Acoustic Resonance Characterization and Numerical Model Including Acoustic Streaming in an HPS Lamp

Transcription

1 Acoustic Resonance Characterization and Numerica Mode Incuding Acoustic Streaming in an HPS Lamp Areski Toumi, Labo Chhun, Souni Bhose, Georges Zissis, Pasca Maussion, Benedict Baumann, M Woff To cite this version: Areski Toumi, Labo Chhun, Souni Bhose, Georges Zissis, Pasca Maussion, et a.. Acoustic Resonance Characterization and Numerica Mode Incuding Acoustic Streaming in an HPS Lamp. IEEE Transactions on Industry Appications, Institute of Eectrica and Eectronics Engineers, 013, vo. 49, pp < /TIA >. <ha > HAL Id: ha Submitted on 19 Feb 014 HAL is a muti-discipinary open access archive for the deposit and dissemination of scientific research documents, whether they are pubished or not. The documents may come from teaching and research institutions in France or abroad, or from pubic or private research centers. L archive ouverte puridiscipinaire HAL, est destinée au dépôt et à a diffusion de documents scientifiques de niveau recherche, pubiés ou non, émanant des étabissements d enseignement et de recherche français ou étrangers, des aboratoires pubics ou privés.

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3 Acoustic Resonance Characterization and Numerica Mode Incuding Acoustic Streaming in an HPS Lamp A. Toumi, L. Chhun, S. Bhose, G. Zissis and P. Maussion Université de Tououse; UPS-INPT; LAPLACE (Laboratoire Pasma et Conversion d'energie) 118, route de Narbonne, F-3106 Tououse cedex 9, France B. Baumann, M. Woff Hamburg University of Appied Sciences, Beriner Tor 1, 0099 Hamburg, Germany Abstract -- This paper presents a numerica mode of High Pressure Sodium (HPS) amps incuding the acoustic streaming. The mode is impemented in COMSOL and based on the finite eements method using a D axi-symmetric geometry. Moreover, a revision concerning AR experimenta characterizations of HPS amps wi aso be provided. The resuts presented in this paper wi contribute to the understanding of AR phenomena and hep in the eectronic baast design methods for AR avoidance. Index Terms- AR characterization, Acoustic streaming, Acoustic waves, HPS amps modeing I. INTRODUCTION High Pressure Sodium amps (HPS) are artificia ight sources based on the radiation of a sodium discharge. HPS are widey spread in our environment, especiay in pubic ighting, where they can be recognized with their orange characteristic ight coor. Athough ighting systems based on these amps have currenty one of the highest efficacy (typicay 10m/W) higher efficacies can be achieved with high frequency power suppy (some tens or hundreds of khz). However HPS amps operation at high frequency is usuay accompanied by a perturbing phenomenon, provoking amp arc instabiity, known as Acoustic Resonance (AR) [1-]. Nowadays, commony used eectronic baasts for HPS amps usuay operate at ow frequency (around a hundred hertz) square waves in order to avoid the occurrence of arc instabiities. Using higher frequencies woud decrease the baast weight, size and cost. It was shown that the best operation frequency is around 300 khz [3]. Many attempts have been done to increase baasts operating frequency whie avoiding acoustic resonances. In [4] a moduation method based on a constant centra frequency and a frequency moduation band of 10 khz was used. In [5], amp geometry and operating frequency schemes are designed in order to reduce the negative effect of acoustic resonances. Another method referred to as spread spectrum is aso reported to reduce amp instabiities when operated at high frequencies [6]. Lamp AR experimenta characterizations are aso conducted so as to define AR zones and its detections necessary for baast design [7-9]. In [10] a mode of HID amp incuding the acoustic instabiities has been performed. The Acoustic Resonance phenomenon is due to the deveopment of standing acoustic waves in the amp burner, however, the interaction between these acoustic waves and the arc is sti poory understood, especiay their impact on the arc shape. Consequenty, a mode capabe of taking into account this interaction is required in order to improve the phenomenon physica comprehension and evauate the impact of acoustic resonances on arc distortion with the amp frequency. In this paper, a revision of AR characterizations is conducted in section II. A mode deveopment of AR incuding acoustic streaming wi be provided in the foowing sections. Contrary to [10], the physica phenomena of the HID amp have been dissociated in order to see in precise manner the infuence of each parameter (gaz pressure, burner geometry ) on the behavior of the amp under the infuence of acoustic resonances. The resuts obtained with a D axi-symmetric HID amp mode wi aso be presented and discussed. This study wi contribute to the understanding of AR phenomena and hep in eectronic baast design methods for AR avoidance. II. AR EXPERIMENTAL CHARACTERIZATIONS Basicay, the AR is excited when the power suppy frequency is equa to the AR eigenfrequency and its power is higher than certain threshod. An exampe of experimenta power suppy for AR excitation is a ow frequency square wave, superimposed with a high frequency sine wave current source. It shoud be noted that the AR can be different from amp to amp of the same type due to the geometry and gas composition toerances in manufacturing process. Experimenta resuts of power threshod in an HPS 150W amp are iustrated in Fig. 1 [11]. The study of an HPS amp suppy with a sinusoida source aso demonstrates that the degree of arc instabiity and amp parameter variations due to AR depends on the suppy

4 frequency within the unstabe AR zone (Fig. ). This instabiity can aso ead to amp arc extinction. Furthermore, hysteresis phenomenon is presented in the discharge when amp suppy frequency sweeping is appied in increasing or decreasing direction. The experimenta resuts given in Fig. show that the AR zones and parameter variations are more pronounced in decreasing mode than in increasing mode. According to the expanation in [1], arc bending due to AR can shift the eigenfrequency, as a resut, the extension of backward AR band is the consequence of frequency shifting. III. MODEL DESCRIPTION A. Lamp characteristics A typica HPS amp characteristics and shape (Phiips Master Son-T PIA Pus) used in our study are shown in Tabe I and Fig. 3 respectivey. The fiing gases within the amp tube consist mainy of a mixture of sodium, mercury and xenon. TABLE I BURNER DIMENSION AND PARTIAL PRESSURE OF THE FILLING GASES [] Radius [mm].4 Length [mm] 76 Distance between eectrodes [mm] 58 DC current ampitude [A] 1.8 p Na (kpa) 1 p Hg (kpa) 100 p Xe (kpa) 30 Fig. 1: AR threshod in HPS amp SONT 150W [11] Fig. : Lamp eectrica parameter variations in HPS amp SONT 150W [11] The AR excitation phenomenon is hence reated to 3 main subects: eigenfrequency, arc fuctuation ampitude and power threshod. The mode for eigenfrequency estimations has been deveoped so far by many iteratures whie a simpified mode can aso be obtained. Besides, the mode for AR instabiity or fuctuation ampitude at each AR mode is ess deveoped because of the interaction between the AR and the arc is sti ess understood. In this paper, an AR modeing for arc fuctuation ampitude estimation, incuding the acoustic streaming is presented and wi be discussed in the next section. Fig. 3: Geometry of burner used in the mode (burner dimensions in m) B. Genera assumptions The modeing of HID amp is carried out under the foowing assumptions: - the arc coumn is assumed to have a cyindrica symmetry, - the pasma is supposed at the oca thermodynamic equiibrium, under this assumption, the pasma properties can be deduced from the temperature distribution, - the pasma fow is assumed incompressibe, - the couping of the pasma with the eectrodes is

5 negected, The equations governing the physica gas discharge are resoved at steady state and the cacuations are performed using the COMSOL Mutiphysics Finites Eement Method (FEM) too. C. Fuid mode According to the assumption mentioned above, the pasma mechanisms are governed by three differentia equations: - The Eenbaas-Heer equation for the determination of the temperature distribution in the burner, - The incompressibe Navier-Stokes equation to compute the convection veocity, - The current continuity equation to obtain the distribution of the eectrica fied. The Eenbaas-Heer equation (1) is written as foow: TC put St (1) where k is the therma conductivity, T the temperature, the mass density, C p the heat capacity at a constant pressure, U the natura convection veocity and S t the heat source density. The veocity U is set at zero in the eectrodes and was domains as there is no convection. The term source S t is computed from S E () t u rad where is the eectrica conductivity, E the eectrica fied and u rad is the radiations osses. Assuming an idea gas medium, the mass density is given by pm (3) RT where p is the static pressure, M the average atomic mass of fiing gases, R the idea gas constant. The boundary conditions of the externa faces of the was burner is specified according to n. k T q 0 where q 0 is the inward heat fux cacuated from the Stefan- Botzmann aw q 4 0 SBT (4) (5) with SB the Stefan-Botzmann constant. The temperature boundary condition are used for the externa edges of the eectrodes with a constant vaue of T 0 =1500K. The initia vaue of the temperature is taken from [] and is corresponding to the temperature profie of HPS amp 400 W. The veocity U is given by the incompressibe Navier- Stokes equation (6). T U U pi U U F (6) where I is the identity vector, F the voume force due to the gravitation ( F g ), and the dynamic viscosity. This equation is appied ony to the domain corresponding to the pasma. As boundary conditions U 0 is used (no sip). It is important to estabish one point constraint for the pressure on the interior boundary. This point is paced at the vertices formed by the union of the ower eectrode with the interna edge of the wa and its vaue is set at the static pressure of the amp. The initia vaue for this equation is U ( t 0 ) 0 and p ( t 0 ) is set at the static pressure of the amp. To obtain the eectrica fied E in the burner, the current continuity equation has to be soved (7) and it appies ony in the pasma domain. V. E. 0 (7) where V is the eectrostatic potentia and the current density. The boundary conditions of the pasma domain are set as Neumann boundary conditions: n.( T ) J (8) J 0 represents the inward current density. Its vaue on the eectrode tip is obtained by dividing the appied current by the transversa area of one eectrode. The upper eectrode tip is set at a positive vaue and the ower eectrode tip at a negative vaue. The sides of the eectrodes and the was of the amp are defined as the insuation condition (J 0 = 0). The initia vaue of the potentia is set to V(t 0 )=0. The cacuation of the transport coefficients is based on the work of Hirschfeder and a [13] and Devoto [14-15] according to the Chapman-Enskog theory. The pasma composition and the thermodynamic properties are obtained using the chemica equiibrium. The radiation osses is taken from Eenbaas theory and is given by u rad 0 g i E i ( T ) N T A E E 0 ( ) i ( i ) exp (9) i g 0 kbt

6 where N 0 (T) is the atomic density in the ower states, g i and g 0 are the statistica weights of the excited and fundamenta states, A i the atomic transition probabiity and k b is the Botzmann constant. The atomic transition for sodium is taken from [], whie negected the infuence of mercury and xenon on the radiation osses because its impact become ony significant at temperature higher than 5000 K. On the Fig.4(a), the temperature distribution is shown. We can see that the axia temperature is equa to 4400 K and it is in good agreement with the cacuation of de Groot and van Viet (T ax = 4550 K) []. The convection veocity in burner, generated by the gravitationa force ( F g ), is given by Fig.4(b). Because of this convection veocity, the arc discharge is maintained at the axis of the burner. The upward convective veocity in the centre of the arc tube is of the order of 0.1 cm/s. D. Acoustic mode When a high pressure discharge amp operates at certain high frequencies, the discharge path can become unstabe and distorted. These instabiities are due to the acoustic resonance generated by the propagation of an acoustic wave and its interaction with the discharge. The infuence of acoustic resonances on the arc discharge becomes important when amp power frequency is cose to the corresponding AR eigenfrequency. The eigenvaue can be obtained by soving an inhomogeneous Hemhotz equation for the pasma domain [4,17,18]. 1 p p i H (10) cs cs where c s is the sound ceerity of gas compound in the container, denotes heat capacity ratio, and H constitutes the Fourier transform of the power density inected to the gas. The sound veocity c s and the temperature T are reated through c s RT M The inhomogeneous Hemhotz equation in (10) provides ony the eigenfrequencies without the ampitudes of acoustic pressure because the term H is set to 0. The mode does not consider the absorption osses reated to surface osses due to the therma conductivity of burner s was, and voume osses due to the friction in the pasma generated by the therma conductivity and dynamic viscosity. In our simuation, we negected the voumes. E. Post-treatment The ampitude is computed in post-treatment by introducing the quaity factor. On the one hand, the quaity factor k reated to the conduction oss on the boundary ayer with a depth d k, and according to [4,17,18] can be defined as in (11). (a) Fig. 4: (a) The temperature profi [K] in the burner (b) and convection veocity [m/s] due to the gravitationa force. The arrows denote the direction of the veocity. The temperature distribution provides by this mode is used as the input parameter for the computing of the acoustic modes in the next section. (b) k k 1 d 1 p ds V (11) b S b p denotes the acoustica eingenmode for th mode, V b the voume of the burner and S b its intern surface. On the other hands, the quaity factor reated to the viscosity oss term on the boundary ayer described by a given depth d, is defined in (1) [4,13,14]. 1 1 cs ( ) d V B p S B ds (1) where p is the component of the pressure gradient tangentia to the burner wa. In order to compute the pressure ampitude for each

7 acoustic mode without the osses, the foowing equation is appied [4,17,18] A 1 * p V B V B IdV (13) Finay, the AR ampitude in function of discharge inected frequency at a given AR frequency or AR mode is described by the foowing equation [4,17,18]: with 1 1 A k 1 A i i (14) Fig. 6: Pressure integra versus resonance frequency Fig. 5: Simuated acoustic resonances ampitude of HPS amp SON-T Fig.5 iustrates the simuation resuts of AR ampitude over input frequency in HPS amp SON-T 150 W and it is in good agreement with the experimenta resuts shown in Fig.1 and Fig.. The frequency range in our study is defined as 0 khz, nevertheess, it is possibe to simuate the mode at higher frequencies. It can be seen that the maximums ampitudes of AR corresponds to the pair ongitudina modes. These resuts correspond to the experimenta study of Epron [18] on HPS amp SON-T 400 W. Indeed, he denoted that ony the pair modes appear in the sodium amp when it suppied at high frequency. This is due to the integra pressure as shown on Fig.6 and occurs in the computation of A (13). Because the ongitudina pair mode of the acoustic pressure have a sine form with same positive and negative anti-nodes, as we can see on Fig.7, the effect of the positive and negative antinodes is vanished. Fig. 7: Reative vaue of acoustic pressure for some modes (eigenfrequencies 3.06 khz, 5.9 khz, 8.4 khz and 10.8 khz, respectivey). Red indicates positive antinodes whereas bue indicates negative antinodes. F. Acoustic streaming mode The acoustic streaming caused by the spatia variation of Reynods stress by generating a net force per unit voume [19], and infuences the behavior of the pasma in the burner of HID amp. The study carried out by Afshar [0] on acoustic resonances considered its origin to the acoustic streaming. It was demonstrated that the acoustic streaming generates a non-inear acoustic fux with mean vaue different to zero. The force F _ for an axe direction i, can i aco

8 be written as in (15): F v v i i _ aco (15) x Meanwhie, for the axe direction, the corresponding force is described by: viv F _ aco (16) xi where vi and v are the acoustic veocities foowing the direction of axes i and computed by the inhomogeneous Hemhotz equation (10), and vaue. v i v is tempora average These cacuated forces can be impemented in Navier- Stokes equation (6) to obtain the convection veocity meanwhie considering the gravitation and the acoustic streaming in the burner of the amp: F F i F (17) F i F i _ aco (18) F g F _ aco (19) These resuting forces representing the streaming phenomenon need to be integrated into the AR mode given in previous section, in order to impement the numerica simuations. On the Fig.8, we can see severa fuxes of veocity generated by the acoustic streaming force. In addition of these fuxes, the ampitude of the veocity increases noticeaby from 0.1 cm/s (without AR) to 4.5 cm/s (with AR) and it is non uniform ike in the case where the acoustics resonances are not appear (Fig.4.b). This increasing of the ampitude and the generation of the veocity fuxes expain the instabiities in the burner of HPS amp and the dispacement of the eectrica arc. Indeed, because of these fuxes, the arc discharge path it does not stabiized by the natura convection veocity ike in the case where the amp it is not under infuence of the acoustic resonances. Fig. 9: Schematic modeing steps. IV. CONCLUSION Fig. 8: The convection veocity [m/s] incuding the infuence of the acoustic streaming in HPS amp SON-T 150 W and corresponding to the frequency equa to 10.8 khz. The streamines correspond to the veocity. The revision of an AR experimenta characterization method and the AR modeing incuding acoustic streaming are presented in this paper. The experimenta resuts for AR excitation indicated different characteristics of amp parameters responses during its AR excitation at high frequency. Whereas, the AR modeing is based on severa couped equations soved by Comso finite eement method considering D axi-symmetric discharge geometry. The simuated resuts aow to obtain a good estimation of AR eigenfrequency and ampitude. In addition, due to the introduction of acoustic streaming in our cacuation, by taking in account the non-inearity of the acoustic veocity, it is possibe to expain the interaction between the eectrica arc in the burner of HPS amps and acoustic resonances.

9 Despites the simpifications and approximations, the mode provides satisfactory resuts in reativey short computing time with reasonabe memory requirement for a desktop computer. ACKNOWLEDGMENTS We are indebted to John Hirsch, from Phiips Lighting, for his hep on the reaization of this work. REFERENCE [1] J.M. Davenport, and R.J. Petti, Acoustic resonance phenomena in ow wattage meta haide amps J. Ium Eng. Soc., pp , [] J.J. de Groot and J.M. Van Viet, The high pressure sodium Lamp Phiips Technica Library,1986. [3] G. Trestman, Minimizing Cost of HID Lamp Eectronic Baast, 8th Annua Conference of the Industria Eectronics Society, IEEE, 5-8 Nov. 00, pp [4] J. Hirsch, B. Baumann, M. Woff, S. Bhose, and R.Vadivia Barrietos, Acoustic resonances in HID amps : mode and measurements J. App. Phys.43, pp. 1-7,, 010. [5] S. Wada, A. Okada, and S. Morii Study of HID amps with reduced acoustic resonances, J. Iuminating Eng. Soc., pp , [6] R. van Honschooten, Phiips Power Conversion Symp. Aachen, Germany, 007. [7] J. Osen, and W.P. Moskowitz, Optica Measurement of Acoustic Resonance Frequencies in HID amps, IEEE 3 nd IAS annua meeting, New Oreans, USA, Oct 1997, pp [8] J. Osen and W.P. Moskowitz, Time Resoved Measurements of HID Lamp Acoustic Frequency Spectra, IEEE 33 rd IAS annua meeting, St Louis, USA, vo 3, 1998, pp [9] J.C. Anton, C. Banco, F. Ferrero, J. Viera, N. Borde and G. Zissis Acoustic Resonance Band detection Workbench for HID amps, Industry Appications, IEEE Transactions on vo. 43, issue 5, 007, pp [10] T.D. Dreeben and G.P. Chini Two-dimensiona streaming fows in high-intensity discharge amps, Phys. Fuids, vo. 3, issue 5, 011, p. 14. [11] L. Chhun, P. Maussion, S. Bhose and G. Zissis, Characterization of Acoustic Resonance in a High Pressure Sodium Lamp, IAS IEEE transaction on issue 99, 011. [1] C. Juan, A. Avarez, C. Banco, J.F. Ferrero, J.C. Viera, N. Borde, A. Martin, and G. Zissis, An Acoustic Resonance Band Detection Workbench for HID Lamps, Industry Appications, IEEE Transactions, vo 43, pp , 007. [13] J.O. Hirschfeder, C.F. Curtis and R.B. Bird, Moecuar theory of gases and iquids, New York : Wiey, [14] R.S. Devoto, Transport Properties of ionized monatomic gases, Phys. Fuids, vo. 9, pp , [15] R.S. Devoto, Simpified Expression for the transport properties of ionized monatomic gases, Phys. Fuids, vo. 10, pp , [16] B. Baumann, B. Kost, H. Groninga, and M. Woff, Eigenmode anaysis of photoacoustic sensors via finite eement method, Rev. Sci. Instrum., 77, 006. [17] B. Baumann, M. Woff, B. Kost and H. Groninga, Finite eement cacuation of photoacoustic signas, Appied Optics, vo. 46, pp , 007. [18] S. Epron, "Etude et effet des osciations acoustiques dans es ampes à décharges haute pression", Ph.D Thesis, Département Génie éectrique, Univ. Pau Sabatier, Tououse, [19] J. Lighthi, Acoustic streaming, Journa of Sound and Vibration. vo. 61(3), pp , [0] F. Afshar, "The Theory of Acoustic Resonance an Acoustic Instabiity in HID amps," Leukos, 0(1), pp. 7-38, 008.