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A numerical analysis of the radiation distribution produced by a Radiant Protective Performance (RPP) apparatus
International Journal of Thermal Sciences 94 (2015) 170e177
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
A numerical analysis of the radiation distribution produced by a Radiant Protective Performance (RPP) apparatus Xianfu Wan a, c, *, Faming Wang d, Yehu Lu d, Wei Huang b, Jun Wang b, c a
Engineering Research Center of Technical Textiles, Ministry of Education, Donghua University, Shanghai 201620, China Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China c Zhejiang Provincial Key Laboratory of Novel Textiles Research and Development, Hangzhou 310001, China d Laboratory for Clothing Physiology and Ergonomics, National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 September 2014 Received in revised form 28 February 2015 Accepted 28 February 2015 Available online 2 April 2015
In this study, a model based on the Monte Carlo method was developed to investigate the radiation distribution produced by a Radiant Protective Performance (RPP) apparatus. Radiant Protective Performance (RPP) experiments were conducted to validate the model. It was found that the predictions of the model showed good agreement with the experimental data. Further, the results show a uniformly distributed heat flux area with a relatively high level at the center region of the incident surface of the test specimen. The radiation intensity image displays a high degree of similarity to the photo of the inside space of the RPP tester. The radiation intensity is obviously not parallel or uniformly distributed on the hemispherical space at the center of the specimen surface. The high level region corresponds to the lamp chamber. It was also found that the highest radiation intensity comes from the edge of quartz envelops nearby the gap. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Radiative heat transfer Radiant Protective Performance Monte Carlo method
1. Introduction The protective performance of firefighting clothing was extensively investigated by researchers not only experimentally but also numerically due to its vital role in protecting the life of fire fighters [1e9]. Among the experimental studies, Radiant Protective Performance (RPP) and Thermal Protective Performance (TPP) tests are two widely used methods to evaluate the protective performance of firefighting clothing materials [3,4]. Both standard RPP and TPP apparatuses expose protective materials to a so called uniform heat flux, measure the heat transferred through the test sample using a calorimeter, and predict the time to a second degree burn based on the Stoll Curve [10,11]. This criterion was developed using test data on the bare skin exposed to a uniform heat flux level. Therefore, generating a uniformly distributed incident heat flux at the surface of the test sample is vital. To ensure the consistency of the tests, the standards NFPA 1977 [12] and NFPA 1971 [13] described the design of the RPP and TPP apparatuses, respectively. A close observation of
* Corresponding author. RM 5023, 3 College Building, Donghua University, 2999 People North Road, Songjiang District, Shanghai 201620, China. E-mail address: [email protected] (X. Wan). http://dx.doi.org/10.1016/j.ijthermalsci.2015.02.020 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
the sample after the RPP and/or TPP tests shows that the damage of the clothing material in the center is significantly higher than that at the edge, although the incident heat flux seems to be uniformly distributed around the detecting area. Therefore, it is doubtful whether the incident heat flux at the surface of the test sample on these apparatuses is uniformly distributed or not. Moreover, the protective performance of fire fighting clothing is determined not only by the level of incident heat flux, but also by the incident radiation intensity distribution over the hemispherical space. The radiation source, which produces the same level of incident radiant heat flux but shows non-uniform radiation intensity distribution, could result in significantly different burn injuries. The heat flux distribution may vary in terms of the radiation intensity and direction. The clothing material usually has a significantly different attenuation effect on the radiation from different directions. Even for homogeneous clothing material, different directions may lead to different path lengths for the radiation to travel, resulting in different levels of damage to the skin. Unfortunately, the incident radiations were implicitly assumed to be parallel and normal to the surface of the test sample in various models concerning firefighter's protective clothing [5e7]. They made this assumption due to the unclearness to the incident radiation intensity distribution. Researchers even applied the TPP, RPP or
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similar apparatuses to validate these models, but the incident radiation intensity in these apparatuses is obviously not parallel or normal to the material surface. In order to further analyze the radiation transmission through protective clothing materials, it is essential to examine the distribution of incident radiation intensity on these apparatuses. Therefore, in this study, we attempted to numerically analyze the incident radiation distribution at the test sample surface of an RPP tester. For TPP tests, the fabric samples are exposed to both radiant and convective heat sources, while RPP tests only expose fabrics to the radiant heat source. In order to simplify the problem, we only take the RPP as the object to investigate in this study. For radiation problems, very little research work can be found through the analytical solutions. Under most circumstances, researchers try to solve the differential equations by numerical means. There were many conventional numerical methods such as Spherical Harmonics method, Discrete Transfer method, Discrete Ordinate method, Zonal method, Finite Volume method, Finite Element method and Monte Carlo method [14e17]. Among them, the Monte Carlo method is excellent to solve the most complicated problems [15]. As the complexity of the problem increases, the complexity of formulation and the solution effort increase much more rapidly for convectional techniques. In contrast, the Monte Carlo method can solve it with relative ease [14,15]. Therefore, the Monte Carlo method was adopted in this paper considering the problem's complexity. 2. Model 2.1. Model introduction As shown in Fig. 1, the thermal radiation source of the RPP tester is quartz lamps. These lamps are enclosed by metal and insulation plates. The insulation plate blocks thermal energy to avoid preheating of the test sample. Together with the insulation plate, a shutter plate and a specimen holder plate are also installed between the lamp bank and the test sample. Both the insulation plate
Specimen Holder Plate
Sensor Holder Plate
Shutter Plate Insulation Plate
Sensor
Lamp Bank k
Specimen
Right View Fig. 1. A schematic for the RPP system.
Metal Plate
171
and the specimen holder plate have a window in their center. The test sample is sandwiched between two plates: the specimen holder plate and the sensor holder plate which has a bracket to hold the sensor. When the test begins, the shutter plate would be removed pneumatically, and then thermal radiation would be radiated through the windows and the space left by the shutter plate, finally reach the surface of the test sample. Generally, the convection at the outside of the quartz lamps and at the surface of the walls is large due to the high temperature. In order to eliminate convective heat to be exerted on the surface of the test sample, vertical unimpeded ventilation is designed in the lamps chamber. The convection coupling with radiation would make the problem difficult to analyze. They can be separated if the temperatures of the walls and the quartz envelops are given, and thus the radiation can be calculated independently. To simplify the analysis of the model, the following assumptions were made: (1) The temperature is uniformly distributed at the surfaces of radiant sources; (2) Radiation is emitted diffusely from the surfaces of radiant sources; (3) The quartz in the lamp is either transparent or opaque depending on the wavelength of the incident radiation; the quartz media does not participate the emitting, absorbing or scattering of the radiation, they are assumed to occur at the interface; (4) The air and the gas in quartz lamps are transparent to radiation, thus they do not participate in the emitting, absorbing or scattering of radiation; (5) The radiant effect of the ends of tungsten filaments and quartz envelops can be neglected due to the small size compared with the length; (6) Leakage of radiation through ventilation holes in RPP system can be neglected. Based on the above assumptions, standard Monte Carlo model for the RPP tester was established. A statistically meaningful random sample of energy bundles from the tungsten filament of the lamps and other radiant sources were emitted and traced. After leaving the surface of the sources, these energy bundles would be absorbed, reflected at the surface of walls, or transmitted in quartz envelops. The inside space enclosed by the plates is the boundary for the energy bundles traveling. It consists of four parts: the lamp chamber, the window in the insulting board, the space left by the removed protective shutter, and the window in the specimen holder. The modeling work includes description of the geometry, intersection detection and the simulation for radiation behaviors such as emission, reflection and absorption. The details can be found in literatures [14,15,18,19]. We mainly introduce the particular partdthe quartz lamps. Quartz lamps consist of two parts: tungsten filaments and quartz envelops. The tungsten filament is usually very fine and in the shape of spiral coil. The spiral line is so complex to describe that it was simplified as an open-ended cylinder here; the radiation was emitted from the outer surface of the cylinder. The lighted length was taken as the length of the cylinder. Although the quartz envelop is a closed tube, it was described as an open-ended tube due to the neglecting of its ends. The radiation was emitted from both the inner and outer surface. Quartz envelops are the most sophisticated participators in this system. The radiative properties were found highly wavelength dependent [20,21]. In general, the fused quartz is transparent in the range of 0.2e4.0 mm, but behaves opaque outside the range.
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Therefore, within this band (from 0.2 to 4.0 mm), radiation can be reflected or transmitted at the interfaces of quartz envelops, but can be only reflected or absorbed out of this band. Since the radiant properties of the quartz envelop of the lamps are highly dependent on the wavelength of the radiation, each energy bundle should be assigned a wavelength. The assignment of the wavelength of the energy bundles should be based on the source spectral distributions. The details can be referred in the literature [22]. The reflectivity at gasequartz or quartzegas interface is sensitive to both wavelength and incident angle (qi). Fresnel's equation was used to describe it [23]:
rðqi Þ ¼
1 r ðq Þ þ rp ðqi Þ 2 n i
rn ðqi Þ ¼
a2 þ b2 2a cos qi þ cos2 qi
(1)
a2 þ b2 þ 2a cos qi þ cos2 qi
rp ðqi Þ ¼ rn ðqi Þ
a2 þ b2 2a sin qi tan qi þ sin2 qi tan2 qi a2 þ b2 þ 2a sin qi tan qi þ sin2 qi tan2 qi
where
2a2 ¼
2b2 ¼
h2 k2 sin2 qi
2
þ 4h2 k2
1=2
þ h2 k2 sin2 qi ;
1=2 2 h2 k2 sin2 qi þ 4h2 k2 h2 k2 sin2 qi ;
h and k are the real refractive index ratio and the absorptive index ratio, respectively. h ¼ hq, k ¼ kq for the gas-quartz interface, h
k
q q for the quartzegas interface, where hq and kq are h ¼ h2 þk 2, k ¼ 2 h þk2 q
q
q
q
the real refractive index and the absorptive index of the quartz, respectively. Data for hq and kq versus the wavelength can be found in the reference [22]. If the energy bundles transmit through the interfaces of quartz envelops, the refraction may occur. The Snell's law was applied to calculate the refracted trajectory [24],
sin2 f ¼
sin2 qi h2 þ k2
(2)
where f is the refracted angle. 2.2. Statistics and calculations In this study, the heat flux and the radiation intensity were calculated by statistics. In order to simplify the description, we set a coordinate origin at the center point of the incident surface of the specimen, and established a Cartesian coordinate and a spherical coordinate system on the hemispherical space over the incident surface of the specimen (Fig. 2). 2.2.1. Heat flux When the bundles arrived at the surface of the sensor or a target surface grid, they would be counted to a variable h. The heat flux at the sensor surface can be calculated by
q ¼ lim
N/þ∞
n Qt N A
(3)
where Qt is the total emissive power by all radiant sources, N is the total number emitted by the sources and A is the area of the sensor or the target surface grid.
Fig. 2. Coordinate system in the RPP apparatus: a) Cartesian coordinate. b) Spherical coordinate.
2.2.2. Radiation intensity The radiation intensity may be obtained by counting the number of energy bundles received by the sensor from a direction. However, it would be very inefficient when the target is a small area or a small solid angle in the standard Monte Carlo method [25,26]. This is because only a little portion of the bundles would enter the target. Although it is not a good way, in this study we still attempted to calculate the radiation intensity by emitting a huge amount of energy bundles (1011) to obtain enough quantity for statistics. The radiation intensity Iðq; 4Þ for a direction ðq; 4Þ was calculated by
Iðq; 4Þ ¼
¼
dQ ðq; 4Þ nðq; 4ÞQt ¼ lim A cos qdu N/ þ ∞; NA cos qDu Du/0 nðq; 4ÞQt Z lim N/ þ ∞; NAD4 cos q sin qdq Dq/0; Dq D4/0
(4)
where q is the polar angle, and 4 is the azimuth angle (measured between the positive x direction and the projection of reverse ray incident direction on the incident specimen surface), Du is a solid angle increment around the direction (q,4), Q ðq; 4Þ is the energy of
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173
the radiation incident from the direction (q,4) and nðq; 4Þ is the number of bundles incident from Du into the sensor surface.
Cut out of Specimen Holder Plate
y
3. Validation and experiments
Shutter Plate Specimen Holder Plate
10 5 -54 -40 -20
64
To validate the model, experiments using a RPP apparatus (Richmond, USA) were conducted. The RPP tester is also called RHP tester in ASTM F2702 [27]. ASTM F2702 describes the detailed dimensions of the apparatus. It was found from the measurements that the RPP apparatus used in this study is different from the descriptions in the ASTM F2702. As shown in Fig. 3, the top edge of the cut-out in the insulation plate is 8 mm higher than that in the standard. Besides, the lighted length is about 178 mm, while it is 127 mm in the standard; the gap between two neighboring quartz envelops is about 1 mm, whereas the gap in the standard is 0.4 mm. Our experiments were conducted at a central incident heat flux of 21 kW/m2. The test sample and the sensor holder plate were replaced by the sensor to directly measure the incident heat flux distribution. The sensor was not fixed at the center of the window any more as that in RPP test; it was placed at different sites on the horizontal central line and the vertical central line of the specimen holder window in the XOY plane to measure heat flux (Fig. 4). In these tests, the detecting surface of the sensor was always in the XOY plane. Besides, the heat flux received from different directions was also determined by rotating the sensor around the point (x ¼ 0, y ¼ 0, z ¼ 76 mm) at the front of the specimen holder plate window as shown in Fig. 5. The model was coded using Visual Cþþ (Microsoft, USA). The object orientated programming technology was applied to make an efficient coding. As the Monte Carlo computation needs tracing a large amount of energy bundles, it is CPU-time consuming.
O
-5 20 -10
40
54
152
Specimen Holder Plate
Front View Fig. 4. Locations of the sensor in the measurement of the heat flux on the horizontal central line and the vertical central line.
Therefore, the parallel computation technology was adopted by using twenty threads to trace energy bundles parallel so that the speed increased 20 times. The program was run on a server (Dell Precision T5610, USA) configured with two 6-core CPUs (Intel® Xeon® CPU [email protected] GHz). The temperatures of Quartz envelopes, insulation walls, metal walls, shutter chamber walls and specimen holder window were 894 K, 556 K, 546 K, 370 K and 298 K, respectively. The temperature of filament was estimated as 1625 K according to the Keltner's measurements [3]. The radiative parameters configured in this
Insulation Plate
8.0
Metal Plate
1.0 63.5
0.4
Sensor
Lamp Bank k
Specimen Standard ASTM F2702-08
x
Apparatus(Richmond, USA)
Testing status
Right view Fig. 3. Differences at the cut-out of the insulation plate between the experiment apparatus and that described in the standard ASTM F2702.
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Fig. 5. Locations of the sensor in the measurement of the directional heat flux. Fig. 6. Distribution of the horizontal heat flux at the specimen's incident surface.
model are listed in Table 1. The emissivity for quartz envelops in this table is only used to estimate the emissive power. The properties for the calculation of reflection, absorption and transmission at quartz envelops should be referred to Part 2.1. The absorptivity (a) was not listed in this table because its value equals to the emissivity. In this model, we attempted to replace the tungsten filaments of the complex spiral line geometry by simple cylinders of the same length, an equivalent diameter of the cylinders need to be found out. It was found that an equivalent diameter of 1.3 mm would result in the calculated central heat flux at a reasonable level. Hence, in this model, the diameter of the filament cylinders was set to 1.3 mm. After emitted a large quantity of energy bundles (106), the convergent solution was obtained. Figs. 6e8 show the predicted results of the heat flux at the horizontal central line, the vertical central line and the directional heat flux, respectively. It can be seen that the numerical results fit very well with the experimental ones. The incident heat flux distributes relatively uniform at the central region at the level of 21 kW/m2, while it decreases to 16 kW/ m2 at the edge region. Symmetry about the y-axis for the horizontal heat flux curve can be found from both the numerical and experimental results. However, symmetry about the x-axis for the vertical heat flux distribution curve was only found from the experimental results. The numerical results show a slightly higher value at the top region. This will be discussed in the next section. The directional heat flux is the one with different directions that the target surface faces towards the lamp chamber. Its curve is symmetric about the y-axis with the peak at the zero degree. It denotes that the maximum heat flux occurs when the target plane facing towards the center of the specimen window, while it would decay rapidly as the target rotating away from the center of the window. In order to determine the uncertainty of numerical results due to the uncertainty of radiative parameters in Table 1, sensitivity analysis was carried out. OAT approach was employed to evaluate the sensitivity impacts of each parameter. In OAT approach, only one parameter changes each time while the others keep at the
baseline values. The baseline values were assigned with the values listed in Table 1 for the parameters. The predicted heat flux at the center was used as the target variable of the model for the sensitivity analysis. By changing one of the parameters in a relative range of [5%, 5%], compared with the baseline, the target variable varied in a range of [0.69%, 1.20%], [0.18%, 0.32%], [1.70%, 1.85%], [2.72%, 2.86%], [0.49%, 0.41%] for the emissivity of insulation plates, metal plates, tungsten filaments, quartz envelops and sensor surface, respectively. And it also varied in a range of [0.22%, 0.14%] and [0.57%, 0.45%] for the specula reflectivity of metal plates and quartz envelops, respectively. It shows that the model's outcome is not sensitive to these parameters. This may indicate the reasonableness of the values in Table 1.
Fig. 7. Vertical heat flux distribution at the specimen's incident surface.
Table 1 Radiative parameters of the radiation participators. Radiation participators
Emissivity (ε)
Specula reflectivity (rs)
Diffuse reflectivity (rd)
Insulation plates Metal plates Tungsten filaments Quartz envelops Sensor surface
0.96 0.19 0.39 0.48 0.90
0.00 0.56 0.00 See Part 2.1 0.00
0.04 0.25 [18] 0.61 0.00 0.10
(Asbestos board, [15]) (Aluminum, [15]) ([15]) ([22]) [27]
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Fig. 8. Directional heat flux distribution at the specimen incident surface.
4. Results and discussion The validation roughly presents the numerical results of the heat flux distribution, for that the calculated value actually is the average over the disk area of the sensor surface. The disk area with the diameter of 40 mm is relatively large compared with the size of specimen window (152 mm 64 mm). Therefore, a high resolution image of the incident heat flux is necessary to clearly examine the incident heat flux. Besides, the radiation intensity distribution is another issue we are concerned about.
Fig. 9. The numerical results for the heat flux at the incident surface of the fabric: a) The experiment apparatus. b) The standard apparatus.
4.1. Heat flux distribution at the incident surface of the test sample In order to obtain a high resolution image of the heat flux distribution over the whole incident surface of the specimen, we divided the incident surface of the specimen into 152 64 grids. After tracing an amazing large amount (109) of energy bundles the high resolution image of the incident heat flux was obtained and shown in Fig. 9a. The color (in web version) of a point represents the value of heat flux at this position. Although the image is unsmooth because of the variance distributed in the image in the form of noise, it would not be an accuracy problem as the coefficient of the variation is less than 0.6%. The existence of uncertainty is due to the inherently statistical nature of the Monte Carlo method [25]. Fig. 9a shows an elliptical region with relatively high values at the central area. In this region, the heat flux is almost uniformly distributed with the range of [20.7, 21.9] kW/m2. Obviously, this uniform region almost enclosed the detecting area in RPP test (the circular area with the diameter of 40 mm at the center). Outside this region, the heat flux decreases rapidly with the minimal value of 7.7 kW/m2. The values on the central lines are found to be different from that shown in Figs. 7 and 8. This is mainly because that the predicted heat fluxes in Figs. 7 and 8 is the average value over the sensor surface area. It may not be difficult to understand the heat concentrates in the center of the target surface, but the vertical asymmetry may let you doubt about the correctness. In order to verify it, a piece of plain paper and a moisture barrier for firefighters' ensembles were exposed to the radiation in RPP system; it was found that the surface turned brown (in web version). The depth of the color indicates the level of the heat flux. As shown in Fig. 10, the top region obviously has a deeper color than the bottom, which confirms the correctness of predicted results. The vertical asymmetry of the heat flux distribution can be explained by the vertical asymmetry of the insulation cut-out with respect to the
Fig. 10. The picture of materials after being exposed to the incident radiation of the RPP tester: a) Plain paper. b) Moisture barrier for firefighters' ensembles.
XOZ plane as shown in Fig. 3. The excess 8 mm cut-out on the top of the insulation plate compared with the standard leads to an excess exposure to thermal radiation. To further prove this point, a numerical simulation was made for the standard RPP apparatus. The numerical results (in Fig. 9b) for the standard RPP apparatus clearly demonstrate the vertical symmetry of heat flux distribution. The vertical symmetry results in the experiments can be explained that the sensor is not sensitive enough to distinguish the fine difference for the averaged heat flux over a 40 mm-diameter disk area. 4.2. The radiation intensity distribution at the specimen's incident surface Fig. 11 shows the radiation intensity received by the sensor located at the center of the incident surface. This figure uses twodimensional polar coordinates to present the radiation intensity Iðq; 4Þ under three-dimensional spherical coordinates. The radius in polar coordinates represents the polar angle q in the spherical
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X. Wan et al. / International Journal of Thermal Sciences 94 (2015) 170e177
radiation intensity for the brightest bands (621.8 C) can be found to be 11.6 kW/m2sr. It's close to the numerical result (around 12 kW/m2sr).
I¼
εsT 4 p
(5)
where s is StefaneBoltzmann's constant and T is temperature. It can be seen from Fig. 12 that the highest intensity bands are at around the gap region. However, the bands' width (about 3 mm) is obviously larger than that of the gap. By counting the source of the energy bundles incident from the direction (q ¼ 6 , f ¼ 90 ), we found that the maximum fraction (51.0%) is from transmitting through neighboring quartz envelops, and only 16.2% is from the reflection at the metal wall behind the gap. Therefore, the highest intensity bands are attributed to the radiation transmitting from the edge of quartz envelops nearby the gap. 5. Conclusions Fig. 11. The numerical results for radiation intensity received by the sensor at the center of the incident surface of the specimen.
coordinates, and the polar angle in polar coordinates represents the azimuth angle 4 in the spherical coordinates. Each point ðq; 4Þ in this image corresponds a direction of ðq; 4Þ in the spherical coordinates. The value of Iðq; 4Þ is indicated by the color of the point ðq; 4Þ. The image shows a surprisingly high similarity to the picture of the RPP chamber taken from a hemispherical camera. The red part (I > 9 kW/m2sr) corresponds to the lamp bank; the yellow (I z 8 kW/m2sr) and the light blue (I z 6 kW/m2sr) are the walls in the lamp chamber; and the deep blue (in web version) (I z 2 kW/ m2sr) are the low-temperature walls in the shielding chamber and the sample holder. The top weak light blue area should be the uncovered part due to the excess cut-out in the insulation plate. It should also be noted that the highest value of radiation intensity emerges on the two horizontal lines that symmetrically lying within the red region. There are another two lines at the outside of them. These four lines correspond to the gap region between two neighboring lamps. The next task is to determine whether the highest intensity is from the gap of the quartz envelop. This may be proved from the photo taken by an infrared camera (FLIR T440, FLIR system Inc., USA) as shown in Fig. 12. Although it is usually used to measure temperatures, the infrared camera essentially detects the radiation intensity, and converts it to a temperature value by assuming that it originates from isotropic radiation emission. Therefore, the radiation intensity values can be obtained by converting backward using Equation (5). For convenience, we preset the emissivity parameter to 1.0 for the camera. By conversion, the
A model based on the Monte Carlo method was developed to numerically analyze the radiation distribution in the Radiant Protective Performance test apparatus. The incident radiant heat flux distribution at the surface of test specimen and the incident radiation intensity distribution in the hemispherical space upon the center of the specimen surface were calculated for a RPP apparatus. The heat fluxes show a uniformly distributed area with a relatively high level at the center region. The heat flux at the top area of the whole incident surface is higher than that at the bottom due to the uncovered excessive 8 mm cut-out at the top of the insulation plate in the RPP apparatus. The radiation intensity image demonstrates a highly degree similarity to the picture of the inside space of RPP taken by a hemispherical camera located at the center point of the specimen window. It is evident that the radiation intensity is not parallel or uniformly distributed on the hemispherical space. The high level region corresponds to the lamp chamber and the highest radiation intensity comes from the edge of quartz envelops nearby the gap. Acknowledgments This work was supported by the National Natural Science Foundation of China (Project No. 51106021), the Fundamental Research Funds for the Central Universities of China (Project No. 2012D10122, No. 2013D110120 and No. 2014D110139) and Science & Technology Funds of Zhejiang Province of China (Project No. 2013C31006). Nomenclature A d I lim N n O Q q T x,y,z
Fig. 12. Photo taken by the infrared camera.
area, m2 differential radiation intensity, kW/m2sr limit of a function total number of energy bundles emitted by the sources the number of energy bundles coordinate origin the power of radiation, W heat flux, kW/m2 temperature, K Cartesian coordinates
Greek symbols a absorptivity D increment of a variable
X. Wan et al. / International Journal of Thermal Sciences 94 (2015) 170e177
ε
h q k r s
f 4
u
emissivity refractive index polar angle, incident angle or angle between the normal of the sensor surface and z axis absorptive index reflectivity StefaneBoltzmann's constant, 5.67 108 W/m2K4 refracted angle azimuthal angle solid angle
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
A numerical analysis of the radiation distribution produced by a Radiant Protective Performance (RPP) apparatus Xianfu Wan a, c, *, Faming Wang d, Yehu Lu d, Wei Huang b, Jun Wang b, c a
Engineering Research Center of Technical Textiles, Ministry of Education, Donghua University, Shanghai 201620, China Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China c Zhejiang Provincial Key Laboratory of Novel Textiles Research and Development, Hangzhou 310001, China d Laboratory for Clothing Physiology and Ergonomics, National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 September 2014 Received in revised form 28 February 2015 Accepted 28 February 2015 Available online 2 April 2015
In this study, a model based on the Monte Carlo method was developed to investigate the radiation distribution produced by a Radiant Protective Performance (RPP) apparatus. Radiant Protective Performance (RPP) experiments were conducted to validate the model. It was found that the predictions of the model showed good agreement with the experimental data. Further, the results show a uniformly distributed heat flux area with a relatively high level at the center region of the incident surface of the test specimen. The radiation intensity image displays a high degree of similarity to the photo of the inside space of the RPP tester. The radiation intensity is obviously not parallel or uniformly distributed on the hemispherical space at the center of the specimen surface. The high level region corresponds to the lamp chamber. It was also found that the highest radiation intensity comes from the edge of quartz envelops nearby the gap. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Radiative heat transfer Radiant Protective Performance Monte Carlo method
1. Introduction The protective performance of firefighting clothing was extensively investigated by researchers not only experimentally but also numerically due to its vital role in protecting the life of fire fighters [1e9]. Among the experimental studies, Radiant Protective Performance (RPP) and Thermal Protective Performance (TPP) tests are two widely used methods to evaluate the protective performance of firefighting clothing materials [3,4]. Both standard RPP and TPP apparatuses expose protective materials to a so called uniform heat flux, measure the heat transferred through the test sample using a calorimeter, and predict the time to a second degree burn based on the Stoll Curve [10,11]. This criterion was developed using test data on the bare skin exposed to a uniform heat flux level. Therefore, generating a uniformly distributed incident heat flux at the surface of the test sample is vital. To ensure the consistency of the tests, the standards NFPA 1977 [12] and NFPA 1971 [13] described the design of the RPP and TPP apparatuses, respectively. A close observation of
* Corresponding author. RM 5023, 3 College Building, Donghua University, 2999 People North Road, Songjiang District, Shanghai 201620, China. E-mail address: [email protected] (X. Wan). http://dx.doi.org/10.1016/j.ijthermalsci.2015.02.020 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
the sample after the RPP and/or TPP tests shows that the damage of the clothing material in the center is significantly higher than that at the edge, although the incident heat flux seems to be uniformly distributed around the detecting area. Therefore, it is doubtful whether the incident heat flux at the surface of the test sample on these apparatuses is uniformly distributed or not. Moreover, the protective performance of fire fighting clothing is determined not only by the level of incident heat flux, but also by the incident radiation intensity distribution over the hemispherical space. The radiation source, which produces the same level of incident radiant heat flux but shows non-uniform radiation intensity distribution, could result in significantly different burn injuries. The heat flux distribution may vary in terms of the radiation intensity and direction. The clothing material usually has a significantly different attenuation effect on the radiation from different directions. Even for homogeneous clothing material, different directions may lead to different path lengths for the radiation to travel, resulting in different levels of damage to the skin. Unfortunately, the incident radiations were implicitly assumed to be parallel and normal to the surface of the test sample in various models concerning firefighter's protective clothing [5e7]. They made this assumption due to the unclearness to the incident radiation intensity distribution. Researchers even applied the TPP, RPP or
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similar apparatuses to validate these models, but the incident radiation intensity in these apparatuses is obviously not parallel or normal to the material surface. In order to further analyze the radiation transmission through protective clothing materials, it is essential to examine the distribution of incident radiation intensity on these apparatuses. Therefore, in this study, we attempted to numerically analyze the incident radiation distribution at the test sample surface of an RPP tester. For TPP tests, the fabric samples are exposed to both radiant and convective heat sources, while RPP tests only expose fabrics to the radiant heat source. In order to simplify the problem, we only take the RPP as the object to investigate in this study. For radiation problems, very little research work can be found through the analytical solutions. Under most circumstances, researchers try to solve the differential equations by numerical means. There were many conventional numerical methods such as Spherical Harmonics method, Discrete Transfer method, Discrete Ordinate method, Zonal method, Finite Volume method, Finite Element method and Monte Carlo method [14e17]. Among them, the Monte Carlo method is excellent to solve the most complicated problems [15]. As the complexity of the problem increases, the complexity of formulation and the solution effort increase much more rapidly for convectional techniques. In contrast, the Monte Carlo method can solve it with relative ease [14,15]. Therefore, the Monte Carlo method was adopted in this paper considering the problem's complexity. 2. Model 2.1. Model introduction As shown in Fig. 1, the thermal radiation source of the RPP tester is quartz lamps. These lamps are enclosed by metal and insulation plates. The insulation plate blocks thermal energy to avoid preheating of the test sample. Together with the insulation plate, a shutter plate and a specimen holder plate are also installed between the lamp bank and the test sample. Both the insulation plate
Specimen Holder Plate
Sensor Holder Plate
Shutter Plate Insulation Plate
Sensor
Lamp Bank k
Specimen
Right View Fig. 1. A schematic for the RPP system.
Metal Plate
171
and the specimen holder plate have a window in their center. The test sample is sandwiched between two plates: the specimen holder plate and the sensor holder plate which has a bracket to hold the sensor. When the test begins, the shutter plate would be removed pneumatically, and then thermal radiation would be radiated through the windows and the space left by the shutter plate, finally reach the surface of the test sample. Generally, the convection at the outside of the quartz lamps and at the surface of the walls is large due to the high temperature. In order to eliminate convective heat to be exerted on the surface of the test sample, vertical unimpeded ventilation is designed in the lamps chamber. The convection coupling with radiation would make the problem difficult to analyze. They can be separated if the temperatures of the walls and the quartz envelops are given, and thus the radiation can be calculated independently. To simplify the analysis of the model, the following assumptions were made: (1) The temperature is uniformly distributed at the surfaces of radiant sources; (2) Radiation is emitted diffusely from the surfaces of radiant sources; (3) The quartz in the lamp is either transparent or opaque depending on the wavelength of the incident radiation; the quartz media does not participate the emitting, absorbing or scattering of the radiation, they are assumed to occur at the interface; (4) The air and the gas in quartz lamps are transparent to radiation, thus they do not participate in the emitting, absorbing or scattering of radiation; (5) The radiant effect of the ends of tungsten filaments and quartz envelops can be neglected due to the small size compared with the length; (6) Leakage of radiation through ventilation holes in RPP system can be neglected. Based on the above assumptions, standard Monte Carlo model for the RPP tester was established. A statistically meaningful random sample of energy bundles from the tungsten filament of the lamps and other radiant sources were emitted and traced. After leaving the surface of the sources, these energy bundles would be absorbed, reflected at the surface of walls, or transmitted in quartz envelops. The inside space enclosed by the plates is the boundary for the energy bundles traveling. It consists of four parts: the lamp chamber, the window in the insulting board, the space left by the removed protective shutter, and the window in the specimen holder. The modeling work includes description of the geometry, intersection detection and the simulation for radiation behaviors such as emission, reflection and absorption. The details can be found in literatures [14,15,18,19]. We mainly introduce the particular partdthe quartz lamps. Quartz lamps consist of two parts: tungsten filaments and quartz envelops. The tungsten filament is usually very fine and in the shape of spiral coil. The spiral line is so complex to describe that it was simplified as an open-ended cylinder here; the radiation was emitted from the outer surface of the cylinder. The lighted length was taken as the length of the cylinder. Although the quartz envelop is a closed tube, it was described as an open-ended tube due to the neglecting of its ends. The radiation was emitted from both the inner and outer surface. Quartz envelops are the most sophisticated participators in this system. The radiative properties were found highly wavelength dependent [20,21]. In general, the fused quartz is transparent in the range of 0.2e4.0 mm, but behaves opaque outside the range.
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Therefore, within this band (from 0.2 to 4.0 mm), radiation can be reflected or transmitted at the interfaces of quartz envelops, but can be only reflected or absorbed out of this band. Since the radiant properties of the quartz envelop of the lamps are highly dependent on the wavelength of the radiation, each energy bundle should be assigned a wavelength. The assignment of the wavelength of the energy bundles should be based on the source spectral distributions. The details can be referred in the literature [22]. The reflectivity at gasequartz or quartzegas interface is sensitive to both wavelength and incident angle (qi). Fresnel's equation was used to describe it [23]:
rðqi Þ ¼
1 r ðq Þ þ rp ðqi Þ 2 n i
rn ðqi Þ ¼
a2 þ b2 2a cos qi þ cos2 qi
(1)
a2 þ b2 þ 2a cos qi þ cos2 qi
rp ðqi Þ ¼ rn ðqi Þ
a2 þ b2 2a sin qi tan qi þ sin2 qi tan2 qi a2 þ b2 þ 2a sin qi tan qi þ sin2 qi tan2 qi
where
2a2 ¼
2b2 ¼
h2 k2 sin2 qi
2
þ 4h2 k2
1=2
þ h2 k2 sin2 qi ;
1=2 2 h2 k2 sin2 qi þ 4h2 k2 h2 k2 sin2 qi ;
h and k are the real refractive index ratio and the absorptive index ratio, respectively. h ¼ hq, k ¼ kq for the gas-quartz interface, h
k
q q for the quartzegas interface, where hq and kq are h ¼ h2 þk 2, k ¼ 2 h þk2 q
q
q
q
the real refractive index and the absorptive index of the quartz, respectively. Data for hq and kq versus the wavelength can be found in the reference [22]. If the energy bundles transmit through the interfaces of quartz envelops, the refraction may occur. The Snell's law was applied to calculate the refracted trajectory [24],
sin2 f ¼
sin2 qi h2 þ k2
(2)
where f is the refracted angle. 2.2. Statistics and calculations In this study, the heat flux and the radiation intensity were calculated by statistics. In order to simplify the description, we set a coordinate origin at the center point of the incident surface of the specimen, and established a Cartesian coordinate and a spherical coordinate system on the hemispherical space over the incident surface of the specimen (Fig. 2). 2.2.1. Heat flux When the bundles arrived at the surface of the sensor or a target surface grid, they would be counted to a variable h. The heat flux at the sensor surface can be calculated by
q ¼ lim
N/þ∞
n Qt N A
(3)
where Qt is the total emissive power by all radiant sources, N is the total number emitted by the sources and A is the area of the sensor or the target surface grid.
Fig. 2. Coordinate system in the RPP apparatus: a) Cartesian coordinate. b) Spherical coordinate.
2.2.2. Radiation intensity The radiation intensity may be obtained by counting the number of energy bundles received by the sensor from a direction. However, it would be very inefficient when the target is a small area or a small solid angle in the standard Monte Carlo method [25,26]. This is because only a little portion of the bundles would enter the target. Although it is not a good way, in this study we still attempted to calculate the radiation intensity by emitting a huge amount of energy bundles (1011) to obtain enough quantity for statistics. The radiation intensity Iðq; 4Þ for a direction ðq; 4Þ was calculated by
Iðq; 4Þ ¼
¼
dQ ðq; 4Þ nðq; 4ÞQt ¼ lim A cos qdu N/ þ ∞; NA cos qDu Du/0 nðq; 4ÞQt Z lim N/ þ ∞; NAD4 cos q sin qdq Dq/0; Dq D4/0
(4)
where q is the polar angle, and 4 is the azimuth angle (measured between the positive x direction and the projection of reverse ray incident direction on the incident specimen surface), Du is a solid angle increment around the direction (q,4), Q ðq; 4Þ is the energy of
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the radiation incident from the direction (q,4) and nðq; 4Þ is the number of bundles incident from Du into the sensor surface.
Cut out of Specimen Holder Plate
y
3. Validation and experiments
Shutter Plate Specimen Holder Plate
10 5 -54 -40 -20
64
To validate the model, experiments using a RPP apparatus (Richmond, USA) were conducted. The RPP tester is also called RHP tester in ASTM F2702 [27]. ASTM F2702 describes the detailed dimensions of the apparatus. It was found from the measurements that the RPP apparatus used in this study is different from the descriptions in the ASTM F2702. As shown in Fig. 3, the top edge of the cut-out in the insulation plate is 8 mm higher than that in the standard. Besides, the lighted length is about 178 mm, while it is 127 mm in the standard; the gap between two neighboring quartz envelops is about 1 mm, whereas the gap in the standard is 0.4 mm. Our experiments were conducted at a central incident heat flux of 21 kW/m2. The test sample and the sensor holder plate were replaced by the sensor to directly measure the incident heat flux distribution. The sensor was not fixed at the center of the window any more as that in RPP test; it was placed at different sites on the horizontal central line and the vertical central line of the specimen holder window in the XOY plane to measure heat flux (Fig. 4). In these tests, the detecting surface of the sensor was always in the XOY plane. Besides, the heat flux received from different directions was also determined by rotating the sensor around the point (x ¼ 0, y ¼ 0, z ¼ 76 mm) at the front of the specimen holder plate window as shown in Fig. 5. The model was coded using Visual Cþþ (Microsoft, USA). The object orientated programming technology was applied to make an efficient coding. As the Monte Carlo computation needs tracing a large amount of energy bundles, it is CPU-time consuming.
O
-5 20 -10
40
54
152
Specimen Holder Plate
Front View Fig. 4. Locations of the sensor in the measurement of the heat flux on the horizontal central line and the vertical central line.
Therefore, the parallel computation technology was adopted by using twenty threads to trace energy bundles parallel so that the speed increased 20 times. The program was run on a server (Dell Precision T5610, USA) configured with two 6-core CPUs (Intel® Xeon® CPU [email protected] GHz). The temperatures of Quartz envelopes, insulation walls, metal walls, shutter chamber walls and specimen holder window were 894 K, 556 K, 546 K, 370 K and 298 K, respectively. The temperature of filament was estimated as 1625 K according to the Keltner's measurements [3]. The radiative parameters configured in this
Insulation Plate
8.0
Metal Plate
1.0 63.5
0.4
Sensor
Lamp Bank k
Specimen Standard ASTM F2702-08
x
Apparatus(Richmond, USA)
Testing status
Right view Fig. 3. Differences at the cut-out of the insulation plate between the experiment apparatus and that described in the standard ASTM F2702.
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Fig. 5. Locations of the sensor in the measurement of the directional heat flux. Fig. 6. Distribution of the horizontal heat flux at the specimen's incident surface.
model are listed in Table 1. The emissivity for quartz envelops in this table is only used to estimate the emissive power. The properties for the calculation of reflection, absorption and transmission at quartz envelops should be referred to Part 2.1. The absorptivity (a) was not listed in this table because its value equals to the emissivity. In this model, we attempted to replace the tungsten filaments of the complex spiral line geometry by simple cylinders of the same length, an equivalent diameter of the cylinders need to be found out. It was found that an equivalent diameter of 1.3 mm would result in the calculated central heat flux at a reasonable level. Hence, in this model, the diameter of the filament cylinders was set to 1.3 mm. After emitted a large quantity of energy bundles (106), the convergent solution was obtained. Figs. 6e8 show the predicted results of the heat flux at the horizontal central line, the vertical central line and the directional heat flux, respectively. It can be seen that the numerical results fit very well with the experimental ones. The incident heat flux distributes relatively uniform at the central region at the level of 21 kW/m2, while it decreases to 16 kW/ m2 at the edge region. Symmetry about the y-axis for the horizontal heat flux curve can be found from both the numerical and experimental results. However, symmetry about the x-axis for the vertical heat flux distribution curve was only found from the experimental results. The numerical results show a slightly higher value at the top region. This will be discussed in the next section. The directional heat flux is the one with different directions that the target surface faces towards the lamp chamber. Its curve is symmetric about the y-axis with the peak at the zero degree. It denotes that the maximum heat flux occurs when the target plane facing towards the center of the specimen window, while it would decay rapidly as the target rotating away from the center of the window. In order to determine the uncertainty of numerical results due to the uncertainty of radiative parameters in Table 1, sensitivity analysis was carried out. OAT approach was employed to evaluate the sensitivity impacts of each parameter. In OAT approach, only one parameter changes each time while the others keep at the
baseline values. The baseline values were assigned with the values listed in Table 1 for the parameters. The predicted heat flux at the center was used as the target variable of the model for the sensitivity analysis. By changing one of the parameters in a relative range of [5%, 5%], compared with the baseline, the target variable varied in a range of [0.69%, 1.20%], [0.18%, 0.32%], [1.70%, 1.85%], [2.72%, 2.86%], [0.49%, 0.41%] for the emissivity of insulation plates, metal plates, tungsten filaments, quartz envelops and sensor surface, respectively. And it also varied in a range of [0.22%, 0.14%] and [0.57%, 0.45%] for the specula reflectivity of metal plates and quartz envelops, respectively. It shows that the model's outcome is not sensitive to these parameters. This may indicate the reasonableness of the values in Table 1.
Fig. 7. Vertical heat flux distribution at the specimen's incident surface.
Table 1 Radiative parameters of the radiation participators. Radiation participators
Emissivity (ε)
Specula reflectivity (rs)
Diffuse reflectivity (rd)
Insulation plates Metal plates Tungsten filaments Quartz envelops Sensor surface
0.96 0.19 0.39 0.48 0.90
0.00 0.56 0.00 See Part 2.1 0.00
0.04 0.25 [18] 0.61 0.00 0.10
(Asbestos board, [15]) (Aluminum, [15]) ([15]) ([22]) [27]
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Fig. 8. Directional heat flux distribution at the specimen incident surface.
4. Results and discussion The validation roughly presents the numerical results of the heat flux distribution, for that the calculated value actually is the average over the disk area of the sensor surface. The disk area with the diameter of 40 mm is relatively large compared with the size of specimen window (152 mm 64 mm). Therefore, a high resolution image of the incident heat flux is necessary to clearly examine the incident heat flux. Besides, the radiation intensity distribution is another issue we are concerned about.
Fig. 9. The numerical results for the heat flux at the incident surface of the fabric: a) The experiment apparatus. b) The standard apparatus.
4.1. Heat flux distribution at the incident surface of the test sample In order to obtain a high resolution image of the heat flux distribution over the whole incident surface of the specimen, we divided the incident surface of the specimen into 152 64 grids. After tracing an amazing large amount (109) of energy bundles the high resolution image of the incident heat flux was obtained and shown in Fig. 9a. The color (in web version) of a point represents the value of heat flux at this position. Although the image is unsmooth because of the variance distributed in the image in the form of noise, it would not be an accuracy problem as the coefficient of the variation is less than 0.6%. The existence of uncertainty is due to the inherently statistical nature of the Monte Carlo method [25]. Fig. 9a shows an elliptical region with relatively high values at the central area. In this region, the heat flux is almost uniformly distributed with the range of [20.7, 21.9] kW/m2. Obviously, this uniform region almost enclosed the detecting area in RPP test (the circular area with the diameter of 40 mm at the center). Outside this region, the heat flux decreases rapidly with the minimal value of 7.7 kW/m2. The values on the central lines are found to be different from that shown in Figs. 7 and 8. This is mainly because that the predicted heat fluxes in Figs. 7 and 8 is the average value over the sensor surface area. It may not be difficult to understand the heat concentrates in the center of the target surface, but the vertical asymmetry may let you doubt about the correctness. In order to verify it, a piece of plain paper and a moisture barrier for firefighters' ensembles were exposed to the radiation in RPP system; it was found that the surface turned brown (in web version). The depth of the color indicates the level of the heat flux. As shown in Fig. 10, the top region obviously has a deeper color than the bottom, which confirms the correctness of predicted results. The vertical asymmetry of the heat flux distribution can be explained by the vertical asymmetry of the insulation cut-out with respect to the
Fig. 10. The picture of materials after being exposed to the incident radiation of the RPP tester: a) Plain paper. b) Moisture barrier for firefighters' ensembles.
XOZ plane as shown in Fig. 3. The excess 8 mm cut-out on the top of the insulation plate compared with the standard leads to an excess exposure to thermal radiation. To further prove this point, a numerical simulation was made for the standard RPP apparatus. The numerical results (in Fig. 9b) for the standard RPP apparatus clearly demonstrate the vertical symmetry of heat flux distribution. The vertical symmetry results in the experiments can be explained that the sensor is not sensitive enough to distinguish the fine difference for the averaged heat flux over a 40 mm-diameter disk area. 4.2. The radiation intensity distribution at the specimen's incident surface Fig. 11 shows the radiation intensity received by the sensor located at the center of the incident surface. This figure uses twodimensional polar coordinates to present the radiation intensity Iðq; 4Þ under three-dimensional spherical coordinates. The radius in polar coordinates represents the polar angle q in the spherical
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radiation intensity for the brightest bands (621.8 C) can be found to be 11.6 kW/m2sr. It's close to the numerical result (around 12 kW/m2sr).
I¼
εsT 4 p
(5)
where s is StefaneBoltzmann's constant and T is temperature. It can be seen from Fig. 12 that the highest intensity bands are at around the gap region. However, the bands' width (about 3 mm) is obviously larger than that of the gap. By counting the source of the energy bundles incident from the direction (q ¼ 6 , f ¼ 90 ), we found that the maximum fraction (51.0%) is from transmitting through neighboring quartz envelops, and only 16.2% is from the reflection at the metal wall behind the gap. Therefore, the highest intensity bands are attributed to the radiation transmitting from the edge of quartz envelops nearby the gap. 5. Conclusions Fig. 11. The numerical results for radiation intensity received by the sensor at the center of the incident surface of the specimen.
coordinates, and the polar angle in polar coordinates represents the azimuth angle 4 in the spherical coordinates. Each point ðq; 4Þ in this image corresponds a direction of ðq; 4Þ in the spherical coordinates. The value of Iðq; 4Þ is indicated by the color of the point ðq; 4Þ. The image shows a surprisingly high similarity to the picture of the RPP chamber taken from a hemispherical camera. The red part (I > 9 kW/m2sr) corresponds to the lamp bank; the yellow (I z 8 kW/m2sr) and the light blue (I z 6 kW/m2sr) are the walls in the lamp chamber; and the deep blue (in web version) (I z 2 kW/ m2sr) are the low-temperature walls in the shielding chamber and the sample holder. The top weak light blue area should be the uncovered part due to the excess cut-out in the insulation plate. It should also be noted that the highest value of radiation intensity emerges on the two horizontal lines that symmetrically lying within the red region. There are another two lines at the outside of them. These four lines correspond to the gap region between two neighboring lamps. The next task is to determine whether the highest intensity is from the gap of the quartz envelop. This may be proved from the photo taken by an infrared camera (FLIR T440, FLIR system Inc., USA) as shown in Fig. 12. Although it is usually used to measure temperatures, the infrared camera essentially detects the radiation intensity, and converts it to a temperature value by assuming that it originates from isotropic radiation emission. Therefore, the radiation intensity values can be obtained by converting backward using Equation (5). For convenience, we preset the emissivity parameter to 1.0 for the camera. By conversion, the
A model based on the Monte Carlo method was developed to numerically analyze the radiation distribution in the Radiant Protective Performance test apparatus. The incident radiant heat flux distribution at the surface of test specimen and the incident radiation intensity distribution in the hemispherical space upon the center of the specimen surface were calculated for a RPP apparatus. The heat fluxes show a uniformly distributed area with a relatively high level at the center region. The heat flux at the top area of the whole incident surface is higher than that at the bottom due to the uncovered excessive 8 mm cut-out at the top of the insulation plate in the RPP apparatus. The radiation intensity image demonstrates a highly degree similarity to the picture of the inside space of RPP taken by a hemispherical camera located at the center point of the specimen window. It is evident that the radiation intensity is not parallel or uniformly distributed on the hemispherical space. The high level region corresponds to the lamp chamber and the highest radiation intensity comes from the edge of quartz envelops nearby the gap. Acknowledgments This work was supported by the National Natural Science Foundation of China (Project No. 51106021), the Fundamental Research Funds for the Central Universities of China (Project No. 2012D10122, No. 2013D110120 and No. 2014D110139) and Science & Technology Funds of Zhejiang Province of China (Project No. 2013C31006). Nomenclature A d I lim N n O Q q T x,y,z
Fig. 12. Photo taken by the infrared camera.
area, m2 differential radiation intensity, kW/m2sr limit of a function total number of energy bundles emitted by the sources the number of energy bundles coordinate origin the power of radiation, W heat flux, kW/m2 temperature, K Cartesian coordinates
Greek symbols a absorptivity D increment of a variable
X. Wan et al. / International Journal of Thermal Sciences 94 (2015) 170e177
ε
h q k r s
f 4
u
emissivity refractive index polar angle, incident angle or angle between the normal of the sensor surface and z axis absorptive index reflectivity StefaneBoltzmann's constant, 5.67 108 W/m2K4 refracted angle azimuthal angle solid angle
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