Chapter 7
Gravity Current Prior to Backdraft Table of contents
1. Introduction............................................................................ 155 2. State of the Art ...................................................................... 155 3. Simplified Methods for Gravity Current ................................. 156 4. Checking the Setup of the Simulation with Saltwater Experiments.................................................................................. 158 4.1 Saltwater Experiment Configuration .................................... 158 4.2 Simulation Setup.................................................................. 160 4.3 Visual Result of the Simulations .......................................... 161 4.4 Qualitative Comparison of the Results................................. 174 4.5 Quantitative Comparison of the Results .............................. 175 5. Effect of Opening Location on the Gravity Current................ 177 5.1 Simulation Setup.................................................................. 177 5.2 New Opening Geometries ..................................................... 177 5.3 Visual Results of the Simulations......................................... 179 5.4 Quantitative Results ............................................................ 186 6. Effect of Compartment Ratio on the Gravity Current............ 187 6.1 Simulation Setup.................................................................. 187
6.2 Visual Results of the Simulations......................................... 188 6.3 Quantitative Results ............................................................ 190 7. Effect of Obstacles on the Gravity Current ............................ 190 7.1 Simulations Setup ................................................................ 191 7.2 Visual Results of the Simulations......................................... 193 7.3 Quantitative Results ............................................................ 196 8. Summary of the Results.......................................................... 197 9. Conclusion .............................................................................. 197
7. Gravity Current Prior to Backdraft
1. Introduction In order to investigate the speed and the mixing that occurs in a gravity current prior to backdraft in building fires, a series of three-dimensional gravity current simulations with different opening geometries and compartment ratios have been carried out. The effect of the presence of obstacles in the compartment has also been simulated. This chapter is divided into four parts: In the first one, the accuracy of the model used for 3-D simulations is checked with saltwater experiments carried out by Fleischmann for different opening geometries and a compartment ratio of 0.5. Upon inspection, the visual observations and the non-dimensional parameters obtained from the saltwater experiments match well with the numerical simulations. The second part deals with the effect of the opening location on the gravity current’s structure (i.e. its speed and mixing). New end-opening geometries and ceiling openings are analysed. The compartment ratio in these simulations is also 0.5. The third part deals with the effect of the compartment ratio on the gravity current. A compartment ratio of 2.0 has been chosen (length-depth ratio). Next, a comparison with the previous simulations is provided. Finally, the last part deals with the effect of obstacles on the gravity current. Two types of obstacles will be analysed for a middle-slot opening. The experiments found in the literature the about gravity current do not consider obstacles on the floor of the compartment. Yet, obstacles affect the gravity current speed and mixing and, therefore, their effect must be studied.
2. State of the Art A gravity current is the flow of one fluid into another, which is caused by a difference in density between the current and the ambient fluid under the influence of gravity. This density difference may be due to a dissolved chemical or a difference in the temperature between the two fluids. There are many common examples of gravity current such as seabreeze fronts, avalanches, lock exchanges, flows following volcanic eruptions, etc. Research on gravity currents prior to backdraft has been published. Fleischmann et al., 1993 conducted a series of scaled saltwater experiments using flow visualizations. Its purpose was to investigate the gravity current speed and the extent of its mixed region. The scale compartment (0.3 m x 0.15 m x 0.15 m) was fitted with a variety of end-opening geometries (full, middle slot, door and window). One conclusion shown in his work is that the mixing layer, which rides on the gravity current in the full opening case, expands to
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7. Gravity Current Prior to Backdraft occupy nearly the entire current, unlike in partial opening cases. In addition, Fleischmann showed that the values of Froude’s number and non-dimensional head height, h*, are independent of the density difference ratio. W.G. Weng, 2002 also conducted saltwater modelling of gravity currents prior to backdraft using flow visualization and digital particle image velocity. The scale compartment (0.6 m x 0.2 m x 0.3 m) was also fitted with the same endopening geometries (full, middle slot, door and window) combined with a ceiling opening. Typically, saltwater models of gravity currents do not provide complete answers to questions about gravity currents. Some important details are lost when a saltwater model is used, e.g. the large vertical structure typically seen in shear flow problems. For this reason, 3-D numerical simulations, with ANSYS-CFX software, are used to analyse the gravity current as it enters a fire compartment. The results of the 3-D computations provide valuable insight into the detailed structure of the gravity current.
3. Simplified Methods for Gravity Current Simple methods exist for predicting the velocity and position of the gravity current in a compartment as a function of the gradient of density between the fluids (inside and outside the compartment) and the dimensions of the compartment (Gladstone, 2000). However, these methods are not very accurate in their predictions and they do not provided complete answers to questions about gravity currents (mixing, vertical structures, etc.). A simplified approach to gravity currents assuming a perfect fluid limit with no mixing or dissipation is given below. In this approach the current is treated as a steady flow of a perfect fluid in a semi-infinite horizontal compartment of arbitrary width, as shown in Figure 7-1. At time zero, far to the right, the entire end of the compartment is instantaneously removed. High density ambient fluid (state 0) flows into the box as low density fluid (states 1 and 2), and then flows out of the compartment due to buoyancy. The parameter indexing considers that buoyancy is the normalized positive density difference. This is expressed in Eq. (7-1). β=
( ρo − ρ1 ) ρ1
(7-1)
Here, ρo is the higher density fluid (cold fluid) and ρ1 is the lower density fluid (hot fluid). Benjamin, 1968 has shown that, in this perfect fluid limit with no mixing or dissipation, the conservation of mass, of momentum and of energy can be written, respectively, as follows: 156
7. Gravity Current Prior to Backdraft
v 1h 1 = v 2 h 2
(conservation of mass)
(7-2)
v21 h1 + β gh12 = 2v22 h2 + β gh22
(conservation of momentum)
(7-3)
v22 = 2β g ( h1 − h2 )
(conservation of energy)
(7-4)
After simplification, the height of the exiting compartment fluid is obtained, Eq. (7-5).
h2 =
h1 = ho 2
h1
(7-5)
ρ1
h2
ho
ρ2 ρo
Figure 7-1: Gravity current diagram. Velocities are indicated in a reference frame fixed on the gravity current. Heights are indicated by h.
Since ho=h1-h2, this result also equals the height of the gravity current. Benjamin, 1968 has shown that for flows with energy losses, the value of ho is lesser than h1/2. This result is used later for comparing which kind of opening involves more mixing. The non-dimensional velocity or Froude number of the fluid exiting the compartment, from Eq. (7-4) and Eq. (7-5) is: v2 = 2 β gh2
(7-6)
where g is the gravitational constant, 9.81 m/s. Since this value is greater than 1, a dissipative hydraulic jump is possible. The velocity of the compartment fluid approaching the gravity current, from Eq. (72), Eq. (7-5) and Eq. (7-6) is: v* =
v1 = 0.5 β gh1
(7-7)
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7. Gravity Current Prior to Backdraft v* = 0.5 represents a flow without energy losses, i.e. no mixing between fluids. Lesser values can be interpreted as a higher level of mixing between fluids. Therefore, this parameter will be used to compare the mixing that occurs in a gravity current scenario with different opening geometries, compartment ratios or the presence of obstacles. Furthermore, knowing v* for each type of opening and compartment ratio provides us the average speed of the gravity current and its approximate position in time in the compartment.
4. Checking the Experiments
Setup
of
the
Simulation
with
Saltwater
The accuracy of the simulations as well as the boundary conditions are checked against the saltwater experiments carried out by Fleischmann, 1993. Four openings are compared: full opening, middle-slot opening, centred window and centred door.
4.1 Saltwater Experiment Configuration 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 kg/m3 to 1.101 kg/m3. The solution temperature was 18ยบC. 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 x 0.15 m), a horizontal slot (0.15 m wide x 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 x 0.05 m wide) centred horizontally with the bottom of the opening at floor level. Figure 7-2 and Figure 7-3 show the saltwater configuration and the opening geometries, respectively. These openings were covered with a vertical sliding partition that was removed at the start of the experiment.
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60 cm
45 cm 15 cm
30 cm
15 cm
30 cm
Figure 7-2: Saltwater configuration. 15 cm
5 cm 15 cm
Middle-slot
Full
5 cm 5 cm
12 cm
5 cm
Centred Window
Centred Door
Figure 7-3: Opening geometries and dimensions used in saltwater experiments.
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7. Gravity Current Prior to Backdraft
4.2 Simulation Setup 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 (18ยบC) 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 of Figure 7-2. 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. From now on in this section, the air initially inside the compartment is termed as inner fluid and the air initially outside the compartment is termed as outer fluid. Therefore, the density of the inner and the outer fluid is 1.205 kg/m3 and 0.833 kg/m3, respectively. These values are obtained by giving an initial temperature of 423K and 293K 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 (Fleischmann, 1993). 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 7-1.
Part of scenario Floor
Boundary type
Characteristics
Wall
Air
Opening
Container
Wall
Wall influence on floor: No slip Wall roughness: Smooth wall Heat transfer: Adiabatic Initial temperature: 293K. Floor direction: Normal to boundary conditions Wall influence on floor: No slip Wall roughness: Smooth wall Heat transfer: Adiabatic
Table 7-1: Characteristics of the floor, container and air for the simulations.
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7. Gravity Current Prior to Backdraft 20 s were simulated with a time step of 0.02 s. The total number of elements (tetrahedrons) for each simulation is around 400000. Figure 7-4 shows a meshed plane for the door opening scenario. The computer used for the simulation is a Pentium(R) 4 CPU 2.40 GHz, 512 Mb RAM.
Figure 7-4: Representation of the mesh in a central plane for the centred door simulation.
4.3 Visual Result of the Simulations The mass fraction of the inner fluid, the temperature and the velocity fields obtained as a function of the opening geometry are represented from Figure 7-5 to Figure 7-8. For each opening geometry, three positions of the gravity current are represented: when it is L/4, 3L/4 and 3H/4 into the compartment. From Figure 7-5 to Figure 7-8, the mass fraction field of the inner fluid is represented. Red represents 100% of mass fraction of the inner fluid and blue is 100% of mass fraction of the outer fluid. Other colours represent different values for the mixture. From Figure 7-9 to Figure 7-12, the temperature fields are shown. Red indicates a temperature of 423K and the blue one represents a temperature of 293K. From Figure 7-13 to Figure 7-16, the velocity field of the gravity current is represented. Its values range from 0.0 to 1.0 m/s. Note that the middle-slot opening and the fully open wall present 2-D effects that cause less mixing and transient flow than the other openings (i.e. window and door).
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7. Gravity Current Prior to Backdraft
Full opening
Mass fraction results for the opening geometries simulated
Geometric arrangement of the simulation for the fully open wall.
Mass fraction profile for the full opening case. Picture taken at 0.21 s. Position of the gravity current: L/4.
Mass fraction profile for the full opening case. Picture taken at 0.69 s. Position of the gravity current: 3L/4.
Mass fraction profile for the full opening case. Picture taken at 1.2 s. Position of the gravity current: 3H/4.
Figure 7-5: Full opening geometry. Mass fraction at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Middle slot
Mass fraction results for the opening geometries simulated
Geometric arrangement of the simulation for the middle-slot opening.
Mass fraction profile for the middleslot opening case. Picture taken at 0.5 s. Position of the gravity current: L/4.
Mass fraction profile for the middle slot opening case. Picture taken at 1.1 s. Position of the gravity current: 3L/4.
Mass fraction profile for the middleslot opening case. Picture taken at 1.8 s. Position of the gravity current: 3H/4.
Figure 7-6: Middle-slot opening geometry. Mass fraction at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Centred window
Mass fraction results for the opening geometries simulated
Geometric arrangement of the simulation for the centred window opening.
Mass fraction profile for the centred window opening case. Picture taken at 0.5 s. Position of the gravity current: L/4.
Mass fraction profile for the centred window opening case. Picture taken at 1.6 s. Position of the gravity current: 3L/4.
Mass fraction profile for the centred window opening case. Picture taken at 3.0 s. Position of the gravity current: 3H/4.
Figure 7-7: Centred
window opening geometry. Mass fraction at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Centred door
Mass fraction results for the opening geometries simulated
Geometric arrangement of the simulation for the centred door opening.
Mass fraction profile for the centred door opening case. Picture taken at 0.2 s. Position of the gravity current: L/4.
Mass fraction profile for the centred door opening case. Picture taken at 0.9 s. Position of the gravity current: 3L/4.
Mass fraction profile for the centred door opening case. Picture taken at 1.6 s. Position of the gravity current: 3H/4.
Figure 7-8:
Centred door opening geometry. Mass fraction at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Full opening
Temperature results for the opening geometries simulated
Geometric arrangement of the simulation for the fully open wall.
Temperature profile for the full opening case. Picture taken at 0.21 s. Position of the gravity current: L/4.
Temperature profile for the full opening case. Picture taken at 0.69 s. Position of the gravity current: 3L/4.
Temperature profile for the full opening case. Picture taken at 1.2 s. Position of the gravity current: 3H/4.
Figure 7-9:
Full opening geometry. Temperature field at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Middle slot
Temperature results for the opening geometries simulated
Geometric arrangement of the simulation for the middle-slot opening
Temperature profile for the middleslot opening case. Picture taken at 0.5 s. Position of the gravity current: L/4.
Temperature profile for the middleslot opening case. Picture taken at 1.1 s. Position of the gravity current: 3L/4.
Temperature profile for the middleslot opening case. Picture taken at 1.8 s. Position of the gravity current: 3H/4.
Figure 7-10: Middle-slot opening geometry. Temperature field at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Centred window
Temperature results for the opening geometries simulated
Geometric arrangement of the simulation for the centred window opening.
Temperature profile for the centred window opening case. Picture taken at 0.5 s. Position of the gravity current L/4.
Temperature profile for the centred window opening case. Picture taken at 1.6 s. Position of the gravity current: 3L/4.
Temperature profile for the centred window opening case. Picture taken at 3.0 s. Position of the gravity current: 3H/4.
Figure 7-11: Centred window opening geometry. Temperature field at different positions of the gravity current.
168
7. Gravity Current Prior to Backdraft
Centred door
Temperature results for the opening geometries simulated
Geometric arrangement of the simulation for the centred door opening.
Temperature profile for the centred door opening case. Picture taken at 0.2 s. Position of the gravity current: L/4.
Temperature profile for the centred door opening case. Picture taken at 0.9 s. Position of the gravity current: 3L/4.
Temperature profile for the centred door opening case. Picture taken at 1.6 s. Position of the gravity current: 3H/4.
Figure 7-12: Centred door opening geometry. Temperature field at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Full opening
Velocity results for the opening geometries simulated
Geometric arrangement of the simulation for the full open wall.
Velocity profile for the full opening case. Picture taken at 0.21 s. Position of the gravity current: L/4.
Velocity profile for the full opening case. Picture taken at 0.69 s. Position of the gravity current: L/4.
Velocity profile for the full opening case. Picture taken at 1.2 s. Position of the gravity current: L/4.
Figure 7-13 Full opening geometry. Velocity field at different position of the gravity current.
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7. Gravity Current Prior to Backdraft
Middle slot
Velocity results for the opening geometries simulated
Geometric arrangement of the simulation for the middle-slot opening.
Velocity profile for the middle-slot opening case. Picture taken at 0.5 s. Position of the gravity current: L/4.
Velocity profile for the middle-slot opening case. Picture taken at 1.1 s. Position of the gravity current: L/4.
Velocity profile for the middle-slot opening case. Picture taken at 1.8 s. Position of the gravity current: L/4.
Figure 14: Middle slot opening geometry. Velocity field at different position of the gravity current.
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7. Gravity Current Prior to Backdraft
Centred window
Velocity results for the opening geometries simulated
Geometric arrangement of the simulation for the centred window opening.
Velocity profile for the centred window opening case. Picture taken at 0.5 s. Position of the gravity current: L/4.
Velocity profile for the centred window opening case. Picture taken at 1.6 s. Position of the gravity current: 3L/4.
Velocity profile for the centred window opening case. Picture taken at 3.0 s. Position of the gravity current: 3H/4.
Figure 7-15: Centred window opening geometry. Velocity field at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft
Centred door
Velocity results for the opening geometries simulated
Geometric arrangement of the simulation for the centred door opening.
Velocity profile for the centred window opening case. Picture taken at 0.2 s. Position of the gravity current: L/4.
Velocity profile for the centred window opening case. Picture taken at 0.9 s. Position of the gravity current: 3L/4.
Velocity profile for the centred window opening case. Picture taken at 1.6 s. Position of the gravity current: 3H/4.
Figure 7-16: Centred door opening geometry. Velocity field at different positions of the gravity current.
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7. Gravity Current Prior to Backdraft In these figures the following phenomena can be observed: • •
• • •
The heavier (outer) fluid entering the compartment and pushing out the lighter (inner) fluid. The head of the gravity current riding over some of the low-density fluid. The overrun fluid causes a gravitational instability that is largely responsible for the three-dimensional effects that are seen in natural gravity currents. The instability is manifested as the lobes and clefts that make up the leading edge of the current and the billows which are formed above and behind the head of the current. The vortex roll at the head of the gravity current. The upward and backward velocity of the outer fluid as the head intrudes. The different gravity current structures for each opening geometry. For example, for the full opening, the gravity current can be divided into two regions: region 1 is purely outer fluid and region 2 is the mixed layer along the shear interface. For the h1/3 centred slot opening geometry (for example), the structure of the gravity current cannot be divided up into two regions. Large scale mixing is occurring, caused by the h1/3 centred slot opening acting as a reward-facing step that is a well-known source of large vertical structures.
4.4 Qualitative Comparison of the Results Figure 7-17 (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. These photographs closely resemble the numerical simulation results shown in Figure 7-17 (b). Red represents 100% of the mass fraction of inner fluid and blue is 100% of the mass fraction of outer fluid. Other colours represent a mixture of these two.
Photograph of the gravity current approximately 3L/4 into the compartment for the fully open condition
Mass fraction profile for the full opening case of the gravity current approximately 3L/4 into the compartment
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7. Gravity Current Prior to Backdraft
Photograph of the gravity current approximately 3L/4 into the compartment for the middle-slot opening condition
Mass fraction profile for the middleslot opening case of the gravity current approximately 3L/4 into the compartment
Photograph of the gravity current Mass fraction profile for the centred approximately 3L/4 into the window opening case of the gravity compartment for the centred window current approximately 3L/4 into the condition compartment (a) (b) Figure 7-17: Visual comparison between (a) saltwater experiments and (b) CFX simulations.
4.5 Quantitative Comparison of the Results To compare the numerical simulations quantitatively with the experiments, the non-dimensional velocity or Froude number is used (Eq. (7-8)). This is defined in terms of the gravity current velocity, Eq. (7-9), that is a function of the transit time, ttrans . v* = v gc
v gc
β gh L = ttrans
(7-8) (7-9)
The transit time is the time required for the leading edge of the gravity current to reach the wall opposite the opening. In these numerical simulations the
175
7. Gravity Current Prior to Backdraft transit time was determined when the mass fraction at the rear wall changed by 10%. For the saltwater experiments, the transit time was taken from a video recording of the gravity current. L is the distance between the opening wall and the end wall, and h is the height of the compartment. 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 Eq. (7-10), where tout is the time from opening to the time the reversed current returns to the opening wall. v gc =
2路L + 2h1 / 3 tout
(7-10)
The 2h1 / 3 factor is used to account for the length the current must travel up the wall opposite the opening (Fleischmann, 1993). Table 7-2 shows ttrans , tout and the buoyancy parameter 尾 obtained from simulations. Table 7-3 compares the Froude numbers (entering and exiting) from saltwater experiments with simulations.
Transit time Full opening Slot opening Centred door Centred window
Entering current s 0.99 1.35 1.20 2.00
Exiting current s 2.3 3.2 2.9 5.1
Bouyancy (--) 0.3072
Table 7-2: ttrans of the entering current and tout of the existing current obtained by CFX simulation for different opening geometries
Froude number Full opening Slot opening Centred door Centred window
Entering current Saltwater CFX Exp. Simulations 0.44 0.45 0.32 0.33 0.35 0.37 0.22 0.22
Exiting current Saltwater CFX Exp. Simulations --0.45 0.32 0.32 0.35 0.36 0.22 0.20
Table 7-3: Froude number from saltwater experiments and CFX simulation for different opening geometries Table 7-4 represents ho obtained from simulation and the average value of h* obtained by simulations and experiments. ho is height of the gravity current
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7. Gravity Current Prior to Backdraft measured over the distance 3L/4 to L. This interval is chosen to reduce any effects caused by the openings. h* is defined as ho/h1.
Full opening Slot opening Door opening Window opening
ho(simulated) [cm] 7.5 5.8 4.8 4.1
h* (simulated) [--] 0.50 0.38 0.32 0.27
h* (Exp.) [--] 0.50 0.38 0.33 0.29
Table 7-4: Comparison of ho 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.
5. Effect of Opening Location on the Gravity Current 5.1 Simulation Setup The compartment dimensions and the setup are identical to those of the Section 4.2: “Simulation Setup�.
5.2 New Opening Geometries The effect of opening location on the gravity current is analysed for five new end-opening geometries (upper slot opening, lower slot opening, side door, lower side window and side-centred window) and two ceiling openings. Figure 7-18 shows a sketch of these new opening geometries in which the grey area indicates the opening.
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7. Gravity Current Prior to Backdraft
5 cm
5 cm
5 cm
Lower slot
Upper slot
Rear ceiling opening
5 cm
12 cm
Side door
lower side window 5 cm
5 cm
22.5 cm
Centred side window
3L/4 Ceiling opening
Figure 7-18: New end-wall and ceiling opening geometries simulated.
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7. Gravity Current Prior to Backdraft
5.3 Visual Results of the Simulations Ceiling openings The mass fraction field of the rear ceiling opening and 3L/4 ceiling opening is represented in Figure 7-19 at t = 1, 1.5, 2.0, 3.0 and 6.0 s. The influence of the rear wall on the structure of the incoming fluid is observed. Whereas, in the case of the 3L/4 ceiling opening, the gravity current is almost symmetric, in the case of rear ceiling opening the gravity current seems to resemble to an end-wall opening case (Figure 7-19 at t=1.5 s). The gravity current propagates in only one direction, from the right to the left. Figure 7-19 also shows a greater level of mixing in the 3L/4 ceiling opening than in the rear ceiling opening.
Centred side window The mass fraction field of the inner fluid for the simulation of the centred side window is represented in Figure 7-20 by an isometric view cut by two planes (one horizontal and the other vertical). The propagation of the gravity current is observed in the horizontal plane. Initially, it tends to propagate circularly; yet due to the interaction with the walls, this circular propagation is altered, acquiring an elliptical form.
Lower side window The mass fraction field of the inner fluid for the simulation of the lower side window is represented in Figure 7-21 also by an isometric view cut by two planes (again, one horizontal and the other vertical). A different propagation than in the previous case is observed. This difference comes from the hydraulic jump created due to the height of the opening. A difference in the height of the head of the gravity current is also seen: it is smaller in the case of the lower side window.
Upper and lower slot opening Figure 7-22 (a) and Figure 7-22 (b) represent the mass fraction field for the case of the upper and lower slot openings, respectively. A hydraulic jump and a difference in the height of the head of the gravity current are also observed.
Side door The mass fraction field is represented in Figure 7-23 also by an isometric view cut by two planes (one horizontal plane and the other vertical plane).
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7. Gravity Current Prior to Backdraft In all these figures, red represents 100% of the mass fraction of the inner fluid and blue is 100% of the mass fraction of the outer fluid. Other colours represent a different ratio of mixing between them.
Ceiling openings
Mass fraction results for the ceiling opening geometries
Geometric arrangement of the simulation for the 3L/4 ceiling opening.
Geometric arrangement of the simulation for the end ceiling opening.
Mass fraction profile for the 3L/4 ceiling opening case at time = 1.0 s
Mass fraction profile for the end ceiling opening case at time = 1.0 s
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7. Gravity Current Prior to Backdraft
Mass fraction profile for the 3L/4 ceiling opening case at time = 1.5 s
Mass fraction profile for the end ceiling opening case at time = 1.5 s
Mass fraction profile for the 3L/4 ceiling opening case at time = 3.0 s
Mass fraction profile for the end ceiling opening case at time = 3.0 s
Mass fraction profile for the 3L/4 ceiling opening case at time = 6.0 s
Mass fraction profile for the end ceiling opening case at time = 6.0 s
Figure 7-19: Mass fraction fields for the ceiling opening geometries at different times.
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7. Gravity Current Prior to Backdraft
Side window
Mass fraction results for the window opening geometries
Geometric arrangement of the simulation for the side window opening.
Mass fraction isometric for the side window opening case of a gravity current 3L/4 into the compartment.
Mass fraction profile for the side window opening case of a gravity current 3L/4 into the compartment.
Mass fraction plan view for the side window opening case of the gravity current 3L/4 into the compartment.
Figure 7-20: Mass fraction fields for the side window opening geometries at different times.
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7. Gravity Current Prior to Backdraft
Lower side window
Mass fraction results for the window opening geometries
Geometric arrangement of the simulation for the lower side window opening.
Mass fraction isometric for the lower side window opening case of a gravity current 3L/4 into the compartment
Mass fraction profile for the lower side window opening case of a gravity current 3L/4 into the compartment.
Mass fraction plan view for the lower side window opening case of a gravity current 3L/4 into the compartment.
Figure 7-21: Mass fraction fields for the lower side window opening geometries at different times.
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7. Gravity Current Prior to Backdraft
Mass fraction results for the slot opening geometries
Geometric arrangement of the simulation for the upper slot opening.
Geometric arrangement of the simulation for the lower slot opening.
Mass fraction profile for the upper slot opening case of the gravity current 3L/4 into the compartment.
Mass fraction profile for the lower slot opening case of the gravity current 3L/4 into the compartment.
Mass fraction plan view for the upper slot window opening case of the gravity current 3L/4.
Mass fraction profile for the lower slot opening case of the gravity current 3L4 into the compartment.
Figure 7-22: Mass fraction fields for the side window opening geometries at different positions. 184
7. Gravity Current Prior to Backdraft
Mass fraction results for the side door opening geometry
Geometric arrangement of the simulation for the side door opening.
Mass fraction isometric for the side door opening case of a gravity current 3L/4 into the compartment
Mass fraction profile for the side door opening case of a gravity current 3L/4 into the compartment.
Mass fraction plan view for the side door opening case of a gravity current 3L/4 into the compartment.
Figure 7-23: Mass fraction fields for the side door opening geometry at different positions.
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7. Gravity Current Prior to Backdraft
5.4 Quantitative Results Three transit times have been considered: ttrans 1, ttrans 2 and ttrans 3. These are the times required for the leading edge of the gravity current to reach the points p1, p2 and p3, respectively. p1 is found in the plane that crosses the opening symmetrically. p2 is found in the plane that crosses the compartment symmetrically and p3 is found the lateral wall (see Figure 7-24).
ttrans _2
ttrans _1 p1
p2
Compartment
d
d
Gravity current
ttrans _ 3 p3 x
L’
x
Opening
Figure 7-24: Schematic plan view of a compartment. Representation of each transit time and its planes.
Results for the end-wall openings are summarized in Table 7-5. Column 1 indicates the type of opening. Columns 2-4 show the value of the transit time at different planes. Column 5 is the Froude number obtained from ttrans 1. Column 6 is the distance from the opening wall to p3. Column 7 and 8 are the height of the gravity current measured over the distance 3L/4 to L and the average height of the gravity current defined as ho/h1.
Fr L’ ho h* entering cm cm Side-centred window 0.24 4.37 3.63 0.24 Lower side window 0.26 9.70 2.72 0.18 Upper-slot opening 0.27 -- 5.35 0.35 Lower-slot opening 0.31 -3.92 0.26 Side door 0.40 6.52 4.41 0.29 * Upper and lower-slot openings act as a 2-D opening, therefore ttrans 3 and L’ are not ttrans 1 s 1.85 1.70 1.60 1.45 1.10
ttrans 2 s 1.95 1.75 1.60 1.45 1.20
ttrans 3 s 1.2 1.1 --0.6
evaluated.
Table 7-5: ttrans1, ttrans2 and ttrans3; Froude number of the entering current
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7. Gravity Current Prior to Backdraft
6. Effect of Compartment Ratio on the Gravity Current In this third set of simulations, the effect of the compartment ratio on the gravity current is analysed. The compartment ratio is defined as the length of the compartment over width. In the previous section, the compartment ratio is given as 0.5. A ratio of 2.0 is now analysed for only two opening geometries: centred door and centred window. The results are compared together in Section 6.3: “Quantitative Results�.
6.1 Simulation Setup The dimensions of the compartment used for simulating the effect of opening location on the gravity current are 0.6 m x 0.3 m x 0.15 m (length x width x depth), Figure 7-25. It is positioned on the far left of the saltwater container, which is 0.8 m long, 0.55 m deep and 0.35 m wide. The enclosure is also lifted 5 cm from the bottom of the container. 55 cm
35 cm 60 cm
15 cm
30 cm
80 cm
Figure 7-25: Saltwater configuration. Dimensions and position of the analysed openings are indicated in Figure 7-26. 30 cm
30 cm
15 cm 5 cm
5 cm
12 cm
Figure 7-26: Dimensions and position of the centred door and window.
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7. Gravity Current Prior to Backdraft The setup of the simulations is identical to that of Section 4.2: “Simulation Setup�.
6.2 Visual Results of the Simulations Figure 7-27 to Figure 7-28 show the mass fraction fields for the inner fluid for the centred door scenario and for the centred window, respectively. Both scenarios are represented by an isometric, profile and plan view. The different heights of the gravity current (higher for the door opening) and different propagations along the compartment (spherical for door-opening; elliptical for window-opening) can be compared visually.
Mass fraction results for the door opening geometry
Geometric arrangement of the simulation for the centred door opening.
Mass fraction isometric for the centred door opening case of a gravity current 3L/4 into the compartment.
Mass fraction profile for centred door opening case of a gravity current 3L/4 into the compartment.
Mass fraction plan view for the centred door opening case of a gravity current 3L/4 into the compartment.
Figure 7-27: Mass fraction fields for the centred door. Compartment ratio: 2.
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7. Gravity Current Prior to Backdraft
Mass fraction results for the window opening geometry
Geometric arrangement of the simulation for the centred window opening.
Mass fraction isometric for the centred window opening case of the gravity current 3L/4 into the compartment.
Mass fraction profile for centred window opening case of the gravity current 3L/4 into the compartment.
Mass fraction plan view for the centred window opening case of the gravity current 3L/4 into the compartment.
Figure 7-28: Mass fraction fields for the centred window. Compartment ratio: 2.
A more significant height for the head of the gravity current occurs in the case of the 0.5 compartment ratio. The reason for this is undoubtedly because in this compartment the wall prevents lateral propagation of the entering fluid, channelling it towards the wall opposite the opening.
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7. Gravity Current Prior to Backdraft
6.3 Quantitative Results Two transit times have been considered: ttrans 1 and ttrans 3. These are the times required for the leading edge of the gravity current to reach the points p1 and p3, respectively. p1 is found in the plane that crosses the opening symmetrically. p3 is found the lateral wall (Figure 7-24). The results are summarized in Table 7-6. Column 1 indicates the type of opening. Columns 2-3 show the value of the transit time at different planes. Column 4 is the Froude number obtained from ttrans 1. Column 5 is the distance from the opening wall to p3. Column 6 and 7 are the height of the gravity current measured over the distance 3L/4 to L and the average height of the gravity current defined as ho/h1.
Compartment ratio 2 Centred door Centred window
ttrans 1 s 1.30 2.5
ttrans 3 s 2.3 3.51
Fr entering 0.34 0.17
L’ cm 15 9.27
ho cm 3.6 2.3
h* 0.24 0.16
Table 7-6: ttrans1 and ttrans3; Froude number of the entering current for a compartment ratio of 2; average value of the height of the gravity current
Compartment ratio 0.5 Centred door Centred window
ttrans 1 s 1.2 2.0
ttrans 3 s -----
Fr entering 0.37 0.22
L’ cm -----
ho cm 4.8 4.1
h* 0.32 0.27
Table 7-7: Froude number of the entering current for a compartment ratio of 0.5; average value of the height of the gravity current Based on the results of Table 7-6 and Table 7-7, increasing the compartment ratio of a compartment reduces the Froude number; therefore, the velocity of the gravity current as well as the average value of the height of the gravity current are also reduced.
7. Effect of Obstacles on the Gravity Current The effect of obstacles on the gravity current prior to backdraft is analysed. Two types of obstacles are chosen for this purpose: Zig-Zag and Up-Down obstacles. Figure 7-29 represents these two scenarios. One more scenario without obstacles is simulated for direct comparison.
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7. Gravity Current Prior to Backdraft
Up-Down scenario
Zig-Zag scenario
Figure 7-29: (a) Up-Down gravity current scenario; (b) Zig-Zag gravity current scenario.
7.1 Simulations Setup Before continuing with the section, it is important to clarify that these scenarios are still under research. The ignition time of the mixture will be calculated for each of them (Up-Down, Zig-Zag and non obstacles scenarios) in the following months and will be compared with Gojkovic’s experiments (Gojkovic, 2001). This justifies the presence of an ignition wire and a well-defined mass concentration of gases inside the compartment in these simulations. The dimensions of the compartment are 5.5 m x 2.2 m and 2.2 m. The enclosure is raised 20 cm from the bottom of the container. The dimensions of the obstacles are summarized in Figure 7-30. 0.3 m
(a) 0.4 m
0.2 m 0.4 m
0.4 m
1.1 m
0.55 m
0.5 m
1.1 m 0.2 m
Wide = 2.2 m
(b)
1.5 m
0.3 m
0.4 m
0.8 m
0.6 m
0.6 m
Wide = 1.55 m Figure 7-30: dimensions and distribution of the obstacles (a) Up-Down, (b) Zig-Zag. 191
7. Gravity Current Prior to Backdraft CH4, CO, CO2, H2O, N2 and O2 are considered gas species accumulated in the compartment. The mass concentration just before the opening time is summarized in Table 7-8. The value of the buoyancy for each simulation is also given in Table 7-9. The characteristics of the scenario without obstacles are identical to the setup of the Up-Down scenario.
Zig-Zag Up-Down
CH4 [%] 0.5 0.14
CO2 [%] 0.25 0.03
H2O [%] 0.25 0.03
N2 [%] 0.0 0.65
O2 [%] 0.0 0.15
Table 7-8: Mass fraction of gas species for Zig-Zag and Up-Down scenario.
Zig-Zag Up-Down
Tin [K] 310 378
Tout [K] 278 278
ρin [kg/m3] 1.265 1.265
ρout [kg/m3] 1.012 0.830
β [--] 0.2 0.34
Table 7-9: Initial parameter for Zig-Zag and Up-Down scenario. 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. 30 s were simulated with a time step of 0.02 s. The total number of elements (tetrahedrons) is around 500000 for each simulation. The computer used for the simulation is a Pentium(R) 4 CPU 2.40 GHz, 512 Mb RAM. To simulate the scenario the Detached Eddy Simulation (DES) turbulent model has been used. An initial k and epsilon equal to 0.0001 m2/s2 and 0.0001 m2/s3, respectively. The boundary conditions for the container, obstacles, ignition wire, floor and air are summarized in Table 7-1.
Part of scenario Floor
Boundary type
Characteristics
Wall
Air
Opening
Container
Wall
Wall influence of floor: No slip. Wall roughness: Smooth wall. Constant temperature of 278K. Initial temperature: 278K. Floor direction: Normal to boundary conditions Wall influence of floor: No slip Wall roughness: Smooth wall Initial temperature of Tin.
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7. Gravity Current Prior to Backdraft Obstacles
Wall
Ignition wire
Wall influence of floor: No slip Wall roughness: Smooth wall Initial temperature of Tin. Region where the ignition of the gas is checked.
Table 7-10: Characteristics of the floor, container and air in the simulations
7.2 Visual Results of the Simulations Figure 7-31 (a) represents the gravity current of the scenario without obstacles (Column a) and Figure 7-31 (b) represents the gravity current of the Zig-Zag scenario at different times. A direct comparison of these scenarios is possible.
(a)
Time = 1 s
(b)
(a)
Time = 3 s
(b)
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7. Gravity Current Prior to Backdraft
(a)
Time = 7 s
(b)
(a)
Time = 10 s
(b)
(a)
Time = 13 s
(b)
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7. Gravity Current Prior to Backdraft
(a)
Time = 30 s
(b)
Figure 7-31: Mass fraction of methane at different times: No-obstacles scenario vs. Up-Down scenario.
Higher velocity is observed when obstacles are not present. Obstacles create more local mixing and turbulence but not necessarily a well-mixed situation throughout the compartment. Figure 7-32 represents the Up-Down scenario. Column a represents the gravity current evolution given in a frontal view and Column b represents a plan view. This scenario present 3-D effects since the obstacles are not symmetrically distributed in the compartment.
(a)
Time = 1 s
(b)
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7. Gravity Current Prior to Backdraft
(a)
Time = 3 s
(b)
(a)
Time = 7 s
(b)
Figure 7-32: Temperature field of the Zig-Zag scenario at 1, 3 and 7 s.
7.3 Quantitative Results The results are summarized in Table 7-5. Column 1 indicates the type of scenario, Columns 2 shows the transit time ttrans 1, and Column 3 is the Froude number. The average height of the gravity current has not been evaluated when obstacles are present in the compartment.
Zig-Zag scenenario Up-Down scenario
ttrans 1 s 14.4 10
Fr entering 0.18 0.20
β 0.2 0.34
Table 7-11: ttrans 1, Froude number and non-dimensional parameters. The comparison shows a great decrease in the Froude number (see Section 8: “Summary of the Results”). This indicates a higher level of mixing and a lower velocity of the gravity current.
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7. Gravity Current Prior to Backdraft
8. Summary of the Results The results obtained regarding the Froude number are shown in the following Table. FROUDE NUMBER Opening geometry Full opening Upper slot Middle slot Lower slot Centred door Side centred door Centred window Side centred window Lower side window
Compartment ratio (length-depth ratio) 0.5 2.0 Without Zig-Zag Up-down Without obstacles obstacles obstacles obstacles 0.45 0.27 0.33 0.31 0.37 0.40 0.22 0.24 0.26
--0.18 -------
--0.20 -------
----0.34 -0.17 ---
Table 7-12: Summary of the simulations carried out.
This table shows the variation of the Froude number as a function of the type of opening, the presence of obstacles and the compartment ratio.
9. Conclusion 12 different gravity current scenarios have been simulated with ANSYS-CFX software. The effect of the compartment ratio and the presence of obstacles in the compartment have been analysed for different opening geometries. The Froude number or non-dimensional parameter has been computed for each gravity current scenario. The Froude number can be used as an indicator of the degree of mixing occurring in the gravity current. The results show that the mixing increases for small openings and with the presence of obstacles in the compartment. For example, taking the case of a compartment provided with a middle-slot opening and Up-Down obstacles, the Froude number is reduced by a factor of 1.65. Obstacles create more turbulence and mixing between the inner fluid and the outer fluid but they do not necessarily create a well-mixed situation in the compartment. The Froude number is also used to obtain the average velocity of the gravity current and, therefore, the position inside the compartment. Knowing the position of the gravity current can inform us of the level of mixing in the compartment (more mixing means more severe backdrafts). These data can play
197
7. Gravity Current Prior to Backdraft an important role in fire fighter security. A practical application of this concept is found in Chapter 12: “Application: Fire in a Building�. In conclusion, for the purposes of creating a simple numerical model for backdraft, if the inner fluid is flammable or is found to be above the upper flammable limit, when creating an opening there will be always a flammable region along the interface between the two streams (i.e. the inner and outer fluid). Because of this, ignition could happen at any moment from the time of opening since the ignition source can be placed anywhere in the building.
198