4.2. Fire Modeling

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4.2. Fire Modeling

CFD simulation of fire incidents (e.g., large-scale jet fire and pool fire) will provide information about the flow field and characteristics of the incident fires, especially in terms of hazards associated with fire events. In the context of process safety, these two incidents are associated with large-scale releases of flammable materials in gas or liquid phases because of loss of primary containment events in industrial settings. Other types of fires such as compartmental fires (e.g., in residential or office buildings or industrial facilities), large-scale fires (e.g., forest fires), and deliberated fire activities (e.g., flare fires or fires in combustion chambers) have been covered extensively in published literature (Novozhilov, 2001). This also limits the boundary of hazards associated with large-scale jet fire and pool fires in process safety. Generally, only radiation hazard and flame impingement on nearby objects, which could set up a sequence of incident events due to the domino effect, are considered in process safety consequence modeling using CFD (Cozzania et al., 2009; Darbra et al., 2012). Other types of fire hazards such as combustion products dispersion, toxic gases dispersion, and fire spread are covered elsewhere.

4.2.1. CFD Modeling of Fire

CFD simulation of fire in the context of process safety is greatly benefitted from CFD studies in combustion engineering and fire safety engineering studies (Baukal et al., 2001; Novozhilov, 2001; Rasbash, 2004). Combustion models, soot formation models, and radiation models, developed in these two disciplines, are used directly in process safety large-scale jet fire and pool fire simulations. Essentially, in CFD simulation of large-scale jet fires and pool fires, there are three important elements: (1) geometry; (2) the mechanism for energy, momentum, and mass transportation provided by the CFD models; and (3) the detailed descriptions of the mechanisms and the kinetics of the fire combustion provided by the fire models (listed in Table 4.3). Extensive reviews on CFD simulation of fire and related physical models have been published (Novozhilov, 2001). Guidelines for using CFD for fire and smoke modeling are listed in a publication provided by the Canadian National Research Council (Hadjisophocleous and McCartney, 2005).

4.2.1.1. Geometry representation

There are typically three factors to be considered in CFD geometry for fire modeling: (1) computational domain, (2) grid size, and (3) boundary conditions. The computational domain of an entire event is the control volume encompassing the affected areas and the surrounding areas. The size of the computational domain for fire incidents is dependent on the size of the fire. The other parameters of the computational domain, including thermal and hydrostatic boundary conditions, are then defined to complete the computational domain. The grid size is determined based on the computational domain sizes and computing resources available to provide grid independent, accurate, and affordable solutions. The smaller the grid size, the more accurate is the solution but the higher is the cost of computing resources. Thus, each scenario is unique and can have its own optimum grid size.

In large-scale jet fire and pool fire modeling, relatively simple geometries are used. It is often rectangular or cylindrical volumes surrounding the incident fire. The grid size is required to be very fine near the fire sources but may be set larger away from the sources. Symmetry rule may be applied to reduce the number of grid cells, thus reducing the computing time.

4.2.1.2. Turbulent model

The use of Reynolds-averaged or Farve-averaged (density averaged) Navier–Stokes (RANS) with two-equation closure for a turbulence k–ε model is the primary type of turbulent model used in fire modeling due to its robustness, balance between accuracy and computational cost (Blazek, 2007; Novozhilov, 2001). Many modifications have been made to the original k–ε turbulence model either as additional terms or additional equations to address phenomena such as buoyancy, stratification, near wall treatment, and fire shapes. The basic assumption for the k–ε model is the eddy viscosity model where k is the turbulence kinetic energy and ε is the energy dissipation rate. The two parameters k and ε arecalculated from the following two equations (Novozhilov, 2001):

$\frac{\partial (ρ k)}{\partial t} + \nabla (ρ \vec{U} k) = \nabla (\frac{μ_{ε}}{σ_{k}} \nabla k) + P + G - ρ ò$ $\frac{\partial (ρ k)}{\partial t} + \nabla (ρ \vec{U} k) = \nabla (\frac{μ_{ε}}{σ_{k}} \nabla k) + P + G - ρ ò$

(4.1)

$\frac{\partial (ρ ò)}{\partial t} + \nabla (ρ \vec{U} ò) = \nabla (\frac{μ_{e}}{σ_{ò}} \nabla ò) + \frac{ò}{k} (c_{1} [P + c_{3} \max (G, 0)] - c_{s} ρ ò)$ $\frac{\partial (ρ ò)}{\partial t} + \nabla (ρ \vec{U} ò) = \nabla (\frac{μ_{e}}{σ_{ò}} \nabla ò) + \frac{ò}{k} (c_{1} [P + c_{3} \max (G, 0)] - c_{s} ρ ò)$

(4.2)

where

$P = μ_{e} {2 [{(\frac{\partial u}{\partial x})}^{2} + {(\frac{\partial v}{\partial y})}^{2} + {(\frac{\partial w}{\partial z})}^{2}] + {(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})}^{2} + {(\frac{\partial v}{\partial z} + \frac{\partial w}{\partial y})}^{2} + {(\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x})}^{2}}$ $P = μ_{e} {2 [{(\frac{\partial u}{\partial x})}^{2} + {(\frac{\partial v}{\partial y})}^{2} + {(\frac{\partial w}{\partial z})}^{2}] + {(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})}^{2} + {(\frac{\partial v}{\partial z} + \frac{\partial w}{\partial y})}^{2} + {(\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x})}^{2}}$

(4.3)

$G = g (\frac{μ_{e}}{σ_{h}}) (\frac{1}{ρ}) (\frac{\partial p}{\partial z})$ $G = g (\frac{μ_{e}}{σ_{h}}) (\frac{1}{ρ}) (\frac{\partial p}{\partial z})$

(4.4)

$μ_{e} = μ_{l a m} + μ_{t}$ $μ_{e} = μ_{l a m} + μ_{t}$

(4.5)

$μ_{t} = ρ c_{μ} \frac{k^{2}}{ò}$ $μ_{t} = ρ c_{μ} \frac{k^{2}}{ò}$

(4.6)

where μ_e is the eddy viscosity, μ_lam is the laminar viscosity, μ_t is the turbulence viscosity, and the constants: σ_h = 0.7, c₁ = 1.44, c₂ = 1.92, and c₃ = 1.0.

Other turbulent models available to be used with RANS, such as the Reynolds normalization group (RNG) k–ε and the realizable k–ε model, or more sophisticated turbulent models, such as the Reynolds stress model, have been used in combustion modeling but have not been used in large-scale fire simulations (Papageorgakis and Assanis, 1999; Novozhilov, 2001; Blazek, 2007). LES and the DNS, because of their high computing power demand, have been only used in small-scale combustion studies (Novozhilov, 2001; Calhoun et al., 2005; Tugnoli et al., 2008; Brennan et al., 2009).

4.2.1.3. Fire models

The fire models, which are used in both jet fire and pool fire modeling, provide the detailed description of the mechanisms and kinetics of the fire combustion, including combustion model, soot formation model, and radiation model.

Combustion model

The combustion chemistry is very complex. Depending on fuels, it could involve hundreds of elementary reactions; thus it requires sophisticated models and extensive computing resources for a complete description of the combustion phenomenon (Baukal et al., 2001; Novozhilov, 2001). In order to simulate fire, especially large-scale fires such as jet fire and pool fire, simplified combustion models are often used. The conserved scalar model with fast chemistry assumption and the eddy break-up model are two simple combustion models, which describe the combustion reaction between fuel and oxygen. The main benefit of these two models is simplicity in implementation, but the main drawback is the inability to predict the formation of species, especially the toxic combustion products such as carbon monoxide.

• The conserved scalar model with fast chemistry (Novozhilov, 2001): The conserved scalar model uses an assumption that the reaction time is significantly shorter than the mixing time and the combustion reaction is a complete, nonreversible reaction. This assumption is somewhat reasonable in certain types of fire modeling such as hydrogen jet fire. The conserved scalar is the quality that does not change during combustion reaction, and using the conserved scalar greatly simplifies the turbulent combustion rate calculation. For example:

$F = n O \to (n + 1) P$ $F = n O \to (n + 1) P$

(4.7)

where F is the fuel; O is the oxidant; P is the combustion products; and n is the stoichiometric number for the combustion reaction.

The scalars in this case are mixture fractions ξ and β:

$β = Y_{F} - \frac{Y_{O}}{n}$ $β = Y_{F} - \frac{Y_{O}}{n}$

(4.8)

$ξ = \frac{β - β_{F}}{β_{F} - β_{O}}$ $ξ = \frac{β - β_{F}}{β_{F} - β_{O}}$

(4.9)

where the indexes F and O refer to the fuel and oxidant streams, respectively.

• The eddy break-up model (Novozhilov et al., 1996; Novozhilov, 2001): The eddy break-up combustion model and its derivatives are very popular models in fire study, especially for large-scale fire modeling. This model uses two variant approaches assuming that the chemical reaction rate is controlled by the rate of molecular mixing of reactants, which in turn is related to the rate of dissipation of turbulent eddies. The reaction rate, R, is calculated by using the following equation:

$R = - C_{R} ρ \frac{ò}{k} \min {{\bar{Y}}_{F}, {\bar{Y}}_{O} / r}$ $R = - C_{R} ρ \frac{ò}{k} \min {{\bar{Y}}_{F}, {\bar{Y}}_{O} / r}$

(4.10)

where

\min {{\bar{Y}}_{F}, {\bar{Y}}_{O} / r}

$\min {{\bar{Y}}_{F}, {\bar{Y}}_{O} / r}$

is the lesser rate in fuel rich stream or in oxygen rich stream and C_R is the eddy break-up constant.

The constant C_R is calculated from:

$C_{R} = 23.6 {(\frac{v ò}{k^{2}})}^{1 / 4}$ $C_{R} = 23.6 {(\frac{v ò}{k^{2}})}^{1 / 4}$

(4.11)

To limit the rate at low temperatures, a controlling term is used. For example, the Arrhenius equation is used to calculate the reaction rate at low temperatures:

$R = {\bar{Y}}_{F} {\bar{Y}}_{O} A_{p} \exp (\frac{- E}{R \bar{T}})$ $R = {\bar{Y}}_{F} {\bar{Y}}_{O} A_{p} \exp (\frac{- E}{R \bar{T}})$

(4.12)

where A_p is the Arrhenius constant, E is the activated energy, R is the gas constant, and

\bar{T}

$\bar{T}$

is the average temperature.

For a complete description of fire, the detailed chemistry models are needed. They allow accurate predictions of toxic gases, such as CO, NO_x, and SO_x, generated in a fire. These toxic gases are also one of the major fire hazards, especially for fire in confined spaces. For example, models available for this type of detailed chemistry include the flamelet model which offers detailed chemistry, based on laminar flamelet considerations. The flamelet approach considers the diffusion flame as a statistical ensemble of thin laminar flames, called flamelets, and assume that the changes in the local mixing environment is much smaller than the mixing time scale (Novozhilov, 2001). The flamelet model is able to describe a complex combustion reaction and is therefore able to predict combustion species. Other more advanced models are the Monte Carlo joint PDF (Pope, 1985) and the conditional moment closure models (Klimenko and Bilger, 1999). These two sophisticated models, although more expensive in terms of computing resources, are becoming more popular in fire modeling to describe the detailed combustion chemistry (Yeoh and Yuen, 2009).

Radiation model

Radiation exchange plays a very important role in fires and is the major hazard in the context of process safety (2005). The radiation model is also a very important part of a realistic CFD fire modeling because, in many situations, radiation is a dominant mode of heat transfer in the vicinity of a fire source, especially in fires of very large scale (Novozhilov, 2001). In large-scale accidental jet fire and pool fire modeling, the radiation model is used to calculate the surface emissivity power (SEP), which in turn is used in a Probit equation to calculate the limit exposure time and safe distances for personnel and equipment. The radiation model calculates the spectral intensity I_λ, defined as the radiant energy (per unit time and per unit wave length interval) passing per unit surface area normal to the direction Ω, into a unit solid angle centered around Ω (Novozhilov, 2001). The spectral intensity is calculated as follows (Novozhilov, 2001):

$\frac{1}{c} \frac{\partial I_{λ}}{\partial t} + \frac{\partial I_{λ}}{\partial s} = W_{λ}$ $\frac{1}{c} \frac{\partial I_{λ}}{\partial t} + \frac{\partial I_{λ}}{\partial s} = W_{λ}$

(4.13)

where s is the distance along a ray in the direction Ω, W_λ is the source term, and c is the characteristic velocity for the radiation exchange.

The source term W_λ is from emission adsorption and scattering of species presented in fires:

$W_{λ} = W_{e m i s s i o n} - W_{a b s o r p t i o n} + W_{s c a t t e r i n g - i n} - W_{s c a t t e r i n g - o u t}$ $W_{λ} = W_{e m i s s i o n} - W_{a b s o r p t i o n} + W_{s c a t t e r i n g - i n} - W_{s c a t t e r i n g - o u t}$

(4.14)

The radiative characteristics of gas mixtures in a fire involve many species and are very complicated; thus, certain simplifications need to be made so that the calculation is justifiable with reasonable computing resources. It is observed that in a fire, soot, CO₂, and H₂O account for more than 95% of the radiation absorption and radiation. This allows the radiation model to be divided into two groups: (1) a gray gas model, where soot presence is significant in the fire; and (2) a nongray gas model, where soot presence is less significant. Hydrocarbon fire, either in a large-scale jet fire or pool fire, often results in gray flame because of a high level of soot formation. The following assumptions are often used in radiation calculation:

• Soot-band emission assumption: A simple model to calculate radiation in a fire, assuming that the fuel-side soot layer of the flame zone is the only source of radiation. This simplification assumption may lead to underestimation of the radiation (Novozhilov, 2001).

• Gray gas assumption: This model assumes that the adsorption and emission coefficients are not dependent on the radiation wavelength, simplifying the radiation calculations. Using this model, the absorption coefficients of the simulated fire can be split into two separated parts: gas and soot. Furthermore, scattering parts of the equation may also be neglected (Novozhilov, 2001).

Using these two assumptions, two methods are available to calculate the radiation of a gray gas fire:

• Flux method (Adiga et al., 1989, 1990; Novozhilov, 2001): The flux method used to calculate fire radiation is popular because it also uses the same numerical techniques used to solve the main hydrodynamic equations (the set of transport equations). In the flux method, radiation equations are solved to calculate the radiating fluxes for three forward and three backward directions in x, y, z coordinates. Several improvements have been made in order for this model to take into account angle dependence in Cartesian coordinates.

• Discrete transfer method (Lockwood and Shah, 1981; Novozhilov, 2001): This model calculates the radiation fluxes by tracing “rays” of radiation through computational domains and solving appropriate equations for the radiation density along each ray. A separated radiation computational grid, besides the main computational grid for the transport equations, is needed; and the accuracy of the method can be adjusted by changing the input parameters to control the numbers and the directions of each ray. This model is widely used because it provides good accuracy with a reasonable computing resource.

Nongray fire is fire having a relatively small amount of soot, like jet fire of non-hydrocarbon fire such as hydrogen jet fire or much diluted hydrocarbon fire. The radiative properties of the non-gray fires can be calculated from methods such as the narrow-band statistical model or the exponential wide-band model (Yan and Holmstedt, 1999; Novozhilov, 2001). The exponential wide-band model takes into account that the infrared radiation of each species in a fire is concentrated into six wide-band regions associated with the principal vibrational transitions of the combustion species. The narrow-band statistical model calculates the radiation by dividing the spectrum into small intervals for each radiating species (i.e., combustion products such as CO₂ and H₂O). These intervals are assumed to follow an exponential probability distribution and have random locations. This method requires a large number of tabulated parameters and has not been used widely in large-scale jet fire or pool fire simulations. Simplified models based on this method have been developed.

Soot formation model

Soot formation is a very complex process in combustion. Soot is very important in fire simulation because of its effect on the radiation through the absorption and scattering process. Whereas in certain combustion processes, such as hydrogen combustion or methane combustion, soot formation may be ignored, in other hydrocarbon combustion processes such as ethylene and acetylene, soot presence is significant to the combustion products.

A number of soot formation models have been introduced (Novozhilov, 2001). For example, a soot formation model can be as simple as a constant factor related to a local value of mixture fraction for each fuel (Bilger, 1977; Orloff et al., 1987), or using a similar eddy break-up approach for combustion process, or more comprehensive using a set of equations for soot fraction and particulate number density (Novozhilov, 2001). Another aspect to be considered of a soot formation model is the coupling between soot production and radiative heat loss from flame because soot is often the primary radiating species (Brookes and Moss, 1999; Novozhilov, 2001).

Fuel source

The fuel source models are used to determine the amount of fuel going into the fire such as the release rate in jet fires or the evaporating rate in pool fires. These parameters are calculated using experimental data or other empirical model programs then incorporated as input into the CFD fire modeling setup.

4.2.2. Applications of CFD Modeling Data into a Radiative Probit Function

Results from CFD simulations can be used to calculate the surface emission power of the accidental fires, which then are used to determine the safe distances for personnel and equipment. The results can also be used in the Probit equation to calculate the maximum allowance time when exposed to radiation (Rew and Hulbert, 1996; Crowl and Louvar, 2002; Mannan and Lees, 2005; Pontiggia et al., 2010; Raj, 2005, 2007a–c; Pontiggia et al., 2010).

$\Pr = a + b \ln (D)$ $\Pr = a + b \ln (D)$

(4.15)

where D is the radiation dose, and a and b are specific parameters for each situation.

The radiation dose is calculated from:

$D = \int_{0}^{\infty} S E P^{n} d t$ $D = \int_{0}^{\infty} S E P^{n} d t$

(4.16)

where SEP is the surface emission power, t is time, and n is specific parameters for each situation.

The relationship between the death probability, P, and the corresponding Probit value, Pr, is:

$P = 0.5 [1 + e r f (\frac{\Pr - 5}{\sqrt{2}})]$ $P = 0.5 [1 + e r f (\frac{\Pr - 5}{\sqrt{2}})]$

(4.17)

4.2.3. CFD Modeling Codes

There are several CFD fire modeling packages available, including commercial codes, government codes, and research codes (Vaagsaether et al., 2007; Skjold, 2010). They can be categorized into two groups: (1) fire modeling codes, which are designed only for modeling fire such as JASMINE (Cox and Kumar, 1987), KAMELON, SMARTFIRE, and SOFIE; and (2) general purpose CFD codes that can be used for fire modeling such as PHOENICS, CFX, and FLUENT. These CFD codes and their developers are listed in Table 4.4.

In a fire event, typically there are five stages involved, including ignition, growth, flashover, fully developed, and decay (Novozhilov, 2001). These five stages have been modeled and studied using CFD, particularly in fire safety engineering. In process safety, CFD simulation of fire is limited to open fields, allowing non-premixed fully developed fires, which results from loss of primary containment events, to release flammable materials. The following sections will discuss CFD simulations in each type of accidental fire (e.g., large-scale jet fire and pool fire).

Table 4.4

Several Commercial Available CFD Packages for Fire Simulations

Name	Developer
CFX	ANSYS
FLUENT	ANSYS
PHOENICS	FRS
JASMINE	FRS
SMARTFIRE	UoG
KAMELON	SINTEF/NTH
SOFIE	Cranfield/FRS
ALOFT-FT	NIST
FDS	NIST
KOBRA-3D	Technik GmbH
SOLVENT	Massachusetts Highway Department; Innovative Research, Inc.; Parsons Brinckerhoff Quade & Douglas, Inc.
STAR-CD	Computational Dynamics Ltd

Figure 4.2 A large-scale jet fire resulted from the release of flammable gas.

4.2.4. Jet Fire

Jet fires are formed when the high-speed releases of various fuel types from pressurized high momentum sources ignite to form flames with trajectories determined by the orientation of the leak. Figure 4.2 illustrates the simplest case of jet fire in which the source is a pressurized flammable gas release, such as compressed natural gas, hydrogen, or other flammable gases. This jet fire was set up as part of a training exercise for firefighters in realistic industrial settings at the Brayton Fire Training Field in College Station, Texas.

Gas phase jet fires are the most encountered jet fire incidents in industry. If material sources contain pressurized gas–liquid mixtures, the ignited flammable streams will be two-phase jet fire. Two-phase jet fires can also form due to the release of highly pressurized liquid if storing conditions allow the liquids to flash evaporation upon release into atmospheric conditions such as liquid natural gas or liquid petroleum gas (LPG).

The main hazards of jet fire are (Lowesmith et al., 2007):

1. Radiation on nearby equipment and personnel, and

2. Possible impingement of the jet flames on nearby objects.

If the impinged objects are storage vessels, this type of incident could lead to vessel failure and other larger incidents such as VCE or boiling liquid expanding vapor explosion (BLEVE) (Crowl and Louvar, 2005; Lowesmith et al., 2007). The radiation is expressed as radiative heat flux iso-surface, which is used as an input parameter in a Probit equation to calculate the maximum allowance exposure time for personnel and equipment. For example, the maximum allowance time for personnel when exposed to radiative heat flux of 4.7 kW/m² is 3 min (Houf et al., 2011). For liquefied natural gas (LNG) facilities (i.e., production, storage, and handling sites), the National Fire and Protection Association (NFPA) specifies 5 kW/m² as a safe level of exposure at a property line (Raj, 2005).

CFD simulations have been used for evaluating the effect of barriers on mitigating the hazards of accidental hydrogen jet release and jet fire at the Sandia National Laboratory in Albuquerque, NM (Houf et al., 2009, 2010, 2011). The purpose of these simulation studies is to assess the effectiveness of barriers in mitigating the consequences including deflecting the jet flame and reducing the extent of the flammable cloud, the magnitude of the radiative heat flux, and the overpressure due to explosion. Several different arrangements of those physical barriers were investigated. The CFD simulations were conducted using Sandia self-developed FUEGO code; the turbulence of the hydrogen flow was modeled using the Farve-averaged RANS RNG k–ε turbulence model; the combustion of hydrogen was modeled as a nonreversible one reaction between hydrogen and oxygen using the Eddy Dissipation Concept model; the radiative heat loss of the hydrogen flames was computed using Sandia-developed gray discrete ordinates SYRINX code with only the spectral band of water vapor radiation absorption in the Lecker model included (Houf et al., 2009, 2010, 2011). The hydrogen jet source was modeled as a subsonic jet inflow boundary condition using the Mach disk model (Houf et al., 2009, 2010, 2011). The simulation results indicate that having appropriate barriers surrounding hydrogen sources could effectively reduce the total emission surface, which is in agreement with experimental data (see Figures 4.3 and 4.4). Figure 4.3 shows graphical rendering of the radiative heat flux iso-surface and Figure 4.5 shows jet deflection from barriers from the CFD simulation results. The study was performed at Sandia National Laboratory to evaluate the effectiveness of a mitigating barrier in accidental hydrogen jet release and jet fire. The iso-surfaces of 4.7 kW/m² are shown in Figure 4.3 including (a) without physical barrier; (b) (top view) with one vertical barrier located 3 feet in front of the hydrogen jet flame; and (c) (side view) with one vertical barrier located 3 feet in front of the hydrogen jet flame (gray color), and the iso-surface of the simulation without barrier (light yellow color). The simulation result clearly shows the reduction of total affected areas when a physical barrier was used.

Figure 4.3 Radiative heat flux iso-surface from the CFD simulation results: (a) jet flame with no barrier; (b) jet flame directed towards a barrier; (c) side view of iso-surfaces shown in (a) and (b). Reprinted with permission from Houf et al. (2011).

Figure 4.4 The comparison between radiative heat flux from experimental (circles) and CFD simulations (line) from a hydrogen jet fire with barriers (dash line) and without barrier (solid line). Reprinted with permission from Houf et al. (2010).

Figure 4.5 shows the effects of mitigation barriers including (a) vertical barrier with the hydrogen jet flame directed at the center of the wall; (b) vertical barrier with the hydrogen jet flame directed at the top of the barrier; (c) 60° tilted barrier with the hydrogen jet flame directed at the center of the barrier; and (d) three vertical barriers for a complete enclosure of the hydrogen jet flame.

Because of the possible impingement, jet fire flame length is one of the important characteristics that could help to determine appropriate separation distances between equipment. Cumber and Spearpoint proposed a CFD methodology that mimics how a camera or human eye senses a fire to calculate the propane jet fire length (Cumber and Spearpoint, 2006). Generally, in CFD simulation, the flame length of a jet fire must be inferred in certain way (i.e., temperature profile of the flame), which may not be accurate in the sense of reality. In this study, the authors calculate the flame length based on the senses of the receiver on the radiation intensity field given off by the incandescent soot particles and participating species. The two-equation k–ε turbulence model was used with modifications to account for the round jet/plane jet anomaly and buoyancy-induced turbulence; a probability density function (PDF) with infinitely fast reaction assumption was used to model propane combustion; and soot formation was modeled using Lindstedt's two-equation soot model (Cumber and Spearpoint, 2006). Radiation heat loss was calculated via the specific enthalpy perturbation transport equation (Cumber and Spearpoint, 2006). The model is calibrated using a selected set of jet fire experiments and then validated against a wider range of data.

Figure 4.5 Graphical interpretation of jet deflection from barriers from the CFD simulation results. Reprinted with permission from Houf et al. (2010).

Kim et al. (2010) used CFD to evaluate the heat load characteristics of steel and concrete tubular members under jet fire in terms of temperature and heat flux. The author used ANSYS, CFX, and KFX codes to conduct their simulations (see Figures 4.6 and 4.7). The jet fire was directed into the bottom of the horizontal bars. They found that CFD simulations were a useful tool to predict jet fire loads on nearby objects; the predicted temperature distribution was similar to those observed in the experiment, although they also noted that the CFD simulation parameters needed to be carefully selected to avoid anomalous results.

Yang et al. (2011) conducted CFD simulations to evaluate the dangerous areas by calculating the shape and size of jet fires on gas pipelines. In this study, the authors used the k–ε turbulence model to describe the jet flow; the turbulent non-premixed combustion process was modeled using the PDF/laminar flamelet model. Radiation heat transfer is described using an adaptive version of the discrete transfer method. The model is compared with experiments on a horizontal jet fire in a wind tunnel in the literature with success. The influence of wind and jet velocity on the fire shape has been investigated, and a correlation based on numerical results for predicting the stoichiometric flame length is proposed.

Figure 4.6 CFD simulation setup for the heat loads of jet fire on steel and concrete tubular bars: (a) dimension of individual objects; (b) the simulation domain. Reprinted with permission from Kim et al. (2010).

Figure 4.7 Evolution of the jet impingement on a pipe structure: (a) 0.02 s; (b) 0.04 s; (c) 0.10 s; (d) 0.50 s; (e) 1.00 s; (f) 5.00 s. Reprinted with permission from Kim et al. (2010).

Aloqaily and Chakrabarty (2010) through implementation of CFD have showed that such approaches are extremely useful in estimating thermal hazards resulting from jet flames to personnel working in process facilities. As illustrated by the same group in a follow-up article (Chakrabarty et al., 2011), upon narrowing down high-risk jet fire scenarios from QRA studies, CFD-based approaches can assist facilities comply with thermal hazard regulation in an more accurate and efficient manner.

4.2.5. Pool Fire

CFD simulation has been used to evaluate many hazards associated with large-scale pool fire events in process safety. Most important among them is the radiation hazard due to the very large size of accidental pool fires often encountered due to loss of primary containment events. Other types of hazards associated with pool fires, such as toxic gases in confined environments, have been covered extensively in fire safety engineering literature (Novozhilov, 2001). Thus, many efforts in CFD modeling are directed at accurately calculating the SEP, an important parameter used to calculate the maximum allowance exposure time for personnel and equipment (see Figure 4.8). CFD simulation of pool fires allows instantaneous and time-averaged temperature fields and iso-surfaces for SEP to be predicted with a high level of accuracy.

CFD modeling was used to investigate the instability of an unconfined kerosene pool fire with a diameter of 20 m in a stagnant, stable atmosphere and in atmosphere having cross wind (Sinai and Owens, 1995; Sinai, 2000). These modeling studies were conducted parallel to the experimental work by Shell Research Ltd at the British Gas Test at Site Spadeadam. A buoyancy-modified k–ε model was used for turbulence, the eddy break-up model for combustion, and the gray-medium model for radiation. The pool was modeled as a stable pool without any extraneous turbulence sources at the pool or within the fire. The modeling results show realistic behavior where large toroidal vortices were generated and rose within the modeled fire, similar to those observed experimentally.

Lin et al. (2010) conducted a CFD simulation to investigate the characteristics of radiative heat transfer in liquid pool fire to predict the thermal radiation and flame characteristics numerically in small to medium-sized heptane pool fires (14–38 cm). This work used an LES model for turbulence, an eddy dissipation concept with extremely fast chemistry for combustion, and a gray gas narrow-band model for radiation. The modeling results are in agreement with experimental data.

Figure 4.8 A pool fire diagram and its associated physical processes. Reproduced by permission with Schalike et al. (2011).

Schalike et al. (2011) conducted CFD simulations to predict the thermal radiation hazards of large LNG pool fires having diameters of 1, 6.1, and 30 m whose radiations were also measured in experimental study (see Figure 4.9). Flow turbulence was modeled by LES, combustion process was modeled using the PDF approach with laminar flamelet for 21 species and elementary reactions, radiation was modeled using discrete ordinates, and soot formation was modeled using the Moos Brookes model. It can be seen from Figure 4.8 that the model pool fire has three rather distinctive surface emission zones (represented as different colors in the figure). The simulation results show that for LNG pool fires having a diameter of 1, 6.1, and 30 m, the averaged flame temperatures of T = 1320, 1298, and 1281 K were observed, and the SEPs of 55, 130, and 230 kW/m² were predicted, respectively. The predicted SEPs as well as their increases with the increase of pool fire diameter agree well with the experimental data. This result indicates that there is a maximum SEP for large-scale pools; that value may be observed for pool fires with diameters greater than 35 m, which have not been simulated. They also found that the higher mass burning rate and the higher flame temperatures lead to the higher SEP values for larger LNG pool fires in comparison with other hydrocarbon pool fires. This modeling result shows that accurate surface emission power can be calculated using a CFD model.

Figure 4.9 Graphic rendering of the surface emission power using a CFD simulation as a result of a large-scale LNG pool fire. Reproduced by permission with Schalike et al. (2011).

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Table of Contents for 4.2. Fire Modeling

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4.2. Fire Modeling

4.2.1. CFD Modeling of Fire

4.2.1.1. Geometry representation

4.2.1.2. Turbulent model

4.2.1.3. Fire models

Combustion model

Radiation model

Soot formation model

Fuel source

4.2.2. Applications of CFD Modeling Data into a Radiative Probit Function

4.2.3. CFD Modeling Codes

4.2.4. Jet Fire

4.2.5. Pool Fire

Table of Contents for
4.2. Fire Modeling