, Qaux=9 lpm Devitrification Limit
2000 1800
T [K]
1600 1400 1200 1000
P = 1.5 kW Devitrified length
Qinj = 0.7 lpm Qp = 0.2 lpm
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z [m]
Fig. 7. Effect frequency on inner and outer surface temperatures of a torch running at P = 1.5 kW. 4. Conclusion In this paper, we developed the necessary mathematical formulation for current carrying induction discs and revisited the boundary conditions on the torch outer surface to account for radiation and natural convection cooling effects. The numerical simulation results indicated that the radiation heat transfer mechanism is more efficient in dissipating heat from the torch outer surface by up to 26 times. The inner and outer surface temperatures are significantly affected by reducing the plasma flow rate and input power whereas the effect of the plasma frequency was evidently negligible.
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