Water Mist Extinguishment of Horizontal Exhaust Duct Fires

Abstract

The efficacy and requirement were investigated for water mist to extinguish fires in circular, horizontally-oriented ducts, in which the air flow was provided by a blower at the duct inlet at velocities ranging from 0.84 m/s to 3.89 m/s under no fire conditions. Water mist was made discharging in the air flow direction. The fire hazard was simulated with propane release into insulated stainless steel ducts of 0.30 and 0.61 m in diameter. The insulation corresponded to the thermal resistance of combustible ducts commonly used for exhaust applications in industrial settings. The investigation was carried out by first estimating the water mist requirement for fire extinguishment, then by a series of evaluation fire tests. For each duct diameter, water mist was discharged inside the duct with a nominal spacing of 3.1 m along the duct length. The 0.30-m duct tests were mainly conducted with a water mist discharge rate of 44 l/min at each duct location, with a volume-median droplet diameter of about 77 μm. Limited testing was also performed with a higher discharge rate of 64 l/min at each location, with a median droplet size of about 88 μm. The tests showed that the fire could be successfully extinguished, and the extinguishment was independent of fire size when the water mist concentration exceeded 300 g/m³ in the air flow. Based on the result, the 0.61-m duct tests were conducted with a water mist discharge rate of 142 l/min at each location. The tests showed that the fire could be extinguished similarly as observed in the 0.30-m duct tests. Based on the duct-wall temperature measurement, the cooling of the tested protection was deemed adequate to maintain the structure integrity of exhaust ducts made of steel, fiber-reinforced-plastic and fiberglass during the process of fire extinguishment.

Appendix: Assessment of Fire Extinguishment Propensity in the 0.30-m Duct

At 41.2 bar, each X1 nozzle discharged 11.0 l/min with a volume median droplet diameter of 77 μm. The total discharge rate from four nozzles at each water mist application location was therefore 44.0 l/min. To evaluate the actual amount of airborne water mist for fire extinguishment, the loss of water discharged from each water mist application location to the duct wall needed to be determined.

1.1 Water Loss to the 0.30-m Duct Wall

The amount of water loss to the duct wall from the upstream nozzle discharge was measured as shown in Fig. 19. The figure shows that the measurement was conducted with a 1.52-m long duct connected to the upstream nozzle location. A similar measurement was made by replacing the 1.52-m long duct with a 3.05-m long duct. The measurement was performed with the designated air flow rate inside the duct by collecting the runoff water at the duct opening during steady nozzle discharge at 41.2 bar, and weighing the collected water with a load cell. The measurement indicated that the loss was 31.8 l/min to the 1.52-m long duct, and 36.0 l/min to the 3.05-m long duct. As a result, the airborne water mist provided from the upstream nozzle discharge was 12.5 l/min at 1.52 m downstream, and 8.0 l/min at 3.05 m downstream. It was assumed that the downstream nozzle discharge provided the same amounts of airborne water mist at the comparable downstream locations.

The above measurements indicated that the amounts of airborne water mist at 1.52 m and 3.05 m downstream from each discharge location were less than the highest amount of 28.8 l/min estimated for the 0.3-m duct for fire extinguishment, as presented in Table 2. However, as pointed out in Sect. 3, the estimate was conservative since the enhanced effect of air vitiation and flow turbulence on fire extinguishment was not considered in the estimate. Also, the water mist discharge at the downstream location should stop the fire spread further downstream due to the high water mist concentration realized at the discharge location. Nevertheless, the question remained whether the fire between the upstream and downstream nozzle locations could be extinguished by the amount of airborne water mist provided from the upstream nozzle discharge alone.

Figure 19

Measurement of water loss to the 0.3-m duct wall from the upstream nozzle discharge. As shown, a 1.52-m long duct was connected to the upstream nozzle location

1.2 Assessment of Fire Extinguishment Propensity

To extinguish a gas fire when air vitiation is insignificant, the water mist concentration needs to be sufficiently high to conduce a global flame extinction in the fire. The concentration should be such that the distance between water mist droplets is comparable to the flame quenching distance, and the water mist cooling per unit volume is sufficient to lower the flame temperature to the extinction temperature for the prevailing flow condition. Under the above condition, fire extinguishment is expected to take place promptly, and independent of the fire size.

It is well known that the flame extinction temperature increases with the strain rate exerting on the flame, and the strain rate increases with the flow turbulence. So, to account for the turbulence effect, the flow condition resulted from the nozzle discharge needs to be evaluated, as well as the water mist concentration in the duct flow. The duct flow induced by the nozzle discharge is governed by the momentum transfer from the discharged water mist to the gas medium, the duct diameter, and the flow resistance of the ductwork.

1.2.1 Spray Thrust Force

Each X1 nozzle had an orifice diameter of 1.61 mm to give a discharge velocity of 77.8 m/s for a discharge rate of 11.0 l/min. Assuming that the spray is uniform and inviscid, the spray thrust force in the nozzle direction can then be estimated with the following expression [15]:

$$\dot{M} = \frac{1}{2}\rho_{w} \dot{V}_{w} U_{d} \left( {\frac{{sin^{2} \theta }}{1 - cos\theta }} \right) ,$$

(7)

where $\rho_{w}$, $\dot{V}_{w}$, $U_{d}$ and $\theta$ are the water density, volumetric discharge rate, angular droplet velocity and spray half angle, respectively.

With $\theta = 45^\circ$, $\dot{V}_{w} = 11.0{\text{ l}}/{\text{min}},{ }$ and $U_{d} = 77.8 {\text{m}}/{\text{s}}$, Eq. (7) yields a thrust force of 12.2 N for the X1 nozzle operating at 41.2 bar. The above thrust force value was examined by conducting the thrust force measurement shown in Fig. 20. In the measurement, the entire downward spray was made to impinge on a horizontal plate of 0.34 m in diameter centered 0.25 m below the nozzle. The thrust force thus measured was 12.5 N, comparable to the above estimate. The measured thrust force was used for the following analysis.

Figure 20

The setup for the spray thrust force measurement

1.2.2 Spray Momentum Transfer

The spray momentum which can be transferred to the air is determined by the droplet size and the droplet’s airborne time before the spray is intercepted by the duct wall. The following analysis assumes that the air in the horizontal duct is quiescent at the beginning of nozzle discharge.

The droplet motion in the horizontal direction is expressed with the following equation:

$$m_{d} \frac{{d\left( {U_{d,H} } \right)}}{dt} = - F_{v,H} ,$$

(8)

where $m_{d}$ and $U_{d,H}$ are the mass and horizontal component of the droplet velocity, and the drag force, $F_{v,H}$, is expressed as:

$$F_{v,H} = \frac{1}{2}C_{D} A_{d} \rho_{a} \left( {U_{d,H} } \right)^{2} ,$$

(9)

where $A_{d}$ is the droplet’s cross-sectional area, and $\rho_{a}$ denotes the air density. For water mist, the drag coefficient $C_{D}$ may be expressed as follows:

$$C_{D} = \frac{{24\mu_{a} }}{{\rho_{a} U_{d,H} }},\quad {\text{ where}}\; \mu_{a} \;{\text{is}}\;{\text{ the}}\;{\text{dynamic}}\;{\text{viscosity}}\;{\text{of}}\;{\text{air}}.$$

With the above expressions, Eq. (8) leads to:

$$U_{d,H} = U_{d,H,i} e^{ - t/\tau } ,$$

(10)

and

$$S_{H} = U_{d,H,i} \tau \left( {1 - e^{{ - \frac{t}{\tau }}} } \right),$$

(11)

where $S_{H}$ is the horizontal travel distance, $U_{d,H,i}$ is the starting horizontal droplet velocity, and $\tau$ is the droplet settling time constant, $\rho_{w} D_{d}^{2} /18\mu_{a}$, in which $D_{d}$ is the droplet diameter. At an air temperature of 300 K, $\tau = 0.0166 s$ for 77-μm droplets, i.e., the median droplet size of the X1 nozzle spray operating at 41.2 bar.

With the discharge rate of 11.0 l/min and thrust force of 12.5 N in the nozzle direction, Eq. (7) gives a bulk droplet discharge velocity of 68.6 m/s in the nozzle direction. Since the nozzle axis was oriented at 45° from the duct wall, the bulk droplet discharge velocity in the duct direction was thus 48.5 m/s.

Assigning $U_{d,H,i} = 48.5\;{\text{m/s}}$ and $\tau = 0.0166 \;{\text{s}}$, Eq. (11) indicates that the momentum transfer in the duct direction from a droplet to the air would complete within a horizontal distance of 0.8 m from discharge. This was well within the distance of 1.52 m from the upstream nozzles to the midpoint propane releasing plenum. So, the airborne water mist was expected to complete its momentum transfer before it reached the midpoint plenum.

Similarly, the motion of a droplet discharged in the axis of the nozzle located at the top of the horizontal duct can be expressed as:

$$m_{d} \frac{{d\left( {U_{d,axis} } \right)}}{dt} = m_{d} gcos45^\circ - F_{v,axis} .$$

(12)

The above equation leads to the following expressions for the droplet velocity and travel distance along the nozzle axis:

$$U_{d,axis} = \tau gcos45^\circ \left( {1 - e^{ - t/\tau } } \right) + U_{d,axis,i} e^{ - t/\tau } ,$$

(13)

and

$$S_{axis} = \tau gtcos45^\circ + \left( { U_{d,axis,i} - \tau gcos45^\circ } \right)\tau \left( {1 - e^{ - t/\tau } } \right) ,$$

(14)

where $g$ is the gravitational acceleration.

With Eqs. (13) and (14) and the angular droplet discharge velocity of $U_{d,axis,i} = 77.8 {\text{m}}/{\text{s}}$, the droplet velocity at the intersect of the nozzle axis and the 0.30-m duct wall was calculated to be about 54.0 m/s, indicating that a droplet traveling along the nozzle axis would at most transfer about 30% of its initial momentum to the air, i.e., (77.8–54.0)/77.8. Since $U_{d,axis,i} \gg \tau gcos45^\circ$, the above momentum transfer estimate for the topmost nozzle was also applicable to the other three nozzles at the same duct location. If the momentum transfer from a droplet traveling along the nozzle axis could represent the overall momentum transfer from the entire nozzle spray, the horizontal component of the momentum transfer from the four discharging nozzles at each location would be:

$$4 \times \left( {12.5 {\text{N}} \times 0.30} \right) \times \cos 45^\circ = 10.6 {\text{N}}{.}$$

Coincidently, the above estimate of 10.6 N at each application location for inducing air flow in the horizontal duct was comparable to the product of the horizontal bulk droplet discharge velocity and the airborne water mist mass flux at 1.52 m from the four discharging nozzles:

$$12.5\frac{{{\text{liter}}}}{{{\text{min}}}} \times \frac{{{\text{min}}}}{{60{\text{ s}}}}{ } \times 1\frac{{{\text{kg}}}}{{{\text{liter}}}} \times 48.5\frac{{\text{m}}}{{\text{s}}} = 10.1{ }\;{\text{N}}{.}$$

The horizontal momentum flux of 10.1 N was used to estimate the air velocity induced by both the upstream and downstream nozzle discharges.

1.2.3 Spray-Induced Air Velocity

In reality, not all the horizontal momentum flux of 10.1 N of the airborne water mist could be transferred to the air, due to the fact that the airborne droplets still possessed some momentum at settling. Based on momentum conservation, the droplets and air would eventually reach a coflowing velocity of around 9.7 m/s. Therefore, the horizontal momentum flux received by the air from each nozzle discharge location would be:

$$T_{a} = 10.1{ }\;{\text{N}} \times \left( {48.5 - 9.7} \right)/48.5 = 8.1\;{\text{ N}}{.}$$

$T_{a}$ is the pumping force provided at each of the two water mist discharge locations to move the air inside the duct.

By factoring in the duct diameter and flow resistance along the ductwork, the air velocity that could be realized inside the duct can be expressed as follows based on the Bernoulli equation:

$$U_{a,duct} = \left[ {\frac{{16T_{a} }}{{\pi \rho_{a} \left( {D^{2} + fDL + K_{f} D^{2} } \right)}}} \right]^{1/2} ,$$

(15)

where $D$ and $L$ are the diameter and length of the fire test ductwork,$f$ is the duct surface friction coefficient, and $K_{f}$ denotes the combined friction coefficient to account for the resistances at the blower, bypass, the flow conditioning screen, and all the junctions along the ductwork. With $D = 0.30 \;{\text{m}}$, $L = 7.7 \;{\text{m}}$, $K_{f} = 9$ and $f = 0.316/Re_{D}^{1/4}$, the air velocity $U_{a,duct}$ induced by the nozzle sprays in the 0.30-m duct was calculated to be around 6 m/s for an air temperature of 300 K.

1.2.4 Flame Extinction Assessment

As stated above, to achieve global flame extinction in the fire, the water mist concentration needs to be sufficiently high so that the distance between water droplets is comparable to the flame quenching distance, and the water mist cooling capacity per unit volume is sufficient to lower the flame temperature to the extinction temperature for the prevailing flow turbulence.

From the water loss measurement, the airborne water mist was determined to be 12.5 l/min and 8.0 l/min at 1.52 m and 3.05 m from the upstream nozzle discharge, corresponding to the midpoint and downstream propane-releasing plenum locations. For an air velocity of 6 m/s in the duct, the water mist concentration was thus 471 g/m³ at the midpoint fire, and 303 g/m³ at the downstream fire.

For a water mist volume fraction α, the droplet spacing may be expressed as [16]:

$$l_{d - d} = D_{d} \left( {\frac{\pi }{6\alpha }} \right)^{1/3} .$$

(16)

With D_d = 77 µm for the X1 nozzle operating at 41.2 bar, the droplet spacing at the midpoint fire was about 0.80 mm, and about 0.92 mm at the downstream fire. Since the quenching distance for stoichiometric hydrocarbon flames ranges from 1.5 to 3 mm [17], the above droplet spacings indicate that the droplets could indeed interact directly with flames for heat extraction in both the upstream and downstream fires.

Stoichiometric propane-air flames have a heat content of about 3400 kJ/m³. With the heat of evaporation of 2595 J/g for water, the heat that could be extracted by complete droplet evaporation was thus about 786 kJ/m³ for the mist concentration of 303 g/m³, and 1222 kJ/m³ for the concentration of 471 g/m³. With the above two heat extraction capacities, the flame temperature could potentially be lowered from the stoichiometric propane-air flame temperature of 2250 K to about 1550 K in the midpoint fire, and 1795 K in the downstream fire.

As stated above, it has been well established that the flame extinction temperature would increase with the strain rate imposed on the flame [18]. The relationship between the flame extinction temperature and strain rate for a propane-air diffusion flame may be expressed as follows [19]:

$$\begin{array}{*{20}l} {T_{C3H8, ext} = 1368.5 a_{c}^{0.1055} } \hfill & {{\text{for}}\;a_{c} = 10 \;{\text{s}}^{ - 1} } \hfill \\ {\quad \quad \quad \; = 1685} \hfill & {{\text{for}}\;a_{c} \le 10 \;{\text{s}}^{ - 1} ,} \hfill \\ \end{array}$$

(17)

where $a_{c} = 0.1\left( {\varepsilon^{2} /k} \right)^{1/4} \left( {g{\overline{\Theta }}/{\Theta }_{o} \nu \alpha } \right)^{1/6}$. In the above expression, $k$ is the turbulence kinetic energy, $\varepsilon$ is the dissipation rate of turbulence kinetic energy, ${\overline{\Theta }}$ is the excess mean gas temperature above ambient, ${\Theta }_{o}$ is the ambient temperature, and $\nu$ and $\alpha$ are the kinematic viscosity and thermal diffusivity of the gas mixture.

The turbulence kinetic energy and dissipation rate are expressed in the following:

$$k = \frac{1}{2}\left( {u^{2} + v^{2} + w^{2} } \right)\quad {\text{and}}\quad \varepsilon = k^{3/2} /l,$$

where $u$, $v$ and $w$ are the fluctuation velocities in the axial, radial, and circumferential directions in the duct, and $l$ is the integral eddy size.

For the largest test fire of 475 kW and the corresponding ventilation rate of 17.0 m³/min employed for the 0.30-m duct test, the free-burn bulk fire gas temperature would be about 1540 K before the water mist application, giving $\left( {g{\overline{\Theta }}/{\Theta }_{o} \nu \alpha } \right)^{1/6} = 28.6\;{\text{m}}^{ - 1/2}$.

In a turbulent duct flow, $u$, $\upsilon$ and $w$ may be related by $u^{2} /v^{2} = 1.5$, $u^{2} /w^{2} = 2.1$ and $u^{2} /\overline{U}^{2} = 0.1$ [20]. For an air velocity of 6 m/s, the turbulence kinetic energy would be about 3.8 m²/s². Assuming $l \approx 0.15\; {\text{m}}$, i.e., half the duct diameter, the turbulence dissipation rate would be about $49 \;{\text{m}}^{2} /{\text{s}}^{3}$. Combining the above values, $\left( {\varepsilon^{2} /k} \right)^{1/4} = 5 \;{\text{m}}^{1/2} \;{\text{s}}^{ - 1}$.

Therefore, the flame would be subjected to a strain rate of $a_{c} = 0.1\left( 5 \right)\left( {28.6} \right) = 14.3 \;{\text{s}}^{ - 1}$. With Eq. (17), the corresponding flame extinction temperature would be around 1800 K. The above analysis indicates that the likelihood of flame extinction in the midpoint fire was high, while the flame extinction in the downstream fire was marginal.