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CHAPTER 2 Transport Phenomena That Affect Heat Transfer in Fully CHAPTER 2 Transport phenomena that affect heat transfer in fully turbulent fi res S.R. Tieszen1 & L.A. Gritzo2 1Fire and Aerosol Sciences Department, Sandia National Laboratories, Albuquerque, NM, USA. 2FM Global, Norwood, MA, USA. Abstract Transport phenomena within large (i.e. fully turbulent) fi res comprise the foundational mechanisms for several principal fi re hazards including smoke production and heat transfer to engulfed and adjacent objects. These phenomena are becoming suffi ciently well known that quantitative descriptions are foreseeable. In this chapter, the authors present the current state of knowledge and emphasize unknown phenomena as well as areas in need of additional research to enable deep understanding and quantitative prediction of hazards posed by these fi res. The tightly coupled, nonlinear transport phenomena of large fi res, as opposed to chemi- cally reacting fl ows in engineered systems which have been more extensively studied by the general combustion community, are discussed. These phenomena include (1) the large length and timescale range of transport phenomena with an emphasis on the challenges of computing and experimentation; (2) fl uid dynamics including turbulence and the effect of buoyancy over the length scale range including the coupling between scalar and momentum fi elds; and (3) radiative properties and transport including local and global characterization of the radiative emission source term. The discussion is supported by physical considerations based on analy- sis of data and established models. The results provide a basis to understand physical transport phenomena in large fi res and lay the foundation for the understanding needed to predict fi re hazards. 1 Introduction Fire is a rich multiphysics phenomenon having a signifi cant impact on mankind from the earliest times to the present. Transport phenomena within a fi re are equally rich and highly nonlinear. In order to have a coherent presentation of the transport phenomena it is useful to have both an application focus and a well defi ned scope. In this chapter, the focus is on heat transfer within a large fi re. As such, the connection between advective and diffusive transport phenomena, and convection and radiation heat transfer, within the fi re will be emphasized. WIT Transactions on State of the Art in Science and Engineering, Vol 31, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/978-1-84564-160-3/02 26 Transport Phenomena in Fires By necessity, the scope of this chapter will be limited. It can be readily argued that hydro- carbon chemistry is as rich and nonlinear as the transport processes themselves. However, pri- oritizing here on the basis of application focus, chemistry will not be discussed except with respect to simplifi ed characteristic time-scale arguments for comparison with transport phenom- ena. Similarly, the chapter will not touch on the very complex topic of fuel decomposition and/ or vaporization from liquid or solid fuels. These are very complex multiphysics processes in themselves in which both chemistry and transport are quite important. It will be assumed in this chapter that the fuel has vaporized under the incident radiative and convective loads. Further, the chapter will focus on transport within a fi re. Fire induced fl ow, particularly in complex struc- tures, is a rich topic in its own right, but is beyond the scope of this chapter. Finally, the chapter will largely focus on large scale fi res, where the laminar to turbulent transition distance is a small fraction of the fi re diameter. All three forms of heat transfer − conduction, convection, and radiation − are present in fi res. In general, for fully turbulent fi res, their importance is in the reverse order, with radiation being the most important and conduction the least important, subject to chemical considerations that might increase the importance of the latter, e.g. the fl ame phenomenology considered in Chapter 9 of this book by DesJardin, Shihn, and Carrara. In large fi res, typical time-mean values of the radiative heat fl ux are of the order of 150 kW/m2 but can range over about an order of magnitude centered on this value. Much of the radiation is from soot with secondary radiation from the gas species in the fl ame [1]. Convection is secondary, but not necessarily second order. Typical time-mean temperatures in a large fi re are of the order of 1300 K (compared to peak fl ame temperatures of 2300 K for many hydrocarbon fuels in air). Convection ranges from free to forced convection depending on local fl ow velocities and temperature differences. Convection coeffi cients in air typically range from 5 to 500 W/m2 K [2]. For a mean temperature difference between the fi re and cold objects of 1000 K (1300 K fi re to 300 K object), convective heat fl uxes will be of the order 5 to 500 kW/m2 for a wide range of heat transfer applications. At the high end, convection can equal radiation and at the low end, it can be of second order importance. Note that the sign of the two modes can, and often will be, different. Convection can cool while radiation is heating, and vice versa. The bal- ance depends on local environmental conditions for convection and more global conditions within the fi re for radiation. In most situations convection is of secondary importance. Within the heat transfer focus and scope outlined, this chapter is structured to fi rst discuss the large length and timescale range of transport phenomena with an emphasis on the challenges of computing and experimentation. Next the effect of buoyancy over the length scale range, includ- ing the coupling between scalar and momentum fi elds, will be addressed. Finally, issues that couple the fl ow fi eld to radiative transport including local and global characterization of the emission source term will be discussed. The future of transport research will be touched on to conclude this chapter. 2 Length and time scales within a fi re 2.1 Overview The challenges associated with understanding transport in turbulent, reacting fl ows are signifi - cant. Fire is an exquisitely complex chemical reaction problem, wrapped in a turbulent, buoyant plume fl ow problem, wrapped inside a participating media radiation heat transfer problem. The time and length scales in fi res are shown in Fig. 1. For large fi res, the primary coupling between (1) WIT Transactions on State of the Art in Science and Engineering, Vol 31, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Heat Transfer in Fully Turbulent Fires 27 Engineering Scale of Interest 10 3 0 10 Heat Transfer in Solids Turbulent& Fuels Transport of Radiative Sources& Convective Products Convection 10 -3 Soot Flames 10 -6 Soot Radiation Time Scale, seconds Diffusive Transport -9 Soot Growth 10 diation Chemical Kinetics Chemical Molecular Ra Molecular Transport 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 2 Length Scale, meters Figure 1: Physics coupling in fi res. the thermal radiation driving fuel vaporization and (2) the turbulent reacting fl ow which pro- duces the high temperature soot (that creates the thermal radiation) can span up to 12 orders of magnitude in length scale. The smallest scales in turbulent sooty fi res of direct interest are those that contribute to thermal radiation, since radiative transport couples this energy back into larger length scales and to fuel pyrolysis/vaporization. The smallest scale is determined by the electronic states of carbon atoms within soot particles O(nm) as these affect soot optical properties [3]. Soot grows from molecular length-scales O(nm) to O(100 nm) in large fi res [4, 5]. Continuum approxima- tions start at length scales of O(100s nm) depending on temperature at ambient pressure [6]. Hence, the nucleation and much of the early growth of soot is a heterogeneous, noncontinuum, process. The large end of the length scale range depends on the application. For laboratory experiments, fi re sizes range from O(cm) to O(m); for building fi res from O(m) to O(10s m); and for forest fi res O(0.1 km) to O(kms). Another consideration in determining the largest length scale of interest is whether the primary interest is within the fi re itself, or in the fi re-induced fl ow which can exceed fi re length scales by several orders of magnitude. The length scale range from nanometers to kilo- meters is 12 orders of magnitude. The time scales involved depend on the length scales and process rates. The shortest timescales relevant to fi re applications in a theoretical sense are determined by the transit time associated with thermal radiation at the speed of light. However, as discussed in Chapter 7 of this book by Modest, the physics of the interaction between radiation transport and momentum/scalar transport is through radiation properties, not radiation transport itself. These properties vary only over transport times- cales of order milliseconds, rather than nanosecond photon transport timescales. Transient times- cales associated with photon transport are therefore typically ignored. Similarly, chemical kinetic (typically high-temperature radical) timescales of order nano- seconds affect heat release within fl ame sheets. For example, for high temperature radicals WIT Transactions on State of the Art in Science and Engineering, Vol 31, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 28 Transport Phenomena in Fires with intermolecular spacings of the order of O(100s nm), molecular velocities at high tem- peratures of the order of 103 m/s, with probabilities of bonding of the order of 10%, have timescales of order nanoseconds [6]. It is often assumed that these very fast timescales reach some statistical equilibrium and can be ignored with good approximation.
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