Investigative Study on Convective Heat Transfer inside Compartment during Fire Situation

Laboratory of Analysis, Simulation and Experiment, University of, Ngaoundéré, Ngaoundéré, Cameroon School of Chemical Engineering and Mineral Industries, University of Ngaoundéré, Ngaoundéré, Cameroon Laboratory of Energetic of Carnot, University of Bangui, Bangui, Central African Republic Higher Polytechnic School of Ouagadougou, Kadiogo Province, Burkina Faso Department of Energy Engineering, IUT, University of Ngaoundéré, Ngaoundéré, Cameroon National Higher Polytechnic School of Douala, University of Douala, Douala, Cameroon


Introduction
Fire in con ned compartment is very complex issue for remen because of its impossibility to describe or predict how it would behave. However, based on re science and experience feedback, it is possible to identify typical phases of the development of con ned re. Indeed, depending on the potential fuels involved, their layout, the geometry of the room, and the level of natural ventilation, it is possible to observe di erent possible evolutions of re, each one leading to particular phenomena with identi able characteristics [1][2][3]. Building re thus constitutes that category of res of which the main characteristic is the lack in fresh air. at di culty in supplying air is due to the presence of walls. e most important parameter, on which other parameters depend, is the heat release rate, which represents the energy released per unit time [4]. Energy rate generated by the re source depends on the quality of the combustion reaction, which depends itself on the type and the availability of fuel as well as the amount of air inside the room in re situation. Partial or total con nement of compartments has two main e ects on the behaviour of building re [5]. Firstly, hot gases accumulating at ceiling heat walls which, along with hot gases, radiate heat far to the re source. e spread of smokes inside compartment accelerates therefore the preheating and the combustion speed of surrounding combustibles. Secondly, confinement tends to restrict the availability of the oxygen necessary for combustion, which, in case of nonconfined building fires, is often supplied through openings such as windows, doors, or cracks. Contrary to confined fires, the spread of fire inside compartment with at least one opening is piloted by ventilation. at means it depends mainly on the flow rate of the entering air, the size, and the position of that opening [6][7][8][9][10][11]. e present paper aims to carry out the impact of natural ventilation on convective heat transfer between hot gases inside compartment in fire and its different walls. To achieve that goal, varying the ventilation factor, fire tests were carried out in an experimental domain in which the heat release rate of the fire source was kept constant. Completed by numerical simulation, results enabled discussing the influence of the variation in the level of natural ventilation on convective heat transfer between burnt gases and walls during fire.

Experimental Trials.
e experimental domain is a room of dimensions L × W × H: 0.50 × 0.50 × 0.50 m, including on its front wall a door of dimensions W 0 × H 0 : 0.20 m × 0.40 m (Figure 1). Walls are designed with wood panels of thickness 0.02 m. As fire source, diesel fuel is introduced in a pan of diameter 0.12 m and then set inside the room precisely at the center of the floor. Seven N-type thermocouples (TC1-TC7), connected to the data acquisition switch (Agilent 34970A), were used to measure temperatures during experiments. Table 1 presents the different positions inside the experimental domain where thermocouples have been installed. e ventilation level in compartment is defined by the parameter called ventilation factor. at parameter is mathematically traduced by the formulae W 0 H 1.5 0 [12,13]. In view of varying the ventilation factor of the experimental room, the width of the door W 0 has been gradually varied while its height H 0 was kept constant. Four geometric configurations with different ventilation factors have thus been tested (Table 2). Each configuration corresponded then to a fire scene to be experimented. To be sure of the repeatability of experiments, each fire scene was repeated three times and only average results were represented and interpreted.
Fire tests consisted of introducing a mass of 0.065 kg of diesel fuel in the fire pan and initiating ignition. at fire source was then left burning inside the room until the amount of fuel initially put in the pan is burned. As illustrated in Figure 2, the fire source was indirectly set on an electronic balance so as to measure the mass loss rate of fuel during tests.

Numerical Simulation.
Numerical simulation can be defined here as the reproduction of physical reality in a computer owing to mathematical models implemented in the simulation software. e choice of numerical model then    depends on the precision, storage space, and the necessary time for performing simulation. Indeed, models are based on algebraic equations or simple analytical approaches, very often resulting from correlations established from experimental data. ese models are thus incorporated in complex models so as to take into account various phenomena implied in the physical reality to be reproduced. One of the most complex models used to simulate uids phenomena is the eld model, commonly called CFD (Computational Fluid Dynamics). Also used in re simulation, that model is established from conservation laws, and the main strongly coupled mathematical equations, describing the physics of compartments res, are continuity equation (1), momentum equation (2), energy equation (3), and transport equation of chemical species (4) [14][15][16][17][18]: Terms ρ, u, h, c p , and λ represent the density, velocity, enthalpy, speci c heat, and thermal conductivity of the uid, respectively. P is the total pressure; τ is the tensor of the viscous stresses. Y k and D k represent the mass fraction of chemical species k and its molecular di usion coe cient, respectively; q r represents the net heat ux due to thermal radiation.
e CFD code used in the present paper is called ISiS. It is a calculation code developed by the Fire and Explosion Laboratory of the IRSN [19]. at code, including a set of combustion, turbulence, soot production, and heat transfer models, can be used to simulate the spread of re in large, naturally ventilated, mechanically ventilated, or con ned compartments. e physical models implemented in ISiS enable 3D simulation of unsteady, low compressibility, and turbulent and reactive or chemically inert ows. ISiS has been validated through a set of tests involving ows with or without combustion reactions [20][21][22]. e di erent steps used to perform numerical simulation of re tests carried out in the present paper are described in Figure 3. Based on Finite Volumes Method, numerical models used to de ne some main re phenomena, such as combustion, turbulence, and heat radiation, are presented in Table 3 [19].

Heat Release Rate.
e behavior of re inside buildings depends mainly on the rate of energy released by the re source. In a predictive study, its determination could give some indications on eventual spread direction of re and then help with de ning the way occupants should leave the building. It could also enable determining whether the structure will resist during re. Estimation of heat release rate enables determining other re parameters such as ame height, position of the hot gas-fresh air interface, hot gas temperature, and concentration in combustion products. ese parameters can be used to determine, for example, the tenability and the resistance of the structure. ere exist in literature di erent models estimating the rate of heat released by re. Some of them are entirely based on experimental data while others try to describe physical phenomena by equations. Pyrolysis and ame propagation are some of those which remain fairly empirical because of their complexity. Heat release rate during compartment re can be calculated using either (5) or (6) [23,24]: where _ m f is the mass loss rate of fuel (kg/s); _ m f ″ is the mass loss rate of fuel per unit of horizontal surface area (kg.m −2 / s −1 ); A f is the horizontal area of the fuel pan; H c is the fuel heat of combustion (kJ.kg −1 ); χ is the e ciency of combustion, for the case of diesel fuel χ and H c are equal to 0.82 and 43.4 MJ kg −1 , respectively [25].

Convective Heat
Transfer. When re evolves in con ned or semicon ned compartment, insu ciency in air supplying the re source could relatively lead to incomplete   [26][27][28][29][30]. e increase in temperature of these hot gases depends on the difference between heat generated by the fire source and heat lost through walls and openings. In addition to heat radiated by flames, heat transferred by convection also plays an important role in energy transfers causing compartment fires. As described in (7), besides the difference between fluid temperature T f and wall temperature T w , convective heat transfer coefficient h cv is also an important parameter necessary to estimate the convective heat flux φ transmitted per unit area [31].
It is therefore important to remember that the convection coefficient, or convective heat transfer coefficient, is a coefficient that quantifies the heat transferred between a fluid moving against a cold or hot wall. With property like density that changes with temperature and pressure, any fluid in contact with hot or cold solid surface tends to rise or fall along that wall, respectively. at phenomenon consequently generates convective currents in the fluid and involves heat transfer between fluid and wall [32]. Depending on the cause of convective currents, value of h cv will depend whether the convection is natural or forced [33].
Regarding precisely heat transfers inside buildings, the convective heat transfer coefficient depends on the interior environment of buildings [34], in particular, parameters such as the shape and dimensions of compartment, the distribution in temperature on the surface, the presence of air movements due to the existence of air currents or ventilation, and the surface roughness. In spite of the variability of case studies, that coefficient remains particularly difficult to determine. However, two alternative methods are mentioned in literature. e first method is to suppose h cv constant according to values determined by Inard (1988) [35]. e second one is to estimate h cv owing to experimental correlations. Concerning experimental correlations, many works exist in literature [36][37][38][39], but the majority expresses the convection coefficient as a function of the difference between the fluid temperature and the wall temperature. Regarding compartment fires, that difference in temperature is not so important. What is rather observed in compartment fires is the strong motion of hot gases. at explains the reason why during compartment fires, the convection heat transfer coefficient could be estimated using the McAdams correlation given by (8) [40].
at correlation takes into account the speed of the fluid V f and the nature of the wall defined by characteristics m and n given in Table 4.

Experimental Results.
After preliminary steps consisting of the preparation and instrumentation of the experimental domain, fire scenes were each performed in its configuration. Figures 4(a)-4(d) show the captured image of flame of fire sources 1, 2, 3, and 4, respectively. According to a visual  point of view, it can be observed that light emitted from ames decreases while the ventilation factor is reduced. One also observes an increase of the ame instability. In other words, as the ventilation factor decreases, the ame becomes increasingly turbulent and production of soot particles also increases. ese observed e ects are obviously due to the progressive lack in oxygen. Having repeated each re scene three times, Figures 5(a)-5(d) show the variation curve over time of burned gases temperature at height h 0.37 m (measured by sensor TC6). In that gure presenting curves of the three repeated tests as well as their mean curve, the three phases of compartment re can clearly be identi ed (growth: from 0 to 200 sec, full development: from 200 to 600 sec, and decline: from 600 to 700 sec). It also appears that   the absolute error between the average and repetition curves is less than 10 K regardless of the re scene. at allows approving the repeatability of each re scene. Exploitation of data collected during experiments enabled determining average values of parameters such as the mass loss rate _ m f of fuel, the maximum temperature T max reached by burned gases at ceiling, and the thermal power released _ Q by the re source (Table 5).
Graphical representation of these data shows regarding the rate consumption of fuel ( Figure 6) that as the ventilation factor decreases, the mass loss rate of fuel increases linearly till a peak value of 0.029 m 2.5 . Starting that peak value, one observes a gradual drop of mass loss rate. Indeed, the literature [41] distinguishes two re control regimes for compartment re: the re controlled by fuel and the re controlled by ventilation. In the present case study, the change over the ventilation level of the direction of variation of the mass loss rate traduces the change of the fire regime. Two variation domains could be highlighted in Figure 6. e first domain is the one where the ventilation factor is less than 0.029 m 2.5 . It corresponds to the range where the flow rate of fuel increases strongly with the ventilation factor. e second domain is the one where the ventilation factor is more than 0.029m 2.5 . It corresponds to the range where the flow rate of fuel gradually decreases while the ventilation factor increases. Indeed, the first domain corresponds to the regime where effects of ventilation on the behavior of fire dominate over effects of fuel. at means the fire is controlled by the ventilation because, in that interval, the increase of the ventilation factor involves the increase of the combustion rate fuel and therefore a rapid development of fire in the compartment. e second domain is the interval where the fire is controlled by fuel. In fact, as the ventilation factor increases, effects of fuel on the behavior of fire gradually take precedence on effects of ventilation. is is manifested by the decrease of the fuel mass loss rate. If the ventilation factor increases indefinitely, the flow rate of fuel will stabilize around a minimum value corresponding to the mass loss rate of the same fire source in an extremely large compartment or in free atmosphere. In other words, effects of ventilation on compartment fire become negligible as the ventilation factor increases. Concerning temperature of hot gases at ceiling, it was found that the change in the fire regime has no influence on it. It increases continuously while the ventilation factor decreases. is is illustrated in Figure 7, where it can be observed that the four fire scenes have the same temperature profile with different peak values. enabled visualizing the temperature contours at that plane of compartment. us, according to a visual analysis (Figures 8(a)-8(d)), one observes an increase in temperature of burned gases at the plume zone depending on the re scenes. e smaller the opening width of the door is, the larger the ame size is. at is illustrated through the height of the plume.

Simulation of
Numerical results were compared to experimental results so as to validate simulations. Indeed, numerical curves giving evolution over time of burned gases temperature in the hot zone (h 0.37 m) were compared to experimental curves (Figures 9(a)-9(d)). In these gures, the rst two phases of the development of compartment res, namely, growth phase (from 0 to 200 sec) and full development phase (from 200 sec to more), are distinguished. During the growth phase, it is observed that numerical curves do not agree with experimental curves. at di erence observed is due to the fact that the average ow rate of fuel de ned in the input le of the ISiS code is those of the full development phase. is means that the variation in the mass loss rate of fuel during growth phase was not taken into account. On the other hand, during that full development phase, simulations are agreed on with experiments. It then means that, during full development phase, simulations are in accordance with experiments. So, following that validation, numerical results obtained during that phase can be exploited and interpreted.

Simulation of Velocity Fields.
During experiments, it was practically impossible to measure velocity of burned gases near the inner part of walls. is is due to the high thermal stresses inside compartment during re. Such environment could be damageable for velocity captor. e other reason is that velocity is easily measurable with uid owing in one direction. is is not the case for burned gases at ceiling of the compartment in re. at justi es the reason to use CFD tool in the present paper. Figures 10(a) near the wall of di erent simulated re scenes. Regarding these curves, and precisely during the full development phases (comprised meanly between 200 and 500 sec), it is observed that velocities of burned gases near walls uctuate around an average value that almost remains constant throughout the full development phase. Numerical simulation enabled characterizing turbulent ow of gases in the hot zone. Manifestations of that turbulence can be observed through the frequency and the amplitude of velocity eld which varies from one re scene to another. Values velocity elds V f were extrapolated into the full-scale situation according to the Froude similarity [42] so as to estimate velocities of burned gas in a real re situation (Table 6). Owing to the deduced full-scale velocities, the convective heat transfer coe cient of each re scene has been determined, and the obtained values are  given in Table 7. Further investigation allowed noting that turbulent ow of hot gases in high part of compartment increases while the ventilation factor decreases. is means that the level of uctuations of hot gases at ceiling of room in re decreases while the ventilation level increases. Graphical representation of convective coe cients deduced from numerical simulation allowed noting that the variation's direction changes according to the re control regime. Indeed, when re is controlled by ventilation, velocity of convective currents of burned gases in the hot zone increases with the ventilation factor, thus implying an increase in the convective heat transfer coe cient. at is for the case of res with a very small ventilation factor such as con ned res. However, as e ects of ventilation begin fading, particularly with the increase of the ventilation factor, velocity of hot gases gradually decreases, leading to the decrease in the convective heat transfer coe cient between hot gases and walls. at variation changing over the ventilation factor is illustrated in Figure 11, where two variation zones, respectively, represented by item (A) and item (B), can be identi ed.
Indeed, the domain where the convective heat transfer coe cient increases with the ventilation factor (A) corresponds to re tests in which the e ects of ventilation are dominant. e re regime is then the fuel-controlled re and really refers to res in nearly con ned environments. On the other hand, the domain where the convective heat transfer coe cient decreases with the ventilation factor (B) corresponds to re scenes during which e ects of ventilation no longer dominate over e ects of fuel. Here, the re regime is the ventilation-controlled re. It refers to cases of res in semienclosed environments such as most building res; this is because during re, it at least one opening will exist which could be a door or a window supplying continuously the compartment in fresh air. For that category of res, it can be denoted that the convective heat exchange coe cient weakly decreases while the ventilation factor increases. A regression of that decreasing curve allowed establishing the mathematical relation (with R 2 0.93) given by (9) and expressing the convective coe cient h cv as a function of the ventilation factor A 0 H 0 : Despite the fact that the convective heat transfer coefcient decreases while the level of ventilation increases, it remains nevertheless close to the average value 8.75W · m − 2 · K − 1 which is lightly higher than value 7.0W · m − 2 · K − 1 recommended in literature [43]. at new value of h cv deducted from experimental and numerical studies could be used in the modeling of con ned res so as to better evaluate thermal balance during buildings res.

Conclusion
Heat transfer between burned gases and walls during compartment fire depends strongly on the convective heat transfer coefficient, which is related to the convective velocity of burned gases in the compartment. Owing to experimental and CFD studies, the present paper aimed to investigate the behavior of burned gases inside room during fire situation. Varying the ventilation level of compartment, temperature, velocity, and convective heat transfer coefficient of burned gases were analyzed. Results revealed that the convective heat transfer coefficient of gases in hot zone increases with the ventilation factor when the fire is piloted by ventilation effects and decreases progressively when effects of ventilation begin fading. However, that convective coefficient remains close to constant value. e maximal temperature of burned gases continuously increases while the ventilation factor of the room decreases.