Heat and mass transfer processes in incandescent lamps and development of gas mixtures for their filling

High Temperatures ^ High Pressures, 2001, volume 33, pages 455 ^ 462 15 ECTP Proceedings pages 1023 ^ 1030 DOI:10.1068/htwu22 Heat and mass transfer processes in incandescent lamps and development of gas mixtures for their filling Anatolij G Shashkov, Olga A Kolenchits Institute of Heat and Mass Transfer, Academy of Sciences of Belarus, P Brovky 15, Minsk 72, 220072 Belarus; fax: +375 172 266 2976; email: koa@ns1.hmti.ac.by Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. A model of a working gas medium for incandescent lamps (ILs) is described. Within the framework of the molecular-kinetic theory, with the help of Langmuir's concept of a stagnant layer about the incandescent tungsten filament, the mathematical model of heat and mass transfer processes for quasistationary operating conditions of the IL was formulated. In this case, the thermodiffusion contribution to tungsten mass transfer and temperature-dependent transfer coefficients of a working mixture were taken into account. With the solution of the transfer equations, the design formulas for the integral heat flux (loss) from the incandescent body and the integral mass flow of tungsten atoms through a filling gas in the IL containing a cylindrical (spherical) incandescent body were obtained. Based on the calculated heat losses from the incandescent body and mass transfer speed of the tungsten atoms in different gas media, effective compositions of multicomponent filling mixtures (N 2 ^ Ar ^ Kr and N 2 ^ Ar ^ Kr ^ Xe) are developed for commonly used bispiral krypton general-purpose ILs. Their applications allow the reduction of the cost of the lamps, while the luminous efficacy and the operating life of the lamps are the same as (or better than) those of lamps with the standard filling mixtures, N 2 ^Kr. 1 Introduction Despite their low power, incandescent lamps (ILs) still remain the most widely used light sources. Such qualities as small size, simplicity of construction, low cost, and the absence of a starting device promote their wide application in private life (general-purpose ILs) and in various spheres of human activity (special-purpose ILs). One of the advantages of ILs in comparison with discharge lamps is their ecological purity and reliability. The performance parameters of ILs (luminous efficacy, Z 1 ; operating life, t) directly depend on the rate of physical processes occurring in the lamp. For the same design, Z 1 and t are limited by heat loss from the incandescent body (IB) through a filling gas to a lamp bulb and through into the surrounding medium, and also by the transfer speed of tungsten atoms sublimating from the IB surface through a filling gas to the bulb inner wall. As the experimental modelling is not very effective it is advisable to solve the problem of perfecting the parameters of production of ILs and of the development of ILs with the needed (1) parameters on the basis of detailed theoretical analysis of heat and mass transfer processes in lamps. The problems of the study of mechanisms of heat transfer from the IB and tungsten particles in a lamp, the investigation of the properties of the filling gas, and the development of an adequate theoretical model of the transfer processes in a lamp were important during the long history of the production and use of ILs (Langmuir 1912; Fonda 1923, 1928; Elenbaas 1963; Covington and Ingold 1975; Almer and de Ridder 1976; (1) At present the problem of energy economy in lighting engineering includes, besides the improvement of light sources as an independent production, also the optimisation of the energetic efficiency of the light source ^ illuminating device system. This means that it is necessary to solve the inverse problem, namely, the development of lamps with the parameters needed for the given illuminating device (Shanda 1993).

456 A G Shashkov, O A Kolenchits 15 ECTP Proceedings page 1024 Berns and de Ridder 1980; Schnedler 1983; Kolenchits et al 1989). Knowledge of the heat and mass transfer processes in lamps has been constantly improving, and the following shortcomings are being overcome: (i) the second-order effects are not taken into account in the description of transfer processes; (ii) incorrect choice of the reference system when writing down the expression of the diffusional flux density of tungsten atoms; (iii) the dependence of working mixture transfer coefficients on temperature is not taken into account or is taken into account incorrectly; (iv) notions about the parameters of a working state of the medium in a lamp are not accurate. 2 Theoretical model of transfer processes in ILs 2.1 Model of working gas medium The real working gas medium in ILs with power higher than 25 W (2) is a vapour ^ gas mixture consisting of tungsten atoms sublimating from an IB surface, filling gases, and gas admixtures. Assuming that the partial pressures of admixtures are small, we can consider the working mixture in the lamp as a binary mixture of tungsten atoms with filling gas. The process of lamp filling (denoted by subscript f) with gas is performed at temperature T f 293 K up to pressure p f ˆ 0:08 ^ 0.09 MPa. The working pressure of the vapour ^ gas mixture in the lamp is constant over the whole bulb volume; p ˆ 0:11 ^ 0.13 MPa. The working medium is continuous (Knudsen number Kn 4 0:01), and it may be considered as a mixture of ideal gases: p ˆ p g p W, pm ˆ rrt, where M ˆ M g M W (c g M W c W M g ) 1, r ˆ r g r W, c W ˆ r W =r, c g ˆ r g =r. In the above, r is density, M is molar volume, T is temperature, c is mass concentration, R is the gas constant, and subscripts g and W refer to gas and tungsten, respectively. Proceeding from the condition of equality of the total number of filling gas molecules in the lamp in working and non-working regimes (Almer and de Ridder 1976), we find: p g ˆ pft g T f, T g ˆ V bi Vfi T fi Vbi V fi dv T 1, (1) where T g is the averaged gas temperature in the bulb, V is volume, subscript fi denotes parameters of the incandescent body, and subscript bi denotes parameters on the internal wall of the bulb. The pressure of tungsten vapour formed as the result of sublimation over the IB with temperature T fi is expressed by the elasticity curve: p W T fi =Pa ˆ exp 64:301047 108944:396 T fi =K 1 0:799435 10 3 T fi =K 4:37526 ln T fi =K Š, the coefficients of which are given by Nesmejanov (1961). For example, at T fi ˆ 2700 K, p W ˆ 2 10 4 Pa. So as p W 5 p g, the tungsten component has a trace (mass) concentration, c W! 0, c g! 1, (2) and further we can assume that p ˆ p g, M ˆ M g, r ˆ r g. (3) 2.2 Stagnant layer model of Langmuir The movements of the working medium in the bulb and transfer processes caused by molecular mechanisms and convection are described by a system of transfer equations, equations of continuity, motion, energy, and diffusion (Hirschfelder et al 1954). (2) ILs of power lower than 25 W are produced in a vacuum variant; above they are filled by heavy inert gases, nitrogen or by mixtures of these gases.

Heat and mass transfer processes in incandescent lamps 457 15 ECTP Proceedings page 1025 The IB of ILs is a tungsten filament (monospiral, bispiral) of radius r fi heated up to T fi ˆ 2300 ^ 3300 K, and the temperature of the internal bulbwall is given by T bi ˆ 400 ^ 450 K. Therefore, difficulties in solving the transfer equations are increased by the necessity of taking into consideration the dependence of the working mixture transfer coefficients (thermal conductivity l ˆ l g, viscosity Z ˆ Z g, diffusion D Wg, thermodiffusion constant a T ) on temperature. Due to the strong viscosity of the filling gas at high T fi, an almost immovable gas layer [the so-called stagnant layer of Langmuir (1912)], is formed near the surface of a thin IB. In the region of this layer the mechanisms of heat and mass transfer in the lamp are mainly molecular, namely thermal conductivity, diffusion, and thermodiffusion (Covington and Ingold 1975; Schnedler 1983; Kolenchits et al 1989). The stagnant layer model of Langmuir [or the reduced film model of Frank-Kamenetskii (1987)] does not allow investigation of the field of stream velocities in the working medium of the lamp but it is convenient for quantitative description of transfer processes. 2.3 Quasistationary problem of heat and mass transfer in ILs With the help of the concept of a stagnant layer around the IB, the real processes of transfer in ILs can be described by an equivalent problem of heat and mass transfer, carried out only by molecular mechanisms (figure 1). In this case the system of transfer equations T fi T(r) T la ˆ T bi r c W (r fi ) c W (r) 0 rfi r la r lb r Figure 1. Scheme of temperature distribution, T(r), and concentration of tungsten component, c W (r), in the gas medium surrounding a cylindrical incandescent body of radius r fi heated up to temperature T fi : r lb is the radius of the boundary layer in the region of which transfer processes are carried out by molecular mechanisms and convection (solid curves); r la is the radius of the stagnant layer in the region of which transfer processes are carried out by molecular mechanisms (dashed curves).

458 A G Shashkov, O A Kolenchits 15 ECTP Proceedings page 1026 reduces to the diffusion equation of the tungsten component of the working mixture and the energy equation, which have the following form in the working regime of the lamp (Hirschfelder et al 1954) H.J q ˆ 0, H.J W ˆ 0. (4) If we take account of conditions (2) and (3), the expressions for density fluxes (3) are reduced to the following form (Hirschfelder et al 1954): J q ˆ lht, J W ˆ r W D Wg c W H ln c W a T H ln T=K Š. (5) The conditions for gas temperature near the surface of the IB and on the `boundary' of the stagnant layer (subscript la) are: T(r fi ) ˆ T fi, T(r la ) ˆ T la. The mass concentration of tungsten atoms near the surface of the IB is assumed to be the same as in vacuum at the same temperature, T fi, and at the external `boundary' of the stagnant layer it is practically zero: c W (r fi ) ˆ M W p W (T fi )=(M g p g ), c W (r la ) ˆ 0. 2.4 Integral fluxes of heat from the IB and mass of tungsten component Let us consider the IB as a horizontal cylinder of radius r fi with uniform temperature distribution T fi along its length, l, and the stagnant layer as a coaxial cylinder of `radius' (4) r la with temperature on its external `boundary', T la. According to equation (1) when r bi 4 r la > r fi, the averaged gas temperature in the bulb, T g, approaches temperature T la, which is equal to the temperature of internal bulb wall, T bi (figure 1), and the pressure of the filling gas is given by p g ˆ p f T bi =T f. For this case integral fluxes are expressed through flux densities in the radial direction (indicated by subscript r): P g ˆ 2plrJ qr (r), M TW ˆ 2plrJ Wr (r). Integrating the system of equations (4) and (5) in cylindrical coordinates (5) with the help of the above-mentioned boundary conditions, we obtain the following expression for heat losses from the IB: P g ˆ 2pl Tfi l ln r la =r fi g T dt, (6) T la and for the mass flux of the tungsten component of the working medium, Tfi 1. (7) a M M TW ˆ P W p W T fi g T a T T fi l g T T fi dt M g p g T la r g D Wg Correct estimations of values of P g and M TW are necessary for the calculation of the parameters of the IB, for the development of optimum sizes of the bulb, and for the solving of other practical problems for ILs. 3 Definition of composition of filling mixtures for krypton ILs The fill-gas mixtures for krypton general-purpose ILs (GPILs) with a bispiral IB consist of N 2 ^Kr, N 2 ^Ar^Kr, N 2 ^ Kr ^ Xe (table 1). Three-component mixtures of N 2 ^ Ar ^ Kr and N 2 ^ Kr ^ Xe (compositions 2, 3) are recommended by Kolenchits et al (1989) and Vugman et al (1984) as more effective replacements for the N 2 ^Kr mixture (composition 1, GOST 239-79), which provides good lamp performance but is expensive because of the high krypton content. (3) Existing estimations have shown that the share of diffusion thermal conductivity in heat flux may be neglected with good accuracy. (4) The radius of the stagnant layer is a hypothetical value which allows us to obtain quantitative results which are close to reality. (5) For the case of a spherical IB, which is important for small and compact halogen ILs, the geometrical parameter {l[ln (r la =r fi )] 1 } is changed to [2r fi r la =(r la r fi )].

Heat and mass transfer processes in incandescent lamps 459 15 ECTP Proceedings page 1027 Table 1. Fill-gas mixtures for krypton general-purpose incandescent lamps. Mixture components Volume concentration of components/% composition 1 composition 2 composition 3 N 2 10 ± 16 10 ± 16 8 ± 12 Argon 24 ± 8 Krypton 90 ± 84 83.7 ± 79.8 68 ± 80 Xenon 6.3 ± 4.2 Compositions 2 and 3 lower the lamp cost by adding inexpensive argon to the N 2 ^Kr fill mixture or by replacing the krypton component with a Kr ^ Xe mixture (GOST 10218-77), which is the industrial precursor of pure krypton and xenon, and thus is less expensive than pure krypton. The use of xenon, which is heavy and has low thermal conductivity, in fill composition 2, as determined by experimental modelling, enhances the operating parameters of krypton GPILs. However, in order to avoid a decrease in the arc discharge starting voltage, Vugman et al (1984) limited the xenon concentration to 4.2% ^ 6.3%, which corresponds to a 5% ^ 7% xenon content in the initial Kr ^ Xe mixture. If this initial mixture contains more than 5% ^ 7% xenon, then the excess must be eliminated in the N 2 ^ Kr ^ Xe fill mixture by adding pure krypton, which negates some of the cost advantage of composition 2 over composition 1. A theoretical approach was used by Kolenchits et al (1989) to identify an N 2 ^Ar^Kr mixture equivalent to composition 1 by calculating and comparing the heat loss from the IB through binary (N 2 ^ Kr) and ternary (N 2 ^ Ar ^ Kr) mixtures of various compositions. Because the addition of 4% argon to the N 2 ^ Kr mixture with a simultaneous decrease of the N 2 content by 1% and krypton content by 3% does not increase the heat loss of the IB (Kolenchits et al 1989), the luminous efficacy, Z 1, of lamps filled with composition 3 should be the same as that of standard bispiral krypton (BK) GPILs. Tests (Vugman et al 1984; Kolenchits et al 1989) of ILs filled with mixtures 2 and 3 confirmed that Z 1 and the operating life, t, of these lamps meet the requirements for BK GPILs. All the advantages of the above-mentioned fill medium can probably be obtained with a mixture consisting of pure N 2 and Kr ^ Xe with the addition of argon. Using the approach taken by Kolenchits et al (1989) to determine composition 3, we undertook a search for the optimum composition of a 4-component mixture of N 2 ^Ar^Kr^Xe by analysing the dependence of the specific heat loss, P gl ˆ P g =l, from the volume concentration components (x N2, x Ar, x Kr, x Xe ). Values of P gl were calculated for 40, 60, 75, and 100 W BK GPILs with fill mixtures containing the standard concentration of N 2 (10% ^ 16%) and small concentrations of argon and xenon (2% ^ 12%). The radius r la of the stagnant gas layer around the coiled-coil filament of radius r fi was determined in accordance with work by Aleinikova et al (1989) with the Kyte ^ Madden ^ Piret (Kyte et al 1953) formula: r la ˆ 1 7:09, (8) 0:37 r fi Ra where Ra is the Rayleigh number. This was calculated as follows: Ra ˆ 32gr fim 3 2 g p 2 f T fi T la T la c pg T av R 2 Tf 2 T fi T la 2 l g T av Z g T av, (9) where the average temperature is given by T av ˆ (T fi T la )=2; g is gravitational acceleration and c p is isobaric specific heat.

460 A G Shashkov, O A Kolenchits 15 ECTP Proceedings page 1028 The value of specific heat, c pg, is determined based on the corresponding contribution of each component: c pg ˆ ( P x i M i ) P 1 x i M i c pi, i ˆ 1, 2,3,4. The thermophysical characteristics of the fill-gas mixtures (l g, Z g ) in equation (9) and the temperature dependence of thermal conductivity, l g (T ), in the temperature range from T la ˆ T bi ˆ 450 KtoT fi ˆ 2700 K in equation (6) were calculated by the Chapman ^ Enskog method (Hirschfelder et al 1954) and the Lennard-Jones potential. The thermal conductivity of mixture components in the range 450 4 T=K 4 2700 was defined from the correction of experimental data obtained by the nonstationary shock tube method and their subsequent generalisation with data of stationary methods at atmospheric pressure: l Ar T =W m 1 K 1 ˆ 2:136 10 3 0:57710 10 4 T=K 0:21790 10 7 T=K 2 0:6466 10 11 T=K 3 0:945 10 15 T=K 4 0:53 10 19 T=K 5, l Kr T =W m 1 K 1 ˆ 0:484 10 3 0:33531 10 4 T=K 0:11121 10 7 T=K 2 0:2555 10 11 T=K 3 0:216 10 15 T=K 4, l Xe T =W m 1 K 1 ˆ 0:059 10 3 0:20790 10 4 T=K 0:06485 10 7 T=K 2 0:1499 10 11 T=K 3 0:128 10 15 T=K 4, where 273 4 T=K 4 5000; 0:781 T=K l N2 T =W m 1 K 1 ˆ 25:91 10 3, 300 4 T=K 4 2700. 300 The coefficient of viscosity of mixture components was determined from generalised experimental data (Golovicher et al 1989). The heat losses in BK 230 ^ 240 V 60 W lamps as calculated from equations (6), (8), and (9) are represented in figure 2 as follows: for N 2 ^ Kr, as the point corresponding to the value P g ˆ P g0 ; for N 2 ^Ar^Kr and N 2 ^ Kr ^ Xe, as border lines (x Xe ˆ 0 and x Ar ˆ 0, respectively); for N 2 ^ Ar ^ Kr ^ Xe, as the lines forming the grid. Certain compositions of the N 2 ^ Ar ^ Kr ^ Xe mixture provide lower heat losses than the conventional N 2 ^ Kr mixture (at the grid nodes below the line P g ˆ P g0 ) and thus a higher Z 1 for the lamp. As the estimations of speed of tungsten atom transfer, m TW J Wr (r) ˆ M TW =(2plr) according to equation (7), have shown in this case, compounds of 4-component mixture are effective from the viewpoint of operating life if they have a molar mass not less than the molar mass of the N 2 ^ Kr mixture (dashed regions in figure 2) (6) : 10% ^ 16% N 2 ^ 4%^10% Ar ^ 82%^64% Kr ^ 4%^10% Xe. (10) The optimum composition is: 13% N 2, 7% Ar, 73% Kr, and 7% Xe. The xenon concentration in the proposed mixture corresponds to a content of 5% ^ 12% in the initial Kr ^ Xe mixture. If the xenon content of the initial Kr ^ Xe mixture is higher, then proportionally more argon must be added to the N 2 ^ Ar ^ Kr ^ Xe fill mixture. The economic advantages of using multicomponent fill mixtures in place of N 2 ^Kr are shown in table 2. Compared with the conventional N 2 ^ Kr fill, the advantage in fill cost is about 10% for the N 2 ^ Ar ^ Kr mixture, 25% for the N 2 ^ Kr ^ Xe mixture, and 31% for the N 2 ^ Ar ^ Kr ^ Xe mixture. (6) This mixture composition also holds for BK 230 ^ 240 V lamps of other wattages.

Heat and mass transfer processes in incandescent lamps 461 15 ECTP Proceedings page 1029 P gl Wm 1 300 290 280 x Xe % xar % N 2 ^Ar^ Kr N 2 ^ Kr ^ Xe N 2 ^Kr x Xe % xar % N 2 ^Ar^ Kr N 2 ^ Kr ^ Xe N 2 ^Kr (a) 270 (b) P gl Wm 1 310 300 290 x Xe % xar % N 2 ^Ar^ Kr N 2 ^ Kr ^ Xe N 2 ^Kr x Xe % 10 8 6 4 2 0 10 8 6 4 2 0 xar % N 2 ^ Ar ^ Kr N 2 ^ Kr ^ Xe N 2 ^Kr (c) 280 60 70 80 90 60 70 80 90 x Kr % (d) xkr % Figure 2. The specific heat losses, P gl ˆ P g =l, of the incandescent body (r fi ˆ 0:269 10 3 m) in a BK 230 ^ 240 V 60 W GPIL for composition of the fill mixture. Horizontal lines are the specific heat losses, P gl, for a lamp with a N 2 ^ Kr fill of composition 1 (table 1). (a) x N2 ˆ 10%; (b) x N2 ˆ 12%; (c) x N2 ˆ 14%; (d) x N2 ˆ 16%. Table 2. Relative cost a, C ˆ cost of mixture/cost of N 2 ^ Kr, of fill-gas mixtures for BK GPILs and operating parameters of BK 230-240-60 lamps with different fills. Fill mixture Volume concentration/% C Z 1 /lm W 1 t 0 /h x N2 x Ar x Kr x Xe N 2 ± Kr 13 87 1 13.20 not less than 700 N 2 ± Ar ± Kr 12 10 78 0.90 13.19 not less than 700 N 2 ± Kr ± Xe 13 81.8 5.2 0.75 N 2 ± Ar ± Kr ± Xe 10 4 82 4 0.69 13.34 not less than 700 13 7 73 7 13.29 not less than 700 16 10 64 10 13.24 not less than 700 a The mixture costs were calculated based on pre-1991 prices of pure gases and mixtures.

462 A G Shashkov, O A Kolenchits 15 ECTP Proceedings page 1030 Brest Electric Lamp Plant (Moskovskaya 204, Brest 633, 224633 Belarus) manufactured a lot of BK 230 ^ 240 V 60 W GPILs filled with either N 2 ^Ar^Kr^Xe (several versions of composition 10) or the conventional N 2 ^ Kr mixture (the optimum version of composition 1) and conducted tests on these lamps. The results for the average Z 1 of samples of 20 lamps and the minimum operating life for each lamp, t 0, are shown in table 2. The average lifetime t for each fill mixture was not less than 1000 h, which conforms to GOST 2239-79. It can be seen from table 2 that the application of fillmulticomponent mixtures permits the luminous efficacy to be kept on the same level (mixture N 2 ^ Ar ^ Kr) or increased (mixture N 2 ^ Ar ^ Kr ^ Xe) in comparison with the sample filling mixture N 2 ^Kr. 4 Conclusion The theory of heat and mass transfer processes in ILs is presented. Based on calculation and comparison of the IB heat losses through a binary N 2 ^ Kr mixture and multicomponent mixtures containing N 2, argon, krypton, and xenon, composition 10 of mixture N 2 ^ Ar ^ Kr ^ Xe was determined and recommended for filling BK GPILs. The effectiveness of this mixture is confirmed by the data in table 2. References Aleinikova V I, Kolenchits O A, Kiseleva N P, Litvinov V S, 1989 Svetotekhnika 1 8^10 Almer F H R, de Ridder J, 1976 Light. Res. Technol. 8 31 ^ 35 Berns E G, de Ridder J, 1980 Philips J. Res. 35 173 ^ 189 Covington E J, Ingold G H, 1975 J. Illum. Eng. Soc. 4 198 ^ 203 Elenbaas W, 1963 Philips Res. Rep. 18 147 ^ 160 Fonda G R, 1923 Phys. Rev. 21 343 ^ 347 Fonda G R, 1928 Phys. Rev. 31 260 ^ 266 Frank-Kamenetskii D A, 1987 Diffuziya i Teploperedacha v Khimicheskoi Kinetike (Diffusion and Heat Transfer in Chemical Kinetics) (Moscow: Nauka) Golovicher L E, Kolenchits O A, Nesterov N A, 1989 Inzh.-fIZ.. Zh. 56 982 ^ 987 GOST 10218-77, 1977 Krypton i Krypton ^ Ksenonovaya Smes' (Krypton and Krypton ^ Xenon Mixture) (Moscow: GOST) GOST 2239-79, 1979 Lampy Nakalivaniya Obshchego Naznacheniya (General-Purpose Incandescent Lamps) (Moscow: GOST) Hirschfelder J O, Curtiss C F, Bird R B, 1954 The Molecular Theory of Gases and Liquids (New York: John Wiley) Kolenchits O A, Aleinikova V I, Turovskaya V I, 1989 Processy Teplomassoperenosa v Lampakh Nakalivaniya (The Processes of Heat and Mass Transfer in Incandescent Lamps) (Minsk: Nauka i Tekhnika) Kyte J, Madden A, Piret E, 1953 Chem. Eng. Prog. 49 653^670 Langmuir I, 1912 Phys. Rev. 34 401 ^ 422 Nesmejanov A N, 1961 Davlenie Para Khimicheskikh Elementov (Vapour Pressure of Chemical Elements) (Moscow: Nauka) Schnedler E, 1983 Philips J. Res. 38 224 ^ 235 Shanda Ja, 1993 Svetotekhnika 5^67^ 9 Vugman S M, Zakhar'evskii A V, Muratov O M, 1984, USSR Inventor's Certificate No 1458907. 1984 Byul. No 6, ``Sostav dlya napolneniya lamp nakalivaniya'' (Filling composition for incandescent lamps) ß 2001 a Pion publication printed in Great Britain