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Experimental and numerical study of high-pressure water-mist nozzle sprays
Fire Safety Journal 81 (2016) 109–117
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Experimental and numerical study of high-pressure water-mist nozzle sprays$ H.M. Iqbal Mahmud n, Khalid A.M. Moinuddin, Graham R. Thorpe Centre for Environmental Safety and Risk Engineering, Victoria University, P.O. Box 14428, Melbourne, Victoria 8001, Australia
art ic l e i nf o
a b s t r a c t
Article history: Received 2 December 2014 Received in revised form 11 January 2016 Accepted 27 January 2016
The performance of extinguishment of fires by water sprays is strongly influenced by the characteristics of the sprays produced by nozzles. Computational fluid dynamics (CFD) based fire models are a tool that can be used for the characterization of sprays. However, it is necessary to evaluate the capability of a CFD based fire model in predicting the behaviour of sprays before using it for such characterization. One of the basic parameters that is important in characterising the water mist spray is the distribution of flux density of water droplets impinging on the floor. This paper reports the study on the characterization of water mists, in terms of distribution of flux density of sprays, produced by a single and a multi-orifice high-pressure jet nozzle. Full-scale experiments were conducted and the distributions of volume flux density of sprays were measured. The sprays were also modelled using a CFD model, Fire Dynamic Simulator (FDS), version 6, to investigate the capability of the model in predicting the distribution behaviour of the spray. The numerical results of distribution are compared with those obtained experimentally. The predicted results of FDS has show good agreement with the experimental results. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Water-mist Single-orifice nozzle Multi-orifice nozzle Distribution of flux density Fire Dynamic Simulator (FDS)
1. Introduction Water-mist fire suppression systems (WMFSS) are increasingly being used in a wide variety of applications ranging from protecting naval vessels and passenger ships through to commercial buildings and industrial structures. WMFSS are not only effective at suppressing fires, but they have low-demands for water compared to conventional sprinkler sprays and they are environmentally friendly compared to gaseous suppression agents [1–3]. However, the performance of WMFSS is crucially dependent on the characteristics of sprays produced by nozzles [4]. One of the important parameters essential for specifying water-mist systems is the distribution of the flux density of the spray [5]. Therefore, a good understanding on the distribution of flux density on surfaces is essential for fire researchers to design an effective WMFSS. In recent years, computational fluid dynamics (CFD) models are increasingly used to investigate the growth and suppression of fires, including the dynamics of sprays. Among the available CFD based tools, Fire Dynamic Simulator (FDS), developed by National Institute of Standards and Technology (NIST), USA, is widely used open-source software used for simulating the spread and suppression of fires in buildings [3,6–10]. In this study, FDS is used to ☆ This work was technically and financially supported by the Defence Science and Technology Organisation (DSTO), Australia. n Corresponding author. E-mail address: [email protected] (H.M.I. Mahmud).
http://dx.doi.org/10.1016/j.firesaf.2016.01.015 0379-7112/& 2016 Elsevier Ltd. All rights reserved.
investigate the dynamics of water-mist sprays. However, to substantiate the accuracy of FDS, full-scale experiments are required. Hence, the object of this study is to investigate the accuracy of FDS in predicting the distribution of flux density of sprays produced by water mist nozzles at a certain distance from the nozzle. In this work, two types of nozzles, a single and a multi-orifice nozzle, were used in the experiments. The distributions of flux density of sprays by single and multi-orifice nozzles are quite different. Single-orifice nozzles result in sprays in which the droplet distribution is concentrated in the vicinity of vertically downward azimuthal axis of the nozzle. However, in case of multiorifice nozzles the flux distribution is concentrated in several regions that correspond to the individual orifices. As a result, the area of distribution of sprays produced by multi-orifice nozzles is higher than that produced by single-orifice nozzles. Moreover, as the peripheral orifices of multi-orifices nozzles sprays in the radial direction, the droplets can reach to fires even though they are far from the nozzle. However, for both type of nozzles, the fine mists produced by them have the desirable features of being able to reach the regions that are otherwise occluded and they cool the surrounding gases and attenuate the thermal radiation by blocking and isolating the fires. Therefore, this work investigates experimentally the distribution of flux density of water emanating from a single and a multiorifice nozzle. The numerical simulations were carried out in FDS using the same input parameters (such as mean droplet diameter, flow rate, spray angle etc) as used for the experiments. FDS,
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version 6, is used for the simulation and the accompanying smokeview tool, version 5.6, is used for the visualization of the sprays. Then the predicted flux distribution data of FDS are compared with the measured data and validation against the experiment are evaluated.
2. Experiment details 2.1. Nozzle specification 2.1.1. Single-orifice nozzle A schematic of the single-orifice nozzle used in the experiment is shown in Fig. 1. The orifice has an opening of 1.524 mm and it is located centrally in the body of the nozzle which discharges an axi-symmetric spray around the nozzle axis. 2.1.2. Multi-orifice nozzle A schematic of the multi-orifice nozzle used in the experiment is shown in Fig. 2. The nozzle comprises a central orifice of 1.524 mm in diameter, placed along the nozzle axis, and six orifices of 0.508 mm in diameter, placed equi-angularly around the perimeter of the nozzle at an azimuthal angle of 60° with the inlet nozzle axis. The central orifice discharges axi-symmetrically around the inlet nozzle axis and the peripheral orifices discharge axi-symmetrically around the axis of that individual orifice. 2.2. Experimental set‐up and procedure An experiment rig was constructed to measure the distribution of flux density produced by the sprays. This was achieved by placing a 2 2 0.1 m water collection tray beneath the nozzles. To spatially resolve the distribution of flux density the tray was divided into 400 compartments, each with dimensions of 10 10 10 cm. The single-orifice and the multi-orifice nozzle heads were clamped at heights of 2.3 m and 2.0 m, respectively, above the floor. A solid boundary wall was present at 2 m away from the nozzle head. Water was supplied to the nozzles by means of a pump that could operate at a pressure of up to 400 bar. The experimental rig is illustrated in Fig. 3. The experiments were designed to measure distribution of the flux densities produced by single and multi-orifice nozzles. It was found that the distribution of flux densities of the spray produced by the single-orifice nozzle was best captured by placing the centre of the water collection tray underneath the nozzle head. This set-up is designated as Case A. However, it was expected that, the maxima of the distributions of the spray by the multi-orifice nozzle would be produced at several locations corresponding to the spray produced by individual orifices. For example, one of the maxima of the distributions would be produced directly beneath the centre of the nozzles by the central orifice, and others would be produced in
regions corresponding to their azimuthal orifices. Hence, in this situation, experiments were carried out with the centre and one of the corner of the water collection tray located underneath the multi-orifice nozzle head. The former set-up is similar to that of the single-orifice nozzle and referred to as Case A, and the latter set-up is referred to as Case B. In both cases, the boundary wall was located at 2 m away from the nozzle head. The locations of the nozzles and boundary wall for these two cases are shown in Fig. 4. To supply the water from the reservoir to the nozzle head, the pump was operated at a pressure of 34.5 bar for single-orifice nozzle spray, which produced a volume flow rate of 1.7 L/min. In case of the multi-orifice nozzle, the pump was operated at a pressure of 70 bar which produced a volume flow rate from the central orifice comparable with that produced by the single-orifice nozzle; the total volume flow rate was 8.8 L/min. The nozzles were allowed to operate for five seconds to have a stable flow. The angles of the sprays for both of the nozzles were determined from the photographs of sprays, as illustrated in Fig. 5. The parameters of the spray, i.e. water flow rates, spray angles and spray heights of the experiment were used as input parameters in FDS model. In the experiment, the volume flow rates of the sprays produced by the nozzles were measured. The flow rate produced by the single-orifice nozzle was 1.7 L/min. In case of multi-orifice nozzle spray, the flow rates for the central and the azimuthal orifices, and for the whole nozzle were measured separately. The measured flow rates for multi-orifice nozzle from the central and azimuthal orifices and for the whole nozzle were 2.2, 1.1 and 8.79 L/min, respectively. The measured flow rate from the nozzle head was corroborated by means of the following correlation [11] –
(1)
Q =K P
where Q is the discharge rate of water and P is the operating pressure of water flow. According to the manufacturer data, the K-factor of the single-orifice and multi-orifice nozzles are 0.073 and 0.02 gam/psi1/2, which give flow rates of 1.69 and 8.74 L/min, respectively, produced by single and multi-orifice nozzles. This also validates the accuracy of the experimental measurement of water flow rates.
3. Numerical model 3.1. FDS model CFD simulations were run using “FDS (version 6)” and accompanying programme, “Smokeview (version 5.6)”, was used for the visualisation of the model. The basic conservation equations of mass, momentum and energy for a Newtonian fluid are presented as a set of partial differential equations and solved by the finite difference technique. In the following few sub-sections, the spray model in FDS is described briefly. Details of these models are given in FDS technical reference guide [12]. FDS takes a sample of spherical droplets to calculate the distribution pattern. The droplet size distribution is expressed in terms of its Cumulative Volume Fraction (CVF), which is represented by a combination of log-normal and Rosin–Rammler distributions [12].
⎧ [ln D ]2 DCVF Dm ⎪ 1 ⎪ (2π )− 2 (σD)−1e 2σ 2 dD (DCVF ≤Dm ) F (d)=⎨ 0 ⎪ ⎪ γ 1 − e−0.693 (DCVF / Dm ) (DCVF > Dm ) ⎩
∫
Fig. 1. Schematic of the single-orifice nozzle (after Tanner and Knasiak [11]).
( )
(2)
where D is the generic droplet diameter, Dm is the median droplet diameter. The median droplet diameter is a function of the sprinkler/nozzle orifice diameter, operating pressure, and geometry. γ and σ are empirical constants used for curve-fitting of distribution
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111
Fig. 2. Schematic view of the multi-orifice nozzle – (a) side view; (b) plan view (after Tanner and Knasiak [11]).
Re=
ρ vd − va 2r μ (T )
where
(6)
μ(T) is the dynamic viscosity of air at temperature T.
3.2. Domain set‐up
Fig. 3. Schematic view of the experimental set‐up.
patterns and they are equal to 2.4 and 0.6, respectively. In FDS, water droplet transport is modelled by a Lagrangian approach. The velocity and position of the droplets are calculated from the theory of conservation of momentum. The position and velocity of each droplet are calculated from the following equations.
d 1 ( mvp )=mg − ρCd πr 2 ( vp−va ) vp−va dt 2
(3)
dxp =vp dt
(4)
where, the drag coefficient, Cd , depends on the following function of the Reynolds number based on the droplet-air relative velocity.
⎧ 24/Re ⎪ Cd=⎨ 24 0.85 + 0.15 Re ⎪ ⎩ 0. 44
(
Re < 1 0.687
)
/Re
1 < Re < 1000 Re >1000
(5)
The Reynolds number of the droplets is defined by
3.2.1. Single-orifice nozzle spray A computational domain for the single-orifice nozzle spray was established that represents a region in space as shown in Fig. 6. The dimensions of the floor are 2 2 m and the vertical height of the domain is 2.4 m. In order to represent the laboratory set-up, one of the vertical boundaries is considered to be an impermeable solid wall. The three other vertical boundaries are considered to be open to flow, as is the upper horizontal boundary. The lower horizontal boundary is the floor on which the mass flux of water emanating from the nozzle impinges. The dots on this surface coincide with the centres of the 10 10 cm regions in which the fluxes were measured. The nozzle head was located at a height of 2.3 m above the floor. 3.2.2. Multi-orifice nozzle spray Two similar computational domain were established to simulate the sprays produced by the multi-orifice nozzle for the two cases – Case A and Case B, as shown in Figs. 7 and 8, respectively. In Case A, the centre of the water collection tray was beneath the nozzle and in Case B, one of the corner of the water collection tray was beneath the nozzle. In both cases, the dimensions of the horizontal floor are 6 6 m and the height of the domain is 2.1 m. To be consistent with the conditions associated with the experiment, one of the vertical boundaries that has dimension of 6 2.1 m is designated as being impermeable, whereas the other three and the horizontal roof are open. The multi-orifice nozzle was located at a height of 2.0 m from the floor. The lower horizontal boundary is the floor on which the mass flux of water emanating from the nozzle impinges. The dots on this surface coincide with the centres of the 10 10 cm regions in which the fluxes were measured. 3.2.3. Grid spacing A computational grid sensitivity analysis was carried out to ensure that the numerical results converged. The grid spacing was
Fig. 4. Locations of the nozzles (a) Case A; (b) Case B.
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Fig. 5. Measurement of angle of spray for single-orifice nozzle; (a) spray produced by single-orifice nozzle; (b) spray produced by multi-orifice nozzle.
manufacturer's data. The angles of sprays for single-orifice nozzle and for the central and peripheral orifices of multi-orifice nozzle were measured from the photographs of sprays, as reported in the previous section. The flow rate of each individual orifice and of the whole nozzle head were measured in the experiment. The velocity of the droplets was calculated from the simple geometrically based relationship between the flow rate and discharge area. The median size of the droplets for the single-orifice nozzle spray was calculated using the corellation between the pressure of water flow, diameter of discharge orifice and median diameter of droplet [13]. According to Fleming [13] the median diameter of droplets generated by a spray has been empirically found to be inversely proportional to the one-third power of water pressure and directly proportional to two-thirds the power of the orifice diameter, i.e.
dm∝
Fig. 6. Computational domain set‐up used to simulate the spray generated by a single-orifice nozzle.
20 cm, 10 cm, 5 cm and 2.5 cm in the x, y and z directions. In all of the simulations the input parameters and boundary conditions were unchanged. The only change was the grid size. The distributed flux density along the centre of the tray parallel to x axis for these four cell sizes were calculated and compared. The results are presented in Fig. 9. It was observed that the computed flux densities were almost identical when the grid sizes were 2.5 cm and 5.0 cm. Hence, in this work a grid size of 5.0 cm was used to discretise the computational domains.
D2/3 P1/3
where dm is the median droplet size, D is the orifice diameter and P is the flow pressure. The details of the procedure is explained in reference [14]. The median size of the droplets for the multi-orifice nozzle spray was taken from the experimental data provided by the manufacturer [11]. The details of the spray parameters for both of the single-orifice and multi-orifice nozzles are presented in Table 1. A Rosin–Rammler-lognormal distribution pattern was used for the distribution of drop sizes. The simulation was allowed to run for 65 seconds; the nozzle was activated at the beginning of the simulation and stopped at 60 seconds; the additional 5 seconds were to allow the water drops to fall down from the nozzle.
3.3. Modelling of sprays
4. Results and discussion
The spray from the single-orifice nozzle was modelled as entering the domain in downwards vertical direction; i.e. 0° azimuthal angle with the nozzle axis. The spray from the multi-orifice nozzle was modelled as a collection of sprays eminating from single nozzles by assigning each nozzle a different orientation and physical characteristics of the sprays. In case of the multi-orifice nozzle, the peripheral orifices were oriented so that they were separated by an azimuthal angle of 60°. The spray from the nozzle was described as a droplet inlet boundary condition.
4.1. Single-orifice nozzle spray
3.4. Input variables Once the computational domains were set-up, the input parameters for the computational measurements were incorporated into the models. The input variables to the model were the flow rate of water, angle of spray, height of spray, median size of droplet size and velocity of droplet. The parameters of the sprays were specified with the aid of the experimental measurements and
(7)
In the experiment, the distribution of flux densities of the spray were measured at a distance 2.3 m below of the nozzle. Input parameters used in the FDS model were obtained from the experimental measurements. These include flow rate of water, velocity of droplet, angle of sprays and height of spray. The numerical simulation was run and the distribution of flux density of the spray was calculated by the model. The flux density distribution of experiment and numerical simulations were calculated in L/m2/min and the contour maps are illustrated in Fig. 10 (a) and (b), respectively. The contour maps are drawn from ordinate 0.4–1.6 on both of the X- and Y-axes, as 90% of the water of the spray were found to be within this region. As expected, the flux density was highest at the centre of the floor, both in the experiment and in the numerical simulation and it decreased monotonically in the radial direction from the centre. The contour maps in Fig. 10 indicate that
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113
Fig. 7. Computational domain used to simulate the spray generated by a multi-orifice nozzle for Case A; (a) isometric view, (b) plan view.
Fig. 8. Computational domain used to simulate the spray generated by a multi-orifice nozzle for Case B; (a) isometric view, (b) plan view.
Table 1 Spray parameters for FDS simulation. Nozzle type
Single-orifice
Input variables Diameter, mm Orientation (azimuthal angle) Flow rate, L/min Spray angle Spray height, m Droplet velocity, m/s Droplet size, μm Spray pattern
Fig. 9. Grid convergence test for spray distribution.
there is discrepancy between the contour maps generated in the experiment and by the computer model. The contour map of the distribution produced by the experimental is elliptical in shape and it has translated 15 and 5 cm from the centre of the tray in the positive X and Y direction, respectively. It was hard to eliminate all non-idealised conditions (including the existence of solid wall mentioned earlier) for this a large scale laboratory experiment. Moreover, water-mists comprise small droplets. So, when they are allowed to fall for 2.3 m, due to even slight non-idealised condition, it can happen that the distribution is not actually circular in shape and concentred with the centre of the tray. The white
Multi-orifice Central
Peripheral
1.524 0° 1.7
1.524 0° 2.2
0.508 60° 1.1
65° 2.3 15.5
45° 2.0 18.8
15° 2.0 89.6
350 Solid
100 Solid
85 Solid
dashed line in the figures are the major and minor axes of the ellipses. The eccentricity of the ellipse for the distribution generated in the experiment is 0.70, whereas the eccentricity of that by the numerical model is 0.2. This indicates that the distribution of spray generated by the numerical model is almost circular. Other than the elliptical in shape of the maps, the predicted distribution pattern and intensity of flux densities of the numerical model is reasonably agreed with that of the experiment. The distribution of water volume flux along the axes of the ellipse and radii of the circle are illustrated in Fig. 11. In the experimental study, the distribution along the major and minor axes of the ellipse are not identical, whereas the simulation results along the centreline showed an almost identical distribution. However, both experimental and numerical data shows a bell shaped distribution patterns.
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Fig. 11. The distribution of flux density of sprays for single-orifice nozzle along the experimental values along the major centreline axes as indicated in Fig. 10; axis, experimental values along the minor axix, numerical values along radii of X direction, numericial values along radii of Y direction.
Fig. 10. Distributions of flux densities of spray produced by the single-orifice nozzle; (a) experimental; (b) numerical.
4.2. Multi-orifice nozzle spray The flux density distribution of the water spray was measured experimentally at a distance 2.0 m beneath the nozzle. The experiments were conducted for two cases; Case A and Case B. In Case A, the position of the nozzle was above the centre of the water collection tray and in Case B, the position of the nozzle was above on one of the corners of the water collection tray. The flux density distributions obtained in the experiment and numerical simulation are displayed as contour plots for Case A and the results are given in Fig. 12 (a) and (b), respectively. The experimental results indicate that the distribution is ellipsoidal and the flux decreases with distance from the centre. The position of highest volume flux is displaced 20 cm from the centre of the tray in both the X and Y directions. A possible reason is that the spray is affected by the wall in the vicinity of the spray. A hint of this artefact is provided in the numerical results that also produced an elliptical flux distribution that is displaced towards the wall. In the numerical case, it is displaced by about 10 cm. The eccentricity of the ellipse for the experimentally obtained distribution is 0.74,
whereas it is 0.58 for the numerically obtained distribution of spray. This confirms that the distribution generated experimentally is more ellipsoidal than that generated by the numerical model. The water fluxes along the major and minor axes of the numerically and experimentally obtained distributions are shown in Fig. 13. The centre of the ellipse of Fig. 12(a) is superimposed on the centre of the ellipse of Fig. 12(b) and corresponding values of the distribution of flux densities are compared. The figures show that the numerical model has under-predicted the distribution of volume flux around the periphery of the ellipse except within the region of 0.0–0.3 m of the tray along the major axis. However, it has predicted the distribution near the centre of the ellipse of the spray with an accuracy greater than 90%, which provides some validation of the model. The distributions are approximately bell shaped in both cases and, the numerical and experimental measurements are generally in good agreement. The distribution of flux densities in the experiment and numerical simulation for case B is shown in Fig. 14(a) and (b), respectively. The maximum flux densities of the sprays for the peripheral orifices are at locations (0.9, 0.4) and (0.9, 0.2) for the experimental and numerical distributions, respectively. The distributions generated by the sprays are elliptical for both experimentaly and numerically generated sprays. The lateral contour axis is depicted by a line connecting the centres of the ellipses of distributions of sprays produced by the central and peripheral orifices. The distances of the centres of ellipses from the corner of the water collection tray along the lateral contour axis for the experimentally and numerically obtaied distribution on the floor is 186 and 200 cm, respectively. The white colour in both of the figures is due to the reason that the flux densities in that region was out of scale (more than 1.05 L/m2/min). The eccenticities of the experimentally and numerically obtained distributions are 0.72 and 0.16, respectively. This signifies that the numerical model has predicted a more circular flux distribution compared to that of the experiment. The peripheral orifices in the body of the nozzle are oriented at an angle of 60° to each other. Therefore, it is expected that the angle separating the peripheral centre (topological) should also be 60°. This expectation is met by the numerical model in simulating the direction of spray produced by the individual orifices. In Case B, one of the lateral contour axes was directed along an edge of the water collection tray and another one along a line at an angle of 60° to the edge as indicated in Fig. 14. In the contour plot of distribution produced by the orifice
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Fig. 12. Distribution of flux density of spray for multi-orifice nozzle for Case A; (a) experimental, (b) numerical.
Fig. 13. The distribution of flux densities of spray for multi-orifice nozzle along the major and minor axes of ellipses for Case A; experimental values along the major axis, experimental values along the minor axix, numerical values along radii of X direction, numerical values along radii of Y direction.
115
Fig. 14. Distribution of flux density generated by a multi-orifice nozzle for Case B; (a) experimental, (b) numerical.
whose axis was directed along an edge of the water collection tray, the half of the ellipse produced by distribution was captured on the water collection tray in the numerical model (Fig. 14(b)); however, no such pattern was observed in the experimentally produced distribution (Fig. 14(a)). A possible reason is that there was as wall 2 m away from the edge of the water collection tray and one of the orifices was directed to the wall. The droplet was injected from the nozzle with a high-speed and it was spread in the room. As a result, it created turbulence in the space of the room. The turbulance created by the spray was affected by the presence of the wall. Moreover, as the droplet size is very small and light in weight, it was suspended surrounding the spray and scattered from its spray path due to the presence of the wall. As a result, no elliptical shape of spray was created by the experiment. The distribution of water fluxes along the lateral axis of contour is illustrated in Fig. 15. It can be seen that the numerical model has over-predicted the distribution near the centre of the ellipse of the spray for both central and peripheral orifices, and under-predicted it around the periphery of the ellipse of the spray for both central
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Table 2 Statistical analysis of standard uncertainty of the experimental data. Nozzle type
Single-orifice
Experimental uncertainty L/m2/min
0.103
Multi-orifice Central
Peripheral
0.169
0.055
Table 3 Statistical analysis of congruence between the measured and calculated distribution of flux densities. Nozzle type
Single-orifice
Multi-orifice Central
Fig. 15. The distribution of flux density of spray for multi-orifice nozzle along the lateral axis of contour for case B.
and peripheral orifices. However, the peak-to-peak differences between the numerical and experimental values for the spray of the central and peripheral orifices are not more than 20%, which indicates the capability of FDS in predicting the distribution of flux density of spray (when away from the wall effect).
5. Statistical analysis 5.1. Experimental uncertainities In physical experiments, assessment of uncertainties deals with evaluating the uncertainty in observation or measurements. An experiment designed to determine a value of a physical variable will be affected by errors due to the experimental procedure, instrumentation, the presence of confounding effects, etc [15]. Therefore, estimation of experimental uncertainty would help to evaluate the confidence in the results. In this section, a statistical analysis has been conducted to quantify the uncertainity of measurements based on the least squares method [16]. Usually, the standard uncertainty, u (xi ), is estimated from the following equations,
⎡ 1 u ( xi )=⎢ ⎢⎣ n (n − 1)
n
⎤1/2
∑ (Xi, k − X¯ i )2⎥ k=1
⎥⎦
(8)
where,
1 xi =X¯ i = n
n
∑ X i, k k=1
(9)
Here, Xi is input quantities which is estimated from n number of independent observations Xi, k of Xi obtained under the same conditions of measurement. If the measured value of any parameter is y, then it can vary with an interval of y ± u (xi ) . The standard uncertainty, u (xi ), of measurements of the distribution of flux densities has been estimated for the sprays produced by the single and multi-orifice nozzles using Eq. (9). The average experimental uncertainty of measurements for the spray produced by the single-orifice nozzle is 0.103 L/m2/min, and for the sprays produced by the central and peripheral orifice of the multi-orifice nozzle are 0.169 and 0.055 L/m2/min, respectively. Therefore, the values of this uncertainty imply that the measured data of the experiments may vary at an amount of less or more of that of the corresponding level of uncertainty. The values of the standard uncertainty of the experimental measurements are presented in Table 2.
Peripheral
Input variables
Exp
Num
Exp
Num
Exp
Num
Uniformity coefficient
0.73
0.96
1.45
1.23
1.02
0.87
5.2. Uniformity coefficient In this section, a quantative statistical analysis has been conducted to identify the uniformity of distribution of flux densities produced by the sprays on the horizontal surface. A uniformity coefficient (b) has been calculated based on the maximum likelihood function. Usually, the uniformity coefficient is used to quantify the resemblance between the measured and calculated distribution of flux densities produced by sprays. The implicit equation for the uniformity coefficient for a set of indepemdent observations, x , is defined as, n
b=
∑i = 1 xib n
(
n
∑i = 1 xib lnxi − ∑i = 1 xib
)(
1 n
n
∑i = 1 ( ln xi )
)
(10)
where n is the number of values in the data set, xi the known data, and it can be calculated from the following equation,
xi =
V˙i′′ max V˙i′′
(11)
where V˙i′′ are the predicted or measured distribution of flux densities for each point of data collection. The value of uniformity coefficient (b) indicates the homogeneity of distribution of flux densities. When the uniformity coefficient (b) is greater than 1, it implies to more uniformity of the distribution. On the other hand, if ‘b’ is less than 1, it indicates to less uniformity of the distribution. The uniformity coefficient for the distribution of sprays produced in the experiment and numerical simulation for both of the single and multi-orifice nozzles are calculated and presented in Table 3.
6. Conclusions Water-mists have the ability to suppress fires, and their efficacy can be explored using computer software packages such as FDS. However, it is essential that the software accurately predicts the behaviour of the mists produced by spray nozzles. In this work, we have assessed the ability of FDS in simulating the distribution of flux densities of sprays that govern the prediction of the behaviour of spray nozzles. It has been found that the distribution of the sprays produced in the experiment and numerical model for both the single and multi-orifice are elliptical in shape.However, the eccenticity of the ellipses for the distribution is less pronounced in the numerical model for both of the single and multi-orifice
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nozzle. In overall, the results obtained using FDS are in close agreement with the experimentally determined distributions of flux densities produced by spray nozzles. In this work, it appears that the presence of a solid wall in the vicinity of the spray influenced the distribution. The experimental and numerical results obtained in this study indicate that the flux distribution was closer to the wall than would otherwise be the case. However, the effect of the boundary wall on the distribution of the spray in the numerical model was pronounced less compared to that of the experimental results. Therefore, a further study would be helpful to quentify the influence of wall on a spray and its effect on the distribution of flux densities produced by the spray.
Acknowledgements The authors wish to acknowledge technical and financial assistance provided by the Defence Science and Technology Organisation (DSTO), Australia. The authors also wish to acknowledge technical support provided by postgraduate students, Mr. Sk Md Kamal Uddin and Mr. Md Mahfuz Sarwar.
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[4] Z. Liu, A.K. Kim, A review of water mist fire suppression systems – fundamental studies, J. Fire Prot. Eng. 10 (3) (2000) 32–50, http://dx.doi.org/10.1177/ 104239159901000303. [5] H.H. Lefebvre, Atomisation and Sprays, Hemisphere Publishing Corporation, New York, 1989. [6] S.C. Kim, H.S. Ryou, An experimental and numerical study on fire suppression using a water-mist in an enclosure, Build. Environ. 38 (2003) 1309–13016, http://dx.doi.org/10.1016/S0360-1323(03)00134-3. [7] B. Yao, B.H. Cong, J. Qin, W.K. Chow, Experimental study of suppressing Poly (methyl methacrylate) fires using water mists, Fire Saf. J. 47 (2012) 32–39, http://dx.doi.org/10.1016/j.firesaf.2011.08.004. [8] A. Jenft, A. Collin, P. Boulet, G. Pianet, A. Breton, A. Muller, Experimental and numerical study of pool fire suppression using water mist, Fire Saf. J. 67 (2014) 1–12, http://dx.doi.org/10.1016/j.firesaf.2014.05.003. [9] L. Yinshui, J. Zhuo, W. Dan, L. Xiaohui, Experimental research on the water mist fire suppression performance in an enclosed space by changing the characteristics of nozzles, Exp. Therm. Fluid Sci. 52 (2014) 174–181, http://dx. doi.org/10.1016/j.expthermflusci.2013.09.008. [10] F. Ura, N. Kawabata, F. Tanaka, Characteristics of smoke extraction by natural ventilation during a fire in a shallow urban road tunnel with roof openings, Fire Saf. J. 67 (2014) 96–106, http://dx.doi.org/10.1016/j.firesaf.2014.05.009. [11] G. Tanner, K.F. Knasiak, Spray characterization of typical fire suppression nozzles, Industrial Products Division, Spraying Systems Co., Wheaton, IL 60189 USA, in: Proceedings of the 3rd International Water Mist Conference (published), Madrid, Spain, September 22–24, 2003. [12] J. Floyd, G. Forney, S. Hostikka, T. Korhonem, R. McDermott, K. McGrattan, C. Weinschenk, Fire Dynamics Simulator (Version 6), Technical Reference Guide, Volume 1: Mathematical Model, NIST Special Publication 1018, Sixth Edition, National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Gaithersburg, Maryland, USA, 2013. [13] R.P. Fleming, Automatic sprinkler system calculations, in: P.J. DiNenno (Ed.), 4th ed.,The SFPE Handbook of Fire Protection Engineering, 02269, National Fire Protection Association, Quincy, MA, 2008, pp. 4–86. [14] H.M.I. Mahmud, Simulation of the Suppression of Fires Using Water Mists (Ph. D. Thesis), Victoria University, Melbourne, Australia, 2015 (submitted). [15] F. Stern, M. Muste, M.L. Beninati, W.E. Eichinger, Summary of Experimental Uncertainty Assessment Methodology with Example, Iowa Institute of Hydraulic Research, College of Engineering, The University of Iowa, Iowa, 1999, IIHR Technical Report No. 406. [16] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, National Institute of Standards and Technology (NIST), Gaithersburg, USA, 1994.
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Fire Safety Journal journal homepage: www.elsevier.com/locate/firesaf
Experimental and numerical study of high-pressure water-mist nozzle sprays$ H.M. Iqbal Mahmud n, Khalid A.M. Moinuddin, Graham R. Thorpe Centre for Environmental Safety and Risk Engineering, Victoria University, P.O. Box 14428, Melbourne, Victoria 8001, Australia
art ic l e i nf o
a b s t r a c t
Article history: Received 2 December 2014 Received in revised form 11 January 2016 Accepted 27 January 2016
The performance of extinguishment of fires by water sprays is strongly influenced by the characteristics of the sprays produced by nozzles. Computational fluid dynamics (CFD) based fire models are a tool that can be used for the characterization of sprays. However, it is necessary to evaluate the capability of a CFD based fire model in predicting the behaviour of sprays before using it for such characterization. One of the basic parameters that is important in characterising the water mist spray is the distribution of flux density of water droplets impinging on the floor. This paper reports the study on the characterization of water mists, in terms of distribution of flux density of sprays, produced by a single and a multi-orifice high-pressure jet nozzle. Full-scale experiments were conducted and the distributions of volume flux density of sprays were measured. The sprays were also modelled using a CFD model, Fire Dynamic Simulator (FDS), version 6, to investigate the capability of the model in predicting the distribution behaviour of the spray. The numerical results of distribution are compared with those obtained experimentally. The predicted results of FDS has show good agreement with the experimental results. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Water-mist Single-orifice nozzle Multi-orifice nozzle Distribution of flux density Fire Dynamic Simulator (FDS)
1. Introduction Water-mist fire suppression systems (WMFSS) are increasingly being used in a wide variety of applications ranging from protecting naval vessels and passenger ships through to commercial buildings and industrial structures. WMFSS are not only effective at suppressing fires, but they have low-demands for water compared to conventional sprinkler sprays and they are environmentally friendly compared to gaseous suppression agents [1–3]. However, the performance of WMFSS is crucially dependent on the characteristics of sprays produced by nozzles [4]. One of the important parameters essential for specifying water-mist systems is the distribution of the flux density of the spray [5]. Therefore, a good understanding on the distribution of flux density on surfaces is essential for fire researchers to design an effective WMFSS. In recent years, computational fluid dynamics (CFD) models are increasingly used to investigate the growth and suppression of fires, including the dynamics of sprays. Among the available CFD based tools, Fire Dynamic Simulator (FDS), developed by National Institute of Standards and Technology (NIST), USA, is widely used open-source software used for simulating the spread and suppression of fires in buildings [3,6–10]. In this study, FDS is used to ☆ This work was technically and financially supported by the Defence Science and Technology Organisation (DSTO), Australia. n Corresponding author. E-mail address: [email protected] (H.M.I. Mahmud).
http://dx.doi.org/10.1016/j.firesaf.2016.01.015 0379-7112/& 2016 Elsevier Ltd. All rights reserved.
investigate the dynamics of water-mist sprays. However, to substantiate the accuracy of FDS, full-scale experiments are required. Hence, the object of this study is to investigate the accuracy of FDS in predicting the distribution of flux density of sprays produced by water mist nozzles at a certain distance from the nozzle. In this work, two types of nozzles, a single and a multi-orifice nozzle, were used in the experiments. The distributions of flux density of sprays by single and multi-orifice nozzles are quite different. Single-orifice nozzles result in sprays in which the droplet distribution is concentrated in the vicinity of vertically downward azimuthal axis of the nozzle. However, in case of multiorifice nozzles the flux distribution is concentrated in several regions that correspond to the individual orifices. As a result, the area of distribution of sprays produced by multi-orifice nozzles is higher than that produced by single-orifice nozzles. Moreover, as the peripheral orifices of multi-orifices nozzles sprays in the radial direction, the droplets can reach to fires even though they are far from the nozzle. However, for both type of nozzles, the fine mists produced by them have the desirable features of being able to reach the regions that are otherwise occluded and they cool the surrounding gases and attenuate the thermal radiation by blocking and isolating the fires. Therefore, this work investigates experimentally the distribution of flux density of water emanating from a single and a multiorifice nozzle. The numerical simulations were carried out in FDS using the same input parameters (such as mean droplet diameter, flow rate, spray angle etc) as used for the experiments. FDS,
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version 6, is used for the simulation and the accompanying smokeview tool, version 5.6, is used for the visualization of the sprays. Then the predicted flux distribution data of FDS are compared with the measured data and validation against the experiment are evaluated.
2. Experiment details 2.1. Nozzle specification 2.1.1. Single-orifice nozzle A schematic of the single-orifice nozzle used in the experiment is shown in Fig. 1. The orifice has an opening of 1.524 mm and it is located centrally in the body of the nozzle which discharges an axi-symmetric spray around the nozzle axis. 2.1.2. Multi-orifice nozzle A schematic of the multi-orifice nozzle used in the experiment is shown in Fig. 2. The nozzle comprises a central orifice of 1.524 mm in diameter, placed along the nozzle axis, and six orifices of 0.508 mm in diameter, placed equi-angularly around the perimeter of the nozzle at an azimuthal angle of 60° with the inlet nozzle axis. The central orifice discharges axi-symmetrically around the inlet nozzle axis and the peripheral orifices discharge axi-symmetrically around the axis of that individual orifice. 2.2. Experimental set‐up and procedure An experiment rig was constructed to measure the distribution of flux density produced by the sprays. This was achieved by placing a 2 2 0.1 m water collection tray beneath the nozzles. To spatially resolve the distribution of flux density the tray was divided into 400 compartments, each with dimensions of 10 10 10 cm. The single-orifice and the multi-orifice nozzle heads were clamped at heights of 2.3 m and 2.0 m, respectively, above the floor. A solid boundary wall was present at 2 m away from the nozzle head. Water was supplied to the nozzles by means of a pump that could operate at a pressure of up to 400 bar. The experimental rig is illustrated in Fig. 3. The experiments were designed to measure distribution of the flux densities produced by single and multi-orifice nozzles. It was found that the distribution of flux densities of the spray produced by the single-orifice nozzle was best captured by placing the centre of the water collection tray underneath the nozzle head. This set-up is designated as Case A. However, it was expected that, the maxima of the distributions of the spray by the multi-orifice nozzle would be produced at several locations corresponding to the spray produced by individual orifices. For example, one of the maxima of the distributions would be produced directly beneath the centre of the nozzles by the central orifice, and others would be produced in
regions corresponding to their azimuthal orifices. Hence, in this situation, experiments were carried out with the centre and one of the corner of the water collection tray located underneath the multi-orifice nozzle head. The former set-up is similar to that of the single-orifice nozzle and referred to as Case A, and the latter set-up is referred to as Case B. In both cases, the boundary wall was located at 2 m away from the nozzle head. The locations of the nozzles and boundary wall for these two cases are shown in Fig. 4. To supply the water from the reservoir to the nozzle head, the pump was operated at a pressure of 34.5 bar for single-orifice nozzle spray, which produced a volume flow rate of 1.7 L/min. In case of the multi-orifice nozzle, the pump was operated at a pressure of 70 bar which produced a volume flow rate from the central orifice comparable with that produced by the single-orifice nozzle; the total volume flow rate was 8.8 L/min. The nozzles were allowed to operate for five seconds to have a stable flow. The angles of the sprays for both of the nozzles were determined from the photographs of sprays, as illustrated in Fig. 5. The parameters of the spray, i.e. water flow rates, spray angles and spray heights of the experiment were used as input parameters in FDS model. In the experiment, the volume flow rates of the sprays produced by the nozzles were measured. The flow rate produced by the single-orifice nozzle was 1.7 L/min. In case of multi-orifice nozzle spray, the flow rates for the central and the azimuthal orifices, and for the whole nozzle were measured separately. The measured flow rates for multi-orifice nozzle from the central and azimuthal orifices and for the whole nozzle were 2.2, 1.1 and 8.79 L/min, respectively. The measured flow rate from the nozzle head was corroborated by means of the following correlation [11] –
(1)
Q =K P
where Q is the discharge rate of water and P is the operating pressure of water flow. According to the manufacturer data, the K-factor of the single-orifice and multi-orifice nozzles are 0.073 and 0.02 gam/psi1/2, which give flow rates of 1.69 and 8.74 L/min, respectively, produced by single and multi-orifice nozzles. This also validates the accuracy of the experimental measurement of water flow rates.
3. Numerical model 3.1. FDS model CFD simulations were run using “FDS (version 6)” and accompanying programme, “Smokeview (version 5.6)”, was used for the visualisation of the model. The basic conservation equations of mass, momentum and energy for a Newtonian fluid are presented as a set of partial differential equations and solved by the finite difference technique. In the following few sub-sections, the spray model in FDS is described briefly. Details of these models are given in FDS technical reference guide [12]. FDS takes a sample of spherical droplets to calculate the distribution pattern. The droplet size distribution is expressed in terms of its Cumulative Volume Fraction (CVF), which is represented by a combination of log-normal and Rosin–Rammler distributions [12].
⎧ [ln D ]2 DCVF Dm ⎪ 1 ⎪ (2π )− 2 (σD)−1e 2σ 2 dD (DCVF ≤Dm ) F (d)=⎨ 0 ⎪ ⎪ γ 1 − e−0.693 (DCVF / Dm ) (DCVF > Dm ) ⎩
∫
Fig. 1. Schematic of the single-orifice nozzle (after Tanner and Knasiak [11]).
( )
(2)
where D is the generic droplet diameter, Dm is the median droplet diameter. The median droplet diameter is a function of the sprinkler/nozzle orifice diameter, operating pressure, and geometry. γ and σ are empirical constants used for curve-fitting of distribution
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111
Fig. 2. Schematic view of the multi-orifice nozzle – (a) side view; (b) plan view (after Tanner and Knasiak [11]).
Re=
ρ vd − va 2r μ (T )
where
(6)
μ(T) is the dynamic viscosity of air at temperature T.
3.2. Domain set‐up
Fig. 3. Schematic view of the experimental set‐up.
patterns and they are equal to 2.4 and 0.6, respectively. In FDS, water droplet transport is modelled by a Lagrangian approach. The velocity and position of the droplets are calculated from the theory of conservation of momentum. The position and velocity of each droplet are calculated from the following equations.
d 1 ( mvp )=mg − ρCd πr 2 ( vp−va ) vp−va dt 2
(3)
dxp =vp dt
(4)
where, the drag coefficient, Cd , depends on the following function of the Reynolds number based on the droplet-air relative velocity.
⎧ 24/Re ⎪ Cd=⎨ 24 0.85 + 0.15 Re ⎪ ⎩ 0. 44
(
Re < 1 0.687
)
/Re
1 < Re < 1000 Re >1000
(5)
The Reynolds number of the droplets is defined by
3.2.1. Single-orifice nozzle spray A computational domain for the single-orifice nozzle spray was established that represents a region in space as shown in Fig. 6. The dimensions of the floor are 2 2 m and the vertical height of the domain is 2.4 m. In order to represent the laboratory set-up, one of the vertical boundaries is considered to be an impermeable solid wall. The three other vertical boundaries are considered to be open to flow, as is the upper horizontal boundary. The lower horizontal boundary is the floor on which the mass flux of water emanating from the nozzle impinges. The dots on this surface coincide with the centres of the 10 10 cm regions in which the fluxes were measured. The nozzle head was located at a height of 2.3 m above the floor. 3.2.2. Multi-orifice nozzle spray Two similar computational domain were established to simulate the sprays produced by the multi-orifice nozzle for the two cases – Case A and Case B, as shown in Figs. 7 and 8, respectively. In Case A, the centre of the water collection tray was beneath the nozzle and in Case B, one of the corner of the water collection tray was beneath the nozzle. In both cases, the dimensions of the horizontal floor are 6 6 m and the height of the domain is 2.1 m. To be consistent with the conditions associated with the experiment, one of the vertical boundaries that has dimension of 6 2.1 m is designated as being impermeable, whereas the other three and the horizontal roof are open. The multi-orifice nozzle was located at a height of 2.0 m from the floor. The lower horizontal boundary is the floor on which the mass flux of water emanating from the nozzle impinges. The dots on this surface coincide with the centres of the 10 10 cm regions in which the fluxes were measured. 3.2.3. Grid spacing A computational grid sensitivity analysis was carried out to ensure that the numerical results converged. The grid spacing was
Fig. 4. Locations of the nozzles (a) Case A; (b) Case B.
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Fig. 5. Measurement of angle of spray for single-orifice nozzle; (a) spray produced by single-orifice nozzle; (b) spray produced by multi-orifice nozzle.
manufacturer's data. The angles of sprays for single-orifice nozzle and for the central and peripheral orifices of multi-orifice nozzle were measured from the photographs of sprays, as reported in the previous section. The flow rate of each individual orifice and of the whole nozzle head were measured in the experiment. The velocity of the droplets was calculated from the simple geometrically based relationship between the flow rate and discharge area. The median size of the droplets for the single-orifice nozzle spray was calculated using the corellation between the pressure of water flow, diameter of discharge orifice and median diameter of droplet [13]. According to Fleming [13] the median diameter of droplets generated by a spray has been empirically found to be inversely proportional to the one-third power of water pressure and directly proportional to two-thirds the power of the orifice diameter, i.e.
dm∝
Fig. 6. Computational domain set‐up used to simulate the spray generated by a single-orifice nozzle.
20 cm, 10 cm, 5 cm and 2.5 cm in the x, y and z directions. In all of the simulations the input parameters and boundary conditions were unchanged. The only change was the grid size. The distributed flux density along the centre of the tray parallel to x axis for these four cell sizes were calculated and compared. The results are presented in Fig. 9. It was observed that the computed flux densities were almost identical when the grid sizes were 2.5 cm and 5.0 cm. Hence, in this work a grid size of 5.0 cm was used to discretise the computational domains.
D2/3 P1/3
where dm is the median droplet size, D is the orifice diameter and P is the flow pressure. The details of the procedure is explained in reference [14]. The median size of the droplets for the multi-orifice nozzle spray was taken from the experimental data provided by the manufacturer [11]. The details of the spray parameters for both of the single-orifice and multi-orifice nozzles are presented in Table 1. A Rosin–Rammler-lognormal distribution pattern was used for the distribution of drop sizes. The simulation was allowed to run for 65 seconds; the nozzle was activated at the beginning of the simulation and stopped at 60 seconds; the additional 5 seconds were to allow the water drops to fall down from the nozzle.
3.3. Modelling of sprays
4. Results and discussion
The spray from the single-orifice nozzle was modelled as entering the domain in downwards vertical direction; i.e. 0° azimuthal angle with the nozzle axis. The spray from the multi-orifice nozzle was modelled as a collection of sprays eminating from single nozzles by assigning each nozzle a different orientation and physical characteristics of the sprays. In case of the multi-orifice nozzle, the peripheral orifices were oriented so that they were separated by an azimuthal angle of 60°. The spray from the nozzle was described as a droplet inlet boundary condition.
4.1. Single-orifice nozzle spray
3.4. Input variables Once the computational domains were set-up, the input parameters for the computational measurements were incorporated into the models. The input variables to the model were the flow rate of water, angle of spray, height of spray, median size of droplet size and velocity of droplet. The parameters of the sprays were specified with the aid of the experimental measurements and
(7)
In the experiment, the distribution of flux densities of the spray were measured at a distance 2.3 m below of the nozzle. Input parameters used in the FDS model were obtained from the experimental measurements. These include flow rate of water, velocity of droplet, angle of sprays and height of spray. The numerical simulation was run and the distribution of flux density of the spray was calculated by the model. The flux density distribution of experiment and numerical simulations were calculated in L/m2/min and the contour maps are illustrated in Fig. 10 (a) and (b), respectively. The contour maps are drawn from ordinate 0.4–1.6 on both of the X- and Y-axes, as 90% of the water of the spray were found to be within this region. As expected, the flux density was highest at the centre of the floor, both in the experiment and in the numerical simulation and it decreased monotonically in the radial direction from the centre. The contour maps in Fig. 10 indicate that
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113
Fig. 7. Computational domain used to simulate the spray generated by a multi-orifice nozzle for Case A; (a) isometric view, (b) plan view.
Fig. 8. Computational domain used to simulate the spray generated by a multi-orifice nozzle for Case B; (a) isometric view, (b) plan view.
Table 1 Spray parameters for FDS simulation. Nozzle type
Single-orifice
Input variables Diameter, mm Orientation (azimuthal angle) Flow rate, L/min Spray angle Spray height, m Droplet velocity, m/s Droplet size, μm Spray pattern
Fig. 9. Grid convergence test for spray distribution.
there is discrepancy between the contour maps generated in the experiment and by the computer model. The contour map of the distribution produced by the experimental is elliptical in shape and it has translated 15 and 5 cm from the centre of the tray in the positive X and Y direction, respectively. It was hard to eliminate all non-idealised conditions (including the existence of solid wall mentioned earlier) for this a large scale laboratory experiment. Moreover, water-mists comprise small droplets. So, when they are allowed to fall for 2.3 m, due to even slight non-idealised condition, it can happen that the distribution is not actually circular in shape and concentred with the centre of the tray. The white
Multi-orifice Central
Peripheral
1.524 0° 1.7
1.524 0° 2.2
0.508 60° 1.1
65° 2.3 15.5
45° 2.0 18.8
15° 2.0 89.6
350 Solid
100 Solid
85 Solid
dashed line in the figures are the major and minor axes of the ellipses. The eccentricity of the ellipse for the distribution generated in the experiment is 0.70, whereas the eccentricity of that by the numerical model is 0.2. This indicates that the distribution of spray generated by the numerical model is almost circular. Other than the elliptical in shape of the maps, the predicted distribution pattern and intensity of flux densities of the numerical model is reasonably agreed with that of the experiment. The distribution of water volume flux along the axes of the ellipse and radii of the circle are illustrated in Fig. 11. In the experimental study, the distribution along the major and minor axes of the ellipse are not identical, whereas the simulation results along the centreline showed an almost identical distribution. However, both experimental and numerical data shows a bell shaped distribution patterns.
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Fig. 11. The distribution of flux density of sprays for single-orifice nozzle along the experimental values along the major centreline axes as indicated in Fig. 10; axis, experimental values along the minor axix, numerical values along radii of X direction, numericial values along radii of Y direction.
Fig. 10. Distributions of flux densities of spray produced by the single-orifice nozzle; (a) experimental; (b) numerical.
4.2. Multi-orifice nozzle spray The flux density distribution of the water spray was measured experimentally at a distance 2.0 m beneath the nozzle. The experiments were conducted for two cases; Case A and Case B. In Case A, the position of the nozzle was above the centre of the water collection tray and in Case B, the position of the nozzle was above on one of the corners of the water collection tray. The flux density distributions obtained in the experiment and numerical simulation are displayed as contour plots for Case A and the results are given in Fig. 12 (a) and (b), respectively. The experimental results indicate that the distribution is ellipsoidal and the flux decreases with distance from the centre. The position of highest volume flux is displaced 20 cm from the centre of the tray in both the X and Y directions. A possible reason is that the spray is affected by the wall in the vicinity of the spray. A hint of this artefact is provided in the numerical results that also produced an elliptical flux distribution that is displaced towards the wall. In the numerical case, it is displaced by about 10 cm. The eccentricity of the ellipse for the experimentally obtained distribution is 0.74,
whereas it is 0.58 for the numerically obtained distribution of spray. This confirms that the distribution generated experimentally is more ellipsoidal than that generated by the numerical model. The water fluxes along the major and minor axes of the numerically and experimentally obtained distributions are shown in Fig. 13. The centre of the ellipse of Fig. 12(a) is superimposed on the centre of the ellipse of Fig. 12(b) and corresponding values of the distribution of flux densities are compared. The figures show that the numerical model has under-predicted the distribution of volume flux around the periphery of the ellipse except within the region of 0.0–0.3 m of the tray along the major axis. However, it has predicted the distribution near the centre of the ellipse of the spray with an accuracy greater than 90%, which provides some validation of the model. The distributions are approximately bell shaped in both cases and, the numerical and experimental measurements are generally in good agreement. The distribution of flux densities in the experiment and numerical simulation for case B is shown in Fig. 14(a) and (b), respectively. The maximum flux densities of the sprays for the peripheral orifices are at locations (0.9, 0.4) and (0.9, 0.2) for the experimental and numerical distributions, respectively. The distributions generated by the sprays are elliptical for both experimentaly and numerically generated sprays. The lateral contour axis is depicted by a line connecting the centres of the ellipses of distributions of sprays produced by the central and peripheral orifices. The distances of the centres of ellipses from the corner of the water collection tray along the lateral contour axis for the experimentally and numerically obtaied distribution on the floor is 186 and 200 cm, respectively. The white colour in both of the figures is due to the reason that the flux densities in that region was out of scale (more than 1.05 L/m2/min). The eccenticities of the experimentally and numerically obtained distributions are 0.72 and 0.16, respectively. This signifies that the numerical model has predicted a more circular flux distribution compared to that of the experiment. The peripheral orifices in the body of the nozzle are oriented at an angle of 60° to each other. Therefore, it is expected that the angle separating the peripheral centre (topological) should also be 60°. This expectation is met by the numerical model in simulating the direction of spray produced by the individual orifices. In Case B, one of the lateral contour axes was directed along an edge of the water collection tray and another one along a line at an angle of 60° to the edge as indicated in Fig. 14. In the contour plot of distribution produced by the orifice
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Fig. 12. Distribution of flux density of spray for multi-orifice nozzle for Case A; (a) experimental, (b) numerical.
Fig. 13. The distribution of flux densities of spray for multi-orifice nozzle along the major and minor axes of ellipses for Case A; experimental values along the major axis, experimental values along the minor axix, numerical values along radii of X direction, numerical values along radii of Y direction.
115
Fig. 14. Distribution of flux density generated by a multi-orifice nozzle for Case B; (a) experimental, (b) numerical.
whose axis was directed along an edge of the water collection tray, the half of the ellipse produced by distribution was captured on the water collection tray in the numerical model (Fig. 14(b)); however, no such pattern was observed in the experimentally produced distribution (Fig. 14(a)). A possible reason is that there was as wall 2 m away from the edge of the water collection tray and one of the orifices was directed to the wall. The droplet was injected from the nozzle with a high-speed and it was spread in the room. As a result, it created turbulence in the space of the room. The turbulance created by the spray was affected by the presence of the wall. Moreover, as the droplet size is very small and light in weight, it was suspended surrounding the spray and scattered from its spray path due to the presence of the wall. As a result, no elliptical shape of spray was created by the experiment. The distribution of water fluxes along the lateral axis of contour is illustrated in Fig. 15. It can be seen that the numerical model has over-predicted the distribution near the centre of the ellipse of the spray for both central and peripheral orifices, and under-predicted it around the periphery of the ellipse of the spray for both central
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Table 2 Statistical analysis of standard uncertainty of the experimental data. Nozzle type
Single-orifice
Experimental uncertainty L/m2/min
0.103
Multi-orifice Central
Peripheral
0.169
0.055
Table 3 Statistical analysis of congruence between the measured and calculated distribution of flux densities. Nozzle type
Single-orifice
Multi-orifice Central
Fig. 15. The distribution of flux density of spray for multi-orifice nozzle along the lateral axis of contour for case B.
and peripheral orifices. However, the peak-to-peak differences between the numerical and experimental values for the spray of the central and peripheral orifices are not more than 20%, which indicates the capability of FDS in predicting the distribution of flux density of spray (when away from the wall effect).
5. Statistical analysis 5.1. Experimental uncertainities In physical experiments, assessment of uncertainties deals with evaluating the uncertainty in observation or measurements. An experiment designed to determine a value of a physical variable will be affected by errors due to the experimental procedure, instrumentation, the presence of confounding effects, etc [15]. Therefore, estimation of experimental uncertainty would help to evaluate the confidence in the results. In this section, a statistical analysis has been conducted to quantify the uncertainity of measurements based on the least squares method [16]. Usually, the standard uncertainty, u (xi ), is estimated from the following equations,
⎡ 1 u ( xi )=⎢ ⎢⎣ n (n − 1)
n
⎤1/2
∑ (Xi, k − X¯ i )2⎥ k=1
⎥⎦
(8)
where,
1 xi =X¯ i = n
n
∑ X i, k k=1
(9)
Here, Xi is input quantities which is estimated from n number of independent observations Xi, k of Xi obtained under the same conditions of measurement. If the measured value of any parameter is y, then it can vary with an interval of y ± u (xi ) . The standard uncertainty, u (xi ), of measurements of the distribution of flux densities has been estimated for the sprays produced by the single and multi-orifice nozzles using Eq. (9). The average experimental uncertainty of measurements for the spray produced by the single-orifice nozzle is 0.103 L/m2/min, and for the sprays produced by the central and peripheral orifice of the multi-orifice nozzle are 0.169 and 0.055 L/m2/min, respectively. Therefore, the values of this uncertainty imply that the measured data of the experiments may vary at an amount of less or more of that of the corresponding level of uncertainty. The values of the standard uncertainty of the experimental measurements are presented in Table 2.
Peripheral
Input variables
Exp
Num
Exp
Num
Exp
Num
Uniformity coefficient
0.73
0.96
1.45
1.23
1.02
0.87
5.2. Uniformity coefficient In this section, a quantative statistical analysis has been conducted to identify the uniformity of distribution of flux densities produced by the sprays on the horizontal surface. A uniformity coefficient (b) has been calculated based on the maximum likelihood function. Usually, the uniformity coefficient is used to quantify the resemblance between the measured and calculated distribution of flux densities produced by sprays. The implicit equation for the uniformity coefficient for a set of indepemdent observations, x , is defined as, n
b=
∑i = 1 xib n
(
n
∑i = 1 xib lnxi − ∑i = 1 xib
)(
1 n
n
∑i = 1 ( ln xi )
)
(10)
where n is the number of values in the data set, xi the known data, and it can be calculated from the following equation,
xi =
V˙i′′ max V˙i′′
(11)
where V˙i′′ are the predicted or measured distribution of flux densities for each point of data collection. The value of uniformity coefficient (b) indicates the homogeneity of distribution of flux densities. When the uniformity coefficient (b) is greater than 1, it implies to more uniformity of the distribution. On the other hand, if ‘b’ is less than 1, it indicates to less uniformity of the distribution. The uniformity coefficient for the distribution of sprays produced in the experiment and numerical simulation for both of the single and multi-orifice nozzles are calculated and presented in Table 3.
6. Conclusions Water-mists have the ability to suppress fires, and their efficacy can be explored using computer software packages such as FDS. However, it is essential that the software accurately predicts the behaviour of the mists produced by spray nozzles. In this work, we have assessed the ability of FDS in simulating the distribution of flux densities of sprays that govern the prediction of the behaviour of spray nozzles. It has been found that the distribution of the sprays produced in the experiment and numerical model for both the single and multi-orifice are elliptical in shape.However, the eccenticity of the ellipses for the distribution is less pronounced in the numerical model for both of the single and multi-orifice
H.M.I. Mahmud et al. / Fire Safety Journal 81 (2016) 109–117
nozzle. In overall, the results obtained using FDS are in close agreement with the experimentally determined distributions of flux densities produced by spray nozzles. In this work, it appears that the presence of a solid wall in the vicinity of the spray influenced the distribution. The experimental and numerical results obtained in this study indicate that the flux distribution was closer to the wall than would otherwise be the case. However, the effect of the boundary wall on the distribution of the spray in the numerical model was pronounced less compared to that of the experimental results. Therefore, a further study would be helpful to quentify the influence of wall on a spray and its effect on the distribution of flux densities produced by the spray.
Acknowledgements The authors wish to acknowledge technical and financial assistance provided by the Defence Science and Technology Organisation (DSTO), Australia. The authors also wish to acknowledge technical support provided by postgraduate students, Mr. Sk Md Kamal Uddin and Mr. Md Mahfuz Sarwar.
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