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42 ANALYTICAL (NUMERICAL) For combustion process modeling, the Eddy-Break-Up FIRE MODELING TECHNIQUE model is generally used. This method may be helpful if the information required from the simulation concerns the fire The CFD simulations of tunnel fires driven by buoyancy zone. The limitation concerns the fire load. It is not always forces with significant energy release require a solution of the possible to provide equivalence in terms of fuel consumption. NavierStokes equations with appropriate boundary condi- tions. The physics of fire modeling is complicated by many In December 2005, NIST performed CFD modeling of uncertainties. A number of assumptions need to be made for the 1982 Caldecott Tunnel Fire (34). They used the FDS numerical modeling. The number of unknown variables and code and a combustion model. They concluded that fire the calculation duration vary according to the hypotheses and consumed roughly 70% of the available oxygen, with an HRR assumptions made. of about 400 MW (1,365 MBtu/hr). However, the authors accepted that this was probably an overestimate because the There are at least eight equations to solve in 3D simulations, model uses a simple "mixed is burnt" combustion model in the unknown variables being , p, T, ux, uy, uz, k, and , and combination with an empirical local extinction algorithm. seven equations to solve in two-dimensional (2D) simulations. The actual combustion processes are far more complicated and potentially much less efficient in the tunnel environment. Additional equations may be required to take into account The model overly predicted the combustion efficiency of the the radiative heat transfer, the combustion process, or the fire, in which case most of the fuel was consumed somewhere heat transfer by conduction inside the walls. Different ways in the tunnel or never consumed at all. Another possibility to model fire have been discussed. Airflow in tunnels is was that the observed flames at the east portal were a result usually turbulent and the user has to make an assumption on of unsteady evaporation of the gasoline. It was assumed the type of turbulence modeling to apply. One of the most that the gasoline evaporated at a constant rate for 40 min common turbulent models is the k- model and its variations. (about 10 kg/s or 22 lb/s). However, had there been periods The user is required to select turbulent length scale along of greater evaporation this would explain the discrepancy with k and coefficients. There is insufficient information from between the observations and the simulation. The maximum a full-scale test to provide recommendations on the coeffi- predicted gas temperature near the ceiling was just below cients to use. With this lack of information, the users apply 1100C (2012F) with ablation and 1150C (2102F) without. the default numbers or follow some recommendations that This high temperature region was located roughly 40 to 120 m may not be applicable to the road tunnel fire test modeling. (131 to 394 ft) east of the overturned truck, near the ceiling The better choice is to calculate the k and coefficients of the and along the tunnel centerline. However, the tunnel inspec- model based on length scale. tion report suggested that the maximum gas temperature could not have exceeded the melting temperature of copper In recent years the development of computers (i.e., speed [1065C (1949F)], because copper wiring in the upper and memory) has allowed for the development of larger and wall light fixtures was not melted. The peak wall surface more complicated numerical models. However, considering temperatures were approximately 950C (1742F). the length of road tunnels, a model may require millions of cells. Even with today's computer power, the transient simu- A more simplified approach is to consider fire as a volume lations of this size of a model may take months of computer source of energy at a given changing FHRR and a source of time. Usually the user has to examine the grid by performing smoke and soot as a function of HRR. The last approach does sensitivity analysis and find the grid scale that will allow for not require combustion and chemical reaction modeling, reasonably accurate simulation results (32, 33). The better but does require knowledge of the heat, smoke, and soot (fine) grid quality is usually in the fire influence zone, whereas release rates. a coarser grid is created in other parts of the tunnel. Fixed HRR in a volume: In this model, the fire source is A road tunnel fire is a combustion process with many represented by an HRR fixed inside a given volume. unknowns, such as the substance that is burning, the method This value is not influenced by ventilation. This method of the burning, and when it is burning. Some conservative leads to a more accurate energy distribution inside the assumptions can be made based on previous experience and tunnel volume, and experience has shown that it can lead full-scale fire tests. Those assumptions may include fire growth to quite realistic temperatures except very near a fire. and decay rates, ignition location, and fire size. However, Fixed heat flux through a horizontal surface: This tech- how the vehicle burns may be one of the most complicated nique imposes a heat flux or a mass flow rate at a fixed questions for the numerical modeler, especially if modeling temperature to get the design HRR. The latter method a fire as a chemical reaction, providing soot particles and leads to the mass flow rate, which is not always in combustion products at high temperatures. One approach is agreement with the combustion's production of burned to represent a vehicle as a blocked volume, consider vehicle gases (it must then be combined with a sink of mass). windows as inlet boundaries, and have hot combustion gases The volume energy distribution is not as good as in the emerge as the flame temperature. previous case, and the results are not as reliable.

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43 Fixed temperature in a volume: The advantage of this Control of heat fluxes at the walls without modeling the method is its ability to control the maximum temperature radiative heat transfer--This solution entails combining reached inside the fire. A disadvantage of this method the radiative and convective heat transfer coefficient to is that the HRR will strongly depend on ventilation form a local empirical transfer coefficient. No additional conditions. equation is required. In France, this method has been applied to simulate the heptane fire test H32, which is The fixed HRR in a volume method is generally preferred carried out during the EUREKA 499 experiments. because it is less expensive (central processing unit time) Results obtained with this method are claimed to be than modeling the combustion process and presents fewer within reason. disadvantages than the other methods. The design HRRs and Reduction of the HRR at the fire source--This considers fire curves can be directly used with this method. reducing the actual heat release source injected in the model by deducing the radiative part. This technique It is always suggested that sensitivity studies be performed has been shown in several publications and the percent- before final design simulations. This may take more time and age of energy lost by radiation at the fire source is esti- effort than the design, but leads to a better understanding of mated to be in the range of 20% to 50% of the total heat the results. energy released by combustion. The major problem There are many other boundary conditions that may affect with this method is caused by not taking into account the end results. the loss in radiative energy from the hot gases to the walls farther from the fire. Initial air movement--Air in the tunnel is never still. There is always some airflow caused either by the piston Smooth wall surfaces are generally the default CFD effect of traffic, by normal tunnel ventilation, or by winds conditions. However, the user may generally define rough and other natural factors. For example, in uni-directional surfaces by modifying the layer parameters to represent the tunnels, the assumption is made that in a fire emergency zone very near the walls. The use of rough surfaces depends traffic will be trapped behind the fire, whereas traffic on the objectives of the simulations; if they concern the downstream of the fire will leave the tunnel. The depart- analysis of the force's balance or the propagation speed of ing traffic will cause a residual piston effect, driving the smoke front, the assumption made on surfaces will influ- smoke and airflow in the direction of travel. Adverse ence the results. winds may also have a significant impact on the airflow. Residual air movement, caused by approaching the fire Heat transfer boundary conditions may also affect the end location traffic, may also drive the airflow. results. Trapped traffic behind the fire incidence--Trapped traffic creates a significant obstruction to the airflow. Fixed temperature or fixed heat fluxes--In this case, This results in substantial resistance to the airflow and the temperatures at the walls or the heat fluxes through obstructions to the air jets developed by the tunnel venti- walls are fixed to constant values. lation system. The last phenomena could be modeled by Combination of fixed temperature with heat fluxes-- CFD; however, it would require complicated geometric This technique may be used to roughly model the heat modeling and many additional computational grid cells. conduction process in the rock (soil). Wall boundary conditions--It is usually considered that Heat conduction inside the rock (soil)--This method approximately 30% of the total heat is transferred to the appears as the best physical interpretation of the prob- tunnel walls by radiation and 70% by convective heat. lem. The heat transfer to the walls may have noticeable There are radiation models available in commercial CFD effects, especially in the case of extended fires. However, products; however, radiation models are complicated and require the use of absorption coefficients and other it leads to larger meshes and longer calculations. empirical information. Often users consider convection portions only. Temperatures inside the fire may reach Boundary conditions at the portals may seriously influence 1300C (2372F). The heat transport is locally more the final results. radiative than convective. Calculations performed with- out radiative models have led to the prediction of higher Fixed pressures at both portals--This directly represents temperatures, even a 100 m from the fire zone. Several the atmospheric effects. The critical size of the out- techniques can be used to take radiation into account. side zone to be modeled is between 3 and 5 hydraulic Radiative heat transfer model coupled with the conser- diameters. However, acceptable results can be obtained vation equation of energy--This technique solves an without an outside domain, provided that some pre- additional equation. The greatest difficulty comes from cautions or even corrections are used. inadequate knowledge of the radiative properties of Specifying fluid properties fixed at one end and fixed smoke, which explains the need for additional research pressure at the other end--This may be justified for the on this topic. analysis of the conditions inside the tunnel with known