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Measurement of gas temperature distributions in a test furnace using spectral remote sensing
Journal of Quantitative Spectroscopy & Radiative Transfer 73 (2002) 517 – 528
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Measurement of gas temperature distributions in a test furnace using spectral remote sensing Hyun Keol Kim, Tae-Ho Song ∗ Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea Received 20 August 2001
Abstract Measurement of a temperature pro/le of a hot gas is made using the Spectral Remote Sensing (SRS) method. Emphasis is placed on the accuracy of the SRS method in a test furnace with intense radiation emerging from the gas as well as from the rear wall. Kerosene is used as the fuel and a 2 m long stainless steel (STS) tube is employed as the test furnace. In calculating spectral intensity, the CK-based WNB model is used. By minimizing the error between the measured spectral intensities and the computed ones, the temperature pro/le along the line-of-sight is recovered. To demonstrate the SRS method, the recovered temperatures are compared with measured temperatures using thermocouples. The recovered temperature pro/le and measured temperatures are in good agreement within an error of 4%. Especially, the hot rear wall is found to a:ect the overall performance of the SRS method signi/cantly through relatively heavily weighted Planck distribution there. The SRS method, however, proves to be applicable in determining the temperature distribution of the gas with a reasonable accuracy whether the rear wall is hot or cold. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: SRS; CO2 4:3 m; CK-based WNB model; Test furnace; Gas temperature pro/les; Hot rear walls
1. Introduction Various optical methods of temperature measurement in hot gases have been introduced [1–3]. Among them, the Spectral Remote Sensing (SRS) method yields temperature pro/les along a line of sight through an inversion procedure using the measured spectral data. It is comprised of compact devices and provides multi-dimensional information of the gas temperature distribution by a simple angular scanning through a few sensing ports. At present, the SRS technique is potentially ∗
Corresponding author. Tel.: +82-428-693-032; fax: +82-428-693-210. E-mail address: [email protected] (T.-H. Song).
0022-4073/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 1 ) 0 0 2 0 6 - 0
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recommended as a strong candidate of practical application, since it has the advantages of relatively simple instrumentation and good accuracy. In this study, the SRS method is applied to a 2 m long Stainless Steel (STS) tube with a hot or cold rear wall to determine the line-of-sight temperature distribution of the gas and also the rear wall. The CO2 4:3 m wide band is used as the sensing spectra because this band does not overlap with other wide bands of CO or H2 O and CO2 is always a product of hydrocarbon combustion likely which is utilized in most practical energy systems. Improvement and /nal determination of the temperature pro/le are made minimizing the error between the measured narrow band intensities and those calculated for a temperature pro/le using the gas absorption database. The absorption coeKcient of the CO2 4:3 m band can be generated using any method in the open literature [4 –7]. In this study, the correlated-k (CK)-based WNB model of Yang and Song [8] is selected since it has the advantage of saving computation time without sacri/cing accuracy compared with the line-by-line (LBL) method [9] and has been reported as an optimal model for the CO2 4:3 m band to be used in the SRS method [4,10]. Application of the SRS method in an engineering problem was /rst made by Krakow [11] in the late 1960s. Since then many researchers have endeavored to improve the accuracy of SRS through various inversion techniques [12,13]. Their results were not very satisfactory possibly due to the poor database of CO2 radiative properties at that time. Only lately, Woo [10] obtained promising results for a 0:8 m long quartz tube. His work veri/es the inversion method using the CO2 4:3 m band suggested by Yang [4], but is limited to a relatively short path length with a cold rear wall. This study is an extension to a realistic industrial situation on the base of Yang’s and Woo’s works [4,10]. The objective of the present study is to investigate e:ects of hot rear walls with a thicker gas layer on the accuracy of the SRS method. For this purpose, the spectral radiation emitted from combustion gas Oowing through a STS tube is measured. The characteristics and actual applicability is discussed in detail. 2. Gas emission model and inversion technique Consider the gas layer /lled with inhomogeneous absorbing and emitting media with an arbitrary temperature pro/le as seen in Fig. 1. For a mathematical formulation, we make two assumptions.
Fig. 1. Schematic of the SRS method.
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First, the system is in local thermodynamic equilibrium, which allows use of the Kircho:’s and the Planck’s laws. Second, the scattering coeKcient is negligibly small compared to the absorption coeKcient. Under these assumptions, the spectral intensity I (0) at location s = 0 is given by the following expression: L L @ (0 − s) ds; (1) Ib [T (s)] I (0) = I (L)e− 0 ds − @s 0 where represents wavenumber, (0−s), transmissivity between s=0 to s, and s, distance into the gas slab. The /rst term is the amount of radiation leaving the rear wall (I (L)), attenuated exponentially by absorption over the gas layer, and the second is the contribution by the gas emission. The above equation shows a simple relationship between the spectral intensity I (0) at location s = 0 and source functions related to emission and absorption in the medium. This fact makes it possible to determine the temperature distribution using the remotely sensed intensity I (0). We take terms of narrow bands in a wide band, and the above equation can be rewritten using the CK-based WNB model as follows: L s − 0L j (s) ds Wj e + Ib (s) Wj e− 0 j (s ) ds j (s) ds; (2) Ii; c (0) = I (L) j
0
j
where the spectral intensity Ii; c is an averaged one over ith narrow band at s = 0, the j ’s are the discrete gray gas absorption coeKcients, and Wj ’s are the spectral weighting factor. Note that here is the average value in a narrow band and it does not change from one temperature to another [4]. In the /rst term, the leaving radiation at the rear wall is assumed to be non-correlated to the /ne gas spectral variation in the narrow band. There are many SRS algorithms to minimize the error between the computation (Eq. (2)) and the measurement as described in detail in Ref. [4]. In brief, the scheme employed in the present study starts with taking several nodal temperatures and assuming a temperature pro/le between them. Terms of spectral intensity measurements are taken to compare with the computations. Since, we take more number of measurements than the nodal temperature, the error is not exactly zero and the most we can expect is a minimum, in other words, the problem is overdeterministic [13]. Here, we introduce the parameters describing the temperature pro/le more in detail. We try two types of temperature pro/les. The /rst is a linear one between the neighboring points with a total of N nodal temperatures. The nodal location will be addressed in detail later. The following equation is the temperature pro/le of the second kind: 1=n T = Tc − (Tc − T0 ) − 1 ; 0 6 6 c ; c − c n ; c 6 6 1; T = Tc − (Tc − TL ) (3) 1 − c where T0 ; Tc and TL mean the temperatures at the exit, at the gas inlet and at the rear end wall of the STS tube (to be explained later from Fig. 2a), respectively. The assumed pro/le usually has a peak at the gas inlet point. is the normalized coordinate (s=L with c that of Tc ), and n is a shape parameter and is preassigned some reasonable value. The e:ect of pro/le parameters when varying nodal points and the shape parameter n will be also discussed later. Note that in both of
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Fig. 2. Measurement system; (a) STS tube used as the test furnace for SRS application; (b) Schematic of the measurement system aligned with optical components for SRS.
the pro/les, the rear wall also has a temperature, either high or low, and it is assumed that there is no temperature jump between the neighboring gas and the rear wall. 3. Experimental study The test furnace is shown in Fig. 2. The STS tube is 2 m long and 0:12 m in inner diameter. Installed in front of the STS tube, a sensing port of 0:025 m diameter allows the gas and the rear wall to be viewed from outside. Basically, the whole test furnace consists of three main parts; i.e., the combustion part, the insulation part, and the cooling part (see Fig. 2a). A domestic Kitturami Turbo-30 burner capable of blowing combustion gas at a velocity of about 2 m=s into the STS tube is selected, and Kerosene is used as the fuel. Typically, the heat capacity for this burner is 30; 000 kcal=h. The combustion part is enclosed with a rock wool of 50 mm thickness for temperature elevation up to about 1500 K. The cooling water jacket leads to a temperature drop in the direction of the sensor. Various gas temperature pro/les can be set up by controlling the water Oow rate through the annular water jacket as the water is supplied from a water tank at a constant height of 4 m. In this research, the experimental conditions have been adjusted to produce a gas temperature drop from about 1500 K to almost 800 K. Note that the rear end wall of the STS tube (opposite to the sensing port), can be either cold or hot depending on whether the water jacket is installed or not. As mentioned in the introduction, one of the objectives of this work is to investigate the e:ect of the rear wall on the accuracy of SRS method. To meet this purpose, various materials, such as refractories and oxidized iron are experimented. The end wall water jacket of Fig. 2a is replaced with di:erent wall conditions. The optical apparatus for spectral measurement is shown in Fig. 2b. All optical components are placed in a dark room to be free from background noise. The emitted light is focused into a 500 m rectangular entrance slit of the ARIES FF500MS monochromator. Dimension of the grating is 65 mm × 65 mm, ruled to 100 g=mm. The optics for light collection is set together with two irises to give a narrow /eld with a solid angle of less than 0:0002 sr. At a distance of 2:6 m, this gives
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a /eld of view of approximately 20 mm in diameter. Therefore, the radiation arriving at the IR sensor is solely from the gas layer and the rear wall. The spectral radiation from the combustion gas is measured using an EG& G Indium antimonide (InSb) detector which has been chosen for its excellent sensitivity in the range of 1.2–5 m. The detector is precisely aligned and /xed on the 200 m exit slit of the monochromator. By doing this the reproducibility under identical experimental conditions can be achieved. Also, as a phase sensitive amplifying circuit, the EG& G 5210 Lock-in Ampli/er is employed with a chopper. Ambient radiation is /ltered out through modulation of the signals. To extract the best performance from the IR sensor, the chopper frequency is set to 1 kHz, the ampli/er sensitivity to 3 V, and time constant to 300 ms. K type thermocouples of diameter in 0:05 mm with a T-shield are applied to measure gas temperature for comparison with the inverted values. The accuracy of the thermocouple reported by the manufacturer is ±0:375% when it is free from other noises; the additional error by radiation=convection interaction is compensated to limit the error within ±2:09%. The calibration test is made for the monochromator and the detector. Also since absorption by atmospheric CO2 in the 4:3 m band is very strong even for the standard atmospheric concentration, this absorption all the way from the port to the detector is taken into account in the following way. The spectral intensity from an electric furnace is measured at a distance equivalent to the sensing port. The furnace is a blackbody reference and the signal is calibrated using the Planck distribution. By doing this, atmospheric absorption in the real experiment is automatically compensated. A blackbody furnace (Barnstead Thermolyne-FB1310M26) is chosen as a reference source since its precise intensity distribution with temperature and wavelength is known a priori. The furnace is aligned with the same solid angle as the monochromator views the gas during an actual experiment. The strength of the output signal is calibrated to the blackbody intensity. The error of calibration is within 2.1% with 95% reliability. Before starting spectral measurements, temperatures and concentrations at three nodal points (i.e., the rear end wall of the STS tube, the gas inlet, and the gas exit) are monitored until it reaches a desired state. The concentration measurement is made using a Horiba MEXA-554JK gas analyzer. First, a gas calibration for CO and CO2 is performed using a high purity standard gas. Sampling is made at the three nodal points. This procedure is repeated until the concentration variation is within 0.5% so that the combustion is complete before the gas enters the STS tube. The CO2 concentration reaches 10:2 ± 0:5% and the CO concentration is as low as 0.001%. In this research, the CO2 concentration is indeed constant over the whole optical path even though a constant CO2 concentration may not be true in real furnaces and especially in combustors. Once a desired temperature pro/le has been reached and a constant concentration is obtained, spectral data are taken at 7 cm−1 intervals from 2045 to 2451 cm−1 . These ‘low resolution’ spectral intensities are regarded as the average intensities of each narrow band. When all spectral radiation measurements are completed, thermocouple scanning is made at every 10 cm and compensated for the error. Fluctuations in the thermocouple reading are within ±5 K. This is most likely due to slight shift of the temperature pro/le caused by Ouctuations in the gas Oow. Data are obtained for three types of the rear wall conditions: the water-jacket wall (cold wall), the gray wall emissivity with high temperature, and variation of the wall temperature. Every experiment is run at least /ve times for reproducibility, and all the results are con/rmed to be nearly identical. Also the Oux emitted by the gas and reOected by the rear wall to the detector can be shown to be negligible in this study. The irradiance G from the gas to the rear wall is approximately Ib; g (1−e−Le )
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where Le is the mean beam length of the gas. The value of Le is of the order of tube diameter D, making Le very small. The overall inversion procedure results in ±0:2% in the /nal temperature. 4. Results and discussion The transmission function means the spatial weighting factor for the Planck’s radiation function. View Eq. (1) for the mathematical expression. If the intensity from the rear wall is solely from self-emission, we can rewrite it, using the rear wall emissivity w , as Eq. (4) to follow: L Ib [T (s)] Kg (s; ) ds; (4) I (0) = Ib [T (L)] w Kw (L; ) + 0
where Kw (L; ) and Kg (s; ) are, respectively, the wall-side transmission function and the gas-side one given by the following de/nitions: Kw (L; ) = e− Kg (s; ) = e−
L 0
s 0
ds
ds
;
:
(5)
The transmission functions show quantitatively on what region along the gas slab, the outgoing radiance I (0) is mainly dependent. Thus proper sensing spectra should be selected to give a fair distribution of transmission function peaks. The expressions for the mean Kw (L; ) and Kg (s; ) over each narrow band are given using the CK-based WNB model as follows (see Eq. (2)): L Kw (L; ) = Wj e− 0 j (s) ds ; j
Kg (s; ) =
W j e−
s 0
j (s ) ds
j :
(6)
j
The /gures to follow show only part of the typical bands describing the spectral behavior of the transmission function. Fig. 3a shows spatial transmission functions at the shorter wavelengths outside the CO2 4:3 m band for a typical temperature pro/le (measured with thermocouples) with the hot rear wall. As can be seen from this information, generally the gas transmission function Kg (s; ) is much smaller than Kw (L; ) and it is almost constant over all distance s. This /gure shows that these outer narrow bands can be used as the sensing spectra of the rear wall temperature. As shown in the open literature [3,4,12], the temperature drop-o: beyond an intervening peak makes the gas in the farther region contribute less to the measured intensity than those near the sensor due to absorption by the front gas layer. Consequently this results in the poor accuracy in determining the temperature beyond the peak, making the inversion ‘ill-posed’ there. On the other hand, we can accurately determine the temperature pro/le in the hot region near the peak, for Kg (s; ) being heavy weighted there. Fig. 3b con/rms this characteristic for the long wavelength region. For the inner spectra of the CO2 4:3 m band, the gas transmission function Kg (s; ) at the CO2 4:3 m band is highly emphasized at s = 0; i.e., these narrow bands are recommended for temperature measurement at s = 0 (see Fig. 3c). In all of the spectra, the temperature beyond the hot peak is weighted very small. For practical applications, transmission functions are unknown in advance. For this reason, a large number of narrow bands having a variety of transmission functions
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Fig. 3. Gas transmission function Kg (s; ) and wall transmission function Kw (L; ) for a typical temperature pro/le (T0 = 924 K; Tc = 1413 K; TL = 1146 K) with the hot rear wall (w = 0:35); (a) at the shorter wavelengths outside the CO2 4:3 m band; (b) at the longer wavelengths outside the CO2 4:3 m band; (c) inside the CO2 4:3 m band.
should be used simultaneously so that favorable transmission functions are likely to be included among them. In this research all 59 narrow bands between 2045 and 2451 cm−1 are used in the inversion procedure. First, the e:ect of the number of nodal points N is examined with the refractory wall condition /xed at emissivity 0.35 and temperature 1135 K while the gas temperature distributions between nodes are assumed to be linear (the /rst kind). Inversion results for N = 3, 5, and 7 are shown in Fig. 4a together with the measured pro/le. The overall error is greater than 10% with this linear pro/le. The result oscillates as N increases. For N = 3 and 5, there is no oscillation, however, the solution does not reveal peak temperature accurately. This underestimation may be due to taking the relative error of temperature as the objective function in this practice. Also, a penalty function to prevent the oscillatory temperature distribution for large N may be helpful.
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1500
measured profile inverted profile (N=3) inverted profile (N=5) inverted profile (N=7)
1400
1300
1300
Tem perature (K)
Temperature (K)
m easured profile inverted profile (n=1.5) inverted profile (n=1.8) inverted profile (n=2.0)
1400
1200
1100
1200
1100
1000
1000
900
900 0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing hole (m)
0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing hole (m )
(a)
(b)
Fig. 4. Result of inversion calculation (w = 0:35); (a) when varying the number of nodal points: N = 3, 5, and 7; (b) when varying the shape parameter n with N = 3. Table 1 Errors of T0 ; TC and TL (K) when varying the shape parameter n with N = 3 (w = 0:35) Measured temp. (K) Computed with
n = 1:5 n = 1:8 n = 2:0
T0 = 924:1
TC = 1409
TL = 1135
925.5 (0.15%) 926.5 (0.26%) 927.1 (0.32%)
1388.7 (1.44%) 1405.9 (0.22%) 1413.3 (0.3%)
1130.2 (0.42%) 1129.8 (0.46%) 1129.6 (0.48%)
Next, the second pro/le (Eq. (3) with n = 1) is tested. The power n of Eq. (3) is given 1.5, 1.8, and 2.0 while the number of nodal points is /xed as 3. Table 1 and Fig. 4b show that all the results for n = 1:5, 1.8, and 2.0 agree well with measured temperatures with an upper limit error of 2%. This practice gives a superior result than the former one. Therefore, only the second pro/le is employed hereafter and the power n is taken as 1.5 throughout. The typical calculation time for the second kind of pro/le is 5 s on an AMD Athlon 600 MHz processor for 10 iterations for the /nal temperature pro/le and it is of a similar magnitude with the /rst kind of temperature pro/le. E:ect of wall emissivities on the accuracy of the SRS method is studied next. Two types of refractories and an oxidized steel plate are tried: a white smooth refractory of = 0:35, a white refractory with = 0:65 by cavities on the surface, and strongly oxidized steel plate of = 0:95. The above are the measured emissivities, which are determined by comparing with the emissions of the blackbody furnace at high temperatures of 1000 K or greater. Fig. 5 shows intensity spectra with the wall emissivity at an instance TL = 1100 to 1200 K(the temperatures of the gas and the rear wall to be shown later). As shown in this /gure, an increase in the wall emissivity gives a considerable increase in the spectral intensity outside the CO2 4:3 m band, while for the inner region it does not. This phenomenon results from the spectral behavior of Kw (L; ) at the wall as seen in Fig. 3a. Consequently the increase in Kw (L; ) outside the strong bands of 4:3 m can be used to accurately measure the wall temperature.
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525
14
re fra c to ry (ε = 0 .3 5 ) re fra c to ry ( ε = 0 .6 5 ) re fra c to ry ( ε = 0 .9 5 )
13
11
-1
Intensity ( W/m cm )
12
2
10 9 8 7 6 5 4 3 2 2000
2100
2200
2300
2400
2500
-1
Wavenumber (cm )
Fig. 5. Intensity spectra with the rear wall emissivity variation at an instance when TL = 1146 K.
9
measured profile (TL=1146K) inverted profile (TL=1138K)
measured intensities inverted intensities
8 -1
Spectral intensity (W/m cm )
1400
7
Temperature (K)
2
1300
1200
1100
1000
6
5
4
3 900
0.0
0.5
1.0
1.5
Distance from the sensing port (m)
(a)
2.0
2.5
2 2000
2100
2200
2300
2400
2500
-1
Wavenumber (cm )
(b)
Fig. 6. Comparison between the measured and the reconstructed temperature pro/les (a) and the spectral intensities (b) at an instance when TL = 1146 K.
One of the inversion results is shown in Fig. 6a and the rest are given in Table 2. As is expected, the spectral intensities outside the 4:3 m band reveal the wall temperature very accurately. Table 2 shows that the error is smaller when the wall emissivity is greater (see the next section for other temperatures). This is due to enhanced intensity from the wall for greater wall emissivity. The recovered temperatures are in good agreement with those measured by thermocouples within an error of 1%. Also, as can be found from Fig. 6b, the spectral intensity reconstructed from the inverted temperature pro/le (Fig. 6a) agrees well with the measurement. In this section, we proceed with discussion on the wall temperature. First, experiments with the cold rear wall with water jacket are conducted. The inversion result shows good agreement with the real pro/le; the results at T0 ; Tc and TL are within relative errors of 0.6%, 1.4% and 12.2%, respectively.
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Table 2 Errors of T0 ; TC and TL (K) when varying wall emissivity Wall emissivity
Thermocouple T0 SRS (error)
Thermocouple TC SRS (error)
Thermocouple TL SRS (error)
w = 0:35
924 926.4 (0.26%) 930 927.6 (0.26%) 930 931.5 (0.16%)
1413.7 1404.4 (0.66%) 1430 1417.9 (0.85%) 1455.5 1466 (0.72%)
1146.8 1138.5 (0.72%) 1148.7 1161.5 (1.11%) 1201.5 1197.5 (0.33%)
w = 0:65 w = 0:95
1500 9
W all tem perature ( ε =0.65) 776K 955K 1100K 1148K
8
1300
-1
Intensity (W /m cm )
7
measured profile (TL=776K) inverted profile (TL=750K)
1400
2
Temperature (K)
6 5 4 3 2
1200 1100 1000 900 800
1
700 0 2000
2100
2200
2300
2400 -1
W avenum ber (cm )
(a)
2500
0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing port (m)
(b)
Fig. 7. Results varying the wall temperature; (a) measured spectral distributions with the rear wall temperature variation; (b) inverted temperature pro/le using spectral data obtained at the rear wall temperature TL = 776 K and emissivity w = 0:65.
An inspection of the results indicates that the error increases slightly near the rear wall. As discussed previously, this trend in the error is due to the low value of Kg (s; ) at the rear wall. Consequently this gives rise to a large inversion error over the gas layer beyond the peak temperature. It is diKcult to improve this error as long as only one side measurement is performed. Next, the hot rear walls are tested while heating up the refractory wall (w = 0:65). Fig. 7a shows spectral intensities for various wall temperatures. Apparently, increase in the wall temperature gives similar results to those in the emissivity variation. However, the results show an increase in the spectral intensities in the inner bands of the CO2 4:3 m band. This phenomenon is related to gas transmission function Kg (s; ) at the front region. Since the intensities in the region are highly weighted at the temperature near the sensor as shown in Fig. 3c, the temperature rise at the front region (see Table 2) gives rise to the increase in the intensities as shown in Fig. 7a.
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Table 3 Errors of T0 ; TC and TL (K) when varying the rear wall temperature (w = 0:65) Thermocouple T0 SRS (error)
Thermocouple TC SRS (error)
Thermocouple TL SRS (error)
821 815.3 852.8 845.3 900 895.4 930 927.6
1413.2 1395.9 1413.2 1396.9 1421 1402.5 1430 1417.9
776.1 750.6 (3.29%) 955.2 952.1 (0.32%) 1100.1 1073.7 (2.40%) 1148.7 1161.5 (1.11%)
(0.69%) (0.88%) (0.51%) (0.26%)
(1.22%) (1.15%) (1.30%) (0.85%)
A temperature pro/le is given in Fig. 7b. Recovered temperature pro/les of Table 3 are in good agreement with the measured ones. Like in the emissivity variation, an increase in the wall temperature is not so inOuential to the overall accuracy of inversion. 5. Conclusion The experimental results demonstrate that the temperature distribution in the gas can be determined using the SRS method to errors within approximately 1% for T0 , 1.5% for Tc , and 3.5% for TL whether or not there is a strong emission from the rear wall. The SRS method is experimentally veri/ed and its limitations are determined by comparison between the measured and the inverted temperatures. Assumption of the temperature pro/le is very critical to the inversion accuracy. For a linear pro/le between nodes, the inversion does not retrieve the peak temperature accurately, regardless of the number of nodal points N . This inaccuracy can be improved by assuming the proper temperature pro/le describing the physical constraints. Next, the rear wall (or the background refractory) temperature can be accurately measured by using a gas-transparent spectral intensity. This increased accuracy is made possible by virtue of the relatively heavily weighted transmission function of short wavelength at the rear wall. The error presented in this work should be considered as an underestimation for a real application, since considerable number of factors a:ecting SRS, such as concentration error, particle scattering, etc are not taken into account in this work. Nonetheless, the present work is believed to be a valuable for future applicability of SRS, for the treatment of closed combustion situations similar to realistic cases. For further study, the SRS method deserves more research regarding the e:ects of particle scattering and concentration error. Acknowledgements This work has been supported by the Brain Korea 21 project and the National Research Laboratory project of the Ministry of Science and Technology, Korea, and the Korea Science and Engineering Foundation (996-1000-001-2).
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Measurement of gas temperature distributions in a test furnace using spectral remote sensing Hyun Keol Kim, Tae-Ho Song ∗ Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea Received 20 August 2001
Abstract Measurement of a temperature pro/le of a hot gas is made using the Spectral Remote Sensing (SRS) method. Emphasis is placed on the accuracy of the SRS method in a test furnace with intense radiation emerging from the gas as well as from the rear wall. Kerosene is used as the fuel and a 2 m long stainless steel (STS) tube is employed as the test furnace. In calculating spectral intensity, the CK-based WNB model is used. By minimizing the error between the measured spectral intensities and the computed ones, the temperature pro/le along the line-of-sight is recovered. To demonstrate the SRS method, the recovered temperatures are compared with measured temperatures using thermocouples. The recovered temperature pro/le and measured temperatures are in good agreement within an error of 4%. Especially, the hot rear wall is found to a:ect the overall performance of the SRS method signi/cantly through relatively heavily weighted Planck distribution there. The SRS method, however, proves to be applicable in determining the temperature distribution of the gas with a reasonable accuracy whether the rear wall is hot or cold. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: SRS; CO2 4:3 m; CK-based WNB model; Test furnace; Gas temperature pro/les; Hot rear walls
1. Introduction Various optical methods of temperature measurement in hot gases have been introduced [1–3]. Among them, the Spectral Remote Sensing (SRS) method yields temperature pro/les along a line of sight through an inversion procedure using the measured spectral data. It is comprised of compact devices and provides multi-dimensional information of the gas temperature distribution by a simple angular scanning through a few sensing ports. At present, the SRS technique is potentially ∗
Corresponding author. Tel.: +82-428-693-032; fax: +82-428-693-210. E-mail address: [email protected] (T.-H. Song).
0022-4073/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 1 ) 0 0 2 0 6 - 0
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recommended as a strong candidate of practical application, since it has the advantages of relatively simple instrumentation and good accuracy. In this study, the SRS method is applied to a 2 m long Stainless Steel (STS) tube with a hot or cold rear wall to determine the line-of-sight temperature distribution of the gas and also the rear wall. The CO2 4:3 m wide band is used as the sensing spectra because this band does not overlap with other wide bands of CO or H2 O and CO2 is always a product of hydrocarbon combustion likely which is utilized in most practical energy systems. Improvement and /nal determination of the temperature pro/le are made minimizing the error between the measured narrow band intensities and those calculated for a temperature pro/le using the gas absorption database. The absorption coeKcient of the CO2 4:3 m band can be generated using any method in the open literature [4 –7]. In this study, the correlated-k (CK)-based WNB model of Yang and Song [8] is selected since it has the advantage of saving computation time without sacri/cing accuracy compared with the line-by-line (LBL) method [9] and has been reported as an optimal model for the CO2 4:3 m band to be used in the SRS method [4,10]. Application of the SRS method in an engineering problem was /rst made by Krakow [11] in the late 1960s. Since then many researchers have endeavored to improve the accuracy of SRS through various inversion techniques [12,13]. Their results were not very satisfactory possibly due to the poor database of CO2 radiative properties at that time. Only lately, Woo [10] obtained promising results for a 0:8 m long quartz tube. His work veri/es the inversion method using the CO2 4:3 m band suggested by Yang [4], but is limited to a relatively short path length with a cold rear wall. This study is an extension to a realistic industrial situation on the base of Yang’s and Woo’s works [4,10]. The objective of the present study is to investigate e:ects of hot rear walls with a thicker gas layer on the accuracy of the SRS method. For this purpose, the spectral radiation emitted from combustion gas Oowing through a STS tube is measured. The characteristics and actual applicability is discussed in detail. 2. Gas emission model and inversion technique Consider the gas layer /lled with inhomogeneous absorbing and emitting media with an arbitrary temperature pro/le as seen in Fig. 1. For a mathematical formulation, we make two assumptions.
Fig. 1. Schematic of the SRS method.
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First, the system is in local thermodynamic equilibrium, which allows use of the Kircho:’s and the Planck’s laws. Second, the scattering coeKcient is negligibly small compared to the absorption coeKcient. Under these assumptions, the spectral intensity I (0) at location s = 0 is given by the following expression: L L @ (0 − s) ds; (1) Ib [T (s)] I (0) = I (L)e− 0 ds − @s 0 where represents wavenumber, (0−s), transmissivity between s=0 to s, and s, distance into the gas slab. The /rst term is the amount of radiation leaving the rear wall (I (L)), attenuated exponentially by absorption over the gas layer, and the second is the contribution by the gas emission. The above equation shows a simple relationship between the spectral intensity I (0) at location s = 0 and source functions related to emission and absorption in the medium. This fact makes it possible to determine the temperature distribution using the remotely sensed intensity I (0). We take terms of narrow bands in a wide band, and the above equation can be rewritten using the CK-based WNB model as follows: L s − 0L j (s) ds Wj e + Ib (s) Wj e− 0 j (s ) ds j (s) ds; (2) Ii; c (0) = I (L) j
0
j
where the spectral intensity Ii; c is an averaged one over ith narrow band at s = 0, the j ’s are the discrete gray gas absorption coeKcients, and Wj ’s are the spectral weighting factor. Note that here is the average value in a narrow band and it does not change from one temperature to another [4]. In the /rst term, the leaving radiation at the rear wall is assumed to be non-correlated to the /ne gas spectral variation in the narrow band. There are many SRS algorithms to minimize the error between the computation (Eq. (2)) and the measurement as described in detail in Ref. [4]. In brief, the scheme employed in the present study starts with taking several nodal temperatures and assuming a temperature pro/le between them. Terms of spectral intensity measurements are taken to compare with the computations. Since, we take more number of measurements than the nodal temperature, the error is not exactly zero and the most we can expect is a minimum, in other words, the problem is overdeterministic [13]. Here, we introduce the parameters describing the temperature pro/le more in detail. We try two types of temperature pro/les. The /rst is a linear one between the neighboring points with a total of N nodal temperatures. The nodal location will be addressed in detail later. The following equation is the temperature pro/le of the second kind: 1=n T = Tc − (Tc − T0 ) − 1 ; 0 6 6 c ; c − c n ; c 6 6 1; T = Tc − (Tc − TL ) (3) 1 − c where T0 ; Tc and TL mean the temperatures at the exit, at the gas inlet and at the rear end wall of the STS tube (to be explained later from Fig. 2a), respectively. The assumed pro/le usually has a peak at the gas inlet point. is the normalized coordinate (s=L with c that of Tc ), and n is a shape parameter and is preassigned some reasonable value. The e:ect of pro/le parameters when varying nodal points and the shape parameter n will be also discussed later. Note that in both of
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Fig. 2. Measurement system; (a) STS tube used as the test furnace for SRS application; (b) Schematic of the measurement system aligned with optical components for SRS.
the pro/les, the rear wall also has a temperature, either high or low, and it is assumed that there is no temperature jump between the neighboring gas and the rear wall. 3. Experimental study The test furnace is shown in Fig. 2. The STS tube is 2 m long and 0:12 m in inner diameter. Installed in front of the STS tube, a sensing port of 0:025 m diameter allows the gas and the rear wall to be viewed from outside. Basically, the whole test furnace consists of three main parts; i.e., the combustion part, the insulation part, and the cooling part (see Fig. 2a). A domestic Kitturami Turbo-30 burner capable of blowing combustion gas at a velocity of about 2 m=s into the STS tube is selected, and Kerosene is used as the fuel. Typically, the heat capacity for this burner is 30; 000 kcal=h. The combustion part is enclosed with a rock wool of 50 mm thickness for temperature elevation up to about 1500 K. The cooling water jacket leads to a temperature drop in the direction of the sensor. Various gas temperature pro/les can be set up by controlling the water Oow rate through the annular water jacket as the water is supplied from a water tank at a constant height of 4 m. In this research, the experimental conditions have been adjusted to produce a gas temperature drop from about 1500 K to almost 800 K. Note that the rear end wall of the STS tube (opposite to the sensing port), can be either cold or hot depending on whether the water jacket is installed or not. As mentioned in the introduction, one of the objectives of this work is to investigate the e:ect of the rear wall on the accuracy of SRS method. To meet this purpose, various materials, such as refractories and oxidized iron are experimented. The end wall water jacket of Fig. 2a is replaced with di:erent wall conditions. The optical apparatus for spectral measurement is shown in Fig. 2b. All optical components are placed in a dark room to be free from background noise. The emitted light is focused into a 500 m rectangular entrance slit of the ARIES FF500MS monochromator. Dimension of the grating is 65 mm × 65 mm, ruled to 100 g=mm. The optics for light collection is set together with two irises to give a narrow /eld with a solid angle of less than 0:0002 sr. At a distance of 2:6 m, this gives
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a /eld of view of approximately 20 mm in diameter. Therefore, the radiation arriving at the IR sensor is solely from the gas layer and the rear wall. The spectral radiation from the combustion gas is measured using an EG& G Indium antimonide (InSb) detector which has been chosen for its excellent sensitivity in the range of 1.2–5 m. The detector is precisely aligned and /xed on the 200 m exit slit of the monochromator. By doing this the reproducibility under identical experimental conditions can be achieved. Also, as a phase sensitive amplifying circuit, the EG& G 5210 Lock-in Ampli/er is employed with a chopper. Ambient radiation is /ltered out through modulation of the signals. To extract the best performance from the IR sensor, the chopper frequency is set to 1 kHz, the ampli/er sensitivity to 3 V, and time constant to 300 ms. K type thermocouples of diameter in 0:05 mm with a T-shield are applied to measure gas temperature for comparison with the inverted values. The accuracy of the thermocouple reported by the manufacturer is ±0:375% when it is free from other noises; the additional error by radiation=convection interaction is compensated to limit the error within ±2:09%. The calibration test is made for the monochromator and the detector. Also since absorption by atmospheric CO2 in the 4:3 m band is very strong even for the standard atmospheric concentration, this absorption all the way from the port to the detector is taken into account in the following way. The spectral intensity from an electric furnace is measured at a distance equivalent to the sensing port. The furnace is a blackbody reference and the signal is calibrated using the Planck distribution. By doing this, atmospheric absorption in the real experiment is automatically compensated. A blackbody furnace (Barnstead Thermolyne-FB1310M26) is chosen as a reference source since its precise intensity distribution with temperature and wavelength is known a priori. The furnace is aligned with the same solid angle as the monochromator views the gas during an actual experiment. The strength of the output signal is calibrated to the blackbody intensity. The error of calibration is within 2.1% with 95% reliability. Before starting spectral measurements, temperatures and concentrations at three nodal points (i.e., the rear end wall of the STS tube, the gas inlet, and the gas exit) are monitored until it reaches a desired state. The concentration measurement is made using a Horiba MEXA-554JK gas analyzer. First, a gas calibration for CO and CO2 is performed using a high purity standard gas. Sampling is made at the three nodal points. This procedure is repeated until the concentration variation is within 0.5% so that the combustion is complete before the gas enters the STS tube. The CO2 concentration reaches 10:2 ± 0:5% and the CO concentration is as low as 0.001%. In this research, the CO2 concentration is indeed constant over the whole optical path even though a constant CO2 concentration may not be true in real furnaces and especially in combustors. Once a desired temperature pro/le has been reached and a constant concentration is obtained, spectral data are taken at 7 cm−1 intervals from 2045 to 2451 cm−1 . These ‘low resolution’ spectral intensities are regarded as the average intensities of each narrow band. When all spectral radiation measurements are completed, thermocouple scanning is made at every 10 cm and compensated for the error. Fluctuations in the thermocouple reading are within ±5 K. This is most likely due to slight shift of the temperature pro/le caused by Ouctuations in the gas Oow. Data are obtained for three types of the rear wall conditions: the water-jacket wall (cold wall), the gray wall emissivity with high temperature, and variation of the wall temperature. Every experiment is run at least /ve times for reproducibility, and all the results are con/rmed to be nearly identical. Also the Oux emitted by the gas and reOected by the rear wall to the detector can be shown to be negligible in this study. The irradiance G from the gas to the rear wall is approximately Ib; g (1−e−Le )
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where Le is the mean beam length of the gas. The value of Le is of the order of tube diameter D, making Le very small. The overall inversion procedure results in ±0:2% in the /nal temperature. 4. Results and discussion The transmission function means the spatial weighting factor for the Planck’s radiation function. View Eq. (1) for the mathematical expression. If the intensity from the rear wall is solely from self-emission, we can rewrite it, using the rear wall emissivity w , as Eq. (4) to follow: L Ib [T (s)] Kg (s; ) ds; (4) I (0) = Ib [T (L)] w Kw (L; ) + 0
where Kw (L; ) and Kg (s; ) are, respectively, the wall-side transmission function and the gas-side one given by the following de/nitions: Kw (L; ) = e− Kg (s; ) = e−
L 0
s 0
ds
ds
;
:
(5)
The transmission functions show quantitatively on what region along the gas slab, the outgoing radiance I (0) is mainly dependent. Thus proper sensing spectra should be selected to give a fair distribution of transmission function peaks. The expressions for the mean Kw (L; ) and Kg (s; ) over each narrow band are given using the CK-based WNB model as follows (see Eq. (2)): L Kw (L; ) = Wj e− 0 j (s) ds ; j
Kg (s; ) =
W j e−
s 0
j (s ) ds
j :
(6)
j
The /gures to follow show only part of the typical bands describing the spectral behavior of the transmission function. Fig. 3a shows spatial transmission functions at the shorter wavelengths outside the CO2 4:3 m band for a typical temperature pro/le (measured with thermocouples) with the hot rear wall. As can be seen from this information, generally the gas transmission function Kg (s; ) is much smaller than Kw (L; ) and it is almost constant over all distance s. This /gure shows that these outer narrow bands can be used as the sensing spectra of the rear wall temperature. As shown in the open literature [3,4,12], the temperature drop-o: beyond an intervening peak makes the gas in the farther region contribute less to the measured intensity than those near the sensor due to absorption by the front gas layer. Consequently this results in the poor accuracy in determining the temperature beyond the peak, making the inversion ‘ill-posed’ there. On the other hand, we can accurately determine the temperature pro/le in the hot region near the peak, for Kg (s; ) being heavy weighted there. Fig. 3b con/rms this characteristic for the long wavelength region. For the inner spectra of the CO2 4:3 m band, the gas transmission function Kg (s; ) at the CO2 4:3 m band is highly emphasized at s = 0; i.e., these narrow bands are recommended for temperature measurement at s = 0 (see Fig. 3c). In all of the spectra, the temperature beyond the hot peak is weighted very small. For practical applications, transmission functions are unknown in advance. For this reason, a large number of narrow bands having a variety of transmission functions
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Fig. 3. Gas transmission function Kg (s; ) and wall transmission function Kw (L; ) for a typical temperature pro/le (T0 = 924 K; Tc = 1413 K; TL = 1146 K) with the hot rear wall (w = 0:35); (a) at the shorter wavelengths outside the CO2 4:3 m band; (b) at the longer wavelengths outside the CO2 4:3 m band; (c) inside the CO2 4:3 m band.
should be used simultaneously so that favorable transmission functions are likely to be included among them. In this research all 59 narrow bands between 2045 and 2451 cm−1 are used in the inversion procedure. First, the e:ect of the number of nodal points N is examined with the refractory wall condition /xed at emissivity 0.35 and temperature 1135 K while the gas temperature distributions between nodes are assumed to be linear (the /rst kind). Inversion results for N = 3, 5, and 7 are shown in Fig. 4a together with the measured pro/le. The overall error is greater than 10% with this linear pro/le. The result oscillates as N increases. For N = 3 and 5, there is no oscillation, however, the solution does not reveal peak temperature accurately. This underestimation may be due to taking the relative error of temperature as the objective function in this practice. Also, a penalty function to prevent the oscillatory temperature distribution for large N may be helpful.
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1500
measured profile inverted profile (N=3) inverted profile (N=5) inverted profile (N=7)
1400
1300
1300
Tem perature (K)
Temperature (K)
m easured profile inverted profile (n=1.5) inverted profile (n=1.8) inverted profile (n=2.0)
1400
1200
1100
1200
1100
1000
1000
900
900 0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing hole (m)
0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing hole (m )
(a)
(b)
Fig. 4. Result of inversion calculation (w = 0:35); (a) when varying the number of nodal points: N = 3, 5, and 7; (b) when varying the shape parameter n with N = 3. Table 1 Errors of T0 ; TC and TL (K) when varying the shape parameter n with N = 3 (w = 0:35) Measured temp. (K) Computed with
n = 1:5 n = 1:8 n = 2:0
T0 = 924:1
TC = 1409
TL = 1135
925.5 (0.15%) 926.5 (0.26%) 927.1 (0.32%)
1388.7 (1.44%) 1405.9 (0.22%) 1413.3 (0.3%)
1130.2 (0.42%) 1129.8 (0.46%) 1129.6 (0.48%)
Next, the second pro/le (Eq. (3) with n = 1) is tested. The power n of Eq. (3) is given 1.5, 1.8, and 2.0 while the number of nodal points is /xed as 3. Table 1 and Fig. 4b show that all the results for n = 1:5, 1.8, and 2.0 agree well with measured temperatures with an upper limit error of 2%. This practice gives a superior result than the former one. Therefore, only the second pro/le is employed hereafter and the power n is taken as 1.5 throughout. The typical calculation time for the second kind of pro/le is 5 s on an AMD Athlon 600 MHz processor for 10 iterations for the /nal temperature pro/le and it is of a similar magnitude with the /rst kind of temperature pro/le. E:ect of wall emissivities on the accuracy of the SRS method is studied next. Two types of refractories and an oxidized steel plate are tried: a white smooth refractory of = 0:35, a white refractory with = 0:65 by cavities on the surface, and strongly oxidized steel plate of = 0:95. The above are the measured emissivities, which are determined by comparing with the emissions of the blackbody furnace at high temperatures of 1000 K or greater. Fig. 5 shows intensity spectra with the wall emissivity at an instance TL = 1100 to 1200 K(the temperatures of the gas and the rear wall to be shown later). As shown in this /gure, an increase in the wall emissivity gives a considerable increase in the spectral intensity outside the CO2 4:3 m band, while for the inner region it does not. This phenomenon results from the spectral behavior of Kw (L; ) at the wall as seen in Fig. 3a. Consequently the increase in Kw (L; ) outside the strong bands of 4:3 m can be used to accurately measure the wall temperature.
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14
re fra c to ry (ε = 0 .3 5 ) re fra c to ry ( ε = 0 .6 5 ) re fra c to ry ( ε = 0 .9 5 )
13
11
-1
Intensity ( W/m cm )
12
2
10 9 8 7 6 5 4 3 2 2000
2100
2200
2300
2400
2500
-1
Wavenumber (cm )
Fig. 5. Intensity spectra with the rear wall emissivity variation at an instance when TL = 1146 K.
9
measured profile (TL=1146K) inverted profile (TL=1138K)
measured intensities inverted intensities
8 -1
Spectral intensity (W/m cm )
1400
7
Temperature (K)
2
1300
1200
1100
1000
6
5
4
3 900
0.0
0.5
1.0
1.5
Distance from the sensing port (m)
(a)
2.0
2.5
2 2000
2100
2200
2300
2400
2500
-1
Wavenumber (cm )
(b)
Fig. 6. Comparison between the measured and the reconstructed temperature pro/les (a) and the spectral intensities (b) at an instance when TL = 1146 K.
One of the inversion results is shown in Fig. 6a and the rest are given in Table 2. As is expected, the spectral intensities outside the 4:3 m band reveal the wall temperature very accurately. Table 2 shows that the error is smaller when the wall emissivity is greater (see the next section for other temperatures). This is due to enhanced intensity from the wall for greater wall emissivity. The recovered temperatures are in good agreement with those measured by thermocouples within an error of 1%. Also, as can be found from Fig. 6b, the spectral intensity reconstructed from the inverted temperature pro/le (Fig. 6a) agrees well with the measurement. In this section, we proceed with discussion on the wall temperature. First, experiments with the cold rear wall with water jacket are conducted. The inversion result shows good agreement with the real pro/le; the results at T0 ; Tc and TL are within relative errors of 0.6%, 1.4% and 12.2%, respectively.
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Table 2 Errors of T0 ; TC and TL (K) when varying wall emissivity Wall emissivity
Thermocouple T0 SRS (error)
Thermocouple TC SRS (error)
Thermocouple TL SRS (error)
w = 0:35
924 926.4 (0.26%) 930 927.6 (0.26%) 930 931.5 (0.16%)
1413.7 1404.4 (0.66%) 1430 1417.9 (0.85%) 1455.5 1466 (0.72%)
1146.8 1138.5 (0.72%) 1148.7 1161.5 (1.11%) 1201.5 1197.5 (0.33%)
w = 0:65 w = 0:95
1500 9
W all tem perature ( ε =0.65) 776K 955K 1100K 1148K
8
1300
-1
Intensity (W /m cm )
7
measured profile (TL=776K) inverted profile (TL=750K)
1400
2
Temperature (K)
6 5 4 3 2
1200 1100 1000 900 800
1
700 0 2000
2100
2200
2300
2400 -1
W avenum ber (cm )
(a)
2500
0.0
0.5
1.0
1.5
2.0
2.5
Distance from the sensing port (m)
(b)
Fig. 7. Results varying the wall temperature; (a) measured spectral distributions with the rear wall temperature variation; (b) inverted temperature pro/le using spectral data obtained at the rear wall temperature TL = 776 K and emissivity w = 0:65.
An inspection of the results indicates that the error increases slightly near the rear wall. As discussed previously, this trend in the error is due to the low value of Kg (s; ) at the rear wall. Consequently this gives rise to a large inversion error over the gas layer beyond the peak temperature. It is diKcult to improve this error as long as only one side measurement is performed. Next, the hot rear walls are tested while heating up the refractory wall (w = 0:65). Fig. 7a shows spectral intensities for various wall temperatures. Apparently, increase in the wall temperature gives similar results to those in the emissivity variation. However, the results show an increase in the spectral intensities in the inner bands of the CO2 4:3 m band. This phenomenon is related to gas transmission function Kg (s; ) at the front region. Since the intensities in the region are highly weighted at the temperature near the sensor as shown in Fig. 3c, the temperature rise at the front region (see Table 2) gives rise to the increase in the intensities as shown in Fig. 7a.
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Table 3 Errors of T0 ; TC and TL (K) when varying the rear wall temperature (w = 0:65) Thermocouple T0 SRS (error)
Thermocouple TC SRS (error)
Thermocouple TL SRS (error)
821 815.3 852.8 845.3 900 895.4 930 927.6
1413.2 1395.9 1413.2 1396.9 1421 1402.5 1430 1417.9
776.1 750.6 (3.29%) 955.2 952.1 (0.32%) 1100.1 1073.7 (2.40%) 1148.7 1161.5 (1.11%)
(0.69%) (0.88%) (0.51%) (0.26%)
(1.22%) (1.15%) (1.30%) (0.85%)
A temperature pro/le is given in Fig. 7b. Recovered temperature pro/les of Table 3 are in good agreement with the measured ones. Like in the emissivity variation, an increase in the wall temperature is not so inOuential to the overall accuracy of inversion. 5. Conclusion The experimental results demonstrate that the temperature distribution in the gas can be determined using the SRS method to errors within approximately 1% for T0 , 1.5% for Tc , and 3.5% for TL whether or not there is a strong emission from the rear wall. The SRS method is experimentally veri/ed and its limitations are determined by comparison between the measured and the inverted temperatures. Assumption of the temperature pro/le is very critical to the inversion accuracy. For a linear pro/le between nodes, the inversion does not retrieve the peak temperature accurately, regardless of the number of nodal points N . This inaccuracy can be improved by assuming the proper temperature pro/le describing the physical constraints. Next, the rear wall (or the background refractory) temperature can be accurately measured by using a gas-transparent spectral intensity. This increased accuracy is made possible by virtue of the relatively heavily weighted transmission function of short wavelength at the rear wall. The error presented in this work should be considered as an underestimation for a real application, since considerable number of factors a:ecting SRS, such as concentration error, particle scattering, etc are not taken into account in this work. Nonetheless, the present work is believed to be a valuable for future applicability of SRS, for the treatment of closed combustion situations similar to realistic cases. For further study, the SRS method deserves more research regarding the e:ects of particle scattering and concentration error. Acknowledgements This work has been supported by the Brain Korea 21 project and the National Research Laboratory project of the Ministry of Science and Technology, Korea, and the Korea Science and Engineering Foundation (996-1000-001-2).
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