Influence of Obstacles on the Development of Gravity Current Prior to Backdraft

Abstract

The phenomenon of backdraft is closely linked to the formation of a flammable region due to the mixing process between the unburned gases accumulated in the compartment and the fresh air entering the compartment through a recently created opening. The flow of incoming fresh air is called the gravity current. Gravity current prior to backdraft has already been studied, Fleischmann (1993, Backdraft phenomena, NIST-GCR-94-646. University of California, Berkeley) and Fleischmann (1999, Numerical and experimental gravity currents related to backdrafts, Fire Safety Journal); Weng et al. (2002, Exp Fluids 33:398–404), but all simulations and experiments found in the current literature are systematically based on a perfectly regular volume, usually parallelipedic in shape, without any piece of furniture or equipment in the compartment. Yet, various obstacles are normally found in real compartments and the question is whether they affect the gravity current velocity and the level of mixing between fresh and vitiated gases. In the work reported here, gravity current prior to backdraft in compartment with obstacles is investigated by means of three-dimensional CFD numerical simulations. These simulations use as a reference case the backdraft experiment test carried out by Gojkovic (2000, Initial Backdraft. Department of Fire Safety Engineering, Lunds Tekniska Högskola Universitet, Report 3121). The Froude number, the transit time and the ignition time are obtained from the computations and compared to the tests in order to validate the model.

Appendices

Annex

1.1 Experimental Setup of Fleischmann’s Experiments

The saltwater experiments were conducted by placing an acrylic compartment within a larger glass tank. The tank (0.3 m wide, 0.6 m long, and 0.45 m deep) contained a dense saline solution ranging in density from 1.003 to 1.101 kg/m³. The solution temperature was 18°C. Standard rock salt crystals were dissolved in tap water to raise the density to the desired level.

The compartment was constructed using 6.0 mm thick acrylic with an interior dimension of 0.15 m wide, 0.3 m long and 0.15 m high. The openings were a fully opened wall (0.15 m × 0.15 m), a horizontal slot (0.15 m wide × 0.05 m high) centred vertically at the end of the wall, a window (0.05 m²) centred vertically and horizontally on the wall and the last opening was a door (0.12 m high × 0.05 m wide) centred horizontally with the bottom of the opening at floor level. Figure 10 shows the saltwater configuration and the opening geometries.

Figure 10

Saltwater configuration and opening geometries used in Fleischmann’s experiments

1.2 Initial and Boundary Conditions

In each of these simulations the fluid used is air. To obtain the difference in density between the inner and outer air, different temperatures are given. In the salt-water experiment, the temperature of both fluids remains constant (18°C) and the difference in density is obtained by adding more or less salt. This difference between the simulation and the physical model has no influence on the results.

The dimensions of the compartment are identical to the experimental setup. The compartment is positioned on the far left of the saltwater container, which is 0.55 m long, 0.35 m deep and 0.3 m wide. The enclosure is also raised 5.0 cm from the bottom of the container (Figure 10).

The density of the inner and the outer fluid is 1.205 and 0.833 kg/m³, respectively. These values are obtained by giving an initial temperature of 423 and 293 K for the inner and outer fluid, respectively, which gives a buoyancy of 0.3072. Only one value of buoyancy is simulated for each opening geometry since the Froude number values are independent of the density difference ratio [1].

To simulate these scenarios, the k-epsilon turbulent model has been used, with an initial k and epsilon equal to 0.0001 m²/s² and 0.0001 m²/s³, respectively. The velocity inside and outside the enclosure was initially set to 0.0. The inner fluid mass fraction was set to 1.0 inside the compartment and 0.0 outside the compartment. For the outer fluid the opposite values are given, i.e. 0.0 inside the compartment and 1.0 outside the compartment. The boundary conditions for the container, floor and air are summarized in Table 5.

Table 5 Boundary Condition for the Container, Obstacles, Floor and the Ambient for the Simulation of the Scaled Saltwater Experiments

About 20 s were simulated with a time step of 0.02 s. The total number of elements (tetrahedrons) for each simulation is around 400,000.

1.3 Qualitative Comparison of the Results: Scaled Saltwater Experiments vs. Simulations

Figure 11(a) represents photographs taken from the saltwater experiments. They represent the mass fraction of the gravity current approximately 3L/4 into the compartment for different opening geometries. Black represents the inner fluid and the lightest colour is for the outer one.

Figure 11

Visual comparison between (a) saltwater experiments and (b) CFX simulation

These photographs closely resemble the numerical simulation results shown in Figure 11(b).

1.4 Quantitative Comparison of the Results: Scaled Saltwater Experiments vs. Simulations

To compare the numerical simulations quantitatively with the experiments, the non-dimensional velocity or Froude number and the transit time, t _trans, is used.

For the saltwater experiments, the transit time was taken from a video recording of the gravity current. Once the gravity current reaches the rear wall, it is reflected up and around until it travels toward the opening. A Froude number is also calculated for the returning current. The returning gravity current is defined in Equation (14), where t _out is the time from opening to the time the reversed current returns to the opening wall.

$$ v_{\text{gc}} = \frac{{2 \cdot L + {{2h_{1} } \mathord{\left/ {\vphantom {{2h_{1} } 3}} \right. \kern-\nulldelimiterspace} 3}}}{{t_{\text{out}} }} $$

(14)

The 2h ₁/3 factor is used to account for the length the current must travel up the wall opposite the opening [1].

Results of the Simulation

Table 6 shows t _trans, t _out, and the buoyancy parameter β obtained from simulations as well as a comparison between the Froude numbers (entering and exiting) from saltwater experiments and simulations.

Table 6 Bouyancy Parameter, t _trans, t _out, and Froude Number from Saltwater Experiments and CFX Simulation for Different Opening Geometries

Table 7 represents h_o obtained from simulation and the average value of h* obtained by simulations and experiments. Note that h _o is height of the gravity current measured over the distance 3L/4 to L. This interval is chosen to reduce any effects caused by the openings, h* is defined as h _o/h ₁.

Table 7 Comparison of h _o and h*: Simulation vs. Experiments

The simulations and the experiments were found to agree. As a result, one may now say that the setup of the model has been well defined. One may then well suppose that the simulations carried out in the following sections will lead to the same accurate results.