CHAPTER 2 Transport phenomena that affect heat transfer … · CHAPTER 2 Transport phenomena that affect heat transfer in fully turbulent ﬁ res S.R. Tieszen 1 & L.A. Gritzo2 1Fire

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.

www.witpress.com, ISSN 1755-8336 (on-line)

© 2008 WIT PressWIT Transactions on State of the Art in Science and Engineering, Vol 31,

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)



Heat Transfer in Fully Turbulent Fires 27

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

Figure 1: Physics coupling in fi res.

Engineering Scale of Interest

Heat T

ransfe

r in

Solids

& F

uels

Flames

Che

mic

al K

inet

ics

Molecular Transport

Diffusive Transport

Soot

Products Convection

Molecular Radiation

Soot Radiation

Soot

Gro

wth

10 -10 10 210 -8 10 -6 10 -4 10 -2 10 0

Length Scale, meters

Tim

e S

cale

, sec

onds

10 -12

10 -9

10 -6

10 -3

10 0

10 3

Turbulent Transport of

Radiative & Convective

Sources




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. There are a spec-trum of chemical kinetic times from nanosecond to tens to hundreds of microseconds that refl ect the interaction of noncontinuum molecular transport and chemical bond rearrangement. Even at ambient temperature and pressure, molecular velocities are typically of the order of 500 m/s [6].

While molecular velocities are high, continuum velocities on the other hand are quite low, even in large fi res. They range from O(0.1 cm/s) to O(cm/s) at the fuel source [7] up to O(10s m/s) at the top of a large O(10 m base) fi re [8]. Hence continuum transport timescales typically range from milliseconds to tens of seconds, depending on the length scales.

The large end of the timescale scale range depends on the application being considered. Under-ground mine fi res in a coal seam can burn for decades, O(108 s). Large forest fi res can last for days, O(105 s). Typical large industrial fi res last for hours, O(104 s).

2.2 Time and length scale range

The shaded bands in Fig. 1 are obtained from partially nondimensionalizing the Navier−Stokes transport equations, which (in addition to the radiative transport equation) describe the dominant transport mechanisms in a fi re. The fundamental continuum equations are expressed in terms of length and time scale gradients. The solution of the fundamental equations is the integration of these gradient based terms over the range of temporal and spatial scales determined by the physi-cal parameters relevant for fi res. By plotting the time and length scales for transport terms in the momentum equations for parameter values that occur in large fi res, a visual, heuristic context is provided.

The Navier−Stokes equations [9] are:

( )( ) .

uuu P g

t

r r s r∂ + ∇ = −∇ + ∇ +∂

� �� ◊ ◊

(1)

For the purpose of nondimensionalization, the following reference values are defi ned:

ref ref ref ref

refref ref ref

ˆ ˆˆ ˆ, , , ,

ˆˆ ˆˆ, , , .

u Pu P

u P

x t gx L t g

L g

r mr m

r r m

t

∞= = = =

−

= ∇ = ∇ = =

��

� ��

(2)

The reference values can be considered as local fi re plume values where tref comparisons are being made at Lref length scales. These reference values provide the coordinate axes in Fig. 1. Substituting the reference values but leaving each term as a rate, i.e. unit of 1/time, gives:

ref

ref ref ref2

ref ref ref ref ref ref

ref ref

ref ref

ˆˆ1 ( ) ˆ ˆ ˆˆ ˆ ˆ ˆ[ ( )] [ ]ˆ

( ) ˆˆ[ ].

u Puuu P

t L u L L

gg

u

mrr s

t r rr r

rr

∞

∂ + ∇ = − ∇ + ∇ ∂ −

−

� ��

�

◊ ◊

(3)




The quantities in the square brackets are assumed to be of order unity due to the nondimension-alization and the relative contribution of each term is from the reference values in front of the brackets. Comparing terms gives the following time-scale/length-scale relations:

v

t t

2ref ref ref ref

ref ref

1 1Advection: ~ Diffusion: ~ .L L

u

(4)

Using the advective time scale defi nition gives:

rt

r r∞

−

1/ 21/ 2ref

ref refref ref

Buoyancy: ~ .( )

Lg

(5)

Note that the same time-scale defi nition for buoyancy comes from a similar partial nondimensional-ization of the vorticity transport equations (curl of the Navier−Stokes equations, see Najm et al. [10] for particular formulation) if the following additional reference scales are defi ned:

w t w r r

r r∞= ∇ = ∇

−� � ref

refref

ˆˆ ˆ, .( )

L

(6)

The result is

2

ref2

ref refref

ref ref ref ref ref3

ref refref ref ref ref

ˆ1 ˆ ˆ ˆˆ ˆ ˆˆ ˆˆ( ) ( ) ( )ˆ

ˆ ˆˆ( ) ( )ˆ ˆ ˆˆ( ) .ˆˆ

uu u u

t L

u g Dug

L DtL

ww w w

tt

m r r r rrs

r rr r t∞ ∞

∂ + ∇ + ∇ − ∇ ∂ − −∇ = ∇ × ∇ + × −

� � � ��

��

◊ ◊ ◊

◊

(7)

The last two terms are, respectively, the gravitational and baroclinic generation of vorticity. The gravitational generation corresponds to the curl of the buoyancy term in the Navier−Stokes equa-tions. The baroclinic part results from density gradients interacting with local acceleration fi elds. Fires are most strongly infl uenced by buoyancy but near the fuel source, strong fl ow acceleration and steep density gradients can produce signifi cant baroclinic generation [11].

Comparing the scaling terms for advection, diffusion and buoyancy, it can be seen that they have different length-scale dependencies. Thus, each term dominates at a different length scale as shown in Fig. 2. At small scales, diffusion is dominant because of the high molecular velocities relative to the bulk gas velocities. Representative values for viscous diffusion in air at 300 and 2300 K are shown in Fig. 2. Random direction, molecular-walk processes which defi ne diffusion are ineffi cient at larger length scales and bulk advection becomes dominant. At still larger scales, buoyancy dominates.

Since large fi res represent turbulent-mixing-limited combustion phenomena which have a spectrum of length-scales contained within the broader length-scale spectrum of radiation trans-port (from noncontinuum soot emission to absorption at global application scales), both fl uid transport and radiative transport contribute in overlapping length scale regimes. In general, all length scales play a role in this coupled multiphysics/multilength scale problem. Therefore, while one process may dominate at a given length scale, it cannot be said that any one of these terms dominates the entire coupled process over all length scales.

The advection to diffusion ratio is the Reynolds number. In fl ames with fast chemistry, (Da >> 1) the balance of these processes defi nes the width of the diffusion fl ame as a function of the




imposed velocity gradient across it. A two order of magnitude increase in imposed velocity will decrease the fl ame thickness one order of magnitude until fi nite rate chemistry results in extinc-tion. Flame widths are typically O(mm) depending on the imposed strain. Above centimeter length scales, advection and buoyancy dominate transport processes.

All the transport physics normally associated with low-Mach number fl ows are present in a fi re. For example, transport of momentum results in a turbulent cascade due to the nonlinear advection term in eqn (1) just like all other fl ows. Fires are also strongly affected by the buoyant source term.

The characterization of the dynamic effects of the buoyant source term has received less atten-tion in the fl uid mechanics community than the turbulence generating nonlinear advection term. In eqn (1), buoyancy is a linear source term for linear momentum. In eqn (7), gravitationally produced buoyancy is a linear source term for vorticity. Equations (1) and (7) are not indepen-dent. Linear momentum generation due to buoyancy is achieved through vorticity generation as will be discussed later in this chapter.

Figure 2 shows two levels of the normalized density difference, (∆r/r), of 3 and 7. The fi rst is roughly representative of the long-time average centerline temperature (~1300 K) difference with ambient (~300 K); this gradient will exist over large length-scales in fi res since this tem-perature difference is relatively constant over large portions of the fi re [12]. The second level is related to the adiabatic fl ame temperature (~2300 K) and is an upper bound that exists only at small scales.

The buoyant time scale is related to the reciprocal of the Brunt−Väisälä frequency [13]. It can be seen in Fig. 2, for moderate velocities typical of fi res, O(1−3 m/s), and a scaled density

Figure 2: Time and length scales in fi res.




difference of 3, that advection is faster, i.e. shorter time scale at a given length scale, than buoy-ancy up to O(10 cm) length scales. At length scales larger than O(10 cm), buoyant time scales are shorter than advection. Experimentally, it is found that fi res become transitionally turbulent for O(10 cm) base diameters and are fully turbulent at O(1−3 m) (see Drysdale [14] for a discussion and references therein), consistent with the view that buoyancy expresses itself as rotational motion whose instability induces turbulent motion. The ratio of the advective time scale to the buoyant time scale is the Richardson number.

For fi res, as chemically reacting fl ows, the ratio of fl uid transport time scales to chemical and heat transfer time scales is important. Chemical time scales are dependent on temperature, com-position, and specifi c reaction metrics (i.e. activation temperature and preexponential factors). For a given chemical time scale, comparison with the transport time scale in Fig. 2 establishes a Dam-kohler number, Da. Comparison can be made to diffusive time scales or advective time scales.

In general, the turbulence intensities in the small-length-scale spectrum in fi res are low com-pared to jet fl ames in combustors [15] and have the appearance of wrinkled fl ame sheets [16]. However, long chemical times may result either from low temperatures or off-stoichiometric com-positions. These conditions possibly occur in two areas in large fi res. (1) In the oxygen-starved vapor dome just above the fuel source, measurements [17] indicate temperatures are of the order of 1000 K. At these conditions, kinetic calculations indicate that pyrolysis reactions can occur but are fairly slow, of the order of tenths of seconds [16]. With advection velocities of O(1 m/s) to O(10 m/s) and vapor dome heights of O(m) for large fi res, signifi cant pyrolysis may occur. (2) The large rolling structures at the edges of large fi res visually appear to end up fi lled with smoke (i.e. rela-tively cold soot on the air side of the fl ame zones), suggesting that some form of quenching has occurred that does not appear to be due to high turbulence levels. Oxygen depletion of fuel rich eddies, perhaps followed by radiative cooling, is a more reasonable hypothesis [16].

While heat transfer to fuels/objects within a fi re is primarily radiative and convective, very often the internal heat transfer of the fuel/objects is limited by conduction. Figure 2 shows ther-mal diffusivities for a good heat conductor, aluminum, O(80 mm2/s), and a poor heat conductor, insulation O(0.3 mm2/s). From an order of magnitude perspective, conduction timescales in sol-ids are not all that different from diffusion times in gases. Both are diffusion processes which are increasingly slow compared to advection processes as the length scale is increased. The ratio of advective to gas-phase diffusive time scales is the Reynolds number, which is O(104−106) for large fi res. At large length scales, a similar disparity exists between convective heating of an object and internal conduction within the object. Due to this convective/conductive disparity, the timescale range from shortest to longest is actually longer than the length scale range in fi res by several orders of magnitude. These very large spans in both length and time scales present chal-lenges to numerical simulation of large fi res.

2.3 Implication for numerical simulation

The largest fi re simulations run to date are of the order of millions [18] to 10s of millions of nodes [19]. Using a simple uniform-spacing scaling rule requires 10 nodes per order of magni-tude of resolved length scale. For three dimensions, this means O(103) times the existing comput-ing power for every order of magnitude of newly resolved length scale as shown in Fig. 3.

Further, an additional factor of 10 increase in processor speed or number of processors is required to capture the shorter time scales associated with the incrementally resolved length scales if the computations are to be done in the advective/buoyancy controlled regime as shown in Fig. 3. In the diffusion controlled regime, where doubling the length scale quadruples the time scale requirements, capturing the time scales requires a factor of 100 increase for every




order of magnitude resolved. Further, as the scales resolved get smaller, the number of species that participate at the short time scales increases, resulting in the need for more transport equa-tions. Therefore, with every order of magnitude of increased resolution, the computing power of the machine needs to be 10,000 to 100,000 times as powerful.

With massively parallel computing, involving O(103−105) processors, it can reasonably be expected that within the next decade an additional single order of magnitude of length scales will be resolved (i.e. billion node fi re calculations). To fully simulate a problem with 12 orders of magnitude in length scale, given that we can reliably simulate 3 orders of magnitude in length scale with machines expected to be built in the near future, the computer processing power would need to be at least 10(4 per order of magnitude × 9 orders needing resolution) or 1036 times the processing power of the world’s largest machines now coming online.

Assuming processing power doubles every 18 months, or roughly a factor of a hundred per decade, it will take almost 18 decades to acquire this kind of computing power.

The example given is for the largest fi re. For smaller laboratory scale fl ames, having 6 total orders of magnitude in length scale, with 3 unresolved, the machines need to be a more modest 10(4−5 orders per order of magnitude × 3 orders of magnitude) more powerful. We could see computing power reach these levels in the next 60−80 years if current trends in the rate of increase in processing power continue.

The above discussion does not imply that numerical simulation is not useful. Quite the oppo-site, it is an extremely valuable complement to experimentation for obtaining both engineering and scientifi c insight. However, due to the extremely large range of length and time scales involved in fi res, numerical simulation’s principal strength is not in its physics content. The strength of numerical simulation is in its diagnostics. All physics variables at all points in space and time are accessible. Correlations in both space and time are available at resolved scales, as well as direct insight into transport dynamics from transient visualization.

910 cells10 4 steps

10 12 cells10 5 steps

Tim

e Sc

ale

(sec

)

10 4

10 2

10 0

10 -2

10 -4

10 -6

10 -8

10 -10

10 -12

Length Scale (meters)10 -4 10 -2 10 010 -610 -810 -10 10 2

10 6 cells10 3 steps

Figure 3: Computational limitations.




In contrast, the strength of experimentation is in its physics content. For fi res that have appli-cation-relevant geometries, initial conditions, and boundary conditions, the experiment contains true physics down to subatomic scales. The relative weakness of experiments is in the diagnos-tics. Unlike numerical simulation, experimental diagnostics are very hard to create. The amount of data recorded from a typical fi re experiment is a vanishingly small fraction of the physics content present, and more often than not, fundamental transport variables cannot be measured directly but must be indirectly inferred. Furthermore, the presence of extensive intrusive diag-nostics can have a signifi cant effect on the fi re physics by introducing additional heat transfer modes, and fl uid mixing.

Thus, numerical simulation and experimentation directly complement each other. Where one is relatively weak, the other is relatively strong. For fi res, experimentation is the full truth par-tially exposed, while simulation is the partial truth fully exposed. Using both in combination is usually the fastest way to gain insight into either physics or engineering applications. The goal of either scientifi c or engineering simulation is typically to make a prediction. Engineering and science simulation use the same tools and approaches but differ on the acceptance standards for the word ‘predictive.’

It can be argued that ‘predictive’ capability already exists in the engineering sense of the term. Evidence for this argument is found in the rapid growth of the use of CFD-based numerical simulations for fi re from early efforts in the 1980s to the present [20]. However, predictive in the scientifi c sense of the term will not be achieved until all scales are resolvable by integration of discrete approximations, or closed form solutions are found. Chapters 1, 3, 7, and, 9 in this book by Nilsson, et al., Smith et al., Modest, and DesJardin et al., respectively, deal specifi cally with numerical simulation in fi res.

2.4 Implications for modeling

The physics in Fig. 1 is continuous across length and time scales. However, it is clear from the discussion above that not all length and time scales can be resolved by solution of the discretized conservation equations. The range must be segmented into three discrete parts. Figure 4 pro-vides a useful visualization of what processes can be captured in a given length scale range. The graph can be divided into three length-scale regimes using two length-scale cutoffs. (For example, imagine vertical lines at 10 cm and 10 m in Fig. 4, capturing two orders of magnitude). Above the larger cutoffs are length scales too large to be captured and these are represented by boundary conditions in a simulation. Below the smaller cutoffs are length scales that have to be modeled and these are represented as source or nonlinear advection terms in the transport equa-tions. Between the boundary conditions and the source terms is the length scale range in which the transport equations are solved by discrete approximation. Implicit in the length scale cutoffs are time scale cutoffs corresponding to the time scales of the transport processes at the cutoff length scales.

This splitting of the time and length scale spectrum into three regimes − boundary conditions, resolution by integration of partial differential equations, and modeling − is permitted mathemat-ically by pre-fi ltering the partial differential conservation (i.e. mass, momentum, and energy) equations. Figure 4 shows graphically that the fi ltering process has separated the time and space regime into discrete parts with the large part of the regime (lower left) being modeled, while the upper right part of the regime is being solved by solution of discrete approximations to the trans-port equations. Boundary conditions are applied at the right boundary of the image (i.e. at all time scales at the largest length scale), and notionally initial conditions at the bottom boundary (i.e. all length scales at the initial, or shortest time scale).




Filtering can be done explicitly in space or in time. As Fig. 4 shows, whichever coordinate is taken there is an implicit fi lter in the other. Explicit spatial fi lters have implicit temporal fi lters (e.g. over the time step which is linked by the Courant number to the spatial fi lter). Similarly, explicit temporal fi lters have implicit spatial fi lters.

Regardless of the fi lter chosen, the necessity of splitting the problem in this manner creates an irreversible loss of information, perhaps best understood in the context of the three processes that occur at the fi lter scale at every time step and discrete element in the solution. Information is passed from the solution of the fi ltered partial differential equations to the model of the high spatial and temporal frequency physics that is unresolved. This model is often called a subgrid model or submodel, but should technically be referred to as a subfi lter model. Based on the infor-mation passed from the partial differential equation solution, the subfi lter model (by various strategies) estimates the evolution of the process within the spatial and temporal domain of the fi lter. After this evolution step, the model values are averaged and used to pass mean information up to the resolved solution to close either source terms or unresolved advective terms.

The most serious effect of this necessary splitting procedure is the loss of information in the down-scale pass from the resolved solution to the subfi lter model of the high spatial and tem-poral frequency physics. The subfi lter model must use the information from the resolved solu-tion as initial and boundary conditions for the spatial and temporal domain within the fi lter. Because the resolved solution is at the limit of its resolution, only mean values can be passed unless additional transport equations are solved. Typically a higher moment (e.g. variance equation) and perhaps a time scale for each physics are passed down. The mean, variance and a time scale are very little information to base initial and boundary condition information on for a subfi lter problem that in itself may contain as many as nine orders of magnitude in length scale. Hence this downscale pass is a ‘one to many’ transfer. It is in this downscale information pass that information is irreversibly lost.

Tim

e Sc

ale

(sec

)

10 4

10 2

10 0

10-2

10 -4

10 -6

10 -8

10 -10

10 -12

Length Scale (meters)10 -4 10 -2 10010-610 -810 -10 10 2

Numerical Solution

τ D( ) 1.5⁄=( )

Slowest mode10m pool fire

Resolved Turbulence Timescales~2 sec

ResolvedLarge Eddies

Time

Gri

dR

eso

luti

on

Minimum filtering to prevent alias-ing of high temporal and spatial frequencies onto lower (resolved) frequencies.

Step

Figure 4: Explicit fi ltering separates modeling from numerics.




The consequence of this loss is that no matter how accurate a subfi lter model is, without fully resolved initial and boundary conditions, the mean value of the evolved process variable will contain uncertainty, the magnitude of which depends on how well the process correlates with the averaged initial and boundary conditions. For most highly nonlinear processes, the mean output is not necessarily highly correlated with the mean input.

Consider the following example. Given that transport physics is well understood in a theoreti-cal sense, it is conceivable that the subfi lter domain could be solved to arbitrary accuracy using partial differential equations, assuming the initial and boundary conditions are known. For such a situation, there would be no ‘modeling error’ in that the physics in the subfi lter domain can be resolved. In this case, all the uncertainty would come from ‘errors’ in applying mean (and per-haps variance) values to what would otherwise be spatially and temporally rich initial and bound-ary conditions. This example is theoretical due to the problems in solving the partial differential equations with high spatial and temporal frequency, or it would have been done without using fi ltering and incurring the errors associated with the ‘one to many’ downscale pass.

Traditional modeling approaches seek to fi nd a correlating variable that can be resolved, and tie the modeled process to that correlating variable. In this manner, the model will have mini-mized the output uncertainty within the context of the information it is being passed. Statistical methods are typically the tools of choice for modelers because statistical tools are well suited to fi nd correlations.

The accuracy of this approach is limited by how well the subfi lter process correlates with resolved variables. Subfi lter processes that are not well correlated with resolved variables often arise because important high frequency content ‘evolves’ in a weakly correlated way with the overall fl ow fi eld. For situations such as these, either the grid resolution must be increased until the resolved fi eld is better correlated with the subfi lter model, or it must be modeled with a sub-fi lter model that evolves the high frequency content.

The only part of the process which does not introduce any information degradation is the upscale pass of the mean value of the subfi lter process to the resolved partial differential equa-tion, either as a source term or a nonlinear unresolved advection term. This upscale pass is of the ‘many to one’ type and is unique. Much emphasis is placed within the mathematically oriented community to ensure that fi ltered equations are used to clearly defi ne the requirements of this upscale pass so that part of the process is free from errors.

With the information from the subfi lter processes, the resolved fi eld is advanced a time step and the fi eld variables updated. The uncertainties in the unresolved source or nonlinear advection terms are then propagated by the equations as the information for the next downscale pass is generated. The process repeats itself as the solution to the resolved equations evolves.

In this manner, the fi lter and the model are linked. There are no universal models except in regimes where the process is independent of the fi lter scale. Arguments are often made for clos-ing the equations in the ‘inertial’ range of turbulence, at length scales smaller than the production range but larger than the dissipation range. This argument makes the assumption that there is a broad spatial distribution between turbulence production and its dissipation. For large fi res, the argument is relatively weak.

As will be discussed later in this chapter, vorticity production occurs across a broad length scale spectrum because density gradients exist across broad length scale spectrums. Therefore the separation of production and dissipation present in shear fl ows is not present in buoyant fl ows. Further, even though the length scales in large fi res are large, the Reynolds numbers are relatively moderate, O(104−106), because the velocities are relatively low.

Note that heat transfer aspects are particularly impacted by modeling. A large fraction of the information content involved in heat transfer is tied up in correlation-based engineering subfi lter




models. For large fi res, Fig. 4 shows that all combustion processes are of higher spatial and tem-poral frequency than can be grid-resolved for practical problems for the foreseeable future. All the soot generation and spatial overlap between soot and high temperature gas fi elds is modeled. Thus the transport terms in the radiation transfer equation have a very high basis in modeling, or ‘mod-eled content’. Similarly for convection, the highest frequency turbulent eddies are created in the near-wall boundary layer region of objects. Ultimately, transport is conductive in the near wall region. None of this physics can be resolved for large fi res with foreseeable technology. Because of the high reliance on modeled physics, the engineering accuracy of heat transfer predictions is strongly dependent on engineering models.

The basic strategy for engineering simulation of fi re for the last couple of decades has been to simulate the fl uid transport at large scales and model the higher spatial and temporal frequency physics. While there is no fundamental reason this approach cannot be altered, it can be expected that as machines become larger, modeling will no longer be necessary for transport physics at length scales below those just resolvable. Figure 5 provides a model taxonomy. Using this tax-onomy, the fi rst models that will be replaced will be the meso-scale mixing models, followed by models for diffusional transport processes, and fi nally, when machines are large enough, by molecular transport and chemical processes.

3 Fluid dynamics within large fi res

Like all continuum fl ows, momentum transport in fi res is given by the Navier−Stokes equations (eqn (1)). Due to the nonlinear advection term (the second term on the left-hand side of eqn (1)), fi res become turbulent for fuel sources above about one meter [14]. Large fi res exhibit the full range of rich vorticity dynamics associated with turbulence including vorticity production at solid boundaries and at density gradients within the fl uid. Visual evidence exists of vorticity scale change including growth in coherence length scales by vorticity rollup and pairing, and decay in coherence length scales by straining and tangling. The result of all these mechanisms is a turbulence cascade in which dynamics across the length scale spectrum discussed with respect to Fig. 2 participates in transport of momentum and scalars in a fi re.

Figure 5: Model taxonomy.




In general, fi res can occur under a very broad set of initial and boundary conditions. By common defi nition, they are low Mach number and have spatially separate fuel and oxidizer sources. Fires induce gas motion themselves. In enclosures, the resulting fl ows may be quite complex, both spa-tially and temporally. Thus, a complete description of the fl uid mechanics of fi res would require a complete description of low Mach number fl uid mechanics. This breadth is beyond the scope of this treatise. Rather, what follows focuses on what makes fi res fl uid-mechanistically unique. To achieve this goal, two canonical fl ows, (1) a round plume issuing from an infi nite ground plane into an otherwise quiescent fl uid, and (2) a round plume issuing from an infi nite ground plane into a hori-zontal cross fl ow will be discussed with respect to the turbulent dynamics.

3.1 Quiescent conditions

If there is no external forcing applied, a fi re is a reacting plume. As such it is a member of the family of jets and plumes as shown in Fig. 6.

(a) (b)

(c)

(d)

Figure 6: Fire as a reacting plume: (a) fi re, (b) reacting jet [21], (c) non-reacting plume [22], and (d) nonreacting jet [23].




3.1.1 Jet versus nonreacting plume dynamicsJets and plumes share all the momentum transport terms in common. Thus, all the nonlinearities associated with advection including turbulence are shared between jets and plumes. The differ-ence between jets and plumes is in the source term. Isothermal jets do not have the source term in eqn (1). On the other hand, jets generally have a high value of inlet momentum. From eqn (3) and Fig. 2, it can be seen that the ratio of the buoyant source term to momentum is given by the Richardson number. Plumes have high values of Richardson numbers, while jets have low values.

A popular alternative expression to the Richardson number is the Froude number, u2/gD, where g is the value of gravity, D is a characteristic length scale, and u is the vertical velocity. Sometimes the square root of this value is used. Further, if the density is used to modify the Froude number, then it is called the density modifi ed Froude number. The Richardson number is the reciprocal of a form of the density modifi ed Froude number.

From a dynamics perspective, the difference between jets and plumes is that vorticity in iso-thermal jets comes entirely from the nozzle boundary layer. In an isothermal fl ow, when a jet enters an unconfi ned, uncluttered domain, all the vorticity that will ever be present in that domain comes from the source boundary layer.

In plumes, the vorticity is generated from the buoyant source term in eqn (1) under the condi-tions expressed in eqn (7). These conditions are shown graphically in Fig. 7 with a notional fl uid

Figure 7: Buoyant vorticity generation.




element overlying a fi re image. The fl uid element shown would be less dense on the left-hand side than the right-hand side because the gases are hotter in the fi re than outside the fi re. The fl uid element has a horizontal density gradient. Even in a quiescent (no velocity) condition, gravity, acting vertically through the element, will result in a force at the mass center of the element. However, the mass and geometric centers are not coincident. The mass center is biased to the right side of the geometric center in the element in Fig. 7 because it is heavier on the right. This condition will result in rotation of the element in Fig. 7 if the geometric center is fi xed and allowed to rotate.

For this heuristic example, the right-hand side would move downward while the left-hand side would rise, thus inducing a rotation under the force of gravity. The rotation would continue until the force through the mass and geometric centers align. In other words, the misalignment between a density gradient and an acceleration fi eld (or equivalently, pressure gradient) will cause the generation of vorticity. More generally, all fl uid elements are connected and the effect is elliptic in nature.

The two parts of eqn (7) that make up the buoyant vorticity generation term can either be thought of as being due to the misalignment of density gradients with hydrostatic and hydrody-namic pressure fi elds, or equivalently, as explicitly stated in the form chosen for eqn (7), the misalignment of density gradients with hydrostatic and hydrodynamic acceleration fi elds. The two terms are called buoyant and baroclinic production of vorticity, respectively.

Since vorticity is generated by the misalignment of density and acceleration fi elds, the length scale of the generated vorticity will be limited by the extent of either the density gradient or the accelerating fi eld. In the case of gravity, the fi eld is very large so that the extent of the vorticity generated is almost always limited by the extent of the density gradient. In turbulent fl ow fi elds, acceleration/deceleration is often experienced across eddy boundaries so that the baroclinic term may be limited by the coherence of the acceleration fi eld. It may change sign rapidly in both space and time unless there is a mean acceleration of the fl ow. Numerical simulation suggests strong acceleration gradients at the base of the plume [11].

It should be noted that the presence of vorticity does not imply the existence of a ‘coherent vortex’ or turbulent eddy. As stated previously, plumes share all the vorticity transport dynam-ics inherent in jets, including the roll-up of vortex sheets, pairing of vortices by amalgamation, etc. [24], as well as the stretching and tangling of vorticity. Thus, as in Fig. 6, both jets and plumes end up with large coherent rotational structures as well as a turbulent cascade through a combination of vorticity source terms and vorticity transport terms. The vorticity transport terms in jets and plumes are shared, whereas the vorticity source terms differ between jets and plumes.

The differing source terms result in quantitative differences in fl ow dynamics corresponding to the magnitude and length scale differences of the source terms. For example, in the far fi eld, both jets and plumes are self-similar, and can be scaled by the same self-similarity laws as long as the overall magnitude of the source term is taken into account [25, 26]. The reason for this equivalence is that the source terms between jets and plumes differ most strongly in the near fi eld. Isothermal jets have their highest velocity at the source and thus have all their vorticity at their injection source.

Plumes accelerate due to buoyant (and baroclinic) production of vorticity. However, as a non-reacting plume moves away from its source the density gradients diminish due to turbulent mixing and diffusion. Thus the rate of production drops and the source term lessens. On the other hand, all the previously generated vorticity continues to be advected. The effect is cumulative in that the circulation grows with elevation.




Since the ratio of production to advection of vorticity drops with elevation in buoyant plumes, at some elevation the decelerative effects of the advected vorticity exceeds accelerative affects of the buoyant vorticity source term and the plume velocity peaks. Eventually the buoyant source term becomes vanishingly small. After vorticity advection dynamics removes the ‘memory’ (i.e. details of the dynamics) of the source term, jets and plumes become similar if the magnitude of the source terms are similar [25, 26].

Between the near and far fi eld regimes, high order turbulent statistics are more strongly affected than mean fl ow statistics. In particular, if the buoyant source term is not zero, vorticity will be generated across a spectrum of length scales corresponding to the spectrum of density gradients. Experimental evidence for this view can be found in nonreacting buoyant plume data [27] which shows a −3 spectral decay as opposed to a −(5/3) spectral decay in velocity over a broad spectrum of length scales above diffusive scales. It is shown that the −3 spectral decay can be obtained from scaling the ratio of buoyant and advective time scales.

3.1.2 Reacting versus non-reacting plume dynamicsThe discussion to this point has compared and contrasted jets and plumes. It is now appropriate to compare and contrast reacting and nonreacting plumes. Note that in eqn (1), or its vorticity equivalent eqn (7), combustion does not appear explicitly. Combustion is coupled to momentum only through density gradients under specifi c conditions, and the temperature dependence of viscosity.

Reacting and nonreacting plumes both have in common the buoyant and baroclinic vorticity generation term in eqn (7). In theory, if a combusting fl ow produced the same magnitude of density gradients in the same spatial locations as a nonreacting plume, then the magnitude of this source term would be the same for each fl ow. In general this is not the case, resulting in quantitative differences between reacting and nonreacting plumes. Examples will be discussed in Section 3.1.3.

Fuel vapor in most fi res is not buoyant relative to air. When at the same temperature, only a limited number of fuels are signifi cantly buoyant relative to air, e.g. hydrogen and methane. Car-bon monoxide and the fuels with two carbon atoms are slightly to neutrally buoyant, while fuels with three or more carbon atoms are negatively buoyant. Without combustion, most fuel vapors will sink and stably stratify.

Combustion products are buoyant due to their high temperature. At ambient temperatures, the products of combustion for the most part are also slightly to neutrally buoyant. Typically for alkanes, CnH2n+2, for large n, the product composition is one CO2 for every H2O. With molecular weights of 44 g/mol and 18 g/mol, respectively, an equal molar solution will give a mean molec-ular weight of 31 g/mol relative to air at 29 g/mol. At peak combustion temperatures that are of the order 2100 K, combustion product density is about 1/7 of air.

Only hot products make a fi re plume buoyant overall. Flame sheets in themselves are buoyant; however, it is the accumulation of the hot products from the fl ame sheets that creates an overall buoyancy in a fi re plume. Figure 8 illustrates this observation. Consider two plumes, one with a plume density equal to that of air (e.g. ethene) and a second with a plume density less than that of air (e.g. products of ethene combustion), shown in Fig. 8(a) and (b), respectively.

Within the fl ame sheet itself, hot products result in a decrease in density, creating a density gradient between the hot products and the air, and between the hot products and the plume [28]. For the case in which the plume density matches that of the air density, then the vorticity gener-ated on each side of the plume is nominally the same (assuming the same diffusivities) since the density gradients are nominally the same. The total vorticity across such a fl ame zone is zero and serves only to accelerate the fl ame sheet at scales corresponding to the fl ame thickness. From a




linear momentum perspective, the fl ame zone is a buoyant sheet and will accelerate upward under gravity. While the air and plume will be drawn into the upwardly accelerating fl ame, there is no net difference to create buoyancy within the plume itself.

Now consider a case in which the density of the plume is less than that of the surrounding air, as in Fig. 8b. As with the fi rst case, within the fl ame sheet itself, hot products result in a decrease in density, creating a density gradient between the hot products and the air, and between the hot products and the plume. Unlike the previous case, the vorticity production is not the same on each side of the fl ame sheet. The vorticity production on the air side will be stronger than on the plume side. This imbalance results in a net vorticity across the fl ame sheet, represents the buoyancy of the plume and is independent of the fl ame sheet itself. So again the fl ame sheet itself is not a net buoyancy source.

A typical fi re plume does not become a buoyant plume until suffi ciently hot products are mixed into the core of the plume such that the overall density becomes less than that of the sur-rounding air. At the base of most fi res, the overall plume is nonbuoyant. The vertical velocity of the fuel vapor is lower than that of the surrounding fl ame sheets. If fl uid mechanics were solely local in nature, the vertical velocity of the fuel vapor would remain at its source value.

However, the elliptic nature of the pressure fi eld results in upward acceleration. From a vortic-ity dynamics perspective, the net vorticity in the buoyant part of the plume (where hot products have mixed to the core) will induce an overall velocity fi eld which tends to accelerate the fuel upward, albeit much more slowly than the surrounding fl ame sheets. A quantitative example will be given in Section 3.1.3.

The nature of the spectrum of turbulent production by buoyant and baroclinic vorticity genera-tion differs somewhat between nonreacting and reacting plumes. As noted previously, the pres-ence of vorticity does not imply the existence of a ‘coherent vortex’ or turbulent eddy. In the simplest case, a density gradient must be contiguous enough so that the vorticity formed from the gradient results in a sheet that can roll up into a coherent structure. Thus, ‘turbulence’ in the form of eddies formed by density gradients is always created at length scales larger than the density gradients creating the vorticity. Implied in Fig. 8b is that the net density gradient across the fl ame sheet is the density gradient that will result in the formation of a coherent eddy. This gradient is shallower, i.e. has a longer length scale, (for the same density difference) in the reacting plume than the nonreacting plume because of the presence of the fl ame sheet in the reacting case. In the nonreacting case, the interface can be much thinner. Thus coherent eddies resulting in dynamics that lead to turbulence will occur at smaller length scales in nonreacting fl ows.

Figure 8: Net vorticity across a fl ame zone: (a) density of plume and air are equal (no net vorticity); (b) density of plume is less than air (net vorticity).




Vorticity generation in reacting fl ows is also suppressed by another effect − dilatation in the fl ame sheets. Combustion produces gradients that result in the net local divergence of the velocity fi eld through dilatation. This effect is explicitly a sink term for vorticity. It is the second compo-nent (∇ ◊ u) of the second term in eqn (7). The term is positive on the left-hand side of the equation, and so would be a negative term if shown on the right-hand side; hence it is a sink.

The dilatation term is a consequence of the local expansion of the fl ow due to the conversion of chemical energy to thermal energy in exothermic reactions. In these regions, the fl ow diverges. The term (∇ ◊ u) is actually the velocity divergence due to the dilatation. It arises due to conserva-tion of mass (continuity equation) in a fl ow with density gradients [10].

A common analogy given to explain the effect is that of an ice skater in a spin. As the skater extends his arms, he slows down, as he pulls them in he speeds up. Similarly, for a point in space with vorticity present, the fl uid expansion will decrease the vorticity. (Less common in fi res, local fl uid contraction, through condensation, for example, will increase the local vorticity.)

Combustion also affects the local viscosity fi eld, since kinematic viscosity is temperature dependent. Because the temperatures in a fi re are distinctly nonuniform, kinematic viscosities will also be nonuniform. In a nonreacting plume, kinematic viscosity can be expected to mono-tonically vary from the plume fl uid to the ambient fl uid. Thus, the spatial distribution of viscosity in a nonreacting plume will be different than that of a fi re, even if the nonreacting plume fl uids are such that the viscosities are of similar magnitude.

The fi rst term on the right-hand side of eqn (7) is the diffusion term. It is not fully expanded so it cannot be seen that viscosity is explicit in this term. Heat release due to exothermic combus-tion increases the kinematic viscosity which increases the diffusion of vorticity. Locally, the term can act like either a local sink or a source term depending on whether higher or lower strength vorticity is being diffused into a region.

The effect of increased viscosity is almost always discussed with respect to kinetic energy as opposed to momentum or vorticity transport. If a moment of the momentum equation is taken, i.e. taking the dot product of velocity with eqn (1), the result is the kinetic energy equation. The diffusion term in the momentum equation now becomes the dissipation term in the kinetic energy equation. Dissipation is always a sink for kinetic energy.

Increasing the viscosity will decrease the turbulent kinetic energy. Gas combustion product kinematic viscosity increases with temperature. Hence, the strongest diffusion and dissipation (with all else equal) will occur within the fl ame zones, where the temperature is the highest. Note that these are also the locations of the highest dilatation.

Physically, the effect of increasing viscosity is that random molecular motion becomes more energetic (higher velocity) with increased temperature (see Fig. 2), so that bulk or directional motion at that scale becomes less signifi cant. In this manner, it is often said that viscosity sets the cutoff scale for turbulent motion. Dissipation is said to convert bulk motion to random motion as a means of dissipating the kinetic energy.

In this manner, bulk or directed energy associated with the introduction of a plume or jet will eventually convert itself into random molecular motion at equilibrium, i.e. after the plume or jet has ‘dissipated’. There is sometimes confusion since in the momentum (and vorticity form) of the equation, diffusion is neither source nor sink, just a local means by which random walk trans-ports momentum or vorticity. It does not ‘dissipate’ momentum; it diffuses it until it uniformly spreads to its lowest value. Higher values of viscosity will therefore result in greater transport of both momentum and vorticity.

Whether viscosity change is considered as diffusion in its effect on momentum, or dissipation in its effect on kinetic energy, the scale over which it operates is defi ned by the velocity gradi-ent. It is strongest at the smallest scales − in the reacting case, in the near fl ame zone regions.




However, to the authors’ knowledge, detailed studies of the effect of local dilatation and enhanced viscosity in combustion zones in turbulent reacting fl ows have not quantifi ed the relative effect of each term as a function of the local turbulence fi eld. Since turbulence is often thought of in terms of the kinetic energy of turbulence, both terms are a direct sink. This observation is consis-tent with qualitative observations that reacting jets are ‘less turbulent’ than nonreacting jets for the same inlet conditions.

Quantifying the effect of dilatation and diffusion on the turbulent spectrum is an open area of research. In the context of a turbulent fl ow fi eld, many questions remain unanswered. Will an active combustion zone affect the spectral distribution of kinetic energy as more than a sink? For example, will the spectral distribution be changed? Will it be changed only near the cutoff scales, or more globally? In fi res, these questions are perhaps more relevant than other forms of combus-tion, because the tighter coupling between the scalar and momentum fi elds.

Further, combustion in fi res is limited by the mixing. From a modeling perspective, since length scales in fi res tend to be large, the scale of the grid relative to molecular scale mixing processes is also large. Therefore, in fi res, a longer range of mixing scales is modeled, and details of the mixing model are more important than perhaps is the case in other reacting fl ow problems. It is worthwhile to note (see Chapter 9 of this book by DesJardin et al.) that virtually all combustion models to date rely on timescales, whose derivation does not take into account local temperature fl uctuations. The viscosity is usually taken from a cell mean temperature.

3.1.3 Rayleigh–Taylor instabilities and buoyancyIn both nonreacting and reacting plumes, momentum transport is triggered by instabilities. Fun-damental observations of the transient dynamics of both nonreacting and reacting laminar and transitionally turbulent plumes [29−33] have resulted in a description of the source of plume dynamics including the puffi ng frequency. Recent temporal and spatially resolved experiments in turbulent nonreacting and reacting plumes have extended this description of dynamics to addi-tional modes [22, 34].

A simple, fully turbulent helium plume taken from [22] will illustrate the near fi eld transport dynamics of a nonreacting plume. Figure 9 shows seven planar laser-induced fl uorescence (PLIF) images, each 1/6 of a ‘puff’ cycle, with the fi rst and the seventh images being the start of a cycle. Each image only shows the left half of a 1 m diameter plume. The plume’s centerline is on the right edge of the image. Notational fl ow dynamics are given on each image, and detailed velocity vector plots are given in [22].

The fi rst image shows a large coherent structure in the upper half of the image with helium entering the domain from a plume source at the base of the image. As the helium enters the domain, it is subject to a Rayleigh−Taylor instability as relatively heavy air overlies the lighter helium entering the domain. The second image in Fig. 9 shows the formation of classical bubble and spike structures, in which the helium forms ‘bubble’ structures that rise relative to the air and air forms ‘spike’ structures that sink relative to the helium. The third image in Fig. 9 shows that as these structures continue to grow, helium and air begin to mix such that by the fourth image in the sequence helium and air have formed a somewhat homogeneous mixture.

The fourth image occurs at ~1/2 the puff cycle. At this point, a helium/air plume exists adja-cent to the surrounding air. This is also a Rayleigh−Taylor unstable situation in which gravity is aligned with the interface instead of perpendicular. As described previously, this situation results in buoyant and baroclinic vorticity generation of the same rotational sense all along the plume air interface.

In the fi fth image in Fig. 9, the resulting vortex sheet begins to roll up into what will be a coherent turbulent structure. As the helium/air plume fl uid rolls outward, surrounding air rolls




underneath the forming structure. In the sixth image in Fig. 9, the coherent structure continues to grow and begins to self-advect upward. In the process, air continues to be pulled in underneath the coherent, turbulent structure and over the top of the source helium, setting up the conditions for the next cycle. The coherent structure continues to grow until it reaches the centerline of the plume as shown in the seventh and fi rst images in Fig. 9. As the structure continues to self-advect upward as shown in the fi rst and second images in Fig. 9, its infl uence on the velocity fi eld at the source decreases, and helium beings to re-reenter the domain and form the bubble and spike structures.

Note that that the Rayleigh−Taylor instability shown in the fi rst image in Fig.9 is not necessar-ily the instability in its classic form, i.e. a quiescent heavy gas layer overlying a quiescent light gas layer, and the distinction can have signifi cant consequences for numerical simulation resolu-tion requirements.

In the fi rst image in Fig. 9, the coherent vortex has moved away from the surface, reducing the induced radial velocity over the helium. However the effect of the moving air may still have a signifi cant infl uence on the instability. In [35], it is noted that the experiments show broader air spikes than would be expected from classical Rayleigh−Taylor instability growth theory. The instabilities look to be of the order of centimeters for the 1 m helium plume shown, instead of the order of millimeters that would be expected from the fastest natural growth mode. This observa-tion suggests that perhaps the instability is forced, not natural. An unstable interface can grow at any forced wavelength in preference to the fastest growing unforced wavelength.

It can be argued that the initial condition for the instability in the fi rst image in Fig. 9 is set up by the radial entrainment of air over the top of the helium during the last half of the previous cycle. A natural suspicion is that Kelvin−Helmholtz instabilities may result from the radial entrainment of air. However, the principal effect may still be Rayleigh−Taylor in nature.

The interface between the helium source and radially entrained air forms a curved mixing layer. At the edge of the source the air has nearly horizontal velocity and near the centerline of

Figure 9: Puffi ng and Rayleigh−Taylor instabilities.

P∇

r∇

P∇

r∇ r∇

P∇




the plume, the air will have nearly vertical velocity. Chuin Wang [36] studied the effects of cur-vature on turbulent mixing layers, including layers with differing densities. Because the fl ow is not quiescent, the transition from nearly horizontal to nearly vertical creates a local acceleration fi eld emanating from approximately the core of the large coherent turbulent structure. In this geometry, the relatively heavy air is being accelerated toward the helium source center point, thus creating a Rayleigh−Taylor unstable situation. Wang [36] studied the conditions in which the velocity between the mixing streams was the same and the density difference was of the order of 7. He notes the importance of the Rayleigh−Taylor instability in this scenario. There are dif-ferences between the fl ow in Fig. 9 and that studied by Wang. For example, his mixing layers were constant velocity. Here, the fl ow is accelerating along the helium/air mixing layer from the edge of the helium source to the centerline of the plume. In spite of the differences, Wang’s results are insightful.

It may be expected that instabilities along the helium/air mixing layer will grow with time away from the source. These instabilities will grow as the air entrains with time over the surface of the helium layer in the fourth through seventh images of Fig. 9, and thus will be present in the fi rst image in Fig. 9, and may be the cause of the larger than expected bubble and spike structures.

Clearly further work is required to quantify the interactions of the various instabilities. There can be important implications. Tieszen et al. [35] report that if too coarse a numerical grid is used, the bubble and spike structure does not form, and the mean statistics can be in error by a factor of two. If the Rayleigh−Taylor instability in the fi rst image in Fig. 9 is natural, rather than forced, the radial spacing of the bubble and spike structures does not depend on a length scale. Thus, if the spacing is centimeters for a 1 meter diameter plume, it would be centimeters for a 10 meter diameter plume. On the other hand, if the initial instability scales with the source diameter, centimeter spacing between structures in the 1 meter diameter plume would be 10 centimeter spacing in the 10 meter diameter plume. The difference in numerical resolution required to pick up the resulting bubble and spike structure is a factor of 10,000 (103 in space and 10 in time).

Movies of fi res in an otherwise quiescent atmosphere suggest that the dynamics of nonreacting plumes are present in fi res. Figure 10 shows a visible image of a 1 m methane fi re [34, 37] at two times during the puff cycle. The left image in Fig. 10 corresponds approximately with the fi rst image in Fig. 9 while the right image in Fig. 10 corresponds to approximately the fourth image in Fig. 9.

Similarly, Fig. 11 shows two still images from a video of a 20 m diameter JP-4 jet fuel fi re at two times in the puff cycle. Only the left half of the fi re is shown (10 m radius at base). The left

Figure 10: 1 m methane fi re at different phases of the puff cycle.




image in Fig. 11 corresponds approximately in time with the fi rst image in Fig. 9, while the right image in Fig. 11 corresponds approximately with the fourth image in Fig. 9.

In a fi re, the bubble and spike structure separates fuel and air and thus is indicated by fl ame sheets. Comparing the left and right images in Fig. 10 near the source, it is clear that the left image has relatively low fl ame surface density compared to the right image. The growth in fl ame surface density corresponds to air/fuel interpenetration, consistent with a Rayleigh−Taylor bub-ble and spike dynamics argument.

The bubble and spike dynamics is perhaps not as apparent in Fig. 11 because of the smoke shielding the fl ame sheets. As will be discussed in Section 4.2, smoke is indicative that a fuel-rich volume has burned out the oxygen and quenched, leaving copious amounts of relatively low temperature soot behind. In this context, it indicates that a fuel bubble has mixed and burned out with an air spike.

In both right-hand images in Figs 10 and 11, the trigger instability for the growth of the large turbulent coherent structure characteristic of puffi ng begins with the fi re base having near vertical slope up to an elevation of 10−20% of the fi re diameter. As with the nonreacting case in image four of Fig. 9, this geometry is unstable if the plume fl uid is reasonably well mixed and buoyant.

Data suggest that the two dynamic modes resulting from Rayleigh−Taylor instabilities have differing strengths for different fi re sizes. For small scale (10 cm diameter and below) fi res, the bubble and spike structure is either not present or relatively weak. This may be because the bubbles and spikes take time to grow into fi nite amplitude instabilities, and the puffi ng period decreases as the inverse of the square root of the diameter [30]. However small the scale, the fl ame sheet is nearly vertical and a fi re will ‘puff’, when the products penetrate to the centerline. The amplitudes of these ‘puffs’ are barely more than bulges, but by their frequency it is clear that they are associated with this instability.

Figure 11: 20 m diameter JP-4 fi re at different phases of the puff cycle.




At the very largest end of the fi re diameter spectrum, the coherent plume structure is postu-lated to break down into individual fi res (see Drysdale [14] for a discussion and Heskestad [38]). This regime is termed a mass fi re. Scaling of the conditions for which this transition occurs is an active research topic. However, the nature of the mass fi re suggests that the bubble and spike mode dominates due to the long timescales involved in large fi re dynamics. For relatively low mass fl ow rates of fuel, it is easy to envision near complete combustion of the fuel in the bubble and spike structures and only the products of combustion are rolled into a fi re plume. The greater the fuel mass fl ux, the longer the timescale needed to combust it and therefore the larger the scale of the fi re in order for it to have the appearance of a mass fi re.

Up to this point in the discussion, continuous uniform fuel sources have been assumed. Studies have been conducted [39] on regular arrays of discontinuous fuel sources, i.e. heterogeneity at small scales relative to the overall fi re size. The studies have been conducted in regard to what is called a ‘fi re storm’, in which individual fi res amalgamate into one large fi re. The transition from individual fi res to a fi re storm and the breakdown of a fi re from a continuous plume into a mass fi re are likely two sides to the same transition. It is the authors’ opinion that these are very much related to the relative strengths of the bubble and spike mode versus the coherent structure mode.

In this description it should be noted that nothing has been said about ‘buoyant turbulence’. This chapter is on large turbulent fi res, for which it has been discussed that buoyancy plays a large role. It is the authors’ opinion that buoyancy does not cause turbulence directly. With respect to eqn (1), and its vorticity equivalent, eqn (7), buoyancy results in vorticity generation through the buoyant source term. The term is linear in nature, and it has been argued throughout this section that the instabilities are initially laminar in nature.

From a linear momentum perspective, turbulence results from the nonlinear advection term (the second term on the left-hand side of eqn (1)). From a vorticity dynamics perspective, all the vorticity transport dynamics inherent in isothermal fl ows, including the roll-up of vortex sheets, pairing of vortices by amalgamation, etc., as well as the stretching and tangling of vorticity, are shared with plumes. The difference is in the source term, the buoyant part of which is linear. Turbulence is a result of the transport of vorticity, not its formation.

Turbulence models have historically been developed to address the unresolved length scales involved in the nonlinear interaction associated with the advection term in eqn (1). For the most part, these models are dissipative in nature. They account for the fact that mechanical energy asso-ciated with advection, in the limit of equilibration, will result in the ‘energy’ being transferred to molecular motion. Modeling of unresolved but linear laminar instabilities that grow by vortex dynamics to become nonlinear and energy bearing, is a virtually nonexistent fi eld in comparison to the vast literature on turbulence models for direct closure of the nonlinear advection terms. One aspect is clear however. Traditional dissipative closure terms will not capture the growth of high frequency (relative to the discrete solution of the partial differential equations) laminar instabili-ties that grow into energy bearing nonlinear structures due to vortex dynamics [35]. Note also that this process is not inherently stochastic in that the laminar instabilities are deterministic, and for them to result in energy bearing vortical structures, the growth mechanisms must also be deter-ministic. However, like all turbulence, the resulting turbulent velocity fi eld may be considered stochastic in a modeling sense, just like turbulence from boundary layers.

3.2 Interaction with cross-winds

This section provides a brief summary of transport dynamics. As with fi res in quiescent condi-tions, the only difference between isothermal jets and fi res is in the location and strength of the




vorticity source term. Figure 12 illustrates four major types of vortical structures found in a jet in cross-fl ow [40]. All have counterparts in fi res in cross-fl ow except the ‘jet shear-layer’ vortices. These shear-layer vortices are due to the boundary layer vorticity generated with the jet source. As discussed above, in a fi re the azimuthal vorticity is buoyantly generated by density gradients between the fi re and the surroundings.

This difference in vorticity sources results in the biggest difference between a jet in cross-fl ow and a plume in cross-fl ow. Figure 13 shows a 20 m diameter JP-8 fi re at three different wind speeds. As the wind speed increases, the fi re plume becomes more defl ected from the vertical as expected. Comparing Figs 12 and 13 highlights two signifi cant differences. The fi rst is that a jet is initially more vertical (less defl ected by the cross-fl ow) than a plume, and becomes more horizontally defl ected away from the jet source.

Figure 12: Vortical structures for a jet in cross-fl ow [40].

Figure 13: Fire in a cross-wind. Wind from the left and increases from the left image to the right image. Long-time exposure of a 20 m diameter JP-8 fi re.




The fi re plume is initially more defl ected in a fi re and becomes (at least within the active com-bustion region) less defl ected away from the fuel source. The reason for this trend is that the jet has its highest vertical momentum at the source, while a fi re starts with its lowest vertical momen-tum at its source. Only after combustion generates a buoyant plume does a fi re begin to have the vertical momentum to alter the trajectory of the cross-wind as seen in Fig. 13.

The second large difference between the jet and the plume is that since the plume has low vertical momentum at its source (fuel is nonbuoyant), fuel is advected downstream so that the apparent ‘source’ of the fi re is elongated while the jet source maintains its original shape. This ‘fl ame drag’ is apparent in Fig. 13 by the elongated base of the fi re in the highest wind condition compared to the lower wind cases.

Fric and Roshko [40] provide a physical explanation for the large columnar vortices as the interaction of the boundary layer fl ow due to the cross-wind with the jet shear-layer vorticity. At the front of the jet, the rotational sense of the boundary layer and shear-layer are different and thus the boundary layer vorticity partially cancels the shear layer vorticity at the leading edge of the fi re. This results in a net decrease in vertical velocity at the leading edge relative to the trailing edge. This velocity difference aligns the azimuthal vorticity in an axial direction causing the columnar vortices.

Figure 14 shows columnar vortices on the downstream side of a 20 m diameter JP-4 fi re. Mov-ies indicate that the columns are not steady, but get stronger and drift downstream until their linkage back to the fuel source grows suffi ciently weak such that combustion within the vortex can no longer be sustained. It appears as though the vortices alternate in strength, and the overall impression is not unlike vortex shedding from a cylinder.

Figure 15 shows a wake vortex similar to that illustrated in Fig. 12. The explanation for the wake vortices given by Fric and Roshko [40] is that some of the boundary layer vorticity that is rolled around the jet into the horseshoe vortex gets caught up in the columnar vortex on one end while the other is attached to the ground. As this vorticity is stretched by the upward acceleration of the fi re plume, it is strengthened. Evidence that this vorticity comes from the boundary layer as opposed to the plume is due to the fl ow being visible from entrainment of sand from the ground (tan color) as opposed to smoke from the plume. Hence, in Fig. 15a the wake vortex was not shed from the plume but pulled up from the ground. The fi re is a 20 m diameter JP-8 fi re at

Figure 14: Columnar vortices on the downwind side of a 20 m diameter JP-4 fi re: (a) twin colum-nar vortices; (b) single columnar vortex.




China Lake, California. Wake vortices are not atypical in large fi res, but for obvious reasons are most commonly seen when the surrounding terrain is dry and dusty.

The major mixing structures in a fi re in a cross-fl ow are due to boundary-layer/fi re interac-tions. This interaction is perhaps the simplest of all interactions between fi res and objects. The more general case of fi re/object interactions includes bluff body dynamics leading to wakes in addition to boundary-layer dynamics. Fundamental fl ows along this path include fl ow over a backward facing step. Because of the value of these bluff body fl ows in inducing high mixing rates in combustors, they have been studied extensively in the combustion community and will not be reviewed here. However, it is worthwhile to note that a fi re placed in a high enough cross-wind in a stabilizing geometry will, in the limit, look very much like a jet engine combustor, because the transport is in effect no different.

4 Scalar transport and radiative properties

4.1 Mixing

The previous sections dealt with the effect of the scalar fi eld on the momentum fi eld. This section examines the effect of the momentum fi eld on the scalar fi eld. Fire is considered a mixing limited phenomenon, that is, the rate of combustion (discussed in Section 4.2) is limited by the rate of mixing of reactants. The rate of mixing is determined by the nonlinear, elliptic growth rate of the instabilities that result in bubble and spike structures, large coherent vortical structures, and resulting turbulent cascade. The growth rate of these structures determines the rate at which air penetrates and mixes into the core of the plume.

Fires are often described by the mixing and combustion characteristics as occurring in three distinct parts [41, 42]. Near the base, the combustion is persistent with continuous combustion around a vapor core. At higher elevations, the combustion is intermittent and characterized by strong turbulent mixing, resulting in complete consumption of the fuel. At still higher elevations, a turbulent, nonreacting plume exists in which surrounding air mixes with the products of com-bustion.

Figure 15: Wake vortex in a fi re: (a) China lake, CA; (b) Albuquerque, NM.




At the lowest elevations, where most hydrocarbon fuels are nonbuoyant, fi res have a fuel vapor core just above the fuel surface termed the vapor dome [14, 41, 42]. Data from both the 1 m methane fi re [34, 37] and the 20 m JP-4 fi re [17] suggest that a nonbuoyant core region exists that is composed primarily of fuel. This fuel vapor region is surrounded by the high temperature products associated with the active combustion region. Qualitatively, the presence of products is indicated by the high fl ame surface area density in Fig. 10 and the smoke in Fig. 11.

The size of the vapor dome is dependent on the scale of the mixing structures penetrating the plume. Both the bubble and spike structures and the large coherent structures result in rapid pen-etration of air into the plume, limiting the size of the vapor dome. As noted by Hamins [41], the time mean extent of the vapor dome is perhaps 20% of the fi re height. Tieszen et al. [34] note that there is a dependency of fuel fl ow rate, but the time mean elevation of the vapor dome is nomi-nally half a fi re diameter.

At higher elevations, the combustion is described in the literature as intermittent. Flow visual-ization [34] of time-resolved data sets strongly suggests that the height of the vapor dome fl uctu-ates with time in accordance with the passage of the large coherent structures. Due to the elliptic nature of the fl ow fi eld, the passage of the large eddies induces an acceleration of the vapor dome along the centerline just underneath the large coherent eddy as it self-advects upward. The large eddy structure associated with the next puff cycle grows underneath this fuel region. This inter-mittent lofting of fuel from the vapor dome may explain the intermittent nature of the combus-tion between one and two diameters above the fi re.

Most large fi res completely deplete their fuel source along a centerline of height approxi-mately equal to two diameters as discussed by a number of authors [43−46]. For noncircular fi res, the minimum dimension is the characteristic length. This observation suggests that the majority of the fuel entrained in large turbulent vortical structures is either consumed or quenched within that structure. Above approximately two source diameters, mixing occurs between the hot products and surrounding air in the absence of combustion.

From a heat transfer perspective, it is obvious that the highest rates of heat transfer will occur in the most active combustion regions, where the time-mean local temperature is the hottest. In large fi res, with vapor domes that can reach meters in elevation, it is perhaps a counter-intuitive result that the lower region in the center of the fi re is not the hottest place. The edge of the fi re has a higher time-mean temperature until elevations are reached where the vapor dome is consumed.

It is worthwhile noting that the presence of the vapor dome in hydrocarbon fi res results in a quantitatively different shape of the velocity fi eld compared to nonreacting plumes in the near source region. Figure 16 shows a comparison of the velocity fi elds for 1 m diameter sources with low inlet velocities [22, 34]. The fi re has ‘W’ shaped vertical velocity contours near the base due to low velocities in the vapor dome relative to the high-temperature combusting surfaces at the fi re edge. Not until nearly 3/4 of a fi re diameter does the peak velocity occur along the centerline. The nonreacting plume on the other hand has ‘U’ shaped vertical velocity contours, and the peak velocity is along the centerline from the outset.

Because the fuel core in most hydrocarbon fi res is nonbuoyant, the bubble and spike structure shown in Fig. 9 for a helium plume in air does not develop in the fuel vapor dome (the exception is for hydrogen as a fuel). The unstable interface is between the hot products and the surrounding air, although clearly from Figs 10 and 11, the instability results in the creation of signifi cant fl ame surface area along the edges of the fi re.

Time scales between fuel vaporization and combustion of that fuel above the vapor dome can reach seconds in duration in large fi res. As discussed by Babrauskas [7], fuel vaporization rates for most hydrocarbon fuels fall in the 0.01−0.1 m/s range. In the vapor dome, the fuel is acceler-ated upward by the elliptic nature of the momentum fi eld.




Velocities even along the centerline quickly reach the order of meter per second levels. How-ever, in large fi res, the time-mean height of the vapor dome can also reach elevations of order meters. Thermocouple measurements in large fi res suggest temperatures can reach about 1000 K allowing for thermal decomposition (pyrolysis, in the absence of oxygen) of the fuel into smaller hydrocarbon fragments [16]. The pyrolyzed fuel can be more neutrally buoyant than the parent hydrocarbon.

Similarly, time scales between the entrainment of fuel and air into one of the large coherent structures and its complete combustion can be of the order of seconds. The characteristic puffi ng period is of the order of seconds for fi res greater than about 2 m diameter [29, 30]. Since large fi res typically complete combustion at a couple of diameters elevation, these structures can last a couple of puff cycles, order of seconds to at most tens of seconds for the largest fi res.

4.2 Combustion

It has been several hundred thousand years, since humankind fi rst learned to utilize fi re to its benefi t, so it is perhaps natural that much of the combustion research has focused on heating, power, and propulsion systems that directly benefi t humans. Since many of the same fuels used in man-made systems are those involved in natural fi res, it can be expected that the chemistry and diffusion transport issues are similar. In both fi res and many man-made systems, combustion is classifi ed as turbulent diffusion fl ame, in which combustion occurs along a gas-phase stoichio-metric mixing surface. Descriptions can be found in a number of good, available, combustion textbooks.

Perhaps three principal differences exist between man-made systems and natural fi res that have an impact on combustion. Relative to man-made combusting systems, fi res have longer time scales, relatively low strain rates, and tighter spatial coupling between the scalar and momentum fi elds. Cox [15] notes that energy release per unit volume measured in fi res is lower than man-made systems’ values by factors of 10−1000.

As mentioned above, fi res are mixing limited and time scales for combustion are of the order of seconds to perhaps tens of seconds. For reference, for typical hydrocarbon fuels, chemical

Figure 16: Difference in vertical velocity fi elds between reacting and non-reacting fl ows: (a) methane fi re, Vo = 0.1 m/s and (b) helium plume, Vo = 0.34 m/s.

(a) (b)




timescales are of the order of tenths of milliseconds for gas phase reactions as evidenced by per-fectly stirred reactor blowout timescales at stoichiometric conditions in air at ambient temperature and pressure [47]. Soot formation timescales are of the order of milliseconds to tens of milliseconds as evidenced by numerous premixed fl ame studies. Hence, from a chemistry perspective, soot formation is a slow process, being of the order of 10−100 times slower than principal gas phase chemistry.

However, compared to the natural turbulent mixing processes in large fi res that are of the order of seconds, both these timescales are short. Mixing times are perhaps 100−1000 times longer than soot formation times and 1000−100,000 times longer than primary gas phase reactions. In man-made systems, particularly propulsion systems, mixing times are much shorter, resulting in higher energy release per unit volume. One of the motivations for short mixing times in propul-sion systems is to achieve combustion without signifi cant soot formation.

Related to the longer time scales in fi res are lower strain rates. While large fi res are fully tur-bulent, the time scales for the dissipation of concentration fl uctuations at the small length scale end of the spectrum tend to be much longer than in jet fl ames [15]. In typical man-made systems, much of the turbulence comes from boundary layers (such as shed or swirled off a backward facing step into a fl ame holding region). Depending on the velocity gradients, the turbulent struc-tures generated in boundary layers with relatively high kinetic energy can have small spatial frequencies relative to fl ame zones [48]. Hence the interaction of these high-energy, small-scale eddies with combustion zones creates local strain-induced quenching, creating a turbulent fl ame brush with triple fl ames and the like. As a result, a signifi cant amount of combustion research has focused on these rapid transient, high-strain-rate interactions.

Small scale strain rates in fi res are not nearly as energetic (unless combustor-like geometries are created in cross-wind conditions). Much of the turbulence is buoyantly generated at scales larger than the fl ame zones. As a result, fi res tend to have what look like manifold wrinkled laminar fl ame sheets. Figure 17 shows a typical view of the base of a medium sized (diameter of the order of meters) fi re. PAH fl uorescence from a laser sheet through the center of the 1 m diameter methane fi re shown in Fig. 10 [37] suggests that there are perhaps of the order of 10 fl ame sheets between the edge and the center of the fi re (exact statistics were not taken). For large fi res, hundreds to perhaps thousands of fl ame sheets could exist between the core and edge of the fi re.

A third attribute of fi res that signifi cantly affects combustion is the close coupling of the com-bustion and mixing zones. In a typical jet fl ame for example, stoichiometric concentrations typi-cal of hydrocarbons place the fl ame outside the core mixing layer [21]. As noted earlier, fl ame sheets do not result in net vorticity. It is the density gradient across the fl ame sheet that is the source of vorticity that drives the mixing. The fl ame surfaces in the right-hand images of both Figs 10 and 11 will roll up to become the large structures halfway up the images on the left-hand side, half a puff cycle later in time. These structures can be quite large as shown in Fig. 18, and of long duration.

The large coherent structures can be idealized as batch reactors in the sense that fuel and air mixed into the structure will react over seconds of time to some state dependent on the ratio of fuel to air within the interfaces of the structure. For heavy hydrocarbon fuels, eddies less than about one meter in diameter burn without producing large amounts of smoke. At greater than nominally one meter, eddies visually appear to change from a tangle of reacting fl ame sheets to a rolling ball of smoke as they age. This effect can be seen in Fig. 19 showing the base of a large fi re. Coherent structures near the base visually appear to be a tangle of fl ame sheets. At higher elevation (imply-ing age of the coherent structure), the eddies appear to be smoke balls.

While quantitative measurements are lacking, one explanation consistent with the observa-tions is that structures over nominally a meter in diameter have suffi cient circulation to entrain a




signifi cant fraction of plume fl uid into the eddy. Because stoichiometric requirements for hydro-carbons are less than 10% by volume of the fuel, the eddies end up being fuel rich. As the oxygen in the interior of the eddy is consumed, the fuel-rich, soot-laden regions quench due to lack of oxygen.

While it is reasonable to postulate that the interior of fuel-rich eddies quench due to oxygen depletion, the eddies are surrounded by air. Thus, there must be another scale-dependent quench mechanism to account for quenching the outer fl ame sheets in an eddy. Soot breakthrough (i.e. incomplete oxidation due to insuffi cient residence time) could explain smoke on the air side of the outermost fl ame surface. Another potential explanation is radiative quenching. T’ien [49] discusses the effect of radiation on quenching with respect to solid surfaces. He notes that as the strain rates decrease, the balance between advection of the reactants into the fl ame sheet and diffusion of products out of the fl ame sheet result in a decrease in heat release rate. On the other hand, radiative losses [42] are quite high for heavy hydrocarbon fuels. Under these conditions, it is perhaps theoretically possible for the radiative losses to exceed the low heat release rates and result in fl ame quenching.

The resulting smoke shielding at the edge of large fi res has a fi rst order effect on radiative transport, as discussed in Chapter 7 by Modest. Clearly, soot (formed on the fuel rich side of a fl ame sheet) has ended up on the lean side. Therefore, some quench mechanism must be respon-sible. A strain-induced quench does not seem consistent with the low strain rates found in fi res or the fact that the eddies appear to be populated with a tangle of fl ame sheets prior to becoming smoke balls. Quantifying the nature of the quenching mechanism is an open opportunity for the research community. It is both important and fundamental in nature.

Figure 17: Typical image from the base of a medium scale JP-8 fi re showing fl ame sheet-like combustion surfaces (see also Fig. 10).




4.3 Absorption properties

The temperatures and volume fraction of soot, fuel and combustion gases present in heavy hydro-carbon fi res [50, 51] result in heat transfer that is dominated by soot emission and absorption [52]. Possible exceptions include heat transfer to very small items, due to the inverse dependence of convection on length scale, in the gaseous fuel-laden vapor dome region.

Soot formation is a subject that has long been studied and yet is still a very active area of research due to its complexity [53−58]. The mechanisms for formation of soot, primarily for laminar fl ames, including models for prediction of soot nucleation (when particles fi rst appear), growth (particles increase in size), agglomeration, and oxidation are provided in several reviews including the work by Kennedy [59]. Soot formation is strongly affected by both chemistry and transport. However, a complete description of this interaction would take a chapter in itself, and is somewhat beyond the scope of this chapter on transport phenomena in fi res that affect heat transfer. Similarly, radiation transport is addressed in this book in Chapter 7 by Modest.

Figure18: Large coherent eddy in a 20 m diameter fi re.




However, the primary connection between fl uid mechanics and heat transfer in fi res is through soot formation and radiation. Thus a brief description of this interaction through soot absorption and emission is in order. Measurements from sampled soot show trends that illus-trate the properties of soot in large fi res as well as the physical formation mechanisms. These data [5, 60] show soot comprised of individual small primary particles typically of the order of <100 nm, agglomerated into wispy chains with fractal patterns and lengths of the order of ~1−4 microns.

Analysis of the radiative properties of the aggregates [61, 62] shows some small infl uence of nonisotropic scattering at the wavelengths of interest, but the primary properties of the soot fi eld are dominated by the absorption coeffi cient of the soot:

v( ).g kf TL=a (8)

The absorption coeffi cient is a function of k (the Planck mean extinction coeffi cient), fv (the soot volume fraction), T (the soot temperature), and L (a path length). The inverse of the absorp-tion coeffi cient determines the length scale for absorption of radiative energy, as discussed in Chapter 7. The mean absorption is temperature dependent. The overlap between soot concentra-tion and temperature will be discussed in Section 4.4. Implicit in eqn (8) is the integration over the wavelength range of interest. Spectral absorption values vary inversely with wavelength.

The mean extinction coeffi cient of the medium in turn is dependent on the optical properties of the soot (i.e. the properties of the material irrespective of its geometric form) as well as the confi guration of the soot aggregates. Optical properties of soot have been expressed in the form of the specifi c spectral extinction coeffi cient as given by

l=e

v

.k

Kf

(9)

Figure 19: Typical smoke shielding in large fi res.




In eqn (9), l is the spectral wavelength. Although measurements of Ke are only available for lim-ited wavelengths, where laser light can be employed in practical diagnostics, results from recent studies seem to converge to values of about 8.5 for visible and near IR, with no indication of strong wavelength dependence into the heat transfer regimes of 3−5 micron wavelengths. Fuels have a minor infl uence on the value, but in general trends tend to indicate that, once formed, soot is approximately the same for all hydrocarbon fi res. Universally accepted models for the progres-sion of nucleation, growth and oxidation for fi res for different fuels have yet to be developed.

The use of optical properties to determine the overall absorption fi eld is still a region of active study and therefore the most common practice is to invoke the Rayleigh approximation whereby the radiative properties of the soot laden fi eld are based solely on the optical properties and the volume fraction. More detailed theories have been proposed, but are diffi cult to employ in prac-tice due to lack of widely applicable data for the fractal parameters of aggregates for fuels, fi re sizes and locations within the fl ame zone.

Additional analyses of the size distribution within aggregates [5], as well as formation time analysis from models and laminar fl ame data support the notion that soot is formed entirely within a single individual fl ame structure. Within this construct, the formation of nonabsorbing soot precursor particles, which have been observed in careful measurements in laminar fl ames, and their subsequent carbonization rate to absorbing particles (as studied by Dobbins [63]) clearly occurs at the fl ame sheet length and time scales.

Oxidation of the soot however, does not universally occur as evidenced by the black tips on fl amelets visible in high resolution photographs of large fi re fl ame structures. In other words, many fl ame sheets exist at conditions beyond the local ‘smoke point’. Additional discussion of this issue will be presented in the section on transport phenomena effect on soot concentrations.

Accordingly, the turbulent mixing region with active combustion occurring in large fi res is comprised of soot within and external to reacting regions of the fl ame sheets. This distribution was cited as the potential explanation for comparison between high temperature soot measured by emission and the integrated effect of all soot obtained by extinction measurements in 6 m × 6 m JP-4 fi res [51]. These data, as well as data from smaller fi res [50], averaged over path lengths of the order of 1 cm provide volume fractions of soot of the order of 1−3 ppm. These integrated measurements are signifi cantly lower than the 3−15 ppm shown in Table 1 as measured within a fl ame sheet in laminar fl ames by Shaddix and Smyth, [64], Santoro et al. [65], and Kent [66] when the same Ke values were employed. Use of newly measured Ke values reduces the overall volume fraction by approximately a factor of two.

Table 1 also shows the volume fraction for methane fl ames to be notably lower, by at least an order of magnitude, in comparison with other hydrocarbon fuels. A consistent trend is observed in large scale fi res burning liquefi ed natural gas (LNG). As noted by Luketa-Hanlin [67], levels of smoke covering the visible soot emission in the noncombusting plume region are signifi cantly lower, resulting in higher emission from the fl ame zone, as will be discussed in Section 4.4.

Current understanding of soot volume fraction and radiative properties for heavy hydrocar-bon fi res leads to absorption coeffi cients within the fl ame zone that correspond to optical thick-ness (i.e. path lengths for exponential absorption) of 0.1−0.3 m. Exponential attenuation of all emission occurs within three path lengths or at lengths of approximately 0.3−1.0 m. This range of paths corresponds to the same range of length scales, where large fi res become fully turbu-lent. Accordingly, the expectation is that for signifi cant regions within fully turbulent, large fi res, the regions are optically thick. Although radiation is the dominant mode of heat transfer, and combustion and the resulting heat release are closely coupled to turbulence, there is no direct physical connection between the length scale regimes for fully turbulent and optically thick fi res.




4.4 Emission properties

The emission of radiative energy in fi res is driven by the temperature and properties of the medium. Subject to the same discussion in the previous section, the relevant simplifi ed, non-scattering, form of the radiative transport equation is given by

4

( ) ( ) .T

s I s I ss

∇ + =πa

a◊

(10)

In eqn (10), s is a direction, I is the irradiance, a is the absorption, s is the Stefan−Boltzmann constant, and T is the temperature. A more detailed description of radiative transport is given in Chapter 7.

Given the previous discussion regarding the formation and growth of soot within the fl ame structures, it is evident that the position of soot within the fl ame structure is important. In par-ticular, the overlap between the soot fi eld and temperature fi eld (note the fourth power depen-dence, even fi fth power, when property dependence is considered) is the dominant contribution to emission. As noted previously, in large fi res there are hundreds to thousands of fl ame sheets between the center of a fi re and an edge.

Table 1: Peak soot concentrations in laminar, low-strain steady diffusion fl ames.

Fuel FlamePeak fv

reported Reference Method AssumptionCurrent best estimate of fv

Methane 79 mm high coannular

3 × 10−7 [64] HeNe extinction

Ke = 4.9 (D&S)

1.7 × 10−7

(Ke = 8.5)

Propane 85 mm high coannular


Ke = 4.9 (D&S)

3.5 × 10−6 (Ke = 8.5)

Ethylene 91 mm high coannular


Ke = 4.9 (D&S)

7.5 × 10−6 (Ke = 8.5)

Ethylene 88 mm high coannular

10 × 10−6 [65] Ar-ion extinction (514 nm)

Ke = 4.9 (D&S)

5.8 × 10−6 (Ke = 8.5)

Ethane 88 mm high coannular

3 × 10−6 [65] Ar-ion extinction (514 nm)

Ke = 4.9 (D&S)

1.7 × 10−6 (Ke = 8.5)

acetylene 6 mm high coannular (smoke pt)

15 × 10−6 [66] Path-ave HeNe

extinction

Ke = 3.5 (L&T)

6.2 × 10−6 (Ke = 8.5)

Ethylene 75 mm high coannular (smoke pt)

6 × 10−6 [66] Path-ave HeNe

extinction

Ke = 3.5 (L&T)

2.5 × 10−6 (Ke = 8.5)

Propane 150 mm high coannular (smoke pt)

4 × 10−6 [66] Path-ave HeNe

extinction

Ke = 3.5 (L&T)

1.6 × 10−6 (Ke = 8.5)




In order to show the importance of fl ame structure, consider the following simplifi ed heuristic scenario. Let all the fl ame sheets and intervening space between the fl ame sheets (fi lled with fuel (and products) on one side and air (and products) on the other side) be the same along a direc-tional path of a particular irradiance direction vector.

From eqn (10), it is clear that the irradiance will increase in the high temperature fl ame sheets and decrease as it is absorbed in the intervening relatively cool fuel, air, and product gases that may contain soot formed elsewhere and transported with bulk fl ow. Since in this heuristic exam-ple, the fl ames are repeated, it is useful to think of an average over a single unit cell (i.e. a fl ame sheet and the surrounding fuel and air, with whatever products they have in them). Using the notation, · Ò to represent this cell average, eqn (10) becomes

4

( ) ( ) .T

s I s I ss

⟨ ⋅∇ ⟩ + ⟨ ⟩ =πa

a

(11)

Since the number of sheets in large fi res is quite large, let the number of fl ame sheets in this heuristic example to be infi nite so boundary conditions are not important. Recall that property measurements indicate that optically thick conditions exist in large hydrocarbon fuel fi res. Under these idealized heuristic conditions, the irradiance along the direction vector normal to the repeat fl ame sheets eventually reaches a ‘saturation’ condition in which the mean value of the irradiation does not change from cell to cell (even though it does change within each cell because of emission and absorption). The gradient of the mean irradiance along the direction vector is zero, i.e.

⟨∇ ⟩ =( ) 0.I s (12)

For the current heuristic example, assuming that the irradiance and absorption are not correlated (again see Chapter 7 by Modest for details), eqn (11) becomes

4

.T

Is⟨ ⟩

⟨ ⟩ =π⟨ ⟩a

a (13)

Note that the absorption is in both the numerator and denominator. The implication is that to lead order, the irradiance is independent of the soot concentration in this heuristic example if the number of fl ame sheets is large enough that the irradiance saturates.

This simplifi ed case of radiative equilibrium therefore illustrates the primary importance of the overlap between the temperature and soot concentration fi elds. For real fi res, not all fl ame sheets are identical as in this heuristic example. However, given that the large fi res are optically thick over large regions, it is likely that radiative heat transfer is very sensitive to the overlap of the soot and temperature fi elds, and only moderately sensitive to the overall soot concentrations. This speculation is supported by recent measurements of emission spectra from 1 to 5 microns by Kearney [68], using fast-scanning spectroscopy from the exterior of the fi res at the lower end of the fully turbulent regime. Both time averaged and time resolved spectra show Planck-like distributions at a temperature of approximately 1400 K.

The results from the example (eqn (13)) also suggest that if the soot concentration overlap with the temperature fi eld is the same between a highly sooting fuel (for example a peak soot concentration of 17 ppm in the fl ame sheet) and a weakly sooting fuel (for example with a peak soot concentration of 0.17 ppm in the fl ame sheet) in a suffi ciently large fi re, the radiative fl ux levels would be similar. Even more dramatically, what is suggested by eqn (13) is that if a low sooting propensity fuel such as methane had an overlap with the temperature fi eld with a higher mean soot temperature (e.g. due to diffi culty in forming soot), then the emission in a large fi re would be even higher for this low sooting fuel.




It is interesting to note that there are signifi cant differences in the heat fl ux from large LNG and heavier hydrocarbon fi res. Typical heavy hydrocarbon fi res without smoke shielding have an effective surface emission of about 120 kW/m2. On the other hand, data from large LNG fi res suggest that the surface emission from LNG fi res is in the range from 150 to 350 kW/m2 (see the review by Luketa-Hanlin [67]). This result is counter-intuitive when compared to small scale fi res. Hamins et al. [42] point out that the radiative fraction from weakly sooting methane fi res (~20%) is smaller than that for more highly sooting fi res (~33%).

Smaller fi res do not have enough fl ame sheets to be optically thick and eqn (12) does not hold. In fact in the optically thin limit where the absorption term goes to zero in eqn (10), the irradi-ance is directly proportional to the soot concentration and path length. So it is not surprising from Table 1, that in small fi res, methane is weakly emitting compared to higher hydrocarbons, while in large fi res, it is more strongly emitting. To the authors’ knowledge, it is not known if the dif-ference in emission between large scale, heavy hydrocarbon and LNG fi res is related primarily to the unique chemical stability of the methane molecule, an absence of cold soot due to an inter-action between low production rates and mixing, a difference in optical properties, or a combina-tion of these effects.

Clearly, both temperature and soot concentration and, in particular, the joint soot concentra-tion and temperature statistics, are very important for quantifying radiation transport. To lead order, temperature is strongly affected by the chemistry of the fuel but also by radiation trans-port. Soot concentration appears to be strongly affected by transport processes. In a series of studies, Gore, Faeth, and colleagues measured the soot concentration in turbulent diffusion fl ames [69] with the hope that the soot concentration would be describable by equilibrium state relations like most of the gas-phase product species. However, these studies clearly showed that soot concentration do not collapse as a function of mixture fraction alone. There is a long time-scale process that prevents this feature from occurring.

The search for what processes are responsible for the nonequilibrium nature of the soot con-centration is currently an active area of research within the fi re community. There are several possibilities. If soot is treated as any other species, each term in the continuum transport equation could be responsible for the rate limiting process. These terms include soot production/destruc-tion, diffusional and advective transport. The relative magnitude of the terms has not been quan-tifi ed for real fi re conditions, so what follows is necessarily a qualitative description of possible important balances. This critical area of research is in fact in its infancy, based on what is known versus what needs to be known to quantify the relative importance of the various terms, and many possibilities exist for signifi cant contributions, experimentally, computationally, and theoreti-cally in this area.

4.4.1 Transport parameters affecting soot production/destructionSoot production/destruction, as it occurs within the length scales of the fl ame structures, is determined by soot chemistry in the context of the enthalpy and species fi elds. As rate pro-cesses, production and destruction compete with transport processes such as advection and diffusion that infl uence the enthalpy and species concentrations within the diffusion fl ame. In particular, the rate of soot destruction is obviously dependent on the soot concentration itself, which is discussed below.

Most obviously, soot production/destruction is infl uenced by the advection and diffusion of gas phase species. Diffusion fl ames, by their very nature, are a balance between diffusion and chemistry and have very strong spatial gradients in species and temperature. For this reason, chemical kineticists have preferred to develop kinetic mechanisms in more homogeneous condi-tions such as in shock tubes and fl at fl ame burners. The characteristic time scale of 1−10 ms




discussed above for soot production is given in this context. Obviously, away from the fl ame itself, where the temperature drops below 1000 K, soot production rates can be expected to com-pletely vanish. Detailed chemical kinetic mechanisms for soot have been evaluated in steady, laminar fl ames, (see e.g. the work of Smooke and colleagues, Smooke et al. [70] being a recent example), but to the authors’ knowledge, not in real turbulent conditions expected in a fi re.

Beyond simple gas-phase diffusion, two additional diffusive transport processes may affect soot production/destruction rates. As soot is formed, it is subject to differential diffusion and thermophoretic transport. Differential diffusion occurs because soot has such a high molecular weight relative to the gas phase species surrounding it that its diffusion relative to the surround-ing gases becomes effectively negligible. For example, diffusion coeffi cients are inversely pro-portional to the square root of the molecular weight. So when soot becomes larger than order 10,000 carbon atoms, the effective diffusivity of the soot drops to order 1% of the gas phase dif-fusivity. The lack of soot diffusion is evident from visualization studies in turbulent diffusion fl ames [71] that show soot as narrow streaks.

Thermophoresis is another diffusional force that can affect soot production. Thermophoresis acts on particles in temperature gradients to drive them to lower temperatures. As mentioned earlier, strong temperature gradients exist in fl ames, of the order of 1000 K/mm. A particle in such an environment will have more energetic collisions on the high temperature side of the particle than the low temperature side of the particle. The imbalance in forces results in a particle drift velocity toward lower temperatures. For a molecule in the gas phase, the collisional imbal-ance is also present, but considered to be differential diffusion based on the different diffusivities at different temperatures in the gradient. The rate balance between soot production and the thermophoretic drift velocity has not been quantifi ed for turbulent fi re conditions.

If signifi cant, thermophoresis may affect the soot emission in several ways. The drift to lower temperatures can slow rates of soot growth. Both the reduced production rates and the lower temperatures directly affect emission. Dehydrogenation, a fi nite rate process, results in soot optical properties switching from banded properties to broadband grey-body properties. If the time scale for dehydrogenation results in signifi cant displacement due to the thermophoretic drift-velocity before the optical properties become broadband, then the soot will effectively begin emission at a lower temperature than that at which incipient formation occurs. Finally, thermophoresis will act to slow down the passage of soot into and through the high temperature oxidation zones of the fl ame. To the authors’ knowledge, the effect of thermophoresis on oxidation rates is unknown.

In addition to diffusive transport processes, advective processes can also strongly affect soot formation rates. Turbulence induced strain on fl ames acts to decrease the residence time within the fl ames (i.e. thinning the fl ame and stretching it at the same time, so that the area increases proportionally). When the residence time is less than the chemical timescale for soot production to occur, soot production will cease. The long chemical time scales for soot production relative to gas phase heat release assures that soot production ceases long before the fl ames themselves are extinguished. Advantage is taken of this fact in the gas turbine industry to run nearly soot free without blowout while using high soot propensity aviation fuels that would otherwise pro-duce copious amounts of smoke, as they do in fi res.

To the authors’ knowledge, the degree to which soot production rates are retarded by turbulent strain rates in real fi res has not been quantifi ed. Clearly, visible evidence suggests that soot pro-duction rates are not completely suppressed to any large degree, which would be evidenced by the dominance of blue gas-phase emission over the ubiquitous red/orange/yellow soot emission. However, in regions of relatively high turbulence, such as behind a wind driven fi re, there is a distinct absence of cold soot (smoke). It is not known if this absence is due to a decrease in production, or due to transport issues or both.




Soot source terms are also likely affected by radiative transport. Overall, it can be expected that the enthalpy loss in the region of overlap between the highest temperatures and soot concen-trations will result in slower soot formation and destruction rates. Ultimately, if the soot loading is high enough, or as discussed previously, if the strain rate is low enough, the radiative loss term can result in fl ame quenching (and consequently, very low production/destruction rates in the quenched region).

It is also possible that soot production/destruction rates can be indirectly, but signifi cantly, affected by the integral effect of the time-history of enthalpy loss in the gas-phase products sur-rounding the soot. Due to the very small size of the soot particles, it is assumed that the particle phase and gas phase equilibrate very quickly in the presence of radiative heat transfer. The com-bustion products lose enthalpy due to soot radiation in addition to the gas phase radiation. As these products mix into the fuel and air streams, the mixture enthalpy is less than if the gases were adiabatic. At increasing elevations, the fuel and air streams will be increasingly diluted with combustion products that have lost energy due to radiative transfer. Hot combustion products are important to maintaining a fl ame. On the other hand, both CO2 and H2O are in use as fi re sup-pressants because of their high heat capacity. So with a history of radiative heat loss, their presence can be an energy sink.

4.4.2 Transport parameters affecting soot concentrationFrom the work of Gore, Faeth and colleagues discussed above, it is clear that soot concentration is dependent on a transport process in addition to chemical processes. There has been much dis-cussion in the community about what this slow transport process is. What follows is a possible physical explanation for turbulent fi res that draws on an analogy with laminar fl ames. In laminar fl ames, it is clear that both differential diffusion between the soot and gases, and thermophoresis result in regions within the fl ame where the balance between soot production and soot destruc-tion vary signifi cantly. For example, near the base of a laminar diffusion fl ame, the fuel diffuses into the air much more readily than the soot being produced by the fl ame diffuses. However, near the top of a steady laminar diffusion fl ame, as the fuel is depleted, the air diffuses much more readily than the soot, forcing the soot through the fl ame.

The turbulent fl ame analog of the laminar diffusion fl ame involves differential diffusion between the soot and gases in regions in which either air pockets, or tongues are depleted in an abundance of fuel, or fuel pockets are depleted in an abundance of air. Using the fl ame sheets as visualiza-tion tools to identify separation of fuel/product and air/product regions, it is clear from Figs 17 and 18, that the surface between these regions is highly convoluted. It is very unlikely that the fl ame sheets will be layered such that the fuel depletes at exactly the same time as the air depletes on either side of a folded fl ame sheet.

In most cases, an eddy will be either fuel rich or fuel lean. If the eddy is fuel rich, there will be a preponderance of fl ame folds that hold air pockets or tongues that will be depleted before the fuel. If the eddy is lean, there will be a preponderance of fl ame folds that hold fuel pockets or tongues that will be depleted before the air. At the base of a large fi re, where air is fi rst entrained deep into the fuel layer by the bubble and spike structure and large eddies, it can be assumed that there is a large preponderance of air tongues that burn out. At the top of the active fl aming region in a fi re, where the last of the fuel is depleted in an abundance of air, the situation will be reversed. This poor mixing effi ciency is perhaps the prime reason that fi res have low heat release rate per unit volume compared to man-made systems as noted by Cox [15].

An analogy can be drawn between the transient depletion of air tongues, and steady laminar inverse diffusion fl ames, and the transient depletion of fuel tongues and normal, steady, laminar




diffusion fl ames. In the case of an air tongue, as the air is depleted, the combustion products will diffuse into the surrounding fuel at a higher rate than the soot. As a consequence, fuel counterdif-fuses into the soot. In this manner soot produced by this fl ame is not consumed by this fl ame, but transported away, initially by differential diffusion, and more generally by convection, to be con-sumed by another fl ame. In analogy, in a laminar inverse diffusion fl ame, soot produced by that fl ame advects away from the producing fl ame. Due to differential diffusion, the combustion prod-ucts diffuse away from the soot to be replaced by counter diffusing fuel. This soot will be consumed by a later fl ame sheet surrounded by ambient air. Since there is a preponderance of air tongues near the base of a large turbulent fi re as air is initially mixed into the fuel plume, it is clear that soot concentrations can accumulate in the fuel rich regions near the base.

On the other hand, near the edge or top of a fi re in which the fuel is rapidly being depleted and is surrounded by an infi nite air supply, the soot within the fuel will be forced to pass through a fl ame sheet as the fuel tongues burn up. If the soot loading is too high, or the enthalpy loss due to radiation is too high, or the combustion has too long of residence time, or a combination of the above, the fl ame can quench and soot will break through to the air side. Clearly from Fig. 19, soot either breaks through or quenches the fl ames often near the edges of large fi res as can be seen by the ubiquitous smoke. The steady laminar analog of the fuel tongue burnout is the normal diffu-sion fl ame, with the quenching marked by the smoke point.

The role of turbulent mixing relative to a laminar fl ame is to create large fl ame surface area that results in relatively rapid reactant depletion. However, differential diffusion followed by advection results in regions near the base of both the laminar fl ame and the turbulent fi re in which the fl ames are net producers of soot, and regions near the top of both laminar fl ames and turbulent fi res in which the fl ames are net destroyers of soot. Due to differential diffusion, soot can exist in all mix-tures richer than stoichiometric, even if production of soot occurs in very narrow mixture fraction bands. Soot can break through to the lean side of stoichiometric, cool and become smoke.

This explanation is consistent with soot morphology which suggests soot growth or destruc-tion occurs mostly within a single fl ame sheet, and with the data that shows that soot concentra-tion is not a unique function of mixture fraction alone. On the other hand, future research may show this view to be overly simplifi ed or incorrect.

5 Future of transport research in fi res

From the theoretical physics perspective of deriving the fundamental mass, force and energy balances, the description of transport, particularly at continuum scales, is complete. It has been understood for about a century that the time rate of change of mass, momentum, and energy is balanced by advection, diffusion, and source terms for conserved quantities. While the useful-ness of this level of understanding cannot be overestimated, it is the solution of the fundamental transport equations that will provide the basis for scientifi c understanding of fi re phenomena.

In the absence of a break-though in mathematics that would permit a closed form solution, the expression of these fundamental equations will be through numerical simulation. As noted in the beginning of this chapter, it will be decades to tens of decades of continuous computational growth before machines are large enough that direct simulation of all the length scales is possi-ble. In the coming decades it will be necessary to formulate the problem by a combination of fi ltered equations with closure models, the desired nature of which is essentially the solution of the transport equations over the length scale ranges that we cannot resolve numerically. So we must have a partial solution (which we do not know in a scientifi c sense) to obtain the whole solution in order to be predictive.




The key scientifi c challenge in the coming decades, then, is to develop an understanding of the nature of the chemistry and physics that is the solution of the fundamental equations in the range of length and time scales that cannot be resolved numerically. The key engineering challenge of the future is to translate that understanding into computationally effi cient models that provide the best possible mean-response (given the available inputs), and to quantify the uncertainty.

While the fundamental expressions are elegant in their simplicity, the expression of the physics and chemistry, while remaining elegant, is anything but simple. In all the complexity, a simple truth is sometimes forgotten: it is only through the understanding of reality that we can obtain informa-tion we need to build the partial solutions, i.e. the models that we need, in order to obtain the whole solution. While science must demonstrate its validity ultimately through experimental means, it is clear that the existence of computational tools that can provide partial solutions to the fundamental equations are a powerful step in gaining scientifi c understanding. Further, laser-based diagnostics developed over the last few decades have permitted unprecedented data sets and insight.

In the context of the hundreds of thousands of years that humankind has interacted with fi re, the next century is the blink of an eye. We are on the threshold of scientifi c understanding of one of humankind’s greatest threats and one of his greatest successes. Historically unique opportuni-ties present themselves to coming generations of scientists to use the rapidly evolving power of computational science in combination with ever more advanced diagnostics to fi nally gain a complete understanding of fi re.

Acknowledgements

The authors would like to thank their many colleagues, particularly at the University of Utah and Stanford, for sharing their insights into transport phenomena in fi res. The authors would also like to acknowledge contributions by Chris Shaddix and John Hewson to this chapter. Sandia is a mul-tiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

References

Markstein, G.H., Radiative energy transfer from turbulent diffusion fl ames. [1] Combustion and Flame, 27, pp. 51−63, 1976.Holman, J.P., [2] Heat Transfer, 4th edn, McGraw-Hill: New York, NY, p. 13, 1976.Solum, M.S., Sarofi m, A.F., Pugmire, R.J., Fletcher, T.H. & Zhang, H., C-13 NMR analy- [3] sis of soot produced from model compounds and a coal. Energy Fuels, 15, pp. 961−971, 2001.Mulholland, G.W., Liggett, W. & Koseki, H., Effect of pool diameter on the properties of [4] smoke produced by crude oil fi res. 26th Symposium (International) on Combustion, The Combustion Institute: Pittsburgh, PA, pp. 1445−1452, 1996.Williams, J.H. & Gritzo, L.A., In situ sampling and transmission electron microscope analy- [5] sis of soot in the fl ame zone of large pool fi res. 27th Symposium (International) on Combus-tion, The Combustion Institute: Pittsburgh, PA, pp. 2707−2714, 1998.Vicente, W.G. & Kruger, Jr., C.H., [6] Introduction to Physical Gas Dynamics, Krieger Pub. Co.: Huntington, NY, 1975.Babrauskas, V., Free burning fi res. [7] Fire Safety Journal, 11, pp. 33−51, 1985.Schneider, M.E., Keltner, N.R. & Kent, L.A., Thermal measurements in the nuclear winter [8] fi re test, SAND88-2839, Sandia National Laboratories, 1989.




Williams, F.A., [9] Combustion Theory, Benjamin/Cummings Pub. Co.: Menlo Park, CA, 1985.Najm, H.N., Schefer, R.W., Milne, R.B., Mueller, C.J., Devine, K.D. & Kempka, S.N., [10] Numerical and experimental investigation of vortical fl ow-fl ame interaction, SAND98-8232, Sandia National Laboratories, 1998.Mell, W.E., McGrattan, K.B. & Baum, H.R., Numerical simulation of combustion in fi re [11] plumes. 26th Symposium (International) on Combustion, The Combustion Institute, Pitts-burgh, PA, pp. 1523−1530, 1996.McCaffrey, B.J., [12] Purely Buoyant Diffusion Flames: Some Experimental Results, National Bureau of Standards, (now NIST), NBSIR 79-1910, 1979.Tennekes, H. & Lumley, J.L., [13] A First Course in Turbulence, The MIT Press: Cambridge, MA, p. 99, 1972.Drysdale, D., [14] An Introduction to Fire Dynamics, Wiley & Sons: NY, 1985.Cox, G. (ed.), Basic Considerations (Chapter 1). [15] Combustion Fundamentals of Fire, Academic Press: London, UK, pp. 1−30, 1995.Tieszen, S.R., Nicolette, V.F., Gritzo, L.A., Holen, J.K., Murray, D. & Moya, J.L., Vortical [16] structures in pool fi res, observations, speculation, and simulation, SAND96-2607, Sandia National Laboratories, 1996.Gritzo, L.A., Gill, W. & Nicolette, V.F., Very large scale fi res. ASTM STP 1336, eds N.R. [17] Keltner, N.J. Alvares & S.J. Grayson, American Society for Testing and Materials, 1998.Baum, H.R., McGrattan, K.B. & Rehm, R.G. (eds.), Three dimensional simulations of fi re [18] plume dynamics. Fire Safety Science – Proceedings of the 5th International Symposium, pp. 511−522, 1997.Krishnamoorthy, G. & Smith, P., Soot in Combustion Simulations. [19] 5th Asia-Pacifi c Confer-ence on Combustion, The University of Adelaide, Adelaide, Australia, 18−20 July 2005.Tieszen, S.R., On the fl uid mechanics of fi re. [20] Annual Review of Fluid Mechanics, 33, pp. 67−92, 2001.Katta, V.R. & Roquemore, W.M., Role of inner and outer structures in transitional jet [21] diffusion fl ames. Combustion and Flame, 92, pp. 274−282, 1993.O’Hern, T.J., Weckman, E.J., Gerhart, A.L., Tieszen, S.R. & Schefer, R.W., Experimental [22] study of a turbulent buoyant helium plume. J. Fluid Mech., 544, pp. 143−171, 2005.Dimotakis, P.E., Miake-Lye, R.C. & Papantoniou, D.A., Structure and dynamics of round [23] turbulent jets. Physics of Fluids, 26, pp. 3185−3192, 1983.Coats, C.M., Coherent structures in combustion. [24] Prog. Energy Combust. Sci., 22, pp. 427−509, 1996.Dai, Z., Tseng, L.K. & Faeth, G.M., Velocity statistics of round, fully developed, buoyant [25] turbulent plumes. Journal of Heat Transfer, 117, pp. 138−145, 1995.Dai, Z., Tseng, L.K. & Faeth, G.M., Velocity/mixture fraction statistics of round, self-pre-[26] serving, buoyant turbulent plumes. Journal of Heat Transfer, 117, pp. 918−926, 1995.Kotsovinos, N.E., Turbulence spectra in free convection fl ow. [27] Physics of Fluids A 3(1), pp. 163−167, 1991.Ashurst, W.T., Vorticity generation in a nonpremixed fl ame sheet, SAND89-8592, Sandia [28] National Laboratories, 1989.Hamins, A., Yang, J.C. & Kashiwagi, T., An experimental investigation of the pulsation fre-[29] quency of fl ames. 24th Symposium (International) on Combustion, pp. 1695−1702, 1992.Cetegen, B.M. & Ahmed, T.A., Experiments on the periodic instability of buoyant plumes [30] and pool fi res. Combustion and Flame, 93, pp. 157−184, 1993.Zhou, X.C. & Gore, J.P., Air entrainment fl ow fi eld induced by a pool fi re. [31] Combustion and Flame, 100, pp. 52−60, 1995.




Zhou, X.C. & Gore, J.P., Experimental estimation of thermal expansion and vorticity [32] distribution in a buoyant diffusion fl ame. 27h Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 2767−2773, 1998.Soteriou, M.S., Dong, Y. & Cetegen, B.M., Lagrangian simulations of the unsteady near [33] fi eld dynamics of planar buoyant plumes. Phys. Fluids, 14(9), 3118−3140, 2002.Tieszen, S.R., O’Hern, T.J., Weckman, E.J. & Schefer, R.W., Experimental study of the [34] effect of fuel mass fl ux on a one meter diameter methane fi re and comparison with a hy-drogen fi re. Combustion and Flame, 139(1–2), pp. 126−141, 2004.Tieszen, S.R., Pitsch, H., Blanquart, G. & Abarzhi, S., Toward the development of a [35] LES-SGS closure model for buoyant plumes. Proceedings of the Summer Program 2004, Center for Turbulence Research, Stanford, University, Stanford CA, pp. 341−352, 2004.Wang, C., [36] The Effects of Curvature on Turbulent Mixing Layers, PhD Dissertation, California Institute of Technology, Pasadena, CA, 1984.Tieszen, S.R., O’Hern, T.J., Schefer, R.W., Weckman, E.J. & Blanchat, T.K., Experimen-[37] tal study of the fl ow fi eld in and around a one meter diameter methane fi re. Combustion and Flame, 129(4), pp. 378−391, 2002.Heskestad, G., A Reduced-Scale Mass Fire Experiment. [38] Combustion and Flame, 83, pp. 293−301, 1991.Vincent, J.R. & Gollahalli, S.R., An experimental study of the interaction of multiple [39] liquid pool fi res. Journal of Energy Resources Technology, 117, pp. 37−42, 1995.Fric, T.F. & Roshko, A., Vortical structures in the wake of a transverse jet. [40] Journal of Fluid Mechanics, 279, pp. 1−47, 1994.Hamins, A., Kashiwagi, T. & Burch, R.R., Characteristics of pool fi re burning. [41] Fire Re-sistance of Industrial Fluids, eds. G.E. Totten, & J. Reichel, American Society for Testing and Materials, Philadelphia, PA, ASTM STP 1284, 1996.Hamins, A., Konishi, K., Borthwick, P. & Kashiwagi, T., Global properties of gaseous [42] pool fi res. 26th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, USA, pp. 1429−1436, 1996.McCaffrey, B., Flame height (Chapter 2-1). [43] The SFPE Handbook of Fire Protection Engi-neering, 2nd edn, National Fire Protection Association: Quincy, MA, pp. 2-1−2-8, 1995.Heskestad, G., Dynamics of the fi re plume. [44] Phil. Trans. R. Soc. Lond. A, 356, pp. 2815−2833, 1998.Heskestad, G., On Q* and the dynamics of turbulent diffusion fl ames. [45] Fire Safety Journal, 30, pp. 215−227, 1998.Heskestad, G., Turbulent jet diffusion fl ames: consolidation of fl ame height data. [46] Combus-tion and Flame, 118, pp. 51−60, 1999.Hewson, J.C., Tieszen, S.R., Sundberg, W.D. & DesJardin, P.E., CFD modeling of fi re [47] suppression and its role in optimizing suppressant distribution. Proceedings of the Halon Options Technical Working Conference, Albuquerque, NM, 2003.White, F.M., [48] Viscous Fluid Flow, McGraw-Hill: New York, NY, pp. 309−402, 1991.T’ien, J.S., Diffusion fl ame extinction at small stretch rates: the mechanism of radiative [49] loss. Combustion and Flame, 65, pp. 31−34, 1986.Murphy, J.J. & Shaddix, C.R., [50] Soot Properties and Species Measurements in a Two-Meter Diameter JP-8 Pool Fire: 2003 Test Series, SAND2005-0337, Sandia National Laborato-ries Report, 2005.Gritzo, L.A., Sivathanu, Y.R. & Gill, W., Transient measurements of radiative properties, [51] soot volume fraction and soot temperature in a large pool fi re. Combust. Sci. and Tech., 139(1–6), p. 113, 1998.




de Ris, J. Fire radiation [52] − a review. Seventeenth Symposium (International) on Combus-tion, The Combustion Institute: Pittsburgh, PA, pp. 1003−1016, 1979.Street, J.C. & Thomas, A., Carbon formation in pre-mixed fl ames. [53] Fuel, 34, pp. 4−36, 1955.Palmer, H.B. & Cullis, H.F., The formation of carbon from gases. ed. P.L. Walker, [54] Chem-istry and Physics of Carbon, Vol. 1, Marcel Dekker: New York, pp. 265−325, 1965.Wagner, H.Gg., Soot formation in combustion.[55] Proc. Combust. Inst., 17, pp. 3−19, 1979.Haynes, B.S., Wagner, H.Gg., Soot formation. [56] Prog. Energy Combust. Sci., 7, pp. 229−273, 1981.Glassman, I., Soot formation in combustion processes. [57] Proc. Combust. Inst., 22, pp. 295−311, 1988.Richter, H. & Howard, J.B., Formation of polycyclic aromatic hydrocarbons and their [58] growth to soot − a review of chemical reaction pathways. Prog. Energy Combust. Sci., 26, pp. 565−608, 2000.Kennedy, I.M., Models of soot formation and oxidation. [59] Prog. Energy Combusti. Sci., 23, pp. 95−132, 1997.Jensen, K.A., Suo-Anttila, J.M. & Blevins, L.G., Characterization of soot properties in [60] two-meter JP-8 pool fi res, SAND2005-0337, Sandia National Laboratories, 2005. Dobbins, R.A. & Megaridis, C.M., Absorption and scattering of light by polydisperse ag-[61] gregates. Applied Optics, 30(33), 1991.Koylu, U.O., Faeth, G.M., Farias, T.L. & Carvalho, M.G., Fractal and projected structure [62] properties of soot aggregates. Combustion and Flame, 100, pp. 621−633, 1995.Dobbins, R.A., Soot inception temperature and the carbonization rate of precursor par-[63] ticles. Combustion and Flame, 130, pp. 204−214, 2002.Shaddix, C.R. & Smyth, K.C., Laser-induced incandescence measurements of soot pro-[64] duction in steady and fl ickering methane, propane, and ethylene diffusion fl ames. Com-bustion and Flame, 107, pp. 418−452, 1996.Santoro, R.J., Yeh, T.T., Horvath, J.J. & Semerjian, H.G., The transport and growth of [65] soot particles in laminar diffusion fl ames. Combustion Science and Technology, 53, pp. 89−115, 1987.Kent, J.H., Quantitative relationship between soot yield and smoke point measurements. [66] Combustion & Flame, 63, pp. 349−358, 1986.Luketa-Hanlin, A., A review of large-scale LNG spills: experiments and modeling. [67] Jour-nal of Hazardous Materials, 132(2–3), pp. 119−140, 2006.Kearney, S., Temporally resolved radiation spectra from a sooting, turbulent pool fi re. [68] Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposi-tion, New York, NY, 11−16 November 2001.Gore, J.P. & Faeth, G.M., Structure and radiation properties of luminous turbulent acety-[69] lene/air diffusion fl ames. ASME Journal of Heat Transfer, 110, pp. 173−181, 1988.Smooke, M.D., Hall, R.J., Colket, M.B., Fielding, J., Long, M.B., McEnally, C.S. & Pfef-[70] ferle, L.D., Investigation of the transition from lightly sooting towards heavily sooting co-fl ow ethylene diffusion fl ames. Combustion, Theory and Modeling, 8(3), pp. 593−606, 2004.Xin, Y., Gore, J.P., Nathan, G.J., Mikofski, M.A. & Geigle, K.P., Two-dimensional soot [71] distributions in buoyant turbulent fi res. Proceedings of the Combustion Institute, 30, pp. 719−726, 2005.



Documents

CHAPTER 2 Transport phenomena that affect heat transfer … · CHAPTER 2 Transport phenomena that affect heat transfer in fully turbulent ﬁ res S.R. Tieszen 1 & L.A. Gritzo2 1Fire