- Email: [email protected]
Thermal behaviour of a LiF crystal mounted in a TLD card and heated by jet impingement
Radiation Measurements 46 (2011) 1432e1435
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Thermal behaviour of a LiF crystal mounted in a TLD card and heated by jet impingement R. Rozenfeld a, T. Bar-Kohany a, M. Weinstein b, A. Abraham b, U. German b, *, Z.B. Alfassi a, G. Ziskind a a b
Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Nuclear Research Centre Negev, P.O.B 9001, Beer-Sheva 84190, Israel
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 November 2010 Received in revised form 28 April 2011 Accepted 13 June 2011
A numerical model is developed to predict the actual temperature profile evolution in a crystal contained in a TLD card that is used in advanced gas heating TLD reader systems. The flow field above the detector and the resulting heat transfer to and within the crystal are obtained directly, and no empirical constants or adjustment parameters are used. It is found that the typical time lag between the crystal temperature and the jet temperature is about 5 s, for the heating rate of 25 K/s. The calculated temperature profile is substituted into a first-order kinetic model equation (RandalleWilkins) to obtain the glow curve, and the results are compared to experimental findings. It is shown that the location of the peaks resulting from the calculated temperature profile overlaps those of the experimental results. Thus, calibration is conducted only to match the intensity of the TL peaks. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Temperature Simulation Crystal LiF
1. Introduction A typical commercial thermo-luminescence dosimeter (TLD) card consists of a LiF crystal covered by a Teflon (PTFE) foil. The most widespread use of TLD is in routine monitoring, where a vast number of cards and limited readout time are the major constraints. As a result, most of the cards must be read employing a high-rate heating profile. Additional constraints, such as the Teflon cover, further limit the temperature for maximum readout, since Teflon can be damaged at temperatures above 300 C. The discussion here focuses on one of the common and modern methods of heating, namely by a hot gas jet. The hot gas reader is described in detail elsewhere (Moscovitch et al., 1990). The TL card is placed in a fitted slot, and then a hot Nitrogen jet is turned on, impacting the card at the detector position in the direction normal to its plane. The jet temperature is pre-determined and measured continuously. However, the temperature of the crystal itself is neither controlled nor measured throughout the readout. It is obvious that heat transfer from the jet to the TL crystal is time-dependent, therefore there is a time lag between the jet temperature and the actual crystal temperature. This lag is influenced by geometrical parameters and material properties, including the presence of the Teflon protecting layer.
Since the crystal temperature is the physical property that determines the shape of the glow curve, it is essential to predict it. Few attempts of modelling the transient temperature behaviour of the crystal can be found in the literature (Piters and Bos, 1994; Kumar et al., 2005; Stadtmann et al., 2002, 2006). In these studies, the temperature of the crystal was assumed to be spatially uniform. Stadtmann et al. (2006, 2002) calculated the gas heated crystal temperature evolution by fitting two parameters. The first describes conduction, forced convection and the second describes thermal radiation. By fitting the first parameter the difference between the theoretical and experimental glow curves was minimized. The second parameter determines the maximum temperature the detector can reach and plays a role only in the last, constant, part of the heating profile. Kumar et al., 2005 fitted the parameter that determines how fast the clamping temperature is achieved, controlling the time lag between the jet and crystal temperatures. The present study deals with a complete numerical solution for a typical TLD package, which includes a 0.9 mm crystal and the Teflon cover. Temperature evolution of the crystal is computed directly, and yields a glow curve which is compared to experimental results. 2. Experimental setup
* Corresponding author. Tel.: þ972 86469632; fax: þ972 86900727. E-mail address: [email protected] (U. German). 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.06.042
The equipment used in the present study included commercially available TLD cards and a Model 6600 hot gas reader, manufactured
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
by Harshaw (now Thermo Scientific). The TLD cards are a 43 30 mm2 rigid aluminium frame with four 9 mm round holes containing 3 3 0.9 mm3 LiF:Mg,Ti (TLD-100) square crystals (the most widespread material used for personnel dosimetry). The crystals are mounted in the holes between two layers of 0.06 mm Teflon. The procedure for card reading was a routine one, with a linear gas heating profile starting at 323 K, a linear heating rate of 25 K/s and consequently a maximum constant temperature of 573 K for a few seconds. As a result of the heating, a glow curve is produced, which can be analyzed for exposure evaluation. 3. Numerical model An attempt was made to reproduce in the model the geometrical and structural parameters of the actual heating chamber, as well as the hydrodynamic and thermal characteristics of the jet and crystal assembly. Still, some simplifications, which did not affect the essential features of the actual device, were required to facilitate the numerical solution. Fig. 1 presents a schematic description of the heating chamber with its relevant physical features and dimensions. 3 3 0.9 mm3 crystals were assumed, fully coated by a 0.06 mm Teflon layer. The numerical approach is based on the solution of transient two-dimensional conservation equations. Accordingly, the numerical model is axisymmetric, i.e. the square-shaped crystal is replaced with a similar round one. The Teflon cover is round-shaped as in the actual card. In reality, the Teflon layers enfold the crystal and then approach one another beyond the crystal edge, enclosing some air. This gradual decrease in the thickness and the presence of air were neglected in this study (see Fig. 1), as it does not affect the heat transfer between the jet and the crystal. It was also decided to model the entire lateral surface of the crystal as being in touch with Teflon. Calculations performed by replacing the Teflon on the side of the LiF crystal by stagnant air yielded results different only by several percent. We note that as the crystal was assumed to be round (rather than square-shaped), an attempt to model the Teflon shape "accurately" would have been rather artificial. However, the influence of different boundary conditions, as well as different physical properties (like the Teflon thickness), will be further investigated in the future. For normal operating conditions, (atmospheric pressure and temperature that varies from 300 K to 573 K), Nitrogen may be considered an ideal gas. Also, within the above mentioned
1433
temperature span (273 K), its thermophysical properties may be considered as constant. No-penetration and no-slip conditions were assumed for the walls. The bottom wall that contacts the card slot was modelled as adiabatic. The discharge orifice, denoted as "jet entry" in Fig. 1, was modelled as "velocity inlet". The adjacent boundary was modelled as an adiabatic wall. The exit port of the model (the right-side wall in Fig. 1) was modelled as "pressure outlet" since it is open to the atmosphere. The maximum heat flux by radiation during the entire heating process was estimated to be at least an order of magnitude smaller than the heat flux by convection. For this reason, radiation has been neglected. The thermal contact resistance between the crystal and Teflon layer is extensively analyzed elsewhere (Rozenfeld, in preparation). ANSYSÒ-12.1 (formerly Fluent) software is used as the platform. A grid of 2100 cells is used as presented in Table 1. The cells are aligned with the direction of flow, as recommended by ANSYSÒ. Very thin cells are used for the Teflon layer because of its small thickness. Overall, there are 60 cells in the axial direction and 35 in the radial one. These values were adopted after a careful grid refinement procedure. Grid independency was checked, and it was found that a further increase in the grid density had a negligible effect on both the velocity and temperature fields: for instance, doubling the number of cells, either in the radial or axial directions, altered the results by less than 0.5%. The model sensitivity to the time step was checked, as well. It was found that the difference in results between time steps of 0.01 s and 0.001 s was less than 0.5%. Therefore, a time step of 0.01 s was used. A comprehensive validation work has been done by solving several models by the present numerical method in order to ensure the reliability of its predictions (Rozenfeld, in preparation). In particular, the numerical results were compared with an analytical solution for the plane stagnation flow (White, 1991), and with the works which investigated transient confined jets (Chiriac and Ortega, 2001). 4. Thermal behaviour analysis First, the thermal behaviour of both the LiF and the Teflon layer, as a result of heating by a Nitrogen jet at a typical constant temperature of 573 K, was modelled. Fig. 2 presents a typical velocity field that evolves as a result of a 100 m/s jet entering from a single round nozzle (SRN). The jet velocity was calculated from the measured Nitrogen flow rate, the geometry of the SNR and the gas properties. A steady velocity distribution is reached after a few milliseconds. The temperature distribution within the crystal is also presented, for the instant of 1 s after jet initiation. It can be observed that the temperature distribution is not spatially uniform. We note that non-uniformity of the crystal temperature in the axial direction would have been more significant without the Teflon cover: the low thermal conductivity of Teflon, (kTeflon ¼ 0.25 W/m/K vs.
Table 1 Cell dimensions. Zone
Cell dimensions
Aspect ratio
Maina FBLb Teflonc Crystal
0.15 0.3 mm2 0.05 0.1 mm2 0.006 0.1 mm2 0.05 0.1 mm2
2 2 16.7 2
a b
Fig. 1. Schematic description of the system.
c
Main flow field, see Fig. 1. FBL denotes a 0.5 mm thick flow boundary layer above the Teflon. The Teflon layer above the crystal.
1434
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
Fig. 2. Simulated flow field and crystal temperature.
kLiF ¼ 4 W/m/K) negatively affects the overall heat transfer between the jet and the crystal, thus less heat is transferred to the crystal. One can also see from Fig. 2 that the radial temperature variation is not significant. This is due to the fact that the crystal and jet diameters are similar. It should be stressed that these results, as well as all other results presented in this work, are given for a crystal thickness of 0.9 mm. Fig. 3 presents the evolution of the maximum and minimum LiF temperatures during the first 10 s of a step heating to 573 K. The difference between the maximum and minimum temperatures across the crystal reaches maximum 24 K during the readout process. The results show that it takes more than 15 s for the crystal to reach the jet temperature. In a routine TLD readout process, a linear gas heating profile with a starting temperature of 323 K, a linear heating rate of 25K /s and a maximum constant temperature of 573 K for some seconds are used. Fig. 4 presents the simulated crystal temperature evolution for this real jet heating profile. The temperature difference across the crystal in this case reaches a maximum of 13 K during the readout process, and the time needed for the crystal to reach the temperature of the jet is about 30 s. 5. Glow curve analysis A first-order kinetic model (Randall and Wilkins, 1945) was applied to describe each peak in the glow curve. In the temperature range to which the crystal is exposed during the readout, mainly peaks no. 1 through 5 are expected. However, since peak 1 decays very fast at room temperature, its contribution will be negligible. For gamma irradiation, the peaks higher than peak 5 are also not significant. In order to facilitate calculations, the original RandalleWilkins equation is substituted with an approximate expression e Eq. (5e16) from Pagonis et al. (2006):
Fig. 3. Simulated temperature evolution for a step heating to 573 K; comparison of the jet and crystal temperatures.
Fig. 4. Simulated temperature evolution for a linear jet heating profile (for a heating rate of 25 K/s up to 573 K): comparison of the jet and crystal temperatures.
" IðTÞ E ¼ s$exp $exp n0 kB T # 2kB T 1 E
! skB T 2 E $exp bE kB T ð1Þ
where I is the intensity; E and S are the activation energy and frequency of the specific peak; n0 is the density of the trapped electrons for that peak; b is the actual heating rate of the crystal, thus being the result of the heating profile used; kB is the Boltzmann constant; T is the time-dependent crystal temperature (in Kelvin). The values of n0 are dependent on the radiation dose absorbed by the crystal. This parameter is different for the different peaks. The heating rate, b, is determined based on the simulation results, as:
bðtÞ ¼
DT T Tt ¼ Dtþt Dt Dt
(2)
where DT is the simulated increase in the crystal temperature over the time period Dt. Typically, we use Dt ¼ 0.02 s in the present calculations. For each peak, the calculation is done as follows: For the whole readout process, from t ¼ 0 to t ¼ 30 s, see Fig. 4, the instant simulation temperatures, T(t), and heating rates, b(t), defined by Eq. (2), are substituted into Eq. (1). The corresponding values of E and S from Taylor and Lilley (1978) were used for each specific peak. As a result, the intensity for each peak, In, normalized by the density of the trapped electrons for that peak, n0n, is obtained. Thus, while the exact shape of the glow curve depends on n02, n03, n04, and n05, the position of each peak (maximum) in time can be
Fig. 5. Comparison of experimental and calculated glow curves for a linear heating rate of 25 K/s and a maximal jet temperature of 573 K.
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
1435
6. Conclusions
Fig. 6. Glow curves based on the jet and crystal temperature profiles for a heating rate of 25 K/s and a maximal jet temperature of 573 K.
determined by the calculation. In other words, the calculation yields the exact "location" of the peaks in time. Since the relative intensity of the different peaks depends on experimental characteristics, experimental data is necessary to fit the complete curve. The experimental data is in the form of intensity-time dependence, which is an experimentally obtained glow curve. A typical example of the experimental results and corresponding calculated glow curve is shown in Fig. 5. The values of n02, n03, n04, and n05 are chosen in order to obtain maximum agreement between the simulated (thick solid line) and measured (connected dots) curves. One can see a very good agreement for peak 2 and a good agreement in the overall shape of the glow curve. A specific comparison for peaks 3e5 can be made only after proper deconvolution of the glow curve. The agreement between experimental and simulated results is due to a rather accurate prediction of the lag between the jet and crystal temperatures. As shown in Fig. 4, this lag is different for different instants. As a result, it is different for different temperatures, and thus for the different peaks. The lag may be expressed either as the jet vs. crystal temperature at the same instant (temperature lag), or the time difference between the jet and crystal reaching the same temperature (time lag). The typical time lag between the crystal temperature and the jet temperature is about 5 s, for the heating rate of 25 K/s. The significance of the lag is further illustrated in Fig. 6. The experimental curve is reproduced from Fig. 5. The dashed curve is calculated using Eq. (1) with the jet temperature instead of the crystal temperature. The values of n0 for each peak are the same as used in Fig. 5.
The crystal temperature profile evolution was obtained by numerical modelling of the flow field of the gas jet and heat transfer from the jet to the crystal covered with a Teflon layer. The simulated temperature profile has been substituted into a firstorder kinetic model equation to obtain the glow curve. The results have been compared to experimental findings. It is shown that the locations of the peaks resulted from the calculated temperature profile overlap those of the experimental results. Calibration is conducted to match the intensity of the TL response of the different peaks by fitting n0 values of the four relevant peaks (peaks 2 to 5), thus only a four-parameter fitting for the peak intensities is conducted. The actual temperature profile in the TLD crystal significantly affects the positions of peak maxima in the glow curve. The effect of the time-dependent lag between the jet and crystal temperatures, for the linear jet-heating rate of 25 K/s, is shown quantitatively. The tool which was developed in this work is versatile and can be employed to check the influence of different experimental parameters (like the Teflon thickness, chip thickness, jet position etc.) on the shape of the glow curve. References ANSYSÒ Academic research, Release 12.1. Chiriac, V., Ortega, A., 2001. A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int. J. Heat Mass Transfer 45, 1237e1248. Kumar, M., Raja, E.A., Prasad, L.C., Popli, K.L., Kher, R.K., Bhatt, B.C., 2005. Studies on automatic hot gas reader used in the coutrywide personnel monitoring programme. Rad. Prot. Dosim. 113, 366e373. Moscovitch, M., Szalanczy, A., Bruml, W.W., Velbeck, K.J., Tawil, R.A., 1990. A TLD system based on gas heating with linear time-temperature profile. Rad. Prot. Dosim. 34, 361e364. Pagonis, V., Kitis, G., Furetta, C., 2006. Numerical and Practical Exercises in Thermoluminescence. Springer (Chapter 5), p. 156. Piters, T.M., Bos, A.J., 1994. Effects on non-ideal heat transfer on the glow curve in thermoluminescence experiments. J. Phys. D: Appl. Phys. 27, 1747e1756. Randall, J.T., Wilkins, M.F.H., 1945. The phosphorescence of various solids. Proc. R. Soc. A. 184, 347e364. Rozenfeld, R., Study of thermal behavior of a thermo-luminescence detector (TLD) due to gas heating, M.Sc. Thesis, Ben Gurion University, Beer Sheva, Israel, in preparation. Stadtmann, H., Delgado, A., Gomez-Ros, J.M., 2002. Study of real heating profiles in routine TLD readout: influence of temperature lags and non-linearities in the heating profiles on the glow curve shape. Rad. Prot. Dosim. 101, 141e144. Stadtmann, H., Hranitzky, C., Brasik, N., 2006. Study of real time temperature profiles in routine TLD read out e influence of detector thickness and heating rate on glow curve shape. Rad. Prot. Dosim. 119, 310e313. Taylor, G.C., Lilley, E., 1978. The analysis of thermoluminescent glow peaks in LiF (TLD-100). J. Phys. D: Appl. Phys. 11, 567e581. White, F.M., 1991. Viscous Fluid Flow. McGraw-Hill.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Thermal behaviour of a LiF crystal mounted in a TLD card and heated by jet impingement R. Rozenfeld a, T. Bar-Kohany a, M. Weinstein b, A. Abraham b, U. German b, *, Z.B. Alfassi a, G. Ziskind a a b
Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Nuclear Research Centre Negev, P.O.B 9001, Beer-Sheva 84190, Israel
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 November 2010 Received in revised form 28 April 2011 Accepted 13 June 2011
A numerical model is developed to predict the actual temperature profile evolution in a crystal contained in a TLD card that is used in advanced gas heating TLD reader systems. The flow field above the detector and the resulting heat transfer to and within the crystal are obtained directly, and no empirical constants or adjustment parameters are used. It is found that the typical time lag between the crystal temperature and the jet temperature is about 5 s, for the heating rate of 25 K/s. The calculated temperature profile is substituted into a first-order kinetic model equation (RandalleWilkins) to obtain the glow curve, and the results are compared to experimental findings. It is shown that the location of the peaks resulting from the calculated temperature profile overlaps those of the experimental results. Thus, calibration is conducted only to match the intensity of the TL peaks. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Temperature Simulation Crystal LiF
1. Introduction A typical commercial thermo-luminescence dosimeter (TLD) card consists of a LiF crystal covered by a Teflon (PTFE) foil. The most widespread use of TLD is in routine monitoring, where a vast number of cards and limited readout time are the major constraints. As a result, most of the cards must be read employing a high-rate heating profile. Additional constraints, such as the Teflon cover, further limit the temperature for maximum readout, since Teflon can be damaged at temperatures above 300 C. The discussion here focuses on one of the common and modern methods of heating, namely by a hot gas jet. The hot gas reader is described in detail elsewhere (Moscovitch et al., 1990). The TL card is placed in a fitted slot, and then a hot Nitrogen jet is turned on, impacting the card at the detector position in the direction normal to its plane. The jet temperature is pre-determined and measured continuously. However, the temperature of the crystal itself is neither controlled nor measured throughout the readout. It is obvious that heat transfer from the jet to the TL crystal is time-dependent, therefore there is a time lag between the jet temperature and the actual crystal temperature. This lag is influenced by geometrical parameters and material properties, including the presence of the Teflon protecting layer.
Since the crystal temperature is the physical property that determines the shape of the glow curve, it is essential to predict it. Few attempts of modelling the transient temperature behaviour of the crystal can be found in the literature (Piters and Bos, 1994; Kumar et al., 2005; Stadtmann et al., 2002, 2006). In these studies, the temperature of the crystal was assumed to be spatially uniform. Stadtmann et al. (2006, 2002) calculated the gas heated crystal temperature evolution by fitting two parameters. The first describes conduction, forced convection and the second describes thermal radiation. By fitting the first parameter the difference between the theoretical and experimental glow curves was minimized. The second parameter determines the maximum temperature the detector can reach and plays a role only in the last, constant, part of the heating profile. Kumar et al., 2005 fitted the parameter that determines how fast the clamping temperature is achieved, controlling the time lag between the jet and crystal temperatures. The present study deals with a complete numerical solution for a typical TLD package, which includes a 0.9 mm crystal and the Teflon cover. Temperature evolution of the crystal is computed directly, and yields a glow curve which is compared to experimental results. 2. Experimental setup
* Corresponding author. Tel.: þ972 86469632; fax: þ972 86900727. E-mail address: [email protected] (U. German). 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.06.042
The equipment used in the present study included commercially available TLD cards and a Model 6600 hot gas reader, manufactured
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
by Harshaw (now Thermo Scientific). The TLD cards are a 43 30 mm2 rigid aluminium frame with four 9 mm round holes containing 3 3 0.9 mm3 LiF:Mg,Ti (TLD-100) square crystals (the most widespread material used for personnel dosimetry). The crystals are mounted in the holes between two layers of 0.06 mm Teflon. The procedure for card reading was a routine one, with a linear gas heating profile starting at 323 K, a linear heating rate of 25 K/s and consequently a maximum constant temperature of 573 K for a few seconds. As a result of the heating, a glow curve is produced, which can be analyzed for exposure evaluation. 3. Numerical model An attempt was made to reproduce in the model the geometrical and structural parameters of the actual heating chamber, as well as the hydrodynamic and thermal characteristics of the jet and crystal assembly. Still, some simplifications, which did not affect the essential features of the actual device, were required to facilitate the numerical solution. Fig. 1 presents a schematic description of the heating chamber with its relevant physical features and dimensions. 3 3 0.9 mm3 crystals were assumed, fully coated by a 0.06 mm Teflon layer. The numerical approach is based on the solution of transient two-dimensional conservation equations. Accordingly, the numerical model is axisymmetric, i.e. the square-shaped crystal is replaced with a similar round one. The Teflon cover is round-shaped as in the actual card. In reality, the Teflon layers enfold the crystal and then approach one another beyond the crystal edge, enclosing some air. This gradual decrease in the thickness and the presence of air were neglected in this study (see Fig. 1), as it does not affect the heat transfer between the jet and the crystal. It was also decided to model the entire lateral surface of the crystal as being in touch with Teflon. Calculations performed by replacing the Teflon on the side of the LiF crystal by stagnant air yielded results different only by several percent. We note that as the crystal was assumed to be round (rather than square-shaped), an attempt to model the Teflon shape "accurately" would have been rather artificial. However, the influence of different boundary conditions, as well as different physical properties (like the Teflon thickness), will be further investigated in the future. For normal operating conditions, (atmospheric pressure and temperature that varies from 300 K to 573 K), Nitrogen may be considered an ideal gas. Also, within the above mentioned
1433
temperature span (273 K), its thermophysical properties may be considered as constant. No-penetration and no-slip conditions were assumed for the walls. The bottom wall that contacts the card slot was modelled as adiabatic. The discharge orifice, denoted as "jet entry" in Fig. 1, was modelled as "velocity inlet". The adjacent boundary was modelled as an adiabatic wall. The exit port of the model (the right-side wall in Fig. 1) was modelled as "pressure outlet" since it is open to the atmosphere. The maximum heat flux by radiation during the entire heating process was estimated to be at least an order of magnitude smaller than the heat flux by convection. For this reason, radiation has been neglected. The thermal contact resistance between the crystal and Teflon layer is extensively analyzed elsewhere (Rozenfeld, in preparation). ANSYSÒ-12.1 (formerly Fluent) software is used as the platform. A grid of 2100 cells is used as presented in Table 1. The cells are aligned with the direction of flow, as recommended by ANSYSÒ. Very thin cells are used for the Teflon layer because of its small thickness. Overall, there are 60 cells in the axial direction and 35 in the radial one. These values were adopted after a careful grid refinement procedure. Grid independency was checked, and it was found that a further increase in the grid density had a negligible effect on both the velocity and temperature fields: for instance, doubling the number of cells, either in the radial or axial directions, altered the results by less than 0.5%. The model sensitivity to the time step was checked, as well. It was found that the difference in results between time steps of 0.01 s and 0.001 s was less than 0.5%. Therefore, a time step of 0.01 s was used. A comprehensive validation work has been done by solving several models by the present numerical method in order to ensure the reliability of its predictions (Rozenfeld, in preparation). In particular, the numerical results were compared with an analytical solution for the plane stagnation flow (White, 1991), and with the works which investigated transient confined jets (Chiriac and Ortega, 2001). 4. Thermal behaviour analysis First, the thermal behaviour of both the LiF and the Teflon layer, as a result of heating by a Nitrogen jet at a typical constant temperature of 573 K, was modelled. Fig. 2 presents a typical velocity field that evolves as a result of a 100 m/s jet entering from a single round nozzle (SRN). The jet velocity was calculated from the measured Nitrogen flow rate, the geometry of the SNR and the gas properties. A steady velocity distribution is reached after a few milliseconds. The temperature distribution within the crystal is also presented, for the instant of 1 s after jet initiation. It can be observed that the temperature distribution is not spatially uniform. We note that non-uniformity of the crystal temperature in the axial direction would have been more significant without the Teflon cover: the low thermal conductivity of Teflon, (kTeflon ¼ 0.25 W/m/K vs.
Table 1 Cell dimensions. Zone
Cell dimensions
Aspect ratio
Maina FBLb Teflonc Crystal
0.15 0.3 mm2 0.05 0.1 mm2 0.006 0.1 mm2 0.05 0.1 mm2
2 2 16.7 2
a b
Fig. 1. Schematic description of the system.
c
Main flow field, see Fig. 1. FBL denotes a 0.5 mm thick flow boundary layer above the Teflon. The Teflon layer above the crystal.
1434
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
Fig. 2. Simulated flow field and crystal temperature.
kLiF ¼ 4 W/m/K) negatively affects the overall heat transfer between the jet and the crystal, thus less heat is transferred to the crystal. One can also see from Fig. 2 that the radial temperature variation is not significant. This is due to the fact that the crystal and jet diameters are similar. It should be stressed that these results, as well as all other results presented in this work, are given for a crystal thickness of 0.9 mm. Fig. 3 presents the evolution of the maximum and minimum LiF temperatures during the first 10 s of a step heating to 573 K. The difference between the maximum and minimum temperatures across the crystal reaches maximum 24 K during the readout process. The results show that it takes more than 15 s for the crystal to reach the jet temperature. In a routine TLD readout process, a linear gas heating profile with a starting temperature of 323 K, a linear heating rate of 25K /s and a maximum constant temperature of 573 K for some seconds are used. Fig. 4 presents the simulated crystal temperature evolution for this real jet heating profile. The temperature difference across the crystal in this case reaches a maximum of 13 K during the readout process, and the time needed for the crystal to reach the temperature of the jet is about 30 s. 5. Glow curve analysis A first-order kinetic model (Randall and Wilkins, 1945) was applied to describe each peak in the glow curve. In the temperature range to which the crystal is exposed during the readout, mainly peaks no. 1 through 5 are expected. However, since peak 1 decays very fast at room temperature, its contribution will be negligible. For gamma irradiation, the peaks higher than peak 5 are also not significant. In order to facilitate calculations, the original RandalleWilkins equation is substituted with an approximate expression e Eq. (5e16) from Pagonis et al. (2006):
Fig. 3. Simulated temperature evolution for a step heating to 573 K; comparison of the jet and crystal temperatures.
Fig. 4. Simulated temperature evolution for a linear jet heating profile (for a heating rate of 25 K/s up to 573 K): comparison of the jet and crystal temperatures.
" IðTÞ E ¼ s$exp $exp n0 kB T # 2kB T 1 E
! skB T 2 E $exp bE kB T ð1Þ
where I is the intensity; E and S are the activation energy and frequency of the specific peak; n0 is the density of the trapped electrons for that peak; b is the actual heating rate of the crystal, thus being the result of the heating profile used; kB is the Boltzmann constant; T is the time-dependent crystal temperature (in Kelvin). The values of n0 are dependent on the radiation dose absorbed by the crystal. This parameter is different for the different peaks. The heating rate, b, is determined based on the simulation results, as:
bðtÞ ¼
DT T Tt ¼ Dtþt Dt Dt
(2)
where DT is the simulated increase in the crystal temperature over the time period Dt. Typically, we use Dt ¼ 0.02 s in the present calculations. For each peak, the calculation is done as follows: For the whole readout process, from t ¼ 0 to t ¼ 30 s, see Fig. 4, the instant simulation temperatures, T(t), and heating rates, b(t), defined by Eq. (2), are substituted into Eq. (1). The corresponding values of E and S from Taylor and Lilley (1978) were used for each specific peak. As a result, the intensity for each peak, In, normalized by the density of the trapped electrons for that peak, n0n, is obtained. Thus, while the exact shape of the glow curve depends on n02, n03, n04, and n05, the position of each peak (maximum) in time can be
Fig. 5. Comparison of experimental and calculated glow curves for a linear heating rate of 25 K/s and a maximal jet temperature of 573 K.
R. Rozenfeld et al. / Radiation Measurements 46 (2011) 1432e1435
1435
6. Conclusions
Fig. 6. Glow curves based on the jet and crystal temperature profiles for a heating rate of 25 K/s and a maximal jet temperature of 573 K.
determined by the calculation. In other words, the calculation yields the exact "location" of the peaks in time. Since the relative intensity of the different peaks depends on experimental characteristics, experimental data is necessary to fit the complete curve. The experimental data is in the form of intensity-time dependence, which is an experimentally obtained glow curve. A typical example of the experimental results and corresponding calculated glow curve is shown in Fig. 5. The values of n02, n03, n04, and n05 are chosen in order to obtain maximum agreement between the simulated (thick solid line) and measured (connected dots) curves. One can see a very good agreement for peak 2 and a good agreement in the overall shape of the glow curve. A specific comparison for peaks 3e5 can be made only after proper deconvolution of the glow curve. The agreement between experimental and simulated results is due to a rather accurate prediction of the lag between the jet and crystal temperatures. As shown in Fig. 4, this lag is different for different instants. As a result, it is different for different temperatures, and thus for the different peaks. The lag may be expressed either as the jet vs. crystal temperature at the same instant (temperature lag), or the time difference between the jet and crystal reaching the same temperature (time lag). The typical time lag between the crystal temperature and the jet temperature is about 5 s, for the heating rate of 25 K/s. The significance of the lag is further illustrated in Fig. 6. The experimental curve is reproduced from Fig. 5. The dashed curve is calculated using Eq. (1) with the jet temperature instead of the crystal temperature. The values of n0 for each peak are the same as used in Fig. 5.
The crystal temperature profile evolution was obtained by numerical modelling of the flow field of the gas jet and heat transfer from the jet to the crystal covered with a Teflon layer. The simulated temperature profile has been substituted into a firstorder kinetic model equation to obtain the glow curve. The results have been compared to experimental findings. It is shown that the locations of the peaks resulted from the calculated temperature profile overlap those of the experimental results. Calibration is conducted to match the intensity of the TL response of the different peaks by fitting n0 values of the four relevant peaks (peaks 2 to 5), thus only a four-parameter fitting for the peak intensities is conducted. The actual temperature profile in the TLD crystal significantly affects the positions of peak maxima in the glow curve. The effect of the time-dependent lag between the jet and crystal temperatures, for the linear jet-heating rate of 25 K/s, is shown quantitatively. The tool which was developed in this work is versatile and can be employed to check the influence of different experimental parameters (like the Teflon thickness, chip thickness, jet position etc.) on the shape of the glow curve. References ANSYSÒ Academic research, Release 12.1. Chiriac, V., Ortega, A., 2001. A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int. J. Heat Mass Transfer 45, 1237e1248. Kumar, M., Raja, E.A., Prasad, L.C., Popli, K.L., Kher, R.K., Bhatt, B.C., 2005. Studies on automatic hot gas reader used in the coutrywide personnel monitoring programme. Rad. Prot. Dosim. 113, 366e373. Moscovitch, M., Szalanczy, A., Bruml, W.W., Velbeck, K.J., Tawil, R.A., 1990. A TLD system based on gas heating with linear time-temperature profile. Rad. Prot. Dosim. 34, 361e364. Pagonis, V., Kitis, G., Furetta, C., 2006. Numerical and Practical Exercises in Thermoluminescence. Springer (Chapter 5), p. 156. Piters, T.M., Bos, A.J., 1994. Effects on non-ideal heat transfer on the glow curve in thermoluminescence experiments. J. Phys. D: Appl. Phys. 27, 1747e1756. Randall, J.T., Wilkins, M.F.H., 1945. The phosphorescence of various solids. Proc. R. Soc. A. 184, 347e364. Rozenfeld, R., Study of thermal behavior of a thermo-luminescence detector (TLD) due to gas heating, M.Sc. Thesis, Ben Gurion University, Beer Sheva, Israel, in preparation. Stadtmann, H., Delgado, A., Gomez-Ros, J.M., 2002. Study of real heating profiles in routine TLD readout: influence of temperature lags and non-linearities in the heating profiles on the glow curve shape. Rad. Prot. Dosim. 101, 141e144. Stadtmann, H., Hranitzky, C., Brasik, N., 2006. Study of real time temperature profiles in routine TLD read out e influence of detector thickness and heating rate on glow curve shape. Rad. Prot. Dosim. 119, 310e313. Taylor, G.C., Lilley, E., 1978. The analysis of thermoluminescent glow peaks in LiF (TLD-100). J. Phys. D: Appl. Phys. 11, 567e581. White, F.M., 1991. Viscous Fluid Flow. McGraw-Hill.