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A theoretical model to predict plume rise in shaft generated by growing compartment fire. (English) Zbl 1209.80025
Summary: A theoretical model for predicting the one-dimensional transient buoyant plume rise in a vertical shaft is developed, with convective heat transfer from hot up-rising flow to the side walls considered. The rising plume is induced by a t-square growing fire in a compartment adjacent to the vertical shaft. The initial plume characteristics at the bottom of shaft nearing the compartment are described using a virtual point source model. The afterward rising of the plume is then solved by considering the conservation law of the mass and energy. Experiments and corresponding CFD simulations are carried out in a 1/8 scale vertical shaft to validate the theoretical model. The measured values are compared with the model proposed in this paper and that of Tanaka. Results show that the Tanaka model somewhat overestimates the up-rising speed of the buoyant flow, while the predictions by the model proposed here agree well with the CFD simulation and measured values.

##### MSC:
 80A20 Heat and mass transfer, heat flow (MSC2010) 76R10 Free convection 76-05 Experimental work for problems pertaining to fluid mechanics
##### Software:
Fire Dynamics Simulator
Full Text:
##### References:
 [1] Markatos, N. C.; Christolis, C.; Argyropoulos, C.: Mathematical modeling of toxic pollutants dispersion from large tank fires and assessment of acute effects for fire fighters, Int. J. Heat mass transfer 52, 4021-4030 (2009) · Zbl 1167.80404 · doi:10.1016/j.ijheatmasstransfer.2009.03.039 [2] Shi, C. L.; Lu, W. Z.; Chow, W. K.; Huo, R.: An investigation on spill plume development and natural filling in large full-scale atrium under retail shop fire, Int. J. Heat mass transfer 50, 513-529 (2007) · Zbl 1112.80314 · doi:10.1016/j.ijheatmasstransfer.2006.07.020 [3] Stavrakakis, G. M.; Markatos, N. C.: Simulation of airflow in one- and two-room enclosures containing a fire source, Int. J. Heat mass transfer 52, 2690-2703 (2009) · Zbl 1167.80367 · doi:10.1016/j.ijheatmasstransfer.2007.10.046 [4] Klote, J. H.; Milke, J. A.: Principles of smoke management, (2002) [5] Chew, M. Y. L.; Liew, P. H.: Smoke movement in atrium buildings, Int. J. Eng. perform.-based fire codes 2, No. 2, 68-76 (2000) [6] Zhang, J. Y.; Lu, W. Z.; Huo, R.; Feng, R.: A new model for determining neutral-plane position in shaft space of a building under fire situation, Build. environ. 43, 1101-1108 (2008) [7] Xiao, G. Q.; Tu, J. Y.; Yeoh, G. H.: Numerical simulation of the migration of hot gases in open vertical shaft, Appl. therm. Eng. 28, 478-487 (2008) [8] E.E. Zukoski, A Review of Flows Driven by Natural Convection in Adiabatic Shafts, NIST-GCR-95-679, National Institute of Standards and Technology, 1995. [9] Lee, J.; Song, D.; Park, D.: A study on the development and application of the E/V shaft cooling system to reduce stack effect in high-rise buildings, Build. environ. 45, No. 2, 311-319 (2010) [10] Cooper, L. Y.: Simulating smoke movement through long vertical shafts in zone-type compartment fire models, Fire safety J. 31, No. 2, 85-99 (1998) [11] Friedman, R.: An international survey of computer models for fire and smoke, J. fire protect. Eng. 4, No. 3, 81-92 (1992) [12] J.B. Cannon, E.E. Zukoski, Turbulent mixing in vertical shafts under conditions applicable to fires in high rise buildings, Technical Fire Report No. 1 to the National Science Foundation, California Institute of Technology, Pasadena, California, USA, 1975. [13] T. Tanaka, T. Fujita, J. Yamaguchi, Investigation into travel time of buoyant fire plume fronts, in: Proceedings of the First International Symposium on Engineering Performance-based Fire Codes, Hong Kong, China, 1998, pp. 220 – 228. [14] Mercier, G. P.; Jaluria, Y.: Fire-induced flow of smoke and hot gases in open vertical enclosures, Exp. therm. Fluid sci. 19, 77-84 (1999) [15] N.L. Benedict, Buoyant flows in vertical channels relating to smoke movement in high-rise building fires, Thesis for the Degree of Doctor of Philosophy, California Institute of Technology, Pasadena, California, USA, 1999. [16] Hu, L. H.; Li, Y. Z.; Huo, R.; Yi, L.; Shi, C. L.; Chow, W. K.: Experimental studies on the rise time of buoyant fire plume fronts induced by pool fires, J. fire sci. 22, No. 1, 69-86 (2004) [17] Heskestad, G.: Fire plumes, SFPE handbook of fire protection engineering, (1995) [18] R. Harrison, Smoke control in atrium buildings: a study of the thermal spill plume, A Thesis for the Master Degree of Engineering in Fire Engineering, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 2004. [19] X.Q. Sun, Y.Z. Li, L. H. Hu, R. Huo, W.K. Chow, N.K. Fong, Gigi C.H. Lui, One-dimensional smoke movement in vertical open shafts at steady state: theoretical prediction and experimental verification, in: 2008 ASME Summer Heat Transfer Conference HT 2008, Jacksonville, Florida, USA, August 10 – 14, 2008. [20] Cianfrini, C.; Corcione, M.; Fontana, D. M.: Laminar free convection from a vertical plate with uniform surface heat flux in chemically reacting systems, Int. J. Heat mass transfer 45, 319-329 (2002) · Zbl 1106.76452 · doi:10.1016/S0017-9310(01)00144-2 [21] Kapoor, K.; Jaluria, Y.: Penetrative flow due to an isothermal vertical wall in a stable two-layer environment generated by a room fire, J. heat mass transfer 39, 3977-3987 (1996) [22] Quintiere, J. G.: Scaling application in fire research, Fire safety J. 15, No. 1, 3-29 (1989) [23] Hu, L. H.; Huo, R.; Li, Y. Z.; Wang, H. B.; Chow, W. K.: Full-scale burning tests on studying smoke temperature and velocity along a corridor, Tunn. undergr. Space technol. 20, No. 3, 223-229 (2005) [24] L.H. Hu, W.K. Chow, R. Huo, Y.Z. Li, H.B. Wang, Comparison of Rise Time of Smoke Plume Front Predicted for High Space by a Field Model with Full-scale Experiments, ASHRAE Transaction, Denver, vol. 111, Part 2, June, 2005, pp.193 – 201. [25] Argyropoulos, C. D.; Sideris, G. M.; Christolis, M. N.; Nivolianitou, Z.; Markatos, N. C.: Modelling pollutants dispersion and plume rise from large hydrocarbon tank fires in neutrally stratified atmosphere, Atmos. environ. 44, 803-813 (2010) [26] Markatos, N. C.; Malin, M. R.; Cox, G.: Mathematical modelling of buoyancy-induced smoke flow in enclosures, Int. J. Heat mass transfer 25, No. 1, 63-75 (1982) · Zbl 0476.76093 · doi:10.1016/0017-9310(82)90235-6 [27] G. Cox, S. Kumar, N.C. Markatos, Some field model validation studies, in: First International Symposium on Fire Safety Science, Gaithersburg, Maryland, October 1985. [28] Papakonstantinou, K. A.; Kiranoudis, C. T.; Markatos, N. C.: Numerical simulation of air flow field in single-sided ventilated buildings, Energy build. 33, 41-48 (2000) [29] Hu, L. H.; Tang, F.; Yang, D.; Liu, S.; Huo, R.: Longitudinal distributions of CO concentration and difference with temperature field in a tunnel fire smoke flow, Int. J. Heat mass transfer 53, 2844-2855 (2010) · Zbl 1194.80113 · doi:10.1016/j.ijheatmasstransfer.2010.02.013 [30] Hu, L. H.; Huo, R.; Yang, D.: Large eddy simulation of buoyancy driven plume dispersion in an urban street canyon under perpendicular wind flow, J. hazard. Mater. 166, No. 1, 394-406 (2009) [31] K. McGrattan, Fire Dynamics Simulator (Version 5) User’s Guide, National Institute of Standards and Technology, 2009. [32] K. McGrattan, Fire Dynamics Simulator (Version 5) Technical Reference Guide, National Institute of Standards and Technology, 2009. [33] Smagorinsky, J.: General circulation experiments with primitive equations – I, the basic experiment, Mon. weather rev. 91, 99-105 (1963) [34] Lax, P. D.: Hyperbolic difference equations: a review of the Courant – Friedrichs – lewy paper in light of recent developments, IBM J. Res. dev. 11, 235-238 (1967) · Zbl 0233.65051 · doi:10.1147/rd.112.0235 [35] Zhang, W.; Hamer, A.; Klassen, M.; Carpenter, D.; Roby, R.: Turbulence statistics in a fire room model by large eddy simulation, Fire safety J. 37, 721-752 (2002) [36] Wen, J. X.; Kang, K.; Donchev, T.; Karwatzki, J. M.: Validation of FDS for the prediction of medium-scale pool fires, Fire safety J. 42, 127-138 (2007) [37] P. Friday, F.W. Mowrer, Comparison of FDS Model Predictions with FM/SNL Fire Test Data, NIST GCR 01-810, National Institute of Standards and Technology, Gaithersburg, Maryland, April 2001. [38] Yang, D.; Hu, L. H.; Jiang, Y. Q.; Huo, R.; Zhu, S.; Li, J.: Comparison of FDS predictions by different combustion models with measured data for enclosure fires, Fire safety J. 45, 298-313 (2010) [39] Jiang, Y.; Chen, Q. Y.: Buoyancy-driven single-sided natural ventilation in building with large openings, Int. J. Heat mass transfer 46, 973-988 (2003) [40] Courant, R.; Friedrichs, K.; Lewy, H.: On partial difference equations of mathematical physics, IBM J. Res. dev. 11, 215-234 (1967) · Zbl 0145.40402 · doi:10.1147/rd.112.0215
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