Journal of Mechanical Science and Technology 27 (6) (2013) 1575~1580 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-013-0402-6
Estimation of convection heat transfer coefficient and surface emissivity of a nonreacting specimen in cone calorimeter using RPSO method† Kyung-Beom Yoon1, Won-Hee Park2,* and Tae-Kuk Kim3 1
Graduate school of Chung-Ang University, Seoul, 156-756, Korea Eco-Transport System Research Division, Korea Railroad Research Institute, Gyeonggi-do, 437-757, Korea 3 Department of Mechanical Engineering, Chung-Ang University, Seoul, 156-756, Korea
2
(Manuscript Received November 23, 2012; Revised February 27, 2013; Accepted March 4, 2013) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract Data for the convection heat transfer coefficient and the surface emissivity of a matter are not easily available from the literature and are usually assumed to be constant values in most studies of pyrolysis. In this study the convection heat transfer coefficient and the surface emissivity of a specimen placed within a cone calorimeter under different external heat fluxes are estimated by using the statistical repulsive particle swarm optimization (RPSO) method. The transient surface temperature distribution of the specimen are measured from the cone calorimeter experiments for different external heat fluxes and these data are then used to determine the convection heat transfer coefficient and the surface emissivity of the specimen inversely. To check the accuracy of this method, we compared the measured temperature and the recalculated temperature of the specimen by using the estimated convection heat transfer coefficient and surface emissivity and we confirmed that they were fairly well matched with each other. We conclude that the proposed RPSO method of estimating the convection heat transfer coefficient and surface emissivity can be an alternative way of obtaining these data for various fire analyses. Keywords: Cone calorimeter experiment; Convective heat transfer coefficient; Repulsive particle swarm optimization; Surface emissivity ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Modern technology results in various kinds of materials developed by using diverse kinds of natural and artificial matters for use in the energy-saving and eco-friendly purposes. Designing lightweight products can be helpful in reducing energy consumption and the research for lightweight products requires new-concepts and compound materials in many fields. According to the increased needs and significance of the newconcept and compound materials, lightweight materials have been adopted on automobile parts, building materials, etc. But the development of the related technologies such as recycling technology and fire safety standards for these new materials are not sufficient for engineering applications. According to statistics published by the National Emergency Management Agency (NEMA) [1] and National Fire Protection Association (NFPA) [2], our living space is susceptible to fire and is not well prepared to cope with fire. The steel frame used widely in our lives expands and loses its strength at approximately 500oC [3] when exposure to heat *
Corresponding author. Tel.: +82 31 460 5358, Fax.: +82 31 460 5279 E-mail address:
[email protected] † This paper was presented at the ISFMFE 2012, Jeju, Korea, October 2012. Recommended by Guest Editor Hyung Hee Cho © KSME & Springer 2013
from fire and these characteristics of the steel frame under fire can cause catastrophic disasters. In Korea we do not have an adequate number of test facilities to evaluate fire safety of structures made with various materials. And the fire safety test has been tried as an event to draw attention by using scaledown mock-up and simplified model, or the test is replaced with the numerical analysis. Computational fluid dynamics (CFD) modeling to predict flame spread and fire growth has been a growing demand because the actual-scale fire test has problems such as high costs and long test time. The CFD modeling can be potentially more useful for fire safety evaluation than the real scale fire test. Due to the fast development of recent computers, fire modeling enables us to get more accurate predictions of fire growth which are comparable to the actual fire situation. Although these prediction technologies do not reach a mature stage, the properties based on the fire model theory can be applied for the purpose of various other fire studies [4, 5]. The fire modeling has been developed for the pyrolysis model of solid materials which is indeed related to the pyrolysis of gaseous matter volatilized from solid materials regardless of the oxygen existence [6]. Generally, the pyrolysis model is an algorithm quantifying the amount of gas-phase pyrolysis material generated from the surface of solid materials whose surface is heated up by a thermal stimulation during
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heat exposure. In fire modeling, the pyrolysis model is used independently or is used as a boundary condition. In a fire modeling, the complex pyrolysis of the fire is simplified and suggested as a simple empirical model that relies on experimental data instead of analyzing the physical and chemical process up to the micro-scale [7-14]. Although different properties are demanded depending on the pyrolysis models, the pyrolysis model of the fire dynamics simulator (FDS) [15] by national institute of standards and technology (NIST) which is frequently used in the field engineering needs properties such as fuel ratio, heat of combustion, heat of reaction, conductivity, specific heat, pre-exponential factor and activation energy. However, obtaining appropriate data for these properties is very difficult because the data in the literature are mostly limited for the pure materials or simple compound products. Furthermore pyrolysis properties data for the composite and newconcept materials are mostly unavailable in the literature. In order to solve these problems, studies on estimating these pyrolysis properties through inverse problem analysis progress are actively performed by using the bench scale experimental data (cone calorimeter test). The inverse problem is a frequently used technique for identifying the internal properties of an object based on the measurable physical amount and is used widely in medical, engineering, and other industries. Recently, the reverse-estimation of pyrolysis properties covers those problems of pyrolysis reactions including conduction, convection and radiation heat transfer together with the combustion phenomenon. It is very important to select a proper technique for optimization in analyzing the inverse problem because the pyrolysis problem involves nonlinearity and very strong directional dependency. The optimization technique for inverse analysis is usually relied on an iterative method to ensure a stable convergence of solutions. There are many iteration methods such as genetic algorithm (GA), hybrid genetic algorithm (HGA), and repulsive particle swarm optimization (RPSO) algorithm, etc. [16, 17] which explore the optimal solutions statistically in a certain solution group. In our previous studies the RPSO algorithm was found to result in more accurate and faster solutions than the GA for pyrolysis problems such as those applied for charring materials [18, 19]. In order to evaluate the effect of fire on specimen a cone calorimeter can be used for various specimens such as steel plate, wood, polymer compounds, etc. For the steel plate, predictions of the convection heat transfer coefficient and surface emissivity had been studied under different conditions of the external heat flux from a cone heater [20, 21]. In order to determine those properties, they used a nonlinear curve fitting algorithm called the generalized reduced gradient and nonlinear optimization method implemented in MS-Excel solver and Powell’s conjugate gradient method. Due to the thin steel plate specimen with high thermal conductivity, the temperature gradient in the direction of thickness was not important and also the chemical deformation and the flame were not observed during the pyrolysis.
Table 1. Pyrometer used in this study. Manufacturer
IMPAC pyrometer IPE 140/39 by LumaSense technologies
IR detector
PbSe
Detection spectral range
3.9 µm
Temperature range
20~700oC
Uncertainty
2oC up to 400oC 0.4~0.6% above 400oC
Operating temperature
0~53oC by completely covered water cooling jacket
Fig. 1. Thermocouple and pyrometer in surface temperature measurement.
In this study the convection heat transfer coefficient and surface emissivity are estimated from the measured surface temperature of the specimen through the cone calorimeter experiment by using the RPSO algorithm. The specimen of synthetic rubber which is frequently used for actual floor material is tested in the cone calorimeter, and the convection heat transfer coefficient and surface emissivity of the synthetic rubber are estimated based on the transient variation of the surface temperature obtained from the experiment.
2. Experimental equipment To measure the surface temperature of the specimen, a cone calorimeter [22] conforming to ISO 5660 is used. Fig. 1 shows the photographs of the experimental apparatus and the specimen exposed to radiation heat from the cone heater. Since the pyrometer used in this study includes targeting laser light to ensure that the correct surface temperature is measured, we can easily pinpoint the measurement location. The surface temperature is measured using the K-type thermocouple and a pyrometer described in Table 1 as a supplementary purpose.
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δρc p
dTs ′′ + h (Ta − Ts ) + εσ (Ta 4 − Ts4 ) = εqɺ ext dt + K s (Ts ) .
(3)
This time, K s (Ts ) includes only the heat flux from the boundary of specimen due to the effect of incomplete insulation. Staggs et al. [20] predicted the convection heat transfer coefficient and surface emissivity of specimen under steady state condition using the steel plate. To calculate the temperature change of the specimen with the time, Staggs et al. [20] revised Eq. (3) as shown below by including the effect of incomplete insulation in ρc p.eff . −λ (t −t0 )
T ∼ T∞ − (T∞ − Ta )e
Fig. 2. Schematic of the heat flux and temperature measurement on the specimen surface.
3. Energy balance and RPSO Fig. 2 presents the schematic drawing of the test specimen and heat transfer over its surface. Total heat flux applied on the surface of specimen is balanced with the change of the internal energy as follows: δρc p
dTs ′′ + h (Ta − Ts ) + εσ (Ta 4 − Ts4 ) = αqɺ ext dt +qɺ ′′fl + K s (Ts ) .
(1)
According to Kirchhoff’s law, the above equation can be reexpressed as follows:
δρc p
dTs ′′ + h (Ta − Ts ) + εσ (Ta 4 − Ts4 ) = εqɺ ext dt +qɺ ′′fl + K s (Ts ) .
(2)
δ represents the thickness of specimen, and ρc p , the volumetric heat capacity. ε denotes the surface emissivity of ′′ , the heat flux from the cone heater. h specimen, and qɺ ext refers to the convection heat transfer coefficient, and Ta , the temperature of atmosphere. Ts represents the surface temperature of specimen, qɺ ′′fl , the heat flux caused by the flame, and σ , the Stefan Boltzmann constant. Finally, K s (Ts ) denotes the heat flux lost due to conduction heat transfer or pyrolysis of the specimen or heat flux from the boundary of the specimen. The steel plate used in this study has very high transfer heat conductivity ( 44.0 ≤ k ≤ 65.0Wm−1K −1 ) and thin thickness ( δ = 4 mm ). In addition, this steel plate does not ignite. Thus, the effect of flame may not need to be examined. Eq. (2) can be expressed as follows:
(4)
.
Here, λ = (h∞ + 4εσT∞ 3 ) / (δρc p.eff ) . h∞ represents the convection heat transfer coefficient under steady state condition, and T∞ , the temperature under steady state condition. t0 denotes the time of initial variations in temperature. Candle soot ( ε = 0.95 ) was coated to the specimen to predict the convection heat transfer coefficient for each external heat flux of the cone heater. Moreover, specimens having different emissivity ( ε = 0.85, 0.50) were coated with paint to measure their temperature. Based on the measured temperature, both convection heat transfer coefficient and emissivity were predicted. RPSO [18] improved the speed equation based on the optimum positions of the randomly selected particles instead of the optimum positions of the entire community based on the speed equation of particle swarm optimization (PSO), which was developed based on the proof of regularity on social behavioral patterns of biological community of birds or fish. ym denotes the position of the particle when the sequence is m; it can be initialized with the following Eq. (5) as, ym = ym, min + r ( ym, max − ym, min ) .
(5)
The subscripts min and max refer to the minimum and maximum values, respectively, whereas r, a random number, is the real number randomly generated between [0, 1]. The fitness to judge whether the position of each particle forming the swarm is appropriate was calculated in this study using the following equation [18] as: 2 N t 2 ∑ φexp (ti ) − φ exp − (φexp (ti ) − φtry (ti )) 1 . fitness = ∑ i=1 Nt 2 Φ φ =1 φexp (ti ) − φ exp ∑ i=1 Φ
(
)
(
)
(6) φ is a physical quantity for the comparison required to assess fitness, i.e., the surface temperature in the cone calorimeter test.
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Table 2. Estimated convection heat transfer coefficients of steel plate for different heat fluxes. Staggs et al. (NCFA) [20]
Present study (RPSO)
Heat flux [kW/m2]
h [W/m K]
h [W/m K]
25
25.6
26.2
30
29.0
29.9
35
27.4
28.3
40
29.7
30.7
45
29.9
30.9
2
2
Table 3. Estimated surface emissivity and convection heat transfer coefficient of steel plate for coatings. Coating
Staggs et al. (NCFA) [20] ε
Candle Soot (ε = 0.95)
-
High emissivity (ε = 0.85)
0.81
Low emissivity (ε = 0.50)
0.49
h [W/m2K]
28.3
Present study (RPSO) ε
h [W/m2K]
-
26.2
0.85
29.18
0.50
22.90
Fig. 3. Temperature-time curve for caldle soot coated specimens along the various heat fluxes.
Fig. 4. Comparison between experimental observation and numerical solutions.
4. Estimation of convection heat transfer coefficient and emissivity
transfer coefficient and the measured surface temperature of the steel specimen. The measured and the predicted results are very well matched with each other.
4.1 Validation of the current method for non-reacting steel plate 4.1.1 Estimation of heat transfer coefficient for varied external heat fluxes with surface emissivity In this study the convection heat transfer coefficient of a steel plate coated with candle soot ( ε = 0.95 ) is predicted for different external heat fluxes of the cone heater. A total of five external heat fluxes of the cone heater are considered, and the results are taken for the heat flux interval of 5 [kW/m2] in the range between 25~45 [kW/m2]. The results reported by Staggs et al. [20] are obtained using the revised Eq. (4) and a nonlinear curve fitting algorithm (NCFA). In the present study, since the surface emissivity of the steel plate is already known in this case, the convection heat transfer coefficient is simply predicted by using the Eq. (3) by using the RPSO. The predicted convection heat transfer coefficients show fairly good agreement with those predicted by Staggs et al. [20] by resulting in errors less than 3.08% as shown in Table 2. Fig. 3 shows the calculated time-dependent surface temperature variations of the specimen by using the predicted convection heat
4.1.2 Estimation of convection heat transfer coefficient and surface emissivity of steel specimen using RPSO The emissivity and convection heat transfer coefficient of the steel specimens coated with candle soot (ε = 0.95), high emissivity paint (ε = 0.85) and low emissivity paint (ε = 0.50) for external heat flux of 25 [kW/m2] are estimated by using the RPSO. In the previous study by Staggs et al. [20], the convection heat transfer coefficient estimated for the same specimens coated with candle soot (ε = 0.95) is used to estimate the surface emissivity for those three surface coatings by using Eq. (4) and a nonlinear curve fitting algorithm (NCFA). In this study, both the surface emissivity and convection heat transfer coefficient are predicted for all specimens using Eq. (3), except for specimens coated with candle soot. In Table 3, current results for the surface emissivity and the convection heat transfer coefficient are compared with those by Staggs et al. [20]. Fig. 4 shows the timely variation of the surface temperatures of the steel specimens coated with those three surface coatings by showing both the measured surface temperature
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Table 4. Estimated surface emissivity and convection heat transfer coefficient over the synthetic rubber plate by using the RPSO. Cone heater heat flux
h [W/m2K]
ε
1 [kW/m2]
4.60
0.80
2 [kW/m2]
6.41
0.80
9.61
0.80
2
3 [kW/m ]
1579
measured for three different external heat fluxes applied by the cone heater, and both surface emissivity and convection heat transfer are estimated by using the RPSO. Experiments are repeated three times for each external heat flux and surface temperature. The standard deviations for the corresponding external heat fluxes are 2.58 [K] (1 [kW/m2]), 3.73 [K] (2 [kW/m2]), 2.79 [K] (3 [kW/m2]) for the surface temperature. Table 4 shows the properties predicted by using the RPSO for respective heat fluxes and Fig. 5 shows the surface temperature distributions as calculated by using Eq. (5) based on the properties shown in Table 4 and the surface temperatures measured for each external heat flux. The surface emissivity of the rubber plate for each external heat flux is predicted to be 0.80, while the convection heat transfer is increased as the heat flux increased. 5. Conclusions
Fig. 5. Comparison surface temperature of synthetic rubber between experimental observation and numerical solutions.
and the calculated surface temperature by using the predicted convection heat transfer coefficient and surface emissivity given in Table 3. As compared to the previous study, the temperature variations of the specimen calculated by using the present results of surface emissivity and convection heat transfer coefficient match better with the measured temperature variations as compare to those by Staggs et al. [20]. 4.2 Non-reacting synthetic rubber plate In the above we confirmed that the convection heat transfer coefficient and surface emissivity could be predicted successfully for the non-reacting steel specimen with very high conductivity by using the RPSO algorithm. We look for the possibility that both the convection heat transfer coefficient and surface emissivity can also be predicted for the non-reacting specimen with low conductivity by using the RPSO.
A synthetic rubber plate with very low conductivity is considered to confirm this possibility of predicting the convection heat transfer coefficient and surface emissivity by using the RPSO. The surface temperature of synthetic rubber plate however is maintained below the ignition point of the rubber by selecting the maximum external heat flux of the cone heater as 3 [kW/m2]. Thus the effect of flame may not need to be examined. Both convection heat transfer coefficient and emissivity are predicted using Eq. (3) through the same method as that used in the foregoing section. The surface temperature of synthetic rubber is
In this study, the measured time dependent surface temperature of a specimen is used to determine inversely both the convection heat transfer coefficient and the surface emissivity of specimen by using the statistical RPSO method. The validity of the method used is successfully examined by comparing the transient temperature variations obtained from the experiment and numerical analysis for non-reacting steel plates with different surface emissivity. The surface emissivity and the convection heat transfer coefficient for a non-reacting rubber plate are successfully determined by using the RPSO method. The recalculated surface temperature distribution using the predicted convection heat transfer coefficient and surface emissivity is fairly well matched with the measured surface temperature distribution. From this study we conclude that the convection heat transfer coefficient and surface emissivity of a non-reacting material can successfully be predicted by using the RPSO with the measured surface temperature in the fire test in the cone calorimeter.
Nomenclature-----------------------------------------------------------------------cp h Ks Ni qɺ ′′ r ym
: Specific heat : Convective heat transfer coefficient : Effect of incomplete insulation : Number of data : Heat flux : Random number : Position of the particle
Greek symbols α δ ε φ ρ
: Absorptivity : Thickness : Surface emissivity : Physical quantity : Density
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σ
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: Stefan-Boltzmann constant
Subscripts a exp ext fl try ∞
: Atmosphere : Experimental result : External : Flame : Assessed data using optimized properties : Steady state
References [1] The state of fire incident in the last 10 years, National Emergency Management Agency (2005) 55-56. [2] M. J. Karter, Jr., Fire loss in the United States during 2009, NFPA 1 (2010). [3] E. Arthur and P. E. Cote, fundamentals of fire protection, Jones & Bartlett Pub, Massachusetts (2004) 151-152. [4] P. A. Croce, The FORUM for international cooperation on fire research: a position paper on evaluation of products and services for global acceptance, FireSafety Journal, 36 (2001) 715-717. [5] L. A. Gritzo, P. E. Senseny, Y. Xin and J. R. Thomas, The international FORUM of fire research directors: a position paper on verification and validation of numerical fire models, Fire Safety Journal, 40 (2005) 495-490. [6] C. Lautenberger, A generalized pyrolysis model for combustible solids, Doctoral thesis, University of California, Berkeley (2007). [7] C. D. Blasi, Modeling and simulation of combustion processes of charring and non-charring solid fuels, Progress in Energy and Combustion Science, 19 (1993) 71-104. [8] T. Kashiwagi, Polymer combustion and flammability-role of the condensed phase, Proceedings of the Combustion Institute, 25 (1994) 1423-1437. [9] A. C. Fernandez-Pello, The solid phase, in Combustion Fundamentals of Fire, Ed. G. Cox Academic Press, New York (1995) 31-100. [10] C. D. Blasi, The state of the art of transport models for charring solid degradation, Polymer International, 49 (2000) 1133-1146. [11] R. E. Lyon and M. L. Janssens, Polymer flammability, DOT/FAA/AR-05/14 (2005). [12] B. Moghtaderi, The state-of-the-art in pyrolysis modeling of lignocellulosic solid fuels, Fire and Materials, 30 (2006) 1-34. [13] C. Lautenberger and A. C. Fernandez-Pello, Pyrolysis modeling, thermal decomposition, and transport processes in combustible solids, to appear in Transport Phenomena in Fires, Ed. M. Faghri and B. Sunden, WIT Press (2008).
[14] C. D. Blasi, Modeling chemical and physical processes of wood and biomass pyrolysis, to appear in Progress in Energy and Combustion Science (2008). [15] C. Lautenberger, S. McAllister, D. Rich and C. FernandezPello, Modeling the effect of environmental variables on opposed-flow flame spread rates with FDS, Fire Safety in Tall Buildings International Congress, University of Cantabria, Santander Spain, October 18-20 (2006). [16] K. W. Kim, S. W. Baek, B. S. Shin, K. J. Kil and K. G. Yeo, Comparison of regularization techniques for an inverse radiation boundary analysis, Tran. KSME(B), 29 (8) (2005) 903-910. [17] 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. [18] H.-C. Chang, Study on inverse property estimation for thermal pyrolysis and radiation by using the RPSO method, Doctoral thesis, Chung-Ang University, Korea (2011). [19] H.-C. Chang, W.-H. Park, K.-B. Yoon and T.-K. Kim, Estimation of the properties for charring material using the RPSO algorithm, Journal of Fluid Machinery, 14 (1) (2011) 34-41. [20] J. E. J. Staggs and H. N. Phylaktou, The effect of emissivity on the performance of steel in furnace tests, Fire Safety Journal, 43 (2008) 1-10. [21] J. E. J. Staggs, Convection heat transfer in the cone calorimeter, Fire Safety Journal, 44 (2009) 469-474. [22] ISO 5660-1, Reaction to fire tests-Heat release, smoke production and mass loss rate - Part 1 : Heat release rate(cone calorimeter method) (2002).
Kyung-Beom Yoon received his M.S. in the school of Mechanical Engineering from Chung Ang University, Korea, in 2008. His current research interest is a numerical analysis of heat transfer, fire dynamics and fire safety.
Won-Hee Park received his B.S., M.S., and Ph.D. in the school of 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 systems.