Critical Conditions for Water-based Suppression of Plastic Pool Fires. H. Li 1, A. S. Rangwala 1 and J.L. Torero 2

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1 Paper # 070FR-0069 Topic: Fire 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Critical Conditions for Water-based Suppression of Plastic Pool Fires H. Li 1, A. S. Rangala 1 and J.L. Torero 2 1 Department of Fire Protection Engineering, Worcester Polytechnic Institute, Worcester, MA 2 University of Queensland, Australia Abstract The study analyzes the critical extinction criteria for a condensed phase pool fire ith ater as suppressing agent. A polymethyl methacrylate (PMMA) rod surrounded by a circular cavity filled ith ater is used to simulate a pool fire. Experiments are conducted ith varying circular cavity idths and PMMA rod diameters. The PMMA rod is ignited and the impact of the surrounding ater on its burning behavior is analyzed. Key parameter influencing the problem is the diameter of the rod. Interesting changes to the geometry and the burning behavior of the PMMA rod are observed. The behavior is remarkably different from earlier studies on pool fires ith solid fuels [1]. The study has found that for small (~2 cm) diameter PMMA rods, the regression rate slos don due to the presence of ater and ultimately the flame extinguishes due to the geometry change. For larger diameter (>~4 cm) PMMA rods, once again the regression rate is decreased. Hoever, in all cases, the flame continues to burn for a longer time due to change in geometry before extinguishes. Phases of burning are classified according to the changing PMMA rod geometry. In each phase, heat transfer beteen the flame and PMMA pool surface is estimated and likely reasons for the observed burning behavior are examined. It is found that heat transfer has forced a geometry hich led to the extinction. Key ords: critical extinction, mass loss rate, ater suppression. 1. Introduction The critical extinction conditions of pool fire of solid material ere studied in several aspects including critical mass pyrolysis rate and critical B-number [2]. Heat transfer models ere built regarding the large scale of luminous radiation [3]. In this study, extinction caused by geometry change is studied. Heat transfer model for small scale (2 ~ 4 cm) is built ith consideration of luminous flame radiation, convection, and conduction to surrounding ater. The heat transfer model compared the importance of different heat transfer modes in terms of forcing the geometry change, and it also verified the experiment results. Based on the results, future study can be focused on the channel idth, PMMA rod height, discussion of critical B-number. 2. Methods 2.1 Experiment setup and procedure A PMMA rod ith ater filled in circular cavity (channel) is used for each experiment. The top and side vies of the container are shon belo (Figure 1). PMMAs are machined using CNC mill to the folloing specifications: 1. The height difference of center PMMA rod to side alls of cavity is 6 mm. This ill allo the fire to spread uniformly before it reaches the ater. 2. Channel depth is 10mm. Height of ater equals to the channel depth. This ill allo enough ater to extinguish the fire gradually ith consideration to the evaporation of ater. 3. Central rod diameter, d, and channel idth,, are variables of this set of experiments. 4. Table 1 belo provides the different scales of channel idth,, corresponding to different center rod diameter, d, that are used.

2 Figure 1. Dimensions of containers Table 1. Center rod diameter and channel idth for PMMAs used (unit: mm) d The schematic side vie of the experiment setup is shon in Figure 2. The PMMA is placed on top of calibrated a Symmetry PR-4200 Load Cell. The data acquisition softare Terminal v1.9b is used to acquire the mass over time measured by the load cell during the experiment. Every to seconds, a picture focusing the interface here the bottom of flame and ater interacts is taken by Canon EOS 5D DSLR camera (C 1 ) controlled by a remote ith Canon EF 100mm f/2.8 Macro USM Macro lens. A video camera (C 2 ) is mounted at the same height as the top surface of load cell to record the flame behavior. Such documentation is made for the study the flame diameter, classification of burning phases, and detailed future study. Center PMMA rod is then ignited. All measurements start at the ignition and end at extinguishment. Figure 2. Side vie of schematic of experimental setup Data of mass change over time can be easily converted to mass loss over time. Average mass loss rate can be calculated using total mass loss divided by total time elapsed from the ignition to extinguishment. A polynomial trend line of order 12 is fitted to mass loss data using Matlab and the normal of residue is very small, hich implies a good fitting. Such high order fitting gives accurate trend for the first 400 seconds of the mass loss curve, hich is good for the study of peak mass loss rate. By obtaining the differentiated function of the trend line function, mass loss rate ith respect to time can be obtained. The mass loss rate data for phase I and phase II are used in the heat transfer model in next section. Peak mass loss rate is obtained at the global maxima of differentiated function. 2

3 Due to the special interest of the extinguishment, another polynomial fitting of order three is conducted on mass loss data of phase II and phase III (after 60 seconds of mass loss curve, hich ill be introduced in the results section) to reduce the error introduced by forcing the polynomial fitting as ell as the noise caused by ignition. First 327 data points of mass loss data (60 seconds, Phase I) are cut off, and the differentiated function of the fitted polynomial is obtained to obtain the mass loss rate at phase III, and at extinguishment. For each center PMMA diameter value, d, a free burn ithout ater in cavity is conducted, and the mass loss is best fitted by linear fitting Heat transfer model A heat transfer model is developed as part of this study. The model assumes a circular a pool of PMMA ith diameter of d surrounded by a ater channel of idth.physical and thermodynamic properties needed for the model are listed in Table 2 and Table 3. Table 2. Nomenclature and values used in heat transfer model Name Symbol Value L effective heat of gasification of PMMA effective heat of gasification of ater specific heat of air mass yield of oxygen per mass of fuel lost to vaporization Heat of combustion per mass of oxygen thermal conductivity of air at T p J/kg L C 3 g J/kg J/(kg K) y ox H J/kg air ox k W/(m K) Prandlt number Pr 1 gravitational acceleration g 9.81 m/s 2 kinematic viscosity of air at 20 C v m 2 /s Stefan-Boltzman constant W/(m 2 K 4 ) temperature of vaporization of PMMA (also surface temperature) T 380 C Euler's number e e emissivity of PMMA surface ε 0.9 thermal conductivity of PMMA k p 0.2 W/(m K) thermal conductivity of ater at 20 C k W/(m K) Table 3. Nomenclature and assumed values used in heat transfer model Name Symbol Value flame temperature environment temperature ater temperature environment temperature radiation fraction of oxygen T f v 1500 K T 20 C T 70 ~ 90 C for d = 20 mm; 50 ~ 70 C for d = 40 mm;, linearly decrease as channel idth increase T 20 C X 0.1 r effective emission coefficient [3] K 2.2 m -1 for d = 20 mm; 2.1 m -1 for d = 40 mm flame diameter D phase I: D = d; phase II: D = 2d/3 (assumed); phase III: D = d/3 (measured) The heat transfer model estimates the mass loss rate of PMMA using an energy balance on to control volumes shon in Figure 2. 3

4 For the control volume of PMMA pool surface: Mass loss rate per unit PMMA top surface area: m q net ; (1) L p The net heat flux gain per unit PMMA top surface area: q q q q ; (2) Net convection heat flux to PMMA pool: q net f c f, r s, r c,, h q f, c [ yox H ox (1 xr ) Cg ( T Tv )] (3) C g here h, heat transfer coefficient for laminar, natural convection at a hot horizontal plate facing up [5], is given by: Nu kair h (4) D here Nu is Nusselt number, and is expressed by: 1/ 4 Nu 0.54 ( Gr Pr) ; (5) Gr is Grashof hich is given by: Gr g D 3 ( T v 2 f T here is the coefficient of volume expansion, and is equal to: 1 T f T v ) ; (7) The radiation heat flux from the flame to PMMA rod surface is: KD 4 ( 1 e T q (8) here, q f, rtop q f, r ) f, f, r, top is the radiation heat flux from flame to ater surface ith respect to PMMA top surface area, hich is converted from the radiation heat flux from flame to ater surface ith respect to ater surface area: The calculation of q, f, r, A ater q f r top q,,,, f r ; (9) Atop is discussed later in Equation (18) to Equation (21), and the area of PMMA rod top surface is: 2 D A top ; (10) 4 The radiation heat flux leaves by PMMA pool is: 4 q T ; (11) s, r v The conduction heat flux from PMMA rod to ater has the area of the side of rod, hich is different from the rod top surface area used in previous heat flux calculations. Thus the heat flux is converted to the rod top surface area: T T A v v side q cd, k ; (12) l Atop For all burning phases, the conduction from the point at the edge of flame to the center point of ater is studied. k is the conductivity of the material beteen the to points ith environment temperature. On phase I, the material is solely ater; on phase II and III, the materials are PMMA and ater. l is the distance beteen the to points. For phase I, the distance is half of the channel idth. For phase II and III, the distance is hatever the distance from the edge of flame to edge of PMMA rod plus half of the channel idth. When to different media is present, heat flux is obtained by using resistance analogy ith negligible contact resistance. (6) 4

5 With the equations above, the calculated PMMA mass loss rate per unit PMMA top surface area is given by: ( q f, c q f, r q s, r q cd, ) m cal, p ; (13) L p And the calculated PMMA mass loss rate is: m m A ; (14) cal p, cal, p top For the control volume of ater surface, the convection from PMMA surface to ater is negligible since the ater has no flo and conduction is dominant, and the radiation from PMMA surface to ater is also neglected since the total radiation from PMMA pool is very small and the vie factor is also very small. Mass loss rate of ater per unit area of ater surface: The net heat flux to the ater: m q, net ; (15) L, ; (16) q net q, f, c q, f, r q, cd The convection heat flux from flame to ater surface: q h ( T T ) (17), f, c 2 f here h 2 is the heat transfer coefficient for external flo of Vertical cylinders and is given by: 1/ 3 h ( Gr Pr) ; (18) D 35 In the equation above, the correlation of h 2 for vertical parallel planes is used, because Gr , and 1/ 4, L Gr here L is the is the characteristic length ith respect to the direction of gravity [5]. The radiation heat flux from flame to ater surface is: KD 4 q A F 1 e T (19), f, r f f ( ) f here A f is the surface area of flame and F f is the vie factor from flame to ater surface. According to Reciprocity Relation, A F A F (20) f f f ater here A ater is the surface area of ater and is given by: 2 2 [( D 2) D ] A ater ; (21) 4 F f is given by simplifying the ater surface as a ring around the base of hemispherical flame. The value of F f is given by Hoell [6] as 1 D 2 2 1/ 2 F f { [( ) 1] D D [( ) 1] D D D 2 ( ) tan ( ) 2 tan ([( ) D D 2 2 1/ 2 [( ) 1] D D f 2 1] 1/ 2 )} ; (22) 5

6 The conduction from PMMA surface to ater per ater surface area is: So the mass loss rate of ater per unit area of ater surface is: And mass loss rate of ater: Calculated total mass loss rate: m cal, A top q cd q, cd, ; (23) Aater ( q, f, c q, f, r q, cd L ) ; (24) m A ; (25) cal m, cal, ater m cal tol m, cal, p m cal, ; (26) The calculated total mass loss rate is then compared to the experimented total mass loss rate. 3. Results and Discussion 4.1 Burning phases By observing the burning, the burning of PMMA pool is classified into three to four different phases based on behavior of the flame and geometry changes of the fuel. Illustrative sketches for classification ith sample photos of each phase are shon in Figure 3 and Figure. Figure 3. Burning phases for d = 20 mm PMMA pool Figure 3 shos the classified burning phases for 20 mm diameter PMMA rod. Before burning, the center PMMA cylindrical in shape. Within approximately 60 seconds after ignition, the PMMA rod s top edge is rounded and eventually become a dome on the top part of the PMMA, such process is classified as Phase I. As the fire propagates don along the PMMA, the bottom of the flame reaches about 1 2 mm higher than ater level. Figure shos an illustrative photo taken using DSLR and Macro lens, here the bottom of flame is about 1 2 mm above the ater surface. In Phase II, the fire stops propagating don and rather, the radius of the dome and thus the radius of flame shrink to form a smaller dome until approximately 360 seconds. In Phase III, the flame radius further shrinks and the in the center a small cavity is formed. At the end of Phase III, the fire is extinguished by itself in approximately seconds. 6

7 Figure 4. Flame - ater interface Figure 5. Burning phases for d = 40 mm PMMA pool The burning phases for 40 mm diameter PMMA pool share the same first three stages as the 20 mm diameter PMMA pool ith different time stamp, (phase II starts from 85 seconds to 355 seconds). But the fire ill not extinguish after Phase III, hich ends approximately at 450 seconds. A smaller dome ill be formed inside the center PMMA rod, and the flame keep burns don until the small dome burns out, hen a bottom hemisphere shape cavity (similar to phase III) is formed at here the small dome as. At that point, hich is at more than 1500 seconds, the flame is extinguished by itself. The geometry before extinction, hich is a hemispherical cavity around the flame, prevents enough oxygen from floing in. Lack of oxygen led to the extinction of the fire. Even though the pool ith diameter of 4 cm or larger has to more phases of creating a smaller dome and another cavity, the cause is the same. 4.2 Mass loss over time Plots of mass loss over time for all experiment cases are shon in Figure and Figure. The dot at the end of a curve denotes a self-extinguishing case; the arro at the end of each curve denotess that the burning keeps going on, since the burning of 40 mm diameter rod after 500 ~ 600 seconds is not logged. 7

8 Figure 6. Mass loss over time for d = 20 mm PMMA pool (unit of : mm) Figure 7. Mass loss over time for d = 40 mm PMMA pool (unit of : mm) As shon in the to figures above, the mass loss for phase I rises more rapidly than phase III and phase IV (for d = 40 mm PMMA pool). The mass loss of free burn differs significantly from the mass loss for cases ith ater surrounded. The slope of the mass loss curve, hich is the mass loss rate, is smaller hen the burning close to its end. Free burn has a linear plot of mass loss over time, and has a higher mass loss rate than that of burning ith ater, and detailed comparison of mass loss rate is shon in next section. 4.3 Mass loss rate Table 4 belo lists the time and mass loss rate (MLR) at extinguishment, average MLR, time at and peak value hen peak MLR occurs, and error. The error is equal to the difference beteen average mass loss rate and the mean value of 8

9 the mass loss rate at each data point, and is to verify the fitting besides using the normal of residue. Figure and Figure sho the MLR comparison for all cases in graph. Table 4. Mass loss rate (MLR) comparison and error d [mm] [mm] d extinguish time [s] Extinguish MLR [mg/s] peak MLR time [s] peak MLR [mg/s] average MLR [mg/s] Error [mg/s] 20 free burn N/A N/A E E E E E E-2 40 free burn N/A E E N/A E E E-2 Figure 8. MLR ith respect to for d = 20 mm Figure 9. MLR ith respect to for d = 40 mm 9

10 It is shon in the table and figures that: 1) The average MLRs of all cases ith ater ithin a diameter set are close to each other, and are all significantly loer than the average MLR of free burn. 2) The time hen the MLR reaches its peak is ranging from approximately seconds for d = 20 mm PMMA pool, and for d = 40 PMMA pool, hich is around the end of phase I to the beginning of phase II. 3) The peak MLRs of all cases ith ater ithin a diameter set are close to each other, and are all loer but close to the peak MLR of free burn. 4) The time of extinguishment is around seconds for d = 20 mm PMMA pool for all cases that are applicable. For d = 40 mm PMMA pool, the mass loss and extinction after phase IV (around 500 seconds) are not measured. 5) The error is very small (1 or 2 magnitude) compare to the average MLR. 6) For d = 20 mm, = 5 mm, the extinguish MLR is significantly loer than other cases. For d = 40 mm, = 10 mm, the average MLR is significantly higher than other cases. Those to values need to be verified by carrying out repeated experiments. 3.4 Heat transfer model The results of applying the modified heat transfer model are shon in Table For each case, the heat flux on PMMA surface control volume is discussed, and the calculated total mass loss rate is compared to the experimental mass loss rate. The error shos the percentage of the difference in mass loss rate to the experimented value. As shon in the error column, more than half cases the model fits in the experiment ell. For rod diameter = 20 mm, small channel idth cases tend not to fit ell. For d = 40 mm, large idth cases tend not to fit ell. The cases here the heat transfer model doesn t fit are marked in bold (and red). Hoever, it can be clearly seen that convection is dominant over radiation in heat flux to the PMMA surface, as suggested by de Ris [3]. For phase I, especially for smaller channel idth cases, thermal conduction from PMMA to ater is more dominant, hich is physically correct because as the flame diameter is relatively large in phase I, and it is closer to ater and has better conductivity. Such high heat flux of conduction prevents the PMMA that closely above the ater surface from being gasified by the heat of flame, and thus forced the burning to go to phase II. 10

11 Table 5. Heat transfer of PMMA and mass loss error 3.5 Error of experiment As discussed in previous sections, the error of mass loss rate calculation, and the error of heat model is ithin the acceptable range. The repeatability of experiment is discussed by doing repeated tests. Table 6. Mass Loss Rate (MLR) Repeatability Test on d = 20 mm, = 12 mm PMMA Extinguish MLR [mg/s] peak MLR [mg/s] average MLR [mg/s] experiment experiment experiment σ σ/average [%] Three experiment of the same PMMA (d = 20 mm, = 12 mm) under same experiment condition has been done. The experiment data is shon above in Table. Standard deviations, σ, of three series of data, mass loss rate (MLR) at extinguishment, peak MLR, and average MLR are calculated. The percentage of standard deviation to the average of 11

12 three experiments is also shon. The relatively high percentage, <~ 10%, could come from polynomial fitting, besides the actual experiment error. 4. Conclusions 1) When a small scale condensed phase polymer pool fire is surrounded by ater, the fire ill be extinguished due to the change in geometry, rather than due to the quenching of ater. 2) The geometry change is dependent to some extent on: a. Material properties. Different fuel ill have different parameters (k, T v, L, ox, etc.) in the heat transfer model hich ill leads to different phase change time and geometry; b. Pool diameter. Different pool diameter has different geometry change, as shon in the experiments here 2 cm rod and 4 cm rod have very different phase change. c. Height of PMMA rod above ater surface. This height ill affect the geometry shape and the time hen phase I ends. More different height can be experimented for future study. d. Channel idth. No obvious dependency of geometry change on the channel idth is shon. Hoever, future experiments can be conducted on more detailed analysis of burning and phase change ith respect to channel idth. 3) The pool ith diameter of 2 cm and diameter of 4 cm extinguishes due to the same reason. The geometry change is forced by the heat loss to ater, especially by thermal conduction. Such geometry caused the extinction due to the lack of oxygen. 4) The results of extinction sho that the extinction of polymers is related to the coupling beteen pool surface and the surrounding boundary. The ater prevents the fire to propagate don and forced a geometry change in fuel pool, hich ultimately leads to the extinction. Acknoledgements Thanks for the kind help in machining PMMA rods provided by Neil Whitehouse, Lab Machinist of WPI. Thanks for the kind help in machining PMMA rods provided by Kevin Arruda, Lab Machinist of WPI. References H 1. Kanury, A. Murty. Modeling of pool fires ith a variety of polymers. Symposium (International) on Combustion, Volume 15, Issue 1, 1975, Pages , ISSN , /S (75) ( 2. Delichatsios, Michael and Delichatsios, Mary. Critical Mass Pyrolysis Rates for Extinction of Fires over Solid Materials. 3. de Ris, J.N. Fire radiation a revie.proceedings of the Combustion Institute, Volume 17, 1979, Pages Quintiere, James. Fundamentals of fire Phenomena. chichester: John Wiley & Sons, Ltd, Print. 5. Drysdale, Dougal. Introduction to Fire Dynamics. 3rd ed. Chichester: John Wiley & Sons, Ltd, Print. 6. Hoell, John. C-57: Ring around base of hemisphere to hemisphere. A Catalog of Radiation Heat Transfer Configuration Factors. Web. 9 Mar < 12