Journal of Mechanical Science and Technology 26 (7) (2012) 2129~2132 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-012-0529-x
Estimation of pyrolysis-related properties using repulsive particle swarm optimization† Won-Hee Park1,*, Kyung-Beom Yoon2, Hee-Chul Chang3 and Tae-Kuk Kim2 1
Eco-Tramsport Systems Research Division, Korea Railroad Research Institute, Gyeonggi-do 437-757, Korea 2 Department of Mechanical Engineering, Chung-Ang University, Seoul, 156-756, Korea 3 Delta ES Co., Bucheonsi, Gyeonggido, 420-020, Korea (Manuscript Received February 22, 2012; Revised March 16, 2012; Accepted April 10, 2012)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract The pyrolysis-related properties of the specimen are obtained by optimizing the repulsive particle swarm optimization technique. Eight pyrolysis-related properties were obtained: virgin thermal conductivity, char thermal conductivity, virgin specific heat, char specific heat, char density, heat of pyrolysis, pre-exponential factor, and activation energy. The surface temperature and the mass loss rate obtained using the optimized properties were consistent with the measured values. In assuming that the properties obtained are physically valid, and that the surface temperature and mass loss rate measured in the experiment are correct, a valid fire phenomenon may be considered for replication if fire analysis is conducted using the properties obtained from the procedures proposed in this study. Keywords: Repulsive particle swarm optimization; Pyrolysis; Fire ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction
2. Tests
The modeling technique can be used to provide the evidence required during the product development stage or by the building code or other regulations. This technique can also reduce the time required for the test as an effective alternative to very expensive full-scale tests. However, techniques in computational fluid dynamics (CFD) can also be used for the precise prediction of fire growth in case fire in the laboratory is not easy to reproduce. The absence of solid fuel properties, as required by the numerical pyrolysis model of CFD, is one of the biggest interference factors restricting the use of fire growth modeling based on CFD. Recently, pyrolysis-related material properties have been obtained using the Genetic Algorithm (GA) optimization technique [1] and its variation [2]. Park et al. [3] compared the performance of repulsive particle swarm optimization (RPSO) and GA by obtaining the pyrolysis-related properties for virtual materials. In the present study, RPSO was used to obtain the eight pyrolysis-related properties using the measured surface temperatures and the pyrolysis mass loss rate of the wood specimen that was subjected to a certain heat flux.
The cone calorimeter was used to estimate the pyrolysisrelated properties. The cone calorimeter test was standardized in ISO 5660 [4]. The mass loss rate and surface temperatures of the specimen were measured as the combustibility of the specimen. Heat must be applied evenly on all parts of the surface of the specimen to cancel out the spatial effects; conductive heat transfer on the specimen is expressed in onedimension in the cone calorimeter. Common specimen holders are made of steel, thus, “edge effects” occur in three dimensions [5]. Accordingly, the shortcomings of the existing steel holder were dealt with in the present work by utilizing ceramic fiberboards (12.5 mm thick) and ceramic blankets. The specimen was enclosed sufficiently within five layers of ceramic fiberboards wherein the middle parts were cut out into 100 mm x 100 mm squares. Nonflammable materials, such as steel wire or pin, were applied to the four corners to prevent the ceramic holders in the layers from shaking. Flexible ceramic blankets, such as textiles, were inserted into the cutout area of the fiberboards up to the height required to have the specimen positioned horizontally in an even line with the surface of the topmost ceramic fiberboard. After placing the specimen holder on the load cell, the k-type thermocouple was fixed on the center of the specimen to measure surface temperature. Since the specimen is wood (charring material), the thermocouple must be fixed, considering that the subject of
*
Corresponding author. Tel.: +82 31 460 5358, Fax.: +82 31 460 5279 E-mail address:
[email protected] † This paper was presented at the ICMR2011, Busan, Korea, November 2011. Recommended by Guest Editor Dong-Ho Bae © KSME & Springer 2012
2130
W.-H. Park et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2129~2132
specimen, and went up to about 22 g/m2s. The mass loss rate reached its maximum value around the ignition time.
3. Energy analysis
Fig. 1. Thermocouple on the surface temperature measurement.
the test may be cracked or deformed by heat while being set on fire and while pyrolysis is still in progress. Various ways in attaching the thermocouple to the surface of the specimen were attempted for measuring surface temperature. Among the various ways was the boring of a backside hole on the surface to insert the thermocouple and to fill the remaining space with high thermal conductive adhesive. These tests were difficult to perform because the specimen cracks or deforms during the experiment. The final and acceptable method used in this study to measure surface temperature is shown in Fig. 1. Surface temperature was measured by enabling the thermocouple to move along the surfaces, even if the wood specimen could be deformed after attaching the bead of the thermocouple to its surface. The mass of the thermocouple was excluded in the consideration of mass loss rates. The test was performed on a 21 mm thick Douglas fir (antisepsis wood) specimen, and the heat fluxes from the cone heater into the specimen were set at 50 and 70 kW/m2. The environmental temperature during the test was 25.7°C, and moisture was maintained evenly at 30% RH. The density of the virgin specimen prior to pyrolysis was 239 kg/m3. The combustibility of the specimen was measured based on the surface temperature and mass loss rate. The surface temperature was confirmed to have increased over time and at a higher rate at the ignition time. The specimen was ignited in 661 seconds and 15 seconds at 50 and 70 kW/m2 heat fluxes, respectively. At 50 kW/m2, the temperature escalated to about 600°C prior to ignition, but went up sharply to about 800°C after ignition. At 70 kW/m2, the graph (Fig. 2) could not confirm that the temperature jumped up after around 660 seconds, as in the case of 50 kW/m2, since the ignition occurred about 15 seconds after the heat flux of the specimen. The temperature went up sharply at 70 kW/m2 of up to 50 seconds, but gradually increased to about 840°C after 100 seconds. Two mass loss rates of the measured heat fluxes were observed in Fig. 3, which implied that the variations of the temperature were comparatively lower but those of the mass loss rate were higher. When the fluxes inserted were at 50 kW/m2, the mass loss rate grew sharply to 7.8 g/m2s at around 670 seconds after ignition and then decreased. At 70 kW/m2, ignition occurred immediately at around 15 seconds after the heat flux in the
Pyrolysis begins to occur on the surface of the charring materials that are heated from the external parts, gradually moving into the internal parts. The material remaining on the affected surfaces is charred during pyrolysis, and the materials remaining on the unaffected surfaces are virgin. Both materials have different values for density, specific heat, and thermal conductivity. The governing equation of this one-dimensional pyrolysis model is as follows [1]:
ρc
∂T ∂ ⎛ ∂T = ⎜k ∂t ∂z ⎝ ∂z
⎞ * ⎟ − m′′′(ΔH p − ΔH p ) ⎠
(1)
where ρ denotes density, c is the specific heat, t is the time, T stands for temperature, k represents thermal conductivity, m ′′′ denotes mass consumption rate per m3, ΔH p is the heat of pyrolysis, and ΔH *p is the revised heat of pyrolysis. If pyrolysis occurs on the surfaces of the affected specimen and with the affected surfaces as reference, the upper volume close to the external heat source classified as char domain is already affected. However, the lower volume that is classified as virgin domain remains unaffected. Density, thermal conductivity, and specific heat have different values in the virgin and char domains, and they are expressed in subscript as v and c, respectively. More details on the singledimensional pyrolysis analysis are given in Ref. [3].
4. RPSO Kennedy and Eberhart developed the particle swarm optimization (PSO) algorithm [6] based on the ideas of the regularity proof of the social behavior patterns of living body groups such as flocks of birds, schools of fish, and others. The PSO algorithm shows better performance in providing solution to the problem (convergence of solution, calculating time, among others), but has a very wide searching area. This could pose as a disadvantage because finding the optimum value for the entire area can be difficult since the particle swarms may converge into the optimum value if the PSO algorithm is applied to optimization matters with complicated optimum values [7]. The RPSO algorithm was improved to supplement such demerit using the optimum location of particles selected at random instead of the optimum position of the entire swarm in the speed formula of the PSO algorithm. The particles forming swarms indicates the solutions to be sought, and the properties of the particles to be determined are the virgin thermal conductivity ( kv ), char thermal conductivity ( kc ), virgin specific heat ( c p ,v ), char specific heat ( c p ,c ), char density ( ρc ), heat of pyrolysis ( ΔH p ), pre-exponential factor ( A ), and activation energy ( E ). The fitness to judge the suitability of each position of the particles forming the swarm for the solution, i.e., the optimum
2131
W.-H. Park et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2129~2132
Table 1. Eight charring material properties found by RPSO.
position of the particle, is calculated as [1] ⎡ ⎢ Φ ⎢ 1 ⎢ fφ pfitness = Φ ⎢ φ =1 ⎢ ⎢⎣
∑
Nt
∑ i=1
2 ⎪⎧⎛ ⎞ ⎨⎜ φexp (ti ) − φ exp ⎟ − φexp (ti ) − φtry (ti ) ⎠ ⎪⎩⎝
(
Nt
∑ i=1
⎛ φ (t ) − φ ⎞ ⎜ exp i exp ⎟ ⎝ ⎠
2
)
2⎪ ⎫⎤
⎬⎥ ⎪⎭ ⎥ ⎥ ⎥ ⎥ ⎥⎦
(2) where Φ is the number of test data sets, with 4 as each surface temperature and mass loss rates at 50 kW and 70 kW. The subscripts “exp” and “try” indicate that the data is assessed numerically, utilizing each test value and the location of the particle. φ exp represents the average value during the test, and Ni expresses the data numbers measured in the test. If the fitness (pfitness) of the particle (p) is better than the individual optimum position (pbest), it is renewed to pbest=p. The optimum position (gbest) among the total particles is also determined using the same method. The position of such particles is identified within the swarm to obtain the estimated optimum solution. The particles move by modifying their positions and velocities among the remaining particles, following the particle closest to the optimum value. The position of each particle may be defined and classified as the pbest and the gbest. If the pfitness of each particle (p) is better than the pbest, it is renewed to pbest=p. The gbest among the group of particles is also determined using the same manner. The positions of all the particles may be renewed using the following speed vector and position update formula: v( j+1)=ωv( j)+α r1 { xbest (j)-x(j)}
+ ωβ r2 { xh,best (j)-x(j)} + ωγ r3ς
(3)
where v denotes the speed of the particle, ω is the inertia weight (category [0.01, 0.7]) [3], and α , β , and γ are constant numbers set as 0.5, 0.5, and 0.0005, respectively. r1 , r2 , and r3 represent the random numbers generated within the category [0, 1]; ς is the randomly chosen velocity component introduced to enhance the searching performance of the particles. x(j) is the particle position, xbest (j) is the optimum position of the particle, and xh,best (j) is the optimum position of the particle that is chosen randomly within the group to the present. The inertia weight ( ω ) plays a role in harmonizing the global search (domain search and new domain search) with the local search (local domain search and minor adjustment of the current domain). If ω becomes larger, the space to be searched expands. The ω used in this study was set to 0.05. The new position of the particles was renewed using the velocity vector obtained from Eq. (2). As a reference data for RPSO, the surface temperatures and pyrolysis mass loss rate of the wood specimen used in the cone heater were 50 kW/m2 and 70 kW/m2, respectively. A population of 100 was established, with eight variables
Property estimated value
Estimated value
Virgin conductivity ( kv , W/m K)
0.488
Char conductivity ( kc , W/m K)
0.274
Virgin specific heat ( c p,v , J/kg K)
2951
Char specific heat ( c p,c , J/kg K)
529
Char density ( ρc , kg/m3)
201
Activation energy ( E , kJ/mol) -1
115
Pre-exponential factor ( A , s )
1.03 x 104
Pyrolysis energy ( ΔH p , kJ/kg)
2036
for optimization of tuple, to calculate the RPSO algorithm. A total of 15 particles were selected for the random topology that helps seek the optimum particle by comparing the individual particle with randomly chosen particles. The traditional RPSO was modified by endowing each particle with wider local search capability. Each particle flies in its local surrounding and searches for a better solution. The domain of its search is controlled by a new parameter.
5. Results Eight pyrolysis-related properties (virgin/char thermal conductivity, virgin/char specific heat, char density, heat of pyrolysis, pre-exponential factor, and activation energy) of wood were obtained using RPSO, as shown in Table 1. The virgin domain was estimated to have a higher conductivity of 0.488 W/mK compared with the 0.274 W/mK of char. The density of char was assessed to have a lower value than that of the virgin domain. However, the specific heat of char was estimated to be lower at 529 J/kg K or 0.18 times the 2,951 J/kg K of the virgin domain. The heat is thus transmitted to the char, which is deformed at the virgin domain after pyrolysis, faster than the transmission to the virgin. The temperature responds more quickly at the char than at the virgin since the former has 0.15 times virgin heat capacity. The heat energy infused in the Douglas fir for the test and estimation was transmitted faster from the outer cone heater to the virgin underneath the char, which was not decomposed by heat. Fig. 2 shows the comparison between the temperatures obtained at 50 and 70 kW/m2 using the RPSO algorithm as well as the actual measured temperatures. The temperatures at 50 and 70 kW/m2 were found to be consistent with the measured values. At 50 kW/m2, the temperatures obtained using the RPSO algorithm tended to remain lower compared with the measured temperature prior to 250 seconds. The estimated temperatures remained higher than the measured temperatures prior to ignition. The estimated temperature using the RPSO algorithm went up sharply after ignition but was still lower than the measured surface temperature. At 70 kW/m2, the estimated temperature using the RPSO algorithm was observed to be comparably lower than the measured temperature. Fig. 3 shows the comparison between the mass loss rate ob-
2132
W.-H. Park et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2129~2132 1000
o
Temperature [C ]
800
600
400
2
50kW/m (RPSO) 50kW/m2(measured) 70kW/m2(RPSO) 70kW/m2(measured)
200
0 0
100
200
300
400
500
600
700
800
900
Time [sec]
lysis-related properties were obtained. The surface temperature and the mass loss rate were obtained using the optimized properties, which were comparably consistent with the measured values. A valid fire phenomenon may be considered for replication if fire analysis is made using the properties obtained through the procedures proposed in this study. This phenomenon is based on the assumption that solid pyrolysis properties are physically valid, and that the surface temperature and mass loss rate measured in the experiment are correct. All the required properties for numerical modeling may be obtained through the procedures done in this study, and by performing the bench-scale fire test using the cone calorimeter and micro-cone calorimeter with optimization techniques.
Fig. 2. Comparison of the measured temperature and those obtained by RPSO.
References 25
2
50kW/m (RPSO) 2 50kW/m (measured) 2 70kW/m (RPSO) 2 70kW/m (measured)
2
Mass loss rate [g/m s]
20
15
10
5
0 0
100
200
300
400
500
600
700
800
900
Time [sec]
Fig. 3. Comparison of the measured mass loss rate and those obtained by RPSO.
tained at 50 kW/m2 and 70 kW/m2 using RPSO and the measured mass loss rate. Comparing the temperatures, the estimated values at the mass loss rate were less consistent with the measured values. The maximum value of the mass loss rate calculated using the RPSO algorithm was 5.3 g/m2s for 723 seconds at 50 kW/m2 and 13.4 g/m2s for 22 seconds at 70 kW/m2. Unlike the measured maximum value, the estimated value at 50 kW/m2 was lower by about 67%, and the mass loss rate increased gradually. Compared with the maximum value measured at 70 kW/m2, the estimated value was lower by around 60%, but the time zones of the maximum value of mass loss rates of both 50 kW/m2 and at 70 kW/m2 were almost the same. The mass loss rate at the 50 kW/m2 test declined rapidly, but the estimated mass loss rate using the RPSO algorithm has dropped slowly.
6. Conclusions In this study, the solid pyrolysis phenomenon on wood was measured through experiments with consistent heat flux. This study aims to measure the combustibility (surface temperature and mass loss rate) using simpler equipment, such as the cone calorimeter, and to obtain the pyrolysis-related properties of the specimen by optimizing the RPSO technique. Eight pyro-
[1] C. Lautenberger, G. Rein and C. Fernandez-Pello, Application of genetic algorithm to estimate the material properties for fire modeling from bench-scale fire test data, Fire Safety Journal, 41 (2006) 204-214. [2] H. Chang, W. Park, T. Kim, D. Lee and W. Jung, Inverse estimation of properties for charring material using a hybrid genetic algorithm, Journal of Mechanical Science and Technology, 25 (2011) 1429-1437. [3] W. Park, H. Chang, T. Kim, D. Lee, W. Jung and I. Thomas, Optimizations of charring material properties, Proceedings of the 6th ICCES International Conference on Meshless and Other Novel Computational Methods, Korea (2010). [4] ISO 5660－1, Reaction to fire tests－Heat release, smoke production and mass loss rate－Part 1：Heat release rate (cone calorimeter method) (2002). [5] S. H. Lee, Material property estimation method using a thermoplastic pyrolysis model, Master thesis, Worcester Polytechnic Institute (2006). [6] J. Kennedy and R. C. Eberhart, Particle swarm optimization, In: Proceedings of the 1995 International Conference on Neural Networks, vol. 4, IEEE Press, Piscataway, NJ (1995) 1942-1948. [7] K. H. Lee, S. W. Baek and K. W. Kim, Inverse radiation analysis using repulsive particle swarm optimization algorithm, International Journal of Heat and Mass Transfer 51 (2008) 2772-2783. [8] S. K. Mishra, Repulsive particle swarm method on some difficult test problems of global optimization, Munich personal repec archive (2006).
Won-Hee Park received his B.S., M.S., and Ph.D in Mechanical Engineering from Chung-Ang University, Korea in 1998, 2000 and 2004, respectively. Dr. Park is currently a Senior Researcher of the Eco-Transport Systems Research Division of Korea Railroad Research Institute, Korea. His research fields are heat transfer, fire dynamics, and fire safety in railway system.
