Design Fire Methodology for Vehicle Spaces Onboard Ships

Abstract

The purpose of this paper is to contribute towards establishing procedures of assessment of the fire safety of Ro–Ro ship cargo spaces, by employing suitable design fires. Data collected from fire experiments involving vehicles are utilized in order to deduce representative heat release rates for common types of passenger cars and heavy goods vehicles (HGVs). An existing mathematical scheme for generating parametric heat release rate curves is extended for handling vehicle fire scenarios. The methodology is demonstrated through a case study. In particular, the Fire Dynamics Simulator (FDS) code is used for investigating fire propagation on the vehicle deck of a Ro–Ro ship, initiated from a single HGV. On this deck are assumed to be transported a combination of cars and HGVs. The evolution of the fire is assessed assuming different ventilation conditions. The circumstances for spreading to adjacent vehicles are examined. Human survivability and the time that the deck remains accessible are evaluated by considering the International Maritime Organization (IMO) life safety performance criteria.

1 Introduction

According to the European Maritime Safety Agency (EMSA), almost 20% of recent accidents on Ro–Ro ships were fire-related [1]. In particular, fires taking place on vehicle decks represent a prevalent safety hazard of ropax and Ro–Ro cargo vessels as well as of pure vehicle carriers [2, 3]. Such fires have potential to spread to vital adjacent spaces of the ship, creating a serious peril for the lives of the people onboard. In two widely publicized fire accidents, namely the fires on the Ro-Pax vessels Norman Atlantic and Sorrento, fire had been initiated from a vehicle and spread to upper decks affecting the evacuation process and resulting in serious injuries and fatalities [4, 5]. The very recent fire on a vehicle deck of the Ro–Ro Euroferry Olympia off the Greek island Corfu, caused several fatalities among the vehicle drivers and triggered serious concern at the International Maritime Organization (IMO) about the fire safety onboard Ro–Ro ferries [6]. Devastating accidents as these, call for further systematic research regarding the mechanisms of ignition and spreading of fires on vehicle decks and also on appropriate effective interventions for mitigating their consequences.

An integrated risk-based method for the assessment of the fire safety of passenger ships, that is applicable at a ship’s design stage, was recently proposed by Spyrou and Koromila [7]. The effective implementation of such a method entails capability to accurately predict fire evolution for the various types of space found onboard a ship. The simulation of fire spreading in accommodation and public spaces of passenger ships (such as, cabin spaces, lounges, restaurants and bars) is already mature to some extent [8,9,10,11,12,13,14]. On the other hand, investigations of ship vehicle deck fires are, so far, very few. Salem [15] employed three fire models and performed comparative scaled fire simulations on a Ro-Pax ship vehicle deck. Themelis and Pagonis [16] investigated the effect of natural openings and wind on the fire development and spreading in a part of a vehicle deck by using computational fluid dynamics (CFD) simulations. Koromila et al. [17] investigated fire spreading from one passenger car to another, considering the entire vehicle deck of a passenger ship. The current paper completes and extends this work.

However, vehicle fires have been extensively studied for land infrastructures, in particular closed parking areas and tunnels. Cheong et al. [18] proposed a performance-based approach for estimating the heat release rate of a vehicle fire. Collier [19] considered modern passenger cars with large combustible mass. Heinisuo and Partanen [20] carried out simulations for examining the spreading of fire in parking areas and for assessing the mitigating effect of sprinklers.

The main aim of the current paper is to advance the concept of “design fire”, in the context of investigations of fire evolution and consequences onboard Ro–Ro cargo spaces of ships. Subsequently, this concept could be effectively integrated within a general ship fire safety risk analysis.

The following studies were undertaken:

First, the literature of fire experiments with various vehicle types, including small, medium and large cars as well as heavy goods vehicles (HGVs), has been compiled in order to deduce representative heat release rate (HRR) curves. As far as HGVs are concerned, solid cargoes were only taken into account. Reefer trucks were not accounted either, notwithstanding that a few fire accidents are known to have been caused by faults in circuit units of these vehicles.

A mathematical scheme earlier developed by Themelis and Spyrou [10] and further by Spyrou and Koromila [7], for generating parametric HRR curves, was appropriately adapted to the vehicle fire scenarios. For implementing this scheme, the quantities and thermal properties of common materials making up a typical car (metals, plastics, rubber etc.) were accounted. On the other hand, HGVs often carry combustible mass varying in nature very substantially (as for example, wood, plastics, furniture, and food stuff). The very large amount of released heat and the large variability of the combustible mass are factors intrinsic to the considered problem of fire evolution.

A closed-type vehicle deck of a certain Ro–Ro passenger ship has been considered as a case study, accommodating cars and HGVs. Ignition was assumed taking place at one of the HGVs and the circumstances of fire evolution and spreading to adjacent vehicles were examined via fire simulation. Two extreme ventilation conditions, namely one with no ventilation at all and the other with constant mechanical supply of air, were investigated, for the purpose of assessing quantitatively the effect of ventilation on the propagation of a fire on a vehicle deck. The simulations were carried out by using the well-known computational thermo-fluid dynamics code Fire Dynamics Simulator (FDS), with the PyroSim interface [21]. Assessment of human survivability on the vehicle deck was also carried out, by considering the IMO life safety performance criteria [22]. One reason for this assessment is that, although prohibited, people remain sometimes on vehicle decks. Such survivability studies can help also to determine the time available for crew’s intervention.

The structure of the paper is as follows: in Sect. 2 is described the background knowledge and the mathematical scheme for constructing design fires. In Sect. 3 are presented, and then processed, the identified experimental results of vehicle design fires. From these are yielded estimations of typical HRR curves for cars and HGVs. In Sect. 4 is demonstrated the application of the current design fire concept through a case study employing a closed-type vehicle deck. The main results of the fire simulations carried out are also found here, together with some discussion. Lastly, the conclusions are summarized in Sect. 5. Specific details contributing to FDS modeling are provided in the Appendix at the end of the paper.

2 Design Fires

2.1 Characteristic Parameters of Fire Modeling

The heat released by a fire indicates the fire’s intensity. It can be expressed through the concept of fire load, implying the energy content of the combustible materials that can be burnt in the event of a fire [23, 24]. The theoretical fire load, $Q$ [kJ], is often apportioned with respect to floor area, as follows [25]:

$$Q =M \Delta {H}_{c}= q {A}_{f}$$

(1)

where, $M$ [kg] is the total mass of the combustible materials; $\Delta {H}_{c}$ [kJ/kg] is the materials’ heat of combustion; $q$ [kJ/m²] is the fire load density; and ${A}_{f}$ [m²] is the floor area occupied by the combustible materials. Fire load density is commonly related to the heat released per mass unit of each of the available materials and it is calculated as [23, 26]:

$$q =(1/{A}_{f}){\sum }_{i}^{n}{M}_{i} \Delta {H}_{ci}$$

(2)

where, $n$ is the number of combustible materials; ${M}_{i}$ [kg] is the mass of the combustible material $i$; and $\Delta {H}_{ci}$ [kJ/kg] is the heat of combustion of material $i$. The total mass of the available combustible materials per unit floor area (${\sum }_{i}^{n}{M}_{i}/{A}_{f}$) expresses the so-called fuel load density $FL$ [kg/m²].

Heat release rate (HRR) is commonly used for describing the intensity of a fire [27]. Assuming that the fire is governed by the amount and type of the fuel, which defines a fuel-controlled fire, the heat release rate $\dot{Q}$ [kW] is commonly expressed as [28]:

$$\dot{Q}=\dot{m} \Delta {H}_{c}$$

(3)

where, $\dot{m}$[kg/s] is the mass burning rate of the combustible mass $M$. Particularly useful is also the heat release rate per unit floor area $\dot{Q}"$ [kW/m²].

In a ventilation-controlled fire, the burning rate of the fuel is mitigated by the rate of the inflow air and the heat release rate is determined by the amount of available oxygen. The heat release rate of such fires is [25, 29],

$${\dot{Q}}_{v}={\dot{m}}_{air}\Delta {H}_{c}{/r}_{s}$$

(4)

where, ${\dot{m}}_{air}$ is the mass flow rate of air via ventilation openings; and ${r}_{s}$ is the stoichiometric air/fuel ratio. ${\dot{m}}_{air}$ depends on the area and the height of the ventilation openings via the relation ${\dot{m}}_{air}=0.5 {A}_{0}\sqrt{{H}_{0}}$ [30]. In principle, when ${\dot{m}}_{air}/\dot{m} <{r}_{s}$, the fire can be considered as ventilation-controlled; otherwise, it is fuel-controlled [25]. A simplified version of Eq. (4) suggests that $\Delta {H}_{c}{/r}_{s}$ represents the heat of combustion per unit mass of air consumed, $\Delta {H}_{c,air}$, which roughly equals $3$ MJ/kg [25, 31].

2.2 Design Fire Mathematical Representation

A fire can be qualitatively modeled through four key fire development phases; namely, the incipient phase, the growth, the full development, and the decay. These phases are quantitatively reflected by the values (in time) of the heat release rate. The curve representing these phases is known as “the HRR curve”. A parametric form of it defines, basically, a design fire [32].

As has been earlier proposed in a more generic context, a design fire can be generated on the basis of the following mathematical representation [7, 10]:

$$\dot{Q}(t)=\left\{\begin{array}{l}{\dot{Q}}_{inc} t/{t}_{inc} ,\\ {\dot{Q}}_{inc}+a{\left(t-{t}_{inc}\right)}^{2},\\ {\dot{Q}}_{max},\\ {\dot{Q}}_{max} {e}^{-(t-{t}_{d})/{\tau }_{d}},\end{array}\right.\begin{array}{c} 0\le t\le {t}_{inc}\\ {t}_{inc}<t\le {t}_{g}\\ {t}_{g}<t\le {t}_{d}\\ t>{t}_{d}\end{array}$$

(5)

where, ${\dot{Q}}_{inc}$ [kW] is the heat release rate at the end of the incipient phase; ${t}_{inc}$ [s] is the time instant when the fire starts to grow; $a$ [kW/s²] is the growth coefficient; ${t}_{g}$ [s] is the time required to reach the maximum heat release rate; ${\dot{Q}}_{max}$ [kW] is the maximum heat release rate; ${t}_{d}$ [s] is the time instant the decay phase starts; and ${\tau }_{d}$ is the decay coefficient.

As a solid combustible material is heated by an external source, above its critical heat flux (CHF), it is ignited. This establishes the incipient phase of the fire, resulting in a linear increase of the heat release rate [33]. A simplified estimate of the incipient time of a fire is given below [34]:

$${t}_{inc}={\left(\frac{TRP}{{\dot{q}}_{e}"-CHF}\right)}^{2}$$

(6)

where, $TRP$ [(kW s^1/2)/m²] is the thermal response parameter indicating the resistance to ignition and fire propagation; ${\dot{q}}_{e}"$ [kW/m²] is the external heat flux; and $CHF$ [kW/m²] is the critical heat flux.

Following the ignition, heat release increases further, and fire growth is realized. At the fire growth phase, the heat release rate is commonly assumed as “time-squared”, rising fast until a plateau is reached where the fire is considered as fully developed [35]. Thereafter, the amount of the available oxygen diminishes until it becomes insufficient, and decay inevitably occurs. This is a typical “ventilation-controlled fire”. It is also possible, however, the heat release rate to begin to decrease immediately after it reached the maximum heat release rate. The reason is because, most of the fuel has been consumed and the decay phase started. Such a scenario would correspond to a “fuel-controlled fire”. Both qualitative types of fire behavior can be accounted by the parametric HRR form given by Eq. (5). As soon as the decay starts, the heat release rate exponentially decreases towards extinction [36].

During the fire, heat energy is transported, exchanged, and redistributed through the mechanisms of conduction, convection, and radiation, thus creating the potential of fire spreading to adjacent objects [37]. The described model generally accounts for fire development based on the combustion of a single burning item called “fuel package”. A fuel package reflects the fire load density associated with a space and it can be defined either with respect to a single combustible material, or with respect to a mix of different materials. Several discrete fuel packages can be distributed on an area to represent the entire available combustible mass.

The various parameters determining the design fire can be derived by calculating the energy released in a period of time, for instance heat released between time instants ${t}_{a}$ and ${t}_{b}$ is:

$$Q({t}_{b}) - Q({t}_{a}) = {\int}_{{t}_{a}}^{{t}_{b}}\dot{Q}(t)dt$$

(7)

Interestingly, it is empirically known that some part of the available combustible material remains unburnt. This is accounted via a factor $k$ resembling the well-known combustion efficiency which is the ratio of the total fire load ${Q}_{T}$ to the theoretical fire load $Q$ ($k={Q}_{T}/Q$) [36]. In incomplete fires, the total fire load is reduced through the combustion efficiency via ${Q}_{T} =kQ$. Therefore, $k$ refers to the percentage of the combustible mass that is finally burned in an incomplete ($k<1$) or a complete ($k=1$) fire. Then, the total area below the heat release rate curve should be $kQ$ as presented in Eq. (8).

$${\int}_{0}^{\infty}\dot{Q}(t)dt={Q}_{T}=kQ$$

(8)

Assuming a ventilation-controlled fire, the maximum heat release rate is reached when a percentage ${b}_{g}$ of the total fire load ${Q}_{T}$ has been consumed. This determines the end of the growth phase. A further percentage ${b}_{d}$ of ${Q}_{T}$ is consumed as the HRR is nearly constant, until the decay starts. In essence, the coefficient ${b}_{d}$ overlaps with the ${b}_{g}$ coefficient. In a fuel-controlled fire, however, decay begins as soon as ${\dot{Q}}_{max}$ is reached (${t}_{g}={t}_{d}$). These assumptions are reflected by the following expressions:

$${\int}_{0}^{{t}_{g}}\dot{Q}(t)dt={b}_{g}{Q}_{T}$$

(9)

$${\int}_{0}^{{t}_{d}}\dot{Q}(t)dt={b}_{d}{Q}_{T}$$

(10)

A fuel-controlled fire can very easily be turned into a ventilation-controlled fire. As the fire rapidly increases with the availability of the fuel and oxygen, the demand for oxygen greatly increases. Then, its supply becomes insufficient, and the fire can no longer be controlled by fuel. Such a behavior can be reproduced also through fire simulation where, although initially sufficient oxygen for growth of the fire is provided, after some time the concentration of fire effluents drastically increases, preventing the supply of further oxygen to the fire. This forces the fire to decay and eventually to become extinguished leaving a lot of the material unburnt.

2.3 Design Fires with Random Elements

One can apply this model within a deterministic or a probabilistic framework. In the first case, the types and the thermal properties of the involved materials are fixed. Such an approach would be suitable for investigating the consequences of a fire for a specific, well-defined, scenario, e.g. in the context of forensics or for evaluating insulation properties of barriers to specific thermal loads. From a more general ship design perspective however, it is essential to handle the uncertainties in the quantity and distribution of cargo’s mass, the mix of participating materials and even in their thermal properties. This entails to assign probability distributions to the essential parameters involved. Midway these two approaches, it is sometimes quite practical and efficient to select several parameters as fixed while handling only a few probabilistically, in particular those most uncertain. Thereafter, families of design fires can be generated describing possible burning behaviors.

The current paper uses an intermediate approach. As soon as the random and fixed parameters are assumed, design fire families are derived and ranked, in terms of severity, in ascending order. To allow their ranking, the below function ${f}_{s}$ is introduced:

$${f}_{s}=\beta \frac{{\dot{Q}}_{{max}_{i}}}{max({\dot{Q}}_{{max}_{i}})}+(1-\beta )\frac{{t}_{{e}_{i}}}{max({t}_{{e}_{i}})}$$

(11)

This function is a weighted linear combination of the normalized maximum heat release rate and of the total time of fire burning ${t}_{e}$. The choice of these two parameters for ranking fire severity is almost obvious as both are known to bear a strong effect on survivability. The value of the weighting coefficient $\beta$ reflects whether, from a consequences perspective, fire severity should be identified more with the maximum heat release rate or with the time duration of the fire. Characteristic HRR curves according to level of severity can be extracted on the basis of ${f}_{s}$ percentiles. Specifically, the 25% percentile of the ${f}_{s}$ can be taken as the representative of a low-severity fire, the 50% percentile can represent the moderate-severity fire, and the 95% percentile can represent the extreme-severity fire.

3 Vehicle Fires

3.1 Fire Experiments

Several large-scale fire tests have been performed since the early nineties. In some, had been employed a calorimeter apparatus to measure the characteristics of the fire in the laboratory. In other cases, a physical setting was selected involving real parking garages or road tunnels. $46$ fire experiments were identified in the literature, accounting for a variety of cars [38, 39]. Another $10$ experiments were identified concerning HGVs [40,41,42,43]. Experiments have been carried out also for vehicles carrying dangerous liquid cargo. However, these were neglected here as the transport of such vehicles by Ro-Ro passenger ships is formally prohibited.

A summary of mean values and ranges, as obtained from these experiments, is provided in Table 1 concerning: (a) the maximum heat release rate; (b) the time for reaching the maximum heat release rate; and (c) the total energy released. We adopted a quite standard vehicle classification of cars and HGVs that is based, respectively, on the curb¹ and gross weight of the vehicle. More specifically, the cars were classified in seven groups as proposed in ANSI [44]: (a) mini, (b) light, (c) compact, (d) medium, (e) heavy, (f) van, and (g) SUV. The heat energy released during these experiments ranged quite widely; from $0.09$ GJ to $8.50$ GJ. In a few of these experiments, however, fire did not develop at all, presumably owning to the prevailing ventilation conditions combined with the presence of a high amount of highly fire-resistant materials. Indeed, most of the cars burned in these experiments had been constructed in the seventies, eighties, and nineties when a lot of steel and limited plastics were used, releasing much less heat energy. As for the HGVs, in the experiments had been examined semi-trailers consisting of the tractor unit and the detachable cargo trailer. These were classified according to their weight as: (a) medium and (b) heavy [44]. The experiments considered merely fires in cargo units consisted of, either, wooden and plastic pallets, or furniture. The released heat energy ranged between $10$ GJ and $247$ GJ; that is, one or higher order of magnitude compared to the heat released from car fires.

Table 1 Representative Values for Characteristic Quantities of the Heat Release Rate Curve, per Vehicle Type, Obtained from Experiments

3.2 Combustible Mass of Modern Passenger Cars

Modern cars meet several requirements for functionality, cost, weight minimization and minimum environmental impact. These requirements have led to the extensive use of plastics, polymers, and composite materials [45]. The mean amount of combustible materials has gradually increased from $9$ kg in the ‘60s to $160$ kg in the 2010s [46, 47]. The mass of the plastics relates of course with the total mass of the vehicle. In the last decade, the weight of plastics typically ranges between $100$ kg for mini cars to $300$ kg for heavy cars [48]. Despite this great increase, at the same time, the fuel is stored in well-protected tanks avoiding its immediate release and therefore its participation to the fire, resulting in the modern cars producing levels of fire load quite similar to the older ones. All these contribute to fire loads that are capable of reaching about $10$ GJ (by assuming for plastics an average heat of combustion $35$ MJ/kg).

In Table 2 are presented the most common materials found in a modern car, their contribution to the combustible mass, their thermal properties and the species yields. The key materials are roughly divided into the next four generic material groups: (a) plastics, (b) metals, (c) rubber, and (d) miscellaneous. By assuming an average mass per material group over a decade (2010–2020), the contribution of each group to the total mass is $17\%$, $58\%$, $6\%$ and $19\%$ respectively [48, 49]. As a matter of fact, some of the most widely used plastics, both in the interior and the exterior parts, arranged in a descending order are polypropylene (PP, $44\%$), polyurethane (PU, $9.5\%$), polyamide (PA, $8\%$), polyethylene (PE, $7\%$), acrylonitrile–butadiene–styrene (ABS, $4.5\%$), poly-butylene-terephthalate (PBT, $2\%$), and poly-ethylene-terephthalate (PET, $2\%$) [48]. Of course, metals make up an essential part of a car. These are mostly, steel, aluminum and magnesium. Steel presents extremely high ignition temperature and for many fires it can be reasonably considered as a non-combustible material. Miscellaneous other materials are found in vehicles, including engine fuels, oils and lubricants, other composites and metals, textiles, ceramics, glass, coatings and others. Some of the materials of this category can contribute significantly to the fire load.

Table 2 Thermal Properties of the Materials Appearing in a Typical Modern Car (Mainly from Appendices of the SFPE Handbook [50])

3.3 Combustible Mass of Heavy Goods Vehicles

Ro–Ro passenger ships are allowed to carry HGVs, in addition to passengers and cars. Such vehicles are designed to carry a wide variety of cargoes from huge pieces of machinery, vehicles, chemicals, and radioactive materials, to foodstuff, condiments, furniture, textiles, and toys. As a matter of fact, Ro-Ro passenger ships normally transport large quantities of daily necessities to remote areas, while, less often, they may carry dangerous goods and timber, though in very limited quantities. Goods are stowed in cardboard packages, pallets or bulk in trailers or containers, and they are loaded on Ro-Ro passenger ships either as cargo alone or together with the tractor. Cardboard packaging and wooden or plastic stowage pallets constitute the main combustible mass of these HGVs [41]. Of course, there are other combustible materials present in the trailer unit, for example the main cargo that can be foodstuff. Yet, their contribution to a fire is considered modest and, therefore, it can be neglected [41]. The available fire load of a HGV cargo can reach very high values ($250$ GJ).

Table 3 lists the key combustible materials commonly found in HGVs transported by Ro-Ro passenger ships, their thermal properties and the species yields. Wooden and plastic pallets are taken into account [41]. The contribution of each material to the total fire load is estimated to be about $80\%$ for wood and $20\%$ for plastics [41, 43]. In the case the tractor section is further considered to be contributing to the fire load, additional combustible mass including a combination of furniture, tires and cab shall be estimated. It has been suggested that about $52\%$ of the combustible mass corresponds to the tractor [41]. The combustible mass of the tractor can be considered as composed of materials similar to those found in a modern car.

Table 3 Thermal Properties of the Materials Appearing in Typical HGVs Transported via Ro-Ro Passenger Ships (Mainly from Appendices of the SFPE Handbook [50])

4 Application

4.1 Deck Layout and Vehicles Arrangement

As a case study, a realistic closed-type cargo space of a Ro–Ro passenger ship, accommodating $38$ cars and $11$ HGVs, was assumed. In Fig. 1 appears the general arrangement of this deck which is $97.8$ m in length, $18.9$ m in width and $5$ m in height. Τhe main exterior and interior wall boundaries and the floor of the vehicle deck are designed as obstacles made of steel. On the other hand, cars and HGVs are shown as orthogonal parallelepipeds, each having volume, respectively, $13.2$ m³ and $138.9$ m³. They are capable to generate fire with the appropriate HRR characteristics. Such a representation of vehicles has been used also in the past for studying the evolution of heat and smoke from car fires in tunnels (see for example [61]).

Figure 1

Considered vehicle deck of Ro–Ro passenger ship. Green rectangles indicate the passenger cars, blue rectangles indicate HGVs, and the red rectangle indicates the initially ignited HGV. Yellow circles indicate the locations of the fire indicator meters measuring the temperature, visibility, radiation, FED, and the CO, O₂ and CO₂ concentrations. Arrows indicate the location and the direction of the air flow of the available mechanical ventilation system (Color figure online)

Two ventilation scenarios are investigated. In the first, the vehicle deck space is assumed fully enclosed with no mechanical ventilation. It is, indeed, completely airtight. Therefore, the available oxygen is the initially contained in the enclosure. This represents of course an extreme scenario since internal or external openings for air circulation always exist. Nevertheless, this scenario is useful for observing differences with a fire evolving under continuous supply of oxygen. In the second, the vehicle deck is mechanically-ventilated. This scenario considers two openings of $5.76$ m² in the bow area supplying air at a rate of 16 m³/s each. Two more openings of the same size are placed in the stern area for discharging air and hazardous indoor gases at the same rate each.

In the specific scenarios examined, the fire is assumed to initiate from a HGV located at the port side of the ship. Cars ignite when their surface temperature reaches $230$°C. This is an average temperature assuming the ignition point of the materials of the engine cover, seats, console shell and tires [62]. HGVs, on the other hand, ignite when the wooden pallets ignite, namely at $250$°C (the required temperature for piloted ignition of wood is as discussed in Lowden & Hull [63]).

Particular attention was on monitoring temperature, visibility, radiation, fractional effective dose (FED), and the concentrations of carbon monoxide (CO), oxygen (O₂), and carbon dioxide (CO₂). These characteristic fire effluents were monitored throughout the deck space, with meters placed at $17$ points along the evacuation routes, at height $1.6$ m. Additional meters were placed above the first ignited vehicle at height $4.4$ m (device 6 in Fig. 1). Moreover, temperature, soot and mass fractions of CO₂, CO and O₂, were further recorded in three dimensions.

One of the most widely used fire simulation models, the Fire Dynamics Simulator (FDS), enhanced with the PyroSim interface, has been employed. As well-known, in this simulator is applied a Large Eddy Simulation (LES) approach for solving the Navier–Stokes equations, optimized for low-speed, thermally-driven flows. FDS has been extensively verified and validated (e.g. [64, 65]). As recommended there, the grid resolution should be selected on the basis of recommended values of the nondimensional ratio of the characteristic fire diameter versus the nominal size of a grid cell (${D}^{*}/\delta x$). The greater this ratio, the finer the resolution. ${D}^{*}$ depends on the heat release rate $\dot{Q}$ (calculated in the next sub-section) and the ambient conditions, via the next expression [66]:

$${D}^{*}={\left(\frac{\dot{Q}}{{\rho }_{\infty }{c}_{p}{T}_{\infty }\sqrt{g}}\right)}^{2/5}$$

(12)

The selection of suitable grid should take however into account also the geometrical characteristics of the space and of the objects in it (in the current application was selected a fine grid corresponding to $20$ cm cells; however, optimal grid selection for vehicle deck spaces requires a separate focused study). More details about the input data used for the FDS model are found in the Appendix.

4.2 HRR Characteristics of Vehicles

Design fires for the cars and HGVs were created by utilizing the parametric model of Eq. (5). Each vehicle was assumed capable to generate a fire with a predetermined theoretical fire load, calculated by combining expressions (1) and (2), taking into account the materials’ contribution to the combustible mass as presented in Tables 2 and 3. First, compact-sized cars with nominal mean mass $1280$ kg were considered [44]. Their mass participating in the combustion was calculated, according to the contribution of each group of materials to the total mass of the car as shown in Table 2: $218$ kg plastics, $51$ kg metals (Al and Mg), $77$ kg rubber and $13$ kg miscellaneous materials [48, 49]. The corresponding fire load for such a car was calculated via expression (1) to about $11.9$ GJ. On the other hand, every HGV considered in the current case study was assumed to belong to the “straight truck” category having around $16$ tons mass [67]. The tractor mass corresponds to approximately $52\%$ of the total mass of a HGV, so it was estimated to be equal to $8.32$ tons [41]. Its flammable mass is estimated as $2.24$ tons following the procedure applied for cars. Therefore, it accrues that the trailer carries the remaining combustible mass, namely $48\%$ of the total HGV which corresponds to $7.68$ tons of wooden and plastic pallets. The contribution of steel was neglected as this is ignited at very high temperature. The total fire load of such a vehicle was estimated via Eq. (1) at $277$ GJ. Table 4 collects the assumptions made for the combustible mass of cars and HGVs as well as the estimated fire loads. As has become already apparent, the total fire loads were assumed as fixed quantities, whilst other parameters describing fire behavior were treated as random. In particular, ignition heat flux ${\dot{q}}_{e}{^{\prime}}{^{\prime}}$, heat release rate at the incipient phase ${\dot{Q}}_{inc}$, fire growth coefficient $a$, and coefficients ${b}_{g}$, ${b}_{d}$, and $k$, were assumed distributed, in the first instance, uniformly within the ranges indicated in Table 5. The ranges were defined in accordance to the data found in the literature.

Table 4 Assumptions of the Combustible Mass Involved in Fire of Cars and HGVs and the Corresponding Estimated Fire Loads

Table 5 Ranges for the Random Parameters

As a matter of fact, the ignition heat flux value indicates the ignitability level of the materials involved in the fire. Three standard levels have been identified as describing the ease of ignition [68]: $10$ kW/m² for easily ignitable material; $20$ kW/m² for material of normal ignition; and $40$ kW/m² for materials difficult to ignite. By averaging the ignitability of the materials comprising a car, an ignition heat flux ranging between $30$ kW/m² and $40$ kW/m² was determined [69, 70]. Moreover, for the various ignition heat flux values, the duration of the incipient phase ${t}_{inc}$ could be estimated on the basis of Eq. (6). The weighted average values of $TRP$ and $CHF$ were obtained from Tables 2 and 3. At the end of the incipient phase, the heat release rate ${\dot{Q}}_{inc}$ reaches a characteristic value which is considered uniformly distributed between $20$ kW and $30$ kW [71, 72].

The fire growth coefficient implies how intensely a fire develops. It can be assumed that a typical car fire has a slow to medium growth (respectively $0.003$ kW/s² to $0.012$ kW/s²) [73, 74]. On the other hand, as the HGVs often carry easily ignitable cargoes, the growth coefficient should be assigned a greater value indicating ultra-fast fire growth. The characteristic growth coefficient value adopted here ranged between $0.19$ kW/s² and $0.45$ kW/s² [73, 75]. Then, ${\dot{Q}}_{max}$ is determined by solving Eq. (13).

$${\dot{Q}}_{max}={\dot{Q}}_{inc}+a{\left({t}_{g}-{t}_{inc}\right)}^{2}$$

(13)

The required time ${t}_{g}$ for reaching ${\dot{Q}}_{max}$ is calculated via Eq. (9), the time ${t}_{d}$ at which the decay starts is calculated via Eq. (10), and the value of the decay coefficient ${\tau }_{d}$ is deduced from Eq. (8). To account for possibilities of both fuel-controlled and ventilation-controlled fires, the coefficients ${b}_{g}$ and ${b}_{d}$ were assumed distributed uniformly in the ranges shown in Table 5. These ranges have been selected to approach the behavior of the experimental HRR curves. Since incomplete fires have been considered, the fire load percentage $k$ that participated in the fire was uniformly distributed in the range $65-75\%$ of the total fire load based on the total burnable mass. Taking into account the results of the experiments, the design fire curves of the HGVs were based simply on the truck trailer unit. In this case, a higher percentage $k$ of the fire load was assumed participating in the fire ($75-85\%$).²

In Fig. 2a are shown the HRR curves of $1000$ car design fires generated by the present mathematical scheme. In Fig. 2b they were ranked using the ${f}_{s}$ function. Three characteristic HRR curves are then extracted, as being the representative for low ($25\%$ percentile of the ${f}_{s}$), moderate (median of the ${f}_{s}$), and extreme ($95\%$ percentile of the ${f}_{s}$) severity fire scenarios. The weighting factor $\beta$ was taken equal to $0.7$. In Fig. 3 are contrasted the representative design HRR curves against the HRR curves of the experiments. The comparison covers both cars and HGVs.

Figure 2

(a) $1000$ design fires generated for a typical car. (b) Ranking of the generated fires by exploiting the ${f}_{s}$ function (Eq. 11). The doted horizontal line indicates the representative low-severity fire scenario, the dashed horizontal line indicates the moderate-severity fire scenario, and the continuous horizontal line indicates the extreme-severity fire scenario

Figure 3

Comparison of the experimental and mathematical design fire curves for: (a) cars and (b) HGVs. The experimental design fires data points used are recreated from the literature [38,39,40,41,42,43]. The doted curves indicate the low-severity fire scenarios, the dashed curves indicate the moderate-severity fire scenarios, and the continuous curves indicate the extreme-severity fire scenarios. The thin curves correspond to the case where only the trailer unit of the HGV burns (Color figure online)

4.3 Fire Evolution

Design fires of moderate severity were applied for simulating fire scenarios. A comparison of fire evolution is shown in Fig. 4, considering the two ventilation options. These two simulations yield quite different heat release rates. As a matter of fact, the first scenario constitutes a ventilation-controlled fire. This fire is predicted to self-extinguish in $15$ min due to rapid reduction in oxygen supply. The second scenario represents a fuel-controlled fire, where at approximately $13$ min, the heat release rate deviated from the mathematical design fire indicating that some adjacent material has ignited and has started participating in the fire.

Figure 4

HRR curves of developing vehicle deck fire, obtained for different ventilation conditions. The red curve corresponds to fire simulation for a non-ventilated deck, whereas the yellow curve corresponds to a mechanically-ventilated fire on the same deck. The dashed curve indicates the numerical design fire of moderate severity representative for HGVs. It is considered for the reference simulation time (15 min)

In Fig. 5 are presented two-dimensional slices of the vehicle deck at characteristic time instants, at various heights, which provide insights into the spreading of the fire. It is notable that in the case of the non-ventilated deck, heat is released mainly from the initially ignited HGV reaching great values (namely approximately 100 MW). Adjacent vehicles partly contribute to the fire, although initially only to a minor extend. Indeed, their heat release rate is comparatively low in the very first minutes of the combustion and it cannot be quantitatively attributed to the total HRR shown in Fig. 4. This high HRR values significantly increase the temperature, very profoundly above the burning vehicle. It is evident from Fig. 5a (left figure) that the temperature at $1.5$ m (car height) reaches $160$ to $320$°C for very few minutes not allowing the rapid spread of fire. At the same time, as the temperature and heat release rate increase, the oxygen considerably decreases becoming insufficient not allowing the flame to spread and further develop the fire even at high temperatures. On the other hand, when the fire was constantly supplied with oxygen, fire spreading to adjacent vehicles was easily realized. Thermal energy was initially concentrated in the vicinity of the ceiling. As the time passed, it began to propagate to lower levels by activating adjacent HGVs.

Figure 5

2D slices of the vehicle deck at various heights, for different stages of evolution of the fire (slices per z). The next three heights are illustrated: (a) car height at $1.5$ m, (b) HGV height at $4.0$ m, and (c) near ceiling height at $4.8$ m. Temperature evolution is produced during the fire in the non-ventilated deck (left) and the mechanically-ventilated deck (right)

4.4 Human Survivability

Whilst there should be no humans in vehicle deck spaces during a voyage, a survivability study can nevertheless be quite useful; because several incidents have occurred where human lives were lost due to a fire on a vehicle deck of a ship. These people were, in some cases, truck drivers who had illegally remained in their vehicles; and in other, illegal immigrants. Moreover, members of crew have been injured or even lost their lives while trying to suppress the fire.³ For all these reasons, it is useful to develop quantitative assessment of human survivability on the vehicle deck in the following respects:

• (a) what is the time margin of safe abandonment of a vehicle deck space; and

• (b) for how long after a certain fire started, the deck remains accessible, given specific conditions of ventilation, so that the viability of attempting fire suppression by direct crew intervention can be judged.

Measurements obtained from the numerical fire indicator meters are useful for assessing survivability at various locations on the deck, with respect to an evolving fire. For this, the measured values are continually compared against the normative values of the IMO life safety criteria which address the encounter of life prohibiting levels of temperature and radiation, low visibility, and asphyxia [22]. The limiting conditions, as defined in the criteria, are as follows: (a) maximum air temperature shall not exceed $60$°C; (b) maximum radiant heat flux shall not exceed $2.5$ kW/m²; (c) minimum visibility shall not be less than $10$ m in spaces ≥ $100$ m², and not less than $5$ m in smaller spaces; and (d) either instant exposure to carbon monoxide (CO) shall not exceed $1200$ ppm or cumulative exposure to carbon monoxide (CO) shall not exceed $500$ ppm for $20$ min. IMO requires that these limiting values are not exceeded at any height up to $2$ m. Here we have selected to install the meters at height $1.6$ m; however, in a complete study a number of meters would need to be installed for each deck location, in terms of height.

In Fig. 6 are shown the time histories of the measurements right above the ignited HGV, at height $4.4$ m, where the measurements are expected to be the most extreme (of course, the height of this location is far above that prescribed by the criteria). As heat and fire effluents are concentrated at higher levels, in about $2.5$ min, the temperature and the visibility thresholds were exceeded. Actually, in absence of ventilation, the temperature reached nearly $1200$°C. With ventilation, the temperature at the same location reached about $1100$°C. At the same time, radiation increased rapidly reaching intolerable values within $3$ min, whilst the CO concentration became excessive in $8$ min. CO remained comparatively low, however, on the mechanically-ventilated deck.

Figure 6

Measurements for (a) temperature, (b) radiation, (c) visibility, and (d) CO concentration, obtained from the device located above the ignited HGV (device 6 at height $4.4$ m). The red curves (i) correspond to the non-ventilated deck, whereas the yellow curves (ii) correspond to the mechanically-ventilated one. The black dashed lines indicate the limit values of the IMO life safety criteria

In Fig. 7 are presented more directly relevant data concerning survivability, as the meters were installed at height $1.6$ m, at two critical locations of the deck: (a) near the exit, and (b) next the air vent at the ship’s bow area. In the absence of ventilation, near the exit and at the bow the temperature exceeded the threshold in $5$ min. With mechanical ventilation, near the vent (at bow) the temperature never exceeded $60$°C. Near the exit, this temperature threshold was reached in $6$ min. As for radiation, the limiting value of the IMO criterion is exceeded only for the non-ventilated deck, at approximately $11$ min. Besides the thermal effects of a fire, effluents such as smoke and toxic substances (mainly CO) are also emitted, causing impaired vision, pain, and asphyxia. The smoke entirely blocked the exit in about $8$ min, while in $4$ to $5$ min the visibility limit prescribed for a large space (≥ $100$m long) was exceeded (Fig. 7c). With ventilation, there was sufficient visibility near the bow, basically due to the inlet of air in this area. In Fig. 7d is shown the CO concentration. In the non-ventilated fire, in $9$ min CO reached $500$ ppm near the exit while in $11$ min it reached $1200$ ppm. Concentration above $500$ ppm appears to be maintained for more than $15$ min. It becomes obvious that both criteria referring to CO’s concentration (i.e., $1200$ ppm for instantaneous exposure; and $500$ ppm for cumulative $20$ min exposure) were violated, indicating respiratory system impairment. However, CO’s concentration for the mechanically-ventilated fire remained very low. In both ventilation cases, CO yields are comparatively increased in the area near the air outlets at the stern. It is noteworthy that the non-ventilated fire results in greater CO yields than the mechanically-ventilated fire. This is justified by the fact that the combustion chemistry changes when ventilation is reduced because the CO produced is being more slowly oxidized to CO₂ due to the absence of sufficient oxygen [34, 76]. As a matter of fact, throughout the car deck, CO yields are at least 10 to 100 times larger in the non-ventilated fire than in the ventilated case, whilst near the ventilation inlet CO yields can be 1000 times greater for the non-ventilated fire. Figure 8 presents the evolution of CO yield at $1.6$ m in the non-ventilated fire; it is found that CO increases significantly from $8$ min reaching intolerable levels throughout the entire deck in $12$ to $14$ min. Overall, from the considered case study, it appears that the ventilated fires produce comparatively reduced thermal effects and more tolerable fire effluents. On the other hand, they have potential to burn for very long, until a large part of the available ignitable material on the deck is burnt. Hence, they have much higher potential for leading to an escalation of the fire to adjacent onboard spaces.

Figure 7

Measurements for (a) temperature, (b) radiation, (c) visibility, and (d) CO concentration, obtained from the following devices: near the exit (device 1 at height $1.6$ m, continuous curve) and near the supply ventilation (device 5 at $1.6$ m, dashed curve). The red curves (i) correspond to the non-ventilated deck, whereas the yellow curves (ii) correspond to the mechanically-ventilated deck. The black dashed lines indicate the limit values of the IMO life safety criteria (Color figure online)

Figure 8

2D slices of the vehicle deck at height $1.6$ m, for different stages of evolution of the fire (slices per z). CO yield is produced during the fire in the non-ventilated deck

Survivability with respect to exposure to high temperature (Fig. 9) and toxic dose (Fig. 10) has been evaluated further, considering the two main evacuation routes; that is, the port and the starboard route. When the deck was not ventilated, the temperature reached $60$°C in $5$ to $6$ min, at all considered locations of these two evacuation routes. With ventilation, temperature remained low near air’s inlet. However, as the exit is approached the temperature rises, exceeding the threshold value in about $6$ min. The starboard route was found to be safer. The area near the air supply remained safe in terms of temperature. The maximum value of temperature reached $150$°C to 600°C. In Fig. 11 is shown the relation between the time of human survival and temperature [77]. As evidenced, humans can tolerate higher temperatures if it is for a limited time. Based on such studies, some organizations have adopted less stringent threshold values for the same criteria (a brief review on these is found in [78]).

Figure 9

Measurements for temperature obtained from the devices placed along the evacuation routes (at height $1.6$ m). (a) port side evacuation route in the non-ventilated deck, (b) starboard side evacuation route in the non-ventilated deck, (c) port side evacuation route in the mechanically-ventilated deck, (d) starboard side evacuation route in the mechanically-ventilated deck. Rainbow colors (red, orange, yellow, green, darker green, blue, indigo, purple) indicate the route from bow to stern. The black dashed lines indicate the limit values of the IMO life safety criteria (Color figure online)

Figure 10

Measurements for FED obtained from the devices placed along the evacuation routes (at height $1.6$ m). (a) port side evacuation route in the non-ventilated deck, (b), starboard side evacuation route in the non-ventilated deck, (c) port side evacuation route in the mechanically-ventilated deck, (d), starboard side evacuation route in the mechanically-ventilated deck. Rainbow colors (red, orange, yellow, green, darker green, blue, indigo, purple) indicate the route from bow to stern. The black dashed lines indicate the limit values given in [22, 77] (Color figure online)

Figure 11

Tolerance time of humans to high temperatures in considering that they are at rest and exposed with naked skin in (i) humid and (ii) dry environments (based on [77]). The dashed line indicates the limit for hyperthermia and skin pain

Toxic dose is estimated through the Fractional Effective Dose concept (FED) by combining the cumulative effect, over time, of increased CO, low oxygen, and hyperventilation due to increased CO₂ [77]. Incapacitation is predicted to occur when FED reaches unity and death when FED reaches two. IMO has set the maximum threshold criterion of FED at $0.3$ [22]. FED reached high values for the scenario with no ventilation, especially near the exit. IMO’s threshold value was reached in $10.5$ min. With ventilation, FED remained at a fairly low level providing sufficient time for evacuation. Overall, the rise of temperature and FED for the investigated evacuation routes indicates that the starboard evacuation route had slightly lower concentrations of fire effluents.

5 Concluding Remarks

A methodology for investigating ship vehicle deck fires has been proposed. The method relies on computational fluid dynamics simulations of fire evolution which have reached a good level of maturity in recent years. The methodology takes into account the burning properties of the vehicles, the arrangement of the vehicle deck and the availability of ventilation. Hence it incorporates enough realism for being applied for designing vehicle deck spaces from a fire safety perspective.

Several experiments on cars and HGVs were collected and analyzed in order to determine representative types of fire behavior (from ignition to decay). By incorporating the material content features of the combustible mass, numerical design fires (represented by their HRR curves) for cars and HGVs were constructed.

A closed type vehicle deck, containing cars and HGVs, was investigated in order to demonstrate the method. A moderate severity fire was assumed, originating from a single HGV. Its evolution was examined with the aid of the FDS software. Scenarios of non-ventilated and mechanically-ventilated fire evolution were analyzed. The computations were performed in parallel using 12 computer cores considering almost $1.2$ million cells in total. For the simulation of mechanically-ventilated fires, about $90$ hours were required for $900$ s time evolution of a fire and its effluents, using an Intel core $i7-11700$ processor at frequency $2.50$ GHz and RAM memory $16$ GB. For the other scenario, more time was required due to the high concentration of fire effluents.

As it turned out, the fire on the non-ventilated deck was at some stage deprived of oxygen. It did not burn completely the initially ignited HGV, yet it managed to slightly spread to adjacent vehicles until it rapidly abated due to oxygen depletion. The high concentration of the trapped fire effluents would thwart human survival. When the deck was ventilated, on the other hand, the fire was found to propagate to adjacent vehicles. This fact implies a substantial further increase of the total amount of heat released. Temperature and visibility were not as high as for the non-ventilated deck, yet unacceptable values in terms of IMO life safety criteria were, again, soon reached. However, the concentration of radiation and CO remained low.

In case that humans were present (rather illegally) on the vehicle deck, mechanical ventilation appears to enhance evacuability for the first few minutes. In this case, toxic fire effluents were not too high and, for the simulated time, the FED threshold value was not exceeded. Temperature remained below $60$°C for $6$ min, rising then further up, reaching values that can cause pain and hyperthermia (instead of immediate loss of life) if the person remains in the space for up to $5$ min. Of course, as soon as the fire spreads to adjacent vehicles, the thermal load should have increased very substantially. Well-ventilated fires have the potential to burn until much of the combustible mass is consumed, resulting in very large fires that can spread beyond the deck space, therefore threatening survivability onboard as a whole. About $11$ min were available for evacuating the vehicle deck perhaps with some injuries. On the other hand, the absence of ventilation in the vehicle deck leads to intolerable conditions, in terms of both temperature and toxicity, very quickly. Another factor to consider is that, in both ventilation scenarios, visibility is considerably diminished within $6$ min.

The proposed method can be useful in the context of general risk analysis applied to ships with vehicle spaces. To incorporate modern technological trends, design fires for new vehicle types, such as hybrids and electric cars, should be built as well. Then, different types of HGVs and cargoes, as well as various arrangements with HGVs, trailers and containers can be taken into account. Also, the location of the HGV where the fire is started should be assessed. As is obvious, a probabilistic framework is suitable for taking all these factors into account. Nonetheless, separation of the problem’s parameters into those that are treated deterministically and the others treated probabilistically will still be required, depending on the time requirements of the task.

Appendix: FDS Input Details

In the paper was used the FDS software in order to simulate two fire scenarios, namely a non-ventilated and a mechanically-ventilated fire scenario, onboard a Ro-Ro passenger ship vehicle deck. First, the geometry is constructed; the entire length, width and height are $97.8$ m, $18.9$ m, and $5$ m respectively. Two vehicle types are considered; (a) cars which are represented as rectangles of $4$ m length, $2.2$ m width and $1.5$ m height, and (b) HGVs which are rectangles of $12.4$ m length, $2.8$ m width and $4$ m height. The distance between cars is $0.2$ m, while between HGVs it is $0.6$ m. The non-ventilated fire scenario does not take into account any openings or doors throughout the vehicle deck. It is completely airtight. On the other hand, the mechanically-ventilated fire scenario considers two openings of $5.76$ m² in the bow area supplying air at a rate of $16$ m³/s each (these are placed at x-position $94$ m and extend in z-height from $0.4$ m to $2.8$ m and in y-width from $12.8$ m to $15.2$ m the port side opening, and from $3.8$ m to $6.2$ m the starboard side opening). Two more openings of the same size are placed in the stern area for exhausting air at the same rate each (these are placed at y-position $16.6$ m the port side opening and $3.6$ m the starboard side opening, and extend in z-height from $0.4$ m to $2.8$ m and in x-width from $10.6$ m to $13$ m). For monitoring the evolution of the fire and its effluents in time, devices measuring temperature, visibility, radiation, FED, and the concentrations of CO, CO₂ and O₂ are placed at various points throughout the vehicle deck. Moreover, the 3D plot capability is used to record temperature, soot and mass fractions of CO₂, CO and O₂, in three dimensions. Figure 12 presents a three-dimensional view of the considered geometry as well as a top view showing the dimensions of the spaces and the corridors.

Figure 12

General arrangement of the Ro-Ro passenger ship vehicle deck. (a) Three-dimensional view of the arrangement. (b) Top view showing the detailed layout of the spaces and the corridors. Green rectangles indicate the cars, blue rectangles indicate HGVs, red rectangle indicates the initially burning HGV, black squares indicate the location of air supply and exhaust devices, and yellow circles indicate the location of the measuring devices (Color figure online)

Τhe main exterior and interior wall boundaries, the floor and the arrangement of vehicles through the vehicle deck are designed as obstacles. The following assumptions are taken into account for the materials, boundary conditions and reaction:

• (a) The walls and floor are represented as obstacles whose surfaces are made of steel. Their thickness is $0.2$ m so that it can be accurately recognized by the applied mesh. Their reaction, namely the way in which they ignite and burn, is governed by the thermal properties of the material which are found in Table

  Table 6 Thermal Properties of the Materials Defined in FDS Modeling

  6.

• (b) Vehicles are represented as rectangle obstacles made of materials found either on a car or on a HGV. Indeed, two individual materials are considered, namely “car” and “HGV”, whose thermal properties have been obtained as discussed in Sects. 3.2 and 3.3 of the current paper and are summarized in Table 6. Unlike walls and floor, the burning of the vehicles is governed manually by setting the heat release in time. More specifically, three “layered” surfaces related to the x, y and z planes of the vehicles are created. For these surfaces, are defined the maximum heat release rate per unit volume (HRRPUV) and the “ramp-up” function that determines a fraction of HRRPUV in time. The lower z-plane is not taken into account as a burning surface as it is tangent to the floor. Table

  Table 7 HRRPUV Values for the Considered Surfaces Taking into Account the Maximum HRR Values^a

  7 presents the maximum HRRPUV for the three surfaces of cars and HGVs, while Table

  Table 8 Time Fraction for the “Ramp-Up” Functions for Car and HGV Surfaces

  8 presents the corresponding time fraction for the “ramp-up” functions. Each rectangle is therefore capable of producing fire according to the HRR curves generated for the scope of the current work. Vehicles’ surface has initial temperature $20$°C and is able to transfer heat to the obstacles (backing command is set to “exposed”). Vehicles’ burning is activated when their ignition temperature is reached. Cars are ignited at $230$°C and HGVs at $250$°C. The initially ignited vehicle is a HGV which is represented as a “burner” surface. This surface is defined by the HRRPUV considering, once again, the “ramp-up” time function.

• (c) In order to consider reaction, “simple chemistry” is taken into account by applying the calculated heat of combustion and the post-flame yields of all the fire products as calculated for the HGV burning (these are given in Table 3). The chemical reaction of polyurethane, which comprises of 6.3 Carbon atoms, 7.1 Hydrogen atoms, 2.1 Oxygen atoms and 1.0 Nitrogen atoms, is considered. This is of course a simplification as HGV is composed of a variety of materials whose chemical reaction is complicated to estimate accurately. Such a choice does not appear to significantly affect the concentration of the fire effluents as evidenced in Fig. 

  Figure 13

  

  Measurements for (a) temperature, (b) oxygen, (c) visibility, and (d) CO concentration, obtained from the device located above the ignited HGV (device 6 at height $4.4$ m) for the non-ventilated deck. The red curves (i) correspond to the polyurethane reaction, whereas the yellow curves (ii) correspond to the oak wood reaction (Color figure online)

  13 comparing temperature, oxygen, visibility and CO concentration for reaction of polyurethane and oak wood (oak wood is comprised of 1.0 Carbon atoms, 1.7 Hydrogen atoms, 0.72 Oxygen atoms and 0.001 Nitrogen atoms). This is mainly due to considering the same post-flame yields for the two chemical reaction cases. The considered “simple chemistry” approach, however, has limitations in the application of under-ventilated fires. For the non-ventilated scenario, it is possible to use the “two-step simple chemistry” model to account for the CO increase due to low ventilation. For this purpose, the next command is applied in addition to the “&REAC” command: “&COMB RADIATIVE_FRACTION = 0, EXTINCTION_MODEL = EXTINCTION1, N_SIMPLE_CHEMISTRY_REACTIONS = 2 /”. The “&REAC” command remains as in the “simple chemistry” case. Although the “two-step simple chemistry” is consistently used when there is interest in near-flame phenomena where increased CO concentration and soot have an important role in flame chemistry and radiation emission, in a very recent study, published by FDS developers, it is validated that it can also be safely used for under-ventilated fire compartments [79]. As a matter of fact, this approach first converts the fuel to CO and C and then converts the CO and C to CO₂ with the second step being limited by available oxygen. In under-ventilated areas of the domain this will mean that some CO and C will not be converted to CO₂ resulting a higher than expected accumulation of CO and C. Once CO and C move towards well-ventilated regions of the domain, they will react once again with the oxygen creating CO₂. In essence, post-flame yields are set and FDS automatically produces higher CO and soot yields in low-oxygen regions because there will not be enough oxygen to complete the reaction to CO₂. It should be realized that the “two-step simple chemistry” approach and any assumptions thereof, for simulating under-ventilated spaces, are still an area of active research so the method may not be mature enough yet for direct application in design.

The computations were performed using almost $1.2$ million cells, breaking the grid into $12$ meshes in order to reduce the simulation time. Indeed, parallel computations were performed; each of the 12 computer cores is used to calculate the equations on each of the $12$ meshes. The staggered mesh system is utilized whereby the scalar components are assigned to the cell center, the velocity components are assigned to cell faces, and the vorticity components are assigned to cell edges [80]. In the current application, all meshes consist of cells of size $0.2\times 0.2\times 0.2$ m and all obstacles are adapted to the constraints of this mesh. Figure 14 presents the applied mesh. It is also important to note that, due to the very high values of heat release in the scenarios being examined, the simulations broke down sometimes (this is the reason why the calculations were performed for $15$ min of fire evolution real time, which however were enough for the needs of the current study).

Figure 14

Representation of the meshing applied for the FDS simulations. (a) Yellow outlines indicate the boundaries of the 12 sub-meshes. (b) Part of the vehicle deck showing cells distribution