## 5.4 Physique de la combustion des nappes de combustible liquides

Un nouveau sujet que je souhaite ouvrir est la combustion des nappes combustibles liquides. En particulier, je souhaite me pencher sur la phase liquide et son couplage avec son environnement. Le sujet des bacs de combustible liquide a été largement étudié depuis les années 50. En effet, beaucoup de caractéristiques de ce type de feux ont été étudiées telle que la hauteur des flammes (Hamins et al., 1996; Delichatsios, 1993), la fréquence d'oscillation des flammes (Cetegen and Ahmed, 1993), le taux de production de suies en fonction du type de combustible (Marquardt et al., 1996), la variation des débits de masse en fonction des caractéristiques thermo-physiques (Modak and Croce, 1977), etc... Toutes ces études se sont cependant concentrées uniquement sur les feux de bac à l'air libre. La question que je souhaite étudier est l'effet du confinement et de la sous-ventilation sur tous ces paramètres. L'enjeu est de comprendre par exemple pourquoi le régime de combustion oscillatoire apparaît dans le cas d'un feu de bac de combustible liquide dans un compartiment mécaniquement ventilé.

Pour schématiser, quand une nappe liquide brûle, une partie du rayonnement issu de la flamme pénètre dans le liquide et réchauffe ce dernier jusqu'à évaporation. Les vapeurs issues de ce processus alimentent la flamme et entretiennent la réaction de combustion. Les questions qui se posent sont nombreuses : quelle fraction du rayonnement de la flamme impacte la surface du liquide ? quel effet a ce rayonnement a-t-il en profondeur ? La couche de combustible étant liquide, des écoulements de convection apparaissent-ils ? Quel est le rôle de la convection dans le transport de la chaleur dans les nappes liquides ? Comment se distribue la chaleur dans la couche de liquide ? Quels sont les effets des différents facteurs caractérisant le liquide comme sa viscosité, sa tension de surface, etc... ? L'objectif ici est de construire un modèle simplifié qui sera implémenté dans les codes de calculs pour ingénieurs et qui permettra de prédire des phénomènes aussi complexes que celui du régime de combustion alterné ou oscillatoire.

Pour étudier ce problème, les outils que je souhaite mettre en œuvre sont principalement des outils expérimentaux basés sur une métrologie existante au sein de l'équipe "feux". En effet, nous utiliserons de la PIV pour étudier les écoulements secondaires dans les liquides, des thermocouples pour évaluer la distribution de température au sein du liquide et des fluxmètres totaux et radiatifs pour estimer la part de rayonnement issu de la flamme et venant impacter la surface du liquide. Pour la construction du modèle théorique et son implémentation dans les codes de calculs, l'étude se fera en collaboration avec Tarek Beji de l'Université de Ghent avec qui des premiers échanges portants sur les mesures de température dans le liquides ont d'ores et déjà été réalisés.
Bibliographie

Abaid, N., Adalsteinsson, D., Agyapong, A., and McLaughlin, R. M. (2004). An internal splash : Levitation of falling spheres in stratified fluids. *Phys. Fluids*, 16(5):1567–1580. 63

Abraham, G. (1967). Jets with negative buoyancy in homogeneous fluid. *Journal of Hydraulic Research*, 5(4):235–248. 27

Abraham, G. and Eysink, W. (1969). Jets issuing into fluid with a density gradient. *Journal of Hydraulic Research*, 7(2):145–175. v, 51, 52

Alias, A. A. and Page, M. A. (2017). Low-Reynolds-number diffusion-driven flow around a horizontal cylinder. *J. Fluid Mech.*, 825:1035–1055. 65

Ansong, J. K., Kyba, P. J., and Sutherland, B. R. (2008). Fountains impinging on a density interface. *Journal of Fluid Mechanics*, 595:115–139. 31

Ardekani, A. M., Doostmohammadi, A., and Desai, N. (2017). Transport of particles, drops, and small organisms in density stratified fluids. *Phys. Rev. Fluids*, 2(10):100503. 63

Ardekani, A. M. and Stocker, R. (2010). Stratlets: Low Reynolds number point-force solutions in a stratified fluid. *Phys. Rev. Lett.*, 105:084502. 63, 66, 67

Baddour, R. and Zhang, H. (2009). Density effect on round turbulent hypersaline fountain. *Journal of Hydraulic Engineering*, 135(1):57–59. iv, 41

Baines, W. and Turner, J. (1969). Turbulent buoyant convection from a source in a confined region. *Journal of Fluid mechanics*, 37(1):51–80. 54

Baines, W., Turner, J., and Campbell, I. (1990). Turbulent fountains in an open chamber. *Journal of Fluid Mechanics*, 212:557–592. iii, 29, 30

Blanchette, F. and Shapiro, A. M. (2012). Drops settling in sharp stratification with and without marangoni effects. *Phys. Fluids*, 24(4):042104. 63

Bloomfield, L. J. and Kerr, R. C. (1998). Turbulent fountains in a stratified fluid. *Journal of Fluid Mechanics*, 358:335–356. iv, 31, 32, 33

Bloomfield, L. J. and Kerr, R. C. (2000). A theoretical model of a turbulent fountain. *Journal of Fluid Mechanics*, 424:197–216. 27

Burridge, H. and Hunt, G. (2012). The rise heights of low-and high-froude-number turbulent axisymmetric fountains. *Journal of fluid mechanics*, 691:392–416. iii, iv, vii, 27, 28, 29, 30, 31, 36, 38

Burridge, H., Mistry, A., and Hunt, G. (2015). The effect of source reynolds number on the rise height of a fountain. *Physics of Fluids*, 27(4):047101. 23

Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M., and Parker, R. (2009). Prolonged residence times for particles settling through stratified miscible fluids in the stokes regime. *Phys. Fluids*, 21(3):031702. 63
Campbell, I. and Turner, J. (1985). Turbulent mixing between fluids with different viscosities. *Nature*, 313(5997):39–42. 35

Candelier, F., Mehaddi, R., and Vauquelin, O. (2013). Note on the method of matched-asymptotic expansions for determining the force acting on a particle. *arXiv:1307.6314* 67

Candelier, F., Mehaddi, R., and Vauquelin, O. (2014). The history force on a small particle in a linearly stratified fluid. *J. Fluid Mech.*, 749:183–200. 66, 69

Candelier, F., Mehlig, B., and Magnaudet, J. (2019). Time-dependent lift and drag on a rigid body in a viscous steady linear flow. *Journal of Fluid Mechanics*, 864:554–595. 73

Carazzo, G., Kaminski, E., and Tait, S. (2008a). On the dynamics of volcanic columns: A comparison of field data with a new model of negatively buoyant jets. *Journal of Volcanology and Geothermal Research*, 178(1):94–103. 51

Carazzo, G., Kaminski, E., and Tait, S. (2008b). On the rise of turbulent plumes: Quantitative effects of variable entrainment for submarine hydrothermal vents, terrestrial and extra-terrestrial explosive volcanism. *Journal of Geophysical Research: Solid Earth*, 113(B9). 51

Carazzo, G., Kaminski, E., and Tait, S. (2010). The rise and fall of turbulent fountains: a new model for improved quantitative predictions. *Journal of fluid mechanics*, 657:265–284. 27

Carlotti, P. and Hunt, G. R. (2005). Analytical solutions for turbulent non-boussinesq plumes. *Journal of Fluid Mechanics*, 538:343–58.

Cetegen, B. M. and Ahmed, T. A. (1993). Experiments on the periodic instability of buoyant plumes and pool fires. *Combustion and flame*, 93(1-2):157–184. 78

Chong, M. S., Soria, J., Perry, A., Chacin, J., Cantwell, B., and Na, Y. (1998). Turbulence structures of wall-bounded shear flows found using dns data. *Journal of Fluid Mechanics*, 357:225–247. 29

Crapper, P. and Baines, W. (1978). Some remarks on non-boussinesq forced plumes. *Atmospheric Environment* (1967), 12(10):1939–1941. 38

De Pietro, M., van Hinsberg, M. A. T., Biferale, L., Clercx, H. J. H., Perlekar, P., and Toschi, F. (2015). Clustering of vertically constrained passive particles in homogeneous isotropic turbulence. *Phys. Rev. E*, 91:053002. 63

Delichatsios, M. (1993). Transition from momentum to buoyancy-controlled turbulent jet diffusion flames and flame height relationships. *Combustion and Flame*, 92(4):349–364. 78

Devenish, B., Rooney, G., and Thomson, D. (2010). Large-eddy simulation of a buoyant plume in uniform and stably stratified environments. *Journal of Fluid Mechanics*, 652:75–103. v, 51, 53

Doostmohammadi, A., Dabiri, S., and Ardekani, A. M. (2014). A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. *J. Fluid Mech.*, 750:5–32. 65

Economidou, M. and Hunt, G. (2009). Density stratified environments: the double-tank method. *Experiments in fluids*, 46(3):453–466. 31

Fan, L.-N. (1967). Turbulent buoyant jets into stratified or flowing ambient fluids. v, 51, 52

Fang, J., Jie, J., Hong-Yong, Y., and Yong-Ming, Z. (2006). Early fire smoke movements and detection in high large volume spaces. *Building and Environment*, 41(11):1482–1493. 46
Fanneløp, T. and Webber, D. (2003). On buoyant plumes rising from area sources in a calm environment. *Journal of Fluid Mechanics*, 497:319-58

Friedman, P., Vadakoot, V., Meyer, W., and Carey, S. (2007). Instability threshold of a negatively buoyant fountain. *Experiments in fluids*, 42(5):751-759. 25

Gray, D. D. and Giorgini, A. (1976). The validity of the Boussinesq approximation for liquids and gases. *Int. J. Heat Mass Trans.*, 19(5):545-551. 65

Guasto, J. S., Rusconi, R., and Stocker, R. (2012). Fluid mechanics of planktonic microorganisms. *Ann. Rev. Fluid Mech.*, 44:373-400. 63

Hamins, A., Konishi, K., Borthwick, P., and Kashiwagi, T. (1996). Global properties of gasous pool fires. In *Symposium (International) on Combustion*, volume 26, pages 1429-1436. Elsevier. 78

Haouari-Harrak, S. (2019). *Contributions À l'étude des ecoulements de fumees dans un bâtiment en situation d'incendie*. PhD thesis, Université de Lorraine. 73

Haouari-Harrak, S., Mehaddi, R., Boulet, P., and Koutaiba, E. (2020). Evaluation of the room smoke filling time for fire plumes: Influence of the room geometry. *Fire and materials*, 44(6):793-803. 55, 56

Haouari-Harrak, S., Mehaddi, R., Boulet, P., Koutaiba, E., Giovannelli, G., and Becker, S. (2019). Virtual origin correction for a fire plume in a room under displacement ventilation regime. *International Journal of Thermal Sciences*, 136:243-253. 54

Heskestad, G. (1984). Engineering relations for fire plumes. *Fire Safety Journal*, 7(1):25-32. 56

Heskestad, G. (2016). Fire plumes, flame height, and air entrainment. In *SFPE handbook of fire protection engineering*, pages 396-428. Springer. 47

Hunt, G. and Kaye, N. (2005). Lazy plumes. *Journal of Fluid Mechanics*, 533:329-58

Hunt, G. and Van den Bremer, T. (2011). Classical plume theory: 1937-2010 and beyond. *IMA journal of applied mathematics*, 76(3):424-448. 43, 58

Jacobson, M. Z. (2005). *Fundamentals of atmospheric modeling*. Cambridge university press. 63

Kaminski, E. and Jaupart, C. (2003). Laminar starting plumes in high-prandtl-number fluids. *Journal of fluid mechanics*, 478:287-298. 43

Karlsson, B. and Quintiere, J. (1999). *Enclosure fire dynamics*. CRC press. 75

Kawagoe, K. (1958). Fire behavior in rooms. *Tech. Rep. 27, Building Research Institute*, 27. 75

Kaye, N. and Hunt, G. (2006). Weak fountains. *Journal of Fluid Mechanics*, 558:319-328. iii, 27, 29, 30, 31

Kaye, N. and Hunt, G. (2007a). Overturning in a filling box. *Journal of Fluid Mechanics*, 576:297-323. 54

Kaye, N. and Hunt, G. (2007b). Smoke filling time for a room due to a small fire: the effect of ceiling height to floor width aspect ratio. *Fire safety journal*, 42(5):329-339. 54

Kerber, S. and Milke, J. A. (2007). Using FDS to simulate smoke layer interface height in a simple atrium. *Fire Technology*, 43(1):45-75. 46

Lamorlette, A., Mehaddi, R., and Vauquelin, O. (2011). Unstable modes of laminar round fountains on inclined wall. *Comptes Rendus Mécanique*, 339(4):250-256. iii, 25, 26
Leelőssy, Á., Molnár, F., Izsák, F., Havasi, Á., Lagzi, I., and Mészáros, R. (2014). Dispersion modeling of air pollutants in the atmosphere : a review. *Centr. Eur. J. of Geosci.*, 6:257-278.
63

Lin, W. and Armfield, S. (2000a). Direct simulation of weak axisymmetric fountains in a homogeneous fluid. *Journal of Fluid Mechanics*, 403:67-88. iii, 22, 25, 29, 30

Lin, W. and Armfield, S. (2000b). Very weak fountains in a homogeneous fluid. *Numerical Heat Transfer: Part A: Applications*, 38(4):377-396. 25

Linden, P. F. (1999). The fluid mechanics of natural ventilation. *Annu. Rev. Fluid Mech.*, 31(1):201-238. 61, 63

Linden, P. F., Lane-Serff, G. F., and Smeed, D. A. (1990). Emptying filling boxes : the fluid mechanics of natural ventilation. *J. Fluid Mech.*, 212:309-335. 61

Lovalenti, P. and Brady, J. (1993). The force on a bubble, drop or particle in arbitrary time-dependent motion at small Reynolds number. *Phys. Fluids*, 5(9):2104-2116. 68, 73

Lupton, J., Delaney, J., Johnson, H., and Tivey, M. (1985). Entrainment and vertical transport of deep-ocean water by buoyant hydrothermal plumes. *Nature*, 316(6029):621-623. 43

Malin, M. (1989). Analysis of turbulent forced plumes into a stable environment. *Applied mathematical modelling*, 13(2):122-126. 53

Maluk, C., Woodrow, M., and Torero, J. L. (2017). The potential of integrating fire safety in modern building design. *Fire Safety Journal*, 88:104-112. 46

Marquardt, M., Mauss, F., Jungfleisch, B., Suntz, R., and Bockhorn, H. (1996). Twenty-sixth symposium (international) on combustion. *The Combustion Institute, Pittsburgh*, pages 2343-2350. 78

Maxey, M. R. and Riley, J. J. (1983). Equation of motion for a small rigid sphere in a nonuniform flow. *Phys. Fluids*, 26:883-889. 64

McCaffrey, B., Quintiere, J., and Harkleroad, M. (1981). Estimating room temperatures and the likelihood of flashover using fire test data correlations. *Fire Technology*, 17(2):98-119. 73

McCaffrey, B. J. (1983). Momentum implications for buoyant diffusion flames. *Combust. Flame*, 52:149-167. 56

Mcdougall, T. (1981). Negatively buoyant vertical jets. *Tellus*, 33(3):313-320. 27

Mehaddi, R., Vauquelin, O., and Candelier, F. (2012). Analytical solutions for turbulent bousinesq fountains in a linearly stratified environment. *J. Fluid Mech.*, 691:487-497. 31

Mehaddi, R., Vauquelin, O., and Candelier, F. (2015a). Experimental non-boussinesq fountains. *Journal of Fluid Mechanics*, 784. iv, 35, 41

Mehaddi, R., Vaux, S., Candelier, F., and Vauquelin, O. (2015b). On the modelling of steady turbulent fountains. *Environmental Fluid Mechanics*, 15(6):1115-1134. 27, 47

Meibohm, J., Candelier, F., Rosen, T., Einarsson, J., Lundell, F., and Mehlig, B. (2016). Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number. *Phys. Rev. Fluids*, 1(8):084203. 67

Mense, M., Pizzo, Y., Prétrel, H., Lallemand, C., and Porterie, B. (2019a). Experimental and numerical study on low-frequency oscillating behaviour of liquid pool fires in a small-scale mechanically-ventilated compartment. *Fire Safety Journal*, 108:102824. 77
Mense, M., Pizzo, Y., Prétrel, H., and Porterie, B. (2019b). Experimental study on low-frequency oscillating behavior in mechanically-ventilated compartment fires. *Journal of Applied Fluid Mechanics*, 12(2 (Special Issue)) :49–58. 77

Michaux, G. and Vauquelin, O. (2008). Solutions for turbulent buoyant plumes rising from circular sources. *Physics of Fluids*, 20(6) :066601. 45, 54, 58

Miyazaki, K., Bedeaux, D., and Avalos, J. B. (1995). Drag on a sphere in slow shear flow. *Journal of Fluid Mechanics*, 296 :373–390. 73

Mizushina, T., Ogino, F., Takeuchi, H., and Ikawa, H. (1982). An experimental study of vertical turbulent jet with negative buoyancy. *Wärme-und Stoffübertragung*, 16(1) :15–21. 27

Modak, A. T. and Croce, P. A. (1977). Plastic pool fires. *Combustion and Flame*, 30 :251–265. 78

Morsi, S. and Alexander, A. (1972). An investigation of particle trajectories in two-phase flow systems. *Journal of Fluid mechanics*, 55(2) :193–208. 63

Morton, B. . (1959). Forced plumes. *Journal of Fluid mechanics*, 5(1) :151–163. 27, 58

Morton, B., Taylor, G. I., and Turner, J. S. (1956). Turbulent gravitational convection from maintained and instantaneous sources. *Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences*, 234(1196) :1–23. 43, 44, 50, 51, 61

Mowbray, D. E. and Rarity, B. S. H. (1967). A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. *J. Fluid Mech.*, 28 :1–16. 65

Naumann, Z. and Schiller, L. (1935). A drag coefficient correlation. *Z. Ver. Deutsch. Ing*, 77(318) :e323. 63

Oseen, C. W. (1910). über die Stokes'sche Formel und über eine verwandte Aufgabe in der Hydrodynamik. *Ark. Mat. Astron. Fysik*, 6 :143–152. 68, 73

Oster, G. (1965). Density gradients. *Scientific American*, 213(2) :70–79. 31

Pantzlaff, L. and Lueptow, R. M. (1999). Transient positively and negatively buoyant turbulent round jets. *Experiments in fluids*, 27(2) :117–125. 27

Philippe, P., Raufaste, C., Kurowski, P., and Petitjeans, P. (2005). Penetration of a negatively buoyant jet in a miscible liquid. *Physics of Fluids*, 17(5) :053601. 22

Pierson, J.-L. and Magnaudet, J. (2018). Inertial settling of a sphere through an interface. part 2. sphere and tail dynamics. *J. Fluid Mech.*, 835 :808–851. 63

Proudman, I. and Pearson, J. R. A. (1957). Expansions at small Reynolds numbers for the flow past a sphere and circular cylinder. *J. Fluid Mech.*, 22(2) :385–400. 68

Ricou, F. P. and Spalding, D. (1961). Measurements of entrainment by axisymmetrical turbulent jets. *Journal of fluid mechanics*, 11(1) :21–32. 45

Rooney, G. and Linden, P. (1996). Similarity considerations for non-boussinesq plumes in an unstratified environment. *Journal of fluid mechanics*, 318 :237–250. 45, 56, 58

Rouïl, L., Tognet, F., Meleux, F., Colette, A., Leroy, G., and Truchot, B. (2021). Dispersion and impact of smoke plumes from industrial fires : the case of lubrizol. *Environnement, Risques & Santé*, 20(2) :126–133. 43
Saffman, P. G. (1965). The lift on a small sphere in a slow shear flow. *J. Fluid Mech.*, 22(2):385-400. 66, 67, 68, 70, 73

Schlichting, H. and Gersten, K. (2003). *Boundary-layer theory*. Springer Science & Business Media. 31

Schmidt, W. (1941). Turbulente ausbreitung eines stromes erhitzter luft. *ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik*, 21(5):265-278. 43

Sneck, H. and Brown, D. (1974). Plume rise from large thermal sources such as dry cooling towers. *Tans. ASME : J. Heat Transfer*, 96:232-238. v, 51, 52

Sozza, A., De Lillo, F., Musacchio, S., and Boffetta, G. (2016). Large-scale confinement and small-scale clustering of floating particles in stratified turbulence. *Phys. Rev. Fluids*, 1(5):052401. 63

Srdić-Mitrović, A. N., Mohamed, N. A., and Fernando, H. J. S. (1999). Gravitational settling of particles through density interfaces. *J. Fluid Mech.*, 381:175-198. 63

Torres, C. R., Hanazaki, H., Ochoa, J., Castillo, J., and Van Woert, M. (2000). Flow past a sphere moving vertically in a stratified diffusive fluid. *J. Fluid Mech.*, 417:211-236. 63

Turner, J. (1966). Jets and plumes with negative or reversing buoyancy. *Journal of Fluid Mechanics*, 26(4):779-792. 27, 31

Turner, J. S. (1979). *Buoyancy effects in fluids*. Cambridge University Press. 63

Van Aartrijk, M. and Clercx, H. J. H. (2010). Vertical dispersion of light inertial particles in stably stratified turbulence: The influence of the basset force. *Phys. Fluids*, 22(1):013301. 63

Van Den Bremer, T. and Hunt, G. (2010). Universal solutions for boussinesq and non-boussinesq plumes. *Journal of fluid mechanics*, 644:165. 58

Vauquelin, O. (2015). Oscillatory behaviour in an emptying-filling box. *J. Fluid Mech.*, 781:712-726. 61

Vauquelin, O., Koutaiba, E., Blanchard, E., and Fromy, P. (2017). The discharge plume parameter $\gamma_d$ and its implications for an emptying-filling box. *J. Fluid Mech.*, 817:171-182. 58

Vaux, S., Mehaddi, R., Vauquelin, O., and Candelier, F. (2019). Upward versus downward non-Boussinesq turbulent fountains. *Journal of Fluid Mechanics*, 867:374-391. iii, 22, 39, 48, 54, 71

Vigne, G., Gutierrez-Montes, C., Cantizano, A., Wegrzynski, W., and Rein, G. (2019). Review and validation of the current smoke plume entrainment models for large-volume buildings. *Fire Technology*, 55(3):789-816. 47

Vinoth, B. and Panigrahi, P. (2014). Characteristics of low reynolds number non-boussinesq fountains from non-circular sources. *Physics of Fluids*, 26(1):014106. 25

Williamson, N., Srinarayana, N., Armfield, S., McBain, G., and Lin, W. (2008). Low-reynolds-number fountain behaviour. *Journal of Fluid Mechanics*, 608:297-317. iii, 22, 23, 24, 25

Woods, A. W., Caulfield, C., and Phillips, J. C. (2003). Blocked natural ventilation: the effect of a source mass flux. *Journal of Fluid Mechanics*, 495:119. 61
Yang, R., Ng, C. S., Chong, K. L., Verzicco, R., and Lohse, D. (2022). Do increased flow rates in displacement ventilation always lead to better results? *Journal of Fluid Mechanics*, 932. iv, 44

Yick, K. Y., Torres, C. R., Peacock, T., and Stocker, R. (2009). Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. *J. Fluid Mech.*, 632:49–68. vi, 63, 65, 69

Zeldovich, Y. B. (1937). The asymptotic laws of freely-ascending convective flows. *Zhur. Eksper. Teor. Fiz*, 7(12):1463–1465. 43

Zhang, J., Mercier, M., and Magnaudet, J. (2017). Wake of a vertically moving sphere in a linearly stratified fluid. *16th Eur. Turbulence Conf., Stockholm, Sweden*. vi, 65, 69

Zukoski, E. E., Kubota, T., and Cetegen, B. (1981). Entrainment in fire plumes. *Fire safety journal*, 3(3):107–121. 56

Zvirin, Y. and Chadwick, R. S. (1975). Settling of an axially symmetric body in a viscous stratified fluid. *Int. J. Multiphase Flow*, 1:743–752. 66