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Assessment of cooling effects on extending the maximum operating time for the Syrian miniature neutron source reactor
Progress in Nuclear Energy 49 (2007) 253e261 www.elsevier.com/locate/pnucene
Assessment of cooling effects on extending the maximum operating time for the Syrian miniature neutron source reactor I. Khamis*, W. Alhalabi Department of Nuclear Engineering, Atomic Energy Commission of Syria, P.O. Box 6091, Damascus, Syria
Abstract Various schemes of cooling have been investigated for the purpose of assessing potential benefits on the operational characteristics of the Syrian MNSR reactor. A detailed thermal hydraulic model for the analysis of MNSR has been developed. The analysis shows that an auxiliary cooling system, installed in the pool which surrounds the lower section of the reactor vessel, will significantly offset the consumption of excess reactivity due to the negative reactivity temperature coefficient. Hence, the maximum operating time of the reactor is extended. Compared with experimental data, the suggested model proves to be valid for the analysis of MNSR behavior under both steady state and transient conditions. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: MNSR; Time extension; Assessment; Cooling effect; Thermal hydraulic
1. Introduction Very similar in all aspects to the Canadian SLOWPOKE reactors (IAEA, 1986), the miniature neutron source reactor (MNSR) has a maximum thermal neutron flux of 1 1012 n cm2 s1 in each one of the five inner irradiation sites. The main utilizations of MNSR are neutron activation analysis, production of short-lived radioisotopes, and training. It is a tank-in-pool reactor which uses 89.87% enriched uraniumeAl alloy as fuel, beryllium as a reflector, and water as moderator and coolant. The reactor is designed to be compact with no direct access to the core which is cooled through natural circulation. Normal daily operation at nominal power (30 kW) involves withdrawal of the solely controlled rod, which has a reactivity worth of about 3e4 mk, to compensate for temperature and poison effects. Long-term reactivity adjustment is handled, almost every two years of operation, through the addition of beryllium-reflector shim plate to the top reflector. The principal feature of the MNSR design is its inherent safety resulting from limited initial excess reactivity on one hand, and the reduced ratio of hydrogen to uranium in fuel rod lattice, i.e. large degree of core under moderation which is capable at suppression power excursions on the other hand (SAR, 1992). The operating limiting conditions of MNSR restricts the available cold excess reactivity in the core to less than 4 mk.
* Corresponding author. Tel.: þ963 11 2132580; fax: þ963 11 6112289. E-mail address: [email protected] (I. Khamis). 0149-1970/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.pnucene.2007.01.003
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One of the main disadvantages of the Chinese MNSR is its short time of operation at nominal power (about 2.5 h) (SAR, 1992). At very low power, e.g. 5 kW, the MNSR can operate for a very long time. Whereas if the reactor operates at the nominal value, i.e. 30 kW, the moderator temperature increases, hence, the excess reactivity available for operation is reduced. Therefore, the time available for continuing operation is limited. In fact, it becomes rather cumbersome to make good use of the thermal neutron flux available at nominal power during the analysis of medium or long-lived radionuclides which require relatively longer time of irradiation. In MNSRs, the two most excess reactivity-consuming processes are the increase in moderator temperature due to operation and buildup of xenon poison (IAEA, 1986). Nearly half of the cold excess reactivity is lost due to the temperature effect, hence, hot excess reactivity is relatively small. Furthermore, a small share of this hot excess reactivity will be used to compensate xenon poisoning. The average isothermal reactivity coefficient of moderator in MNSR is 0.092 103 Dk/k/ C, i.e. 0.092 mk/ C (SAR, 1992). After 2 h of operation at nominal power, the average core-coolant temperature rises about 20 C, and the excess reactivity drops from 3.9 mk to 1.1 mk (SAR, 1992). Consequently, the temperature effect is approximately equal to 2.8 mk. As a result, the overall average temperature coefficient is about 0.14 mk/ C (including moderator temperature, flow, and power coefficients). In this paper, focus will be made on developing the thermal hydraulic model of MNSR and improving operational characteristics of the MNSR through various cooling schemes being investigated and presented. 2. Theory The present thermal hydraulic model of MNSR was developed to enable quantitative and qualitative assessments for the benefit of having an auxiliary cooling system capable to overcome the temperature rise in the reactor vessel. Basically, the effectiveness of such cooling system will be demonstrated through detailed analysis of the core parameters, and core temperatures versus operating time. The model considers not only natural circulation and heat transfer across the core, but also the physical coupling between reactor power and rise in coolant temperature on one side and heat transfer to coolant in the reactor vessel and finally towards the pool. The schematic representation of both heat transfer and coolant flow, elaborated in the model, is presented in Fig. 1. Formulation of the mathematical model is based on the lumped parameter model and complete mixing approximations. Based on the actual distribution of fuel elements, dummy-fuel elements, and tie rods on 10 circles with varying pitch in the core, the model calculates the overall coolant flow area in the core, average hydraulic diameter, fuelcoolant and coolant-reflector heat transfer areas. In addition, calculation includes flow areas, hydraulic diameters, and heat transfer areas for the lower and upper parts of the reactor vessel and the pool. The MNSR model considers both steady state and transient conditions using an empirical function for the overshoot and periodicity of thermal power generated in the core. Based on the real reactor startup of the Syrian MNSR, time-related multiplier f(t) is introduced in the value of the reactor operating power during time of operation. Fitting the real experimental data, we found that the reactor power, P, can be expressed as P ¼ f ðtÞPss
ð1Þ
where f ðtÞ ¼ 1 expð0:091745tÞcosð0:055036tÞ and Pss is the reactor power at steady state. f ðtÞ will assume the value 1 when steady state prevails. Heat generated in the core will be partially absorbed by the core constituents, small part transferred to reactor components (according to their masses) as gamma radiation, and the rest transferred from the fuel to the coolant inside the core (El-Wakil, 1962). The latter will contribute to core-coolant heating, heat transfer across the reflector QcB (see Fig. 1) and temperature rise of coolant leaving the core. Heat transported outside the core will result in heating the water bulk present in the upper and lower parts of the reactor vessel. In the upper part, heat will dissipate partially across the vessel wall to the pool Quv and the rest will be transported back downward to the lower part of the vessel. Similarly, heat in the lower part will partially result in an increase of temperature of the coolant at the entrance to the core, and the rest will be transferred to the pool Qlv . Since heating of both the reflector and reactor vessel wall was found to be trivial, an assumption was made to neglect such heating during calculations (Akaho and Maakuu, 2002). Thermal hydraulic model is formulated applying power balance equations for all the considered volumes, Bernoulli and mass conserve equations (Rust, 1979), conduction and natural convection heat transfer equations (Incropera and De Witt, 1981; Wolf, 1984). The model consists of a number of deferential equations with respect to time which
I. Khamis, W. Alhalabi / Progress in Nuclear Energy 49 (2007) 253e261
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Fig. 1. Schematic representation of coolant flow and heat transfer in MNSR.
describe the physical phenomena of thermal and hydraulic aspects (Akaho and Maakuu, 2002; Shi Shuangkai, 1993). The state variables are the average temperature of fuel Tc and coolant Tf in the core, coolant mass flow and velocity, vessel water temperatures in the lower and upper part Tlv ; Tuv , pool water temperatures in the lower and upper part Tlp ; Tup , consequently, the average Tp , as functions of time. dTc ¼ 0:92P Fc ac Tc Tf dt
ð2Þ
dTf _ pf 2 Tf Tin ¼ Fc ac Tc Tf KB FBi Tf Tin mC dt
ð3Þ
ðGUAl Cpu þ GAl CpAl Þ Gf Cpf
Guv Cpuv
dTuv _ f2 Cpuv mT _ uv Kuv Fuvi Tuv Tup ¼ Cpf2 mT dt
ð4Þ
Glv Cplv
dTlv _ puv Tuv mC _ plv Tlv Klv Flvi Tlv Tlp þ KB FBi Tf Tin ¼ mC dt
ð5Þ
Gup Cpup
dTup ¼ Kuv Fuvi Tuv Tup Fup Kupgr Tup Tgr dt
ð6Þ
Glp Cplp
dTlp ¼ Klv Flvi Tlv Tlp Flp Klpgr Tlp Tgr dt
ð7Þ
hp ¼ h l
ð8Þ
Eq. (2) represents the change of average fuel elements’ temperature Tc considering that the fuel meat and cladding have the same temperature because of small heat flux and good conductivity. In this equation, the term Fc ac ðTc Tf Þ
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is the power transferred to the coolant with average temperature Tf in the core and about 8% of the reactor power is considered absorbed gamma power by reactor component. Eq. (3) represents the change of average coolant temperature in the core Tf considering the transferred power from the core across the side reflector QcB ¼ KB FBi ðTf Tin Þ and the transferred power to the coolant from the fuel _ pf 2ðTf Tin Þ. elements mC Eq. (4) represents the change of average water temperature Tuv in the upper section of the vessel considering the _ f2 , the transported power from this volume transported power by the coolant with temperature Tf2 from the core Cpf2 mT _ uv and the transferred power to the reactor pool water Quv ¼ Kuv Fuvi to the lower section of the vessel Cpuv mT ðTuv Tup Þ. Eq. (5) represents the change of average water temperature Tlv in the lower section of the vessel considering the _ plvw Tlvw Qlv ¼ Klv Flvi ðTlv Tlp Þ: transported and transferred power mC Eqs. (6) and (7) represent the change of average water temperatures Tup in the upper and Tlp in the lower section of the pool. The terms Flp Klpgr ðTlp Tgr Þ and Fup Kupgr ðTup Tgr Þ are the transferred powers to the ambient across the side wall in the lower and upper sections of the pool, respectively. Due to natural circulation, Bernoulli Eq. (8) represents balancing the total pressure losses hl for coolant flow (i.e. local and friction pressure losses) against the density head hp produced due to coolant density difference, consequently, the average flow velocity can be evaluated. The density pressure head consist of two components as follows Z H hp ¼ g rf1 rf2 hex þ g rf1 rfz dz ð9Þ 0
The first component is related to the coolant density at the core exit, whereas the second one represents the variance in density due to coolant temperature distribution across the core. Both components can be evaluated once the density is evaluated as a function of temperature as rf ðTÞ ¼ A þ BT þ CT 2 , hence, integration can be carried out considering Tfz ¼ Tf1 þ ð2ðTf Tin Þ=HÞf ðzÞ: The total pressure losses hl consist of local and friction losses. It can be evaluated as follows (Rust, 1979): hl ¼
X
fwj
X Lj 1 1 rfj Wj2 þ xi rfi Wi2 2 dhj 2 i
ð10Þ
fwj
Lj 1 m_ 2 X 1 m_ 2 þ xi 2rfi A2i dhj 2rfj A2j i
ð11Þ
j
or hl ¼
X j
All the symbols are explained in Appendix. The model is able to simulate the following schemes of cooling (see Fig. 2). External chiller with a heat exchanger to be installed in the upper part of pool M.1 having a capacity Qp : External chiller with a heat exchanger to be installed in the upper part of the reactor vessel M.2 having a capacity Qv : External chiller with sprayers (spargers) to be installed in the pool and surround the reactor vessel at the lower section M.3 with cooling water temperature Tcw : For method M.1 Eq. (6) in the model should be modified as follows: Cpup Gup
dTup ¼ Kuv Fuvi Tuv Tup QP Fup Kupgr Tup Tgr dt
ð12Þ
For M.2 Eq. (4) should be modified as follows: Cpuv Guv
dTuv _ f2 Cpuv mT _ uv Kuv Fuvi Tuv Tup QV ¼ Cpf2 mT dt
ð13Þ
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257
Fig. 2. Simulated cooling schemes.
For M.3, the pool water in the lower section is considered constant because of the balance between the cooling capacity and the removed power from the lower section of the vessel and the large heat capacity for pool water, and the temperature of vessel wall in the lower section is equal to cooling water Tcw. Consumption of excess reactivity due to moderator temperature is given as: dRT ¼ aT dTf
ð14Þ
The moderator reactivity factor, aT , is a function of the average coolant temperature Tf K as follows: aT ¼ 0:00034752Tf 0:0026445 mk=K
ð15Þ
IntegratingR Eq. (14) as coolant temperature increases from T0 to Tf , the consumption of excess reactivity, T i.e. RTf T0 ¼ T0 aT dTf is given as: ! Tf2 T02 ð16Þ RTf T0 ¼ 0:00034752 0:0026445 Tf T0 mk 2 During operation, consumption of the excess reactivity due to xenon poison effect Rxe is considered as a function of time and power of the reactor (SAR, 1992) as seen in Fig. 3. Finally, the change of excess reactivity as a function of operation time, ER, is determined as: ER ¼ ER293 ERT0 293 RTf T0 Rxe
ð17Þ
Where, ER293 is the excess reactivity available in the core at 293 K, and RT0 293 is the reduced reactivity when the initial temperature T0 is different from 293 K. The maximum operation time of the reactor tmax can be calculated when ER ¼ 0 for defined power and initial temperature values.
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258
1.6 1.4
Rxe { mk }
1.2
P = 30 kW
1
25 20
0.8
15
0.6
10
0.4
5 0.2 0 1
0
3
2
5
4
6
7
8
9
10
Operation Time { hr } Fig. 3. Xenon poison effect as a function of time and power. 49 Experimental Calculated
Coolant temperature { °C }
44
Tf ,without cooling Tf ,with cooling
39
Tin ,without cooling
34
Tin ,with cooling 29
24
19 0
0.5
1
2
1.5
2.5
Operation time { hr } Fig. 4. Average and inlet coolant temperatures for real operation.
Average Coolant Temperature { °C }
57
Shutdown points for ER293 = 3.7 T0 = 22 °C
52
Without cooling
47
M.1 42
M.3
37
M.2
32 27 22 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Oeration Time { hr } Fig. 5. Average coolant temperature vs. operation time during various cooling modes.
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Table 1 Comparison between real and calculated shutdown time of MNSRs without any cooling Reactor
T0 ½ C
ERT0 ½mk
tmax ½h experimental
tmax ½h calculated
Syrian Chinese Chinese
21.2 20 20
3.71 3.9 3.7
6.05 7.25 6.8
6.3 7.47 6.7
3. Results and discussions Having both a dynamic simulator (Khamis et al., 2000) and experimental data for the real operation of MNSR already established, validation of the thermal hydraulic model was easily made through comparison of results obtained by the model, applying modified Euler method, against the real data as in Fig. 4. Because real data on the reactor console involve only measurement of inlet temperature Tin and temperature difference across the core; hence, core average temperature Tf , Fig. 3 presents these two variables without cooling and with cooling using M.3 having cooling water temperature Tcw ¼ T0 8. Agreement between real and simulated results is rather clear. In order to select the most suitable cooling scheme in the MNSR, the mode of typical operational characteristics was firstly simulated but with an extension of the operating time. The normal operating time is 2.5 h at nominal power. After that, the core average temperature usually increases and almost half of the available excess reactivity is consumed. However, if cooling was to be implemented, the operating time should be extended beyond 2.5 h possibly to about 10e15 h, i.e. long-time operation. Therefore, actual operational characteristics without cooling should be established first. The following calculation is based on a typical operation of MNSR having 30 kW, as a nominal power when the initial condition of temperature for all components is set to T0 ¼ 22 C. Simulation results of the currently developed model of the MNSR, typical operational characteristics without additional cooling are presented in Fig. 5. After 15 h, the average core-coolant temperature reaches about 53 C. Of course such rise in temperature will definitely override the available excess reactivity since the moderator reactivity coefficient in the MNSR is about 0.1 mk/ C. Thus, it is clear as shown in Fig. 5 that the shutdown point after 6 h for ER293 ¼ 3:7 mk. Fig. 5 shows also a comparison of various cooling schemes, i.e. M.1, M.2, and M.3 with specific condition, i.e. the maximum possible cooling capacity. Such capacity is limited to 27 kW for the vessel or pool water cooling system ðQv ; Qp Þ. Whereas, it is 7:5 kW for the sprayers system assuming that the temperature of cooling water to be sprayed on the vessel wall, having a height of 30 cm, is Tcw ¼ T0 8. It can be seen from Fig. 5 that the vessel cooling system, M.2, is the best and its effect begins immediately after the startup of operation. Despite its small cooling capacity, the sprayer system, M.3, is better than the pool cooling system, M.1. It can also be noticed that the shutdown points in Fig. 5 are achieved when all excess reactivity is consumed. In this case, the maximum operation time is 14.5 h, and belongs to the cooling scheme M.2. Verification of calculations was made first for the cold and clean core. Table 1 presents a comparison between the real and calculated shutdown time tmax of the reactor without cooling for three MNSRs, involving the Syrian MNSR and two Chinese reactors having different conditions. From Table 1, one may conclude that the suggested model predicts rather accurately the maximum time of operation taking into consideration coolant temperature changes during the period of reactor operation with and without cooling. The M.3 system, having preferable advantages over all other suggested cooling systems due to easy of installation and being more effective, was selected for further analysis. The model was then utilized for the evaluation of the currently installed cooling system, M.3, with Tcw ¼ T0 8 in the Syrian MNSR for a specified testing case where the total excess reactivity has been reduced from 3:7 mk to 3 mk. Table 2 presents the effect of cooling on maximum operation time and the expected maximum operation time for cold and clean reactor.
Table 2 Effects of M.3 cooling system ER293 ½mk
T0 ½ C
tmax ½h without cooling
tmax ½h with cooling M:3
3 3.7
20 20
3.8 6.7
6.77 10
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Maximum Operation Time { hr }
260
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
M. 2
M. 3
M. 1
Without cooling
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Initial Temperature { °C } Fig. 6. Maximum operation time without and with cooling for ER293 ¼ 3:7 mk:
Finally, Fig. 6 shows the relationship of the maximum operation time with the initial temperature for excess reactivity ER293 ¼ 3:7 mk. Again, one may see that the sprayers M.3 (despite its small capacity) and the vessel cooling systems M.2 are more efficient than pool cooling system M.1 for the complete range being considered for the initial temperatures 20e33 C. However, the pool cooling system M.1 is not much effective for high initial temperature and converges to M.3 system for low initial temperature. The vessel cooling system M.2 without doubt is the best and is capable to guarantee a maximum operation time of 15 h for T0 ¼ 20 C. Acknowledgements The authors are grateful to Prof. Dr. I. Othman, Director General of the Atomic Energy Commission of Syria, for his keen interest and support. Appendix Fc , Surface area of fuel elements. ac , Heat transfer coefficient of fuel elements. GUAl , Fuel meat mass. GAl , Mass of cladding, guide tube and link rods in the core. CpUAl ; CpAl , Specific heat capacity of fuel meat and aluminum. FBi , Internal surface area of side reflector. KB , Overall heat transfer coefficient of side reflector. Tin , Inlet coolant temperature. _ Coolant flow rate. m, Cpf , Average coolant specific heat capacity in the core. Gf , Coolant mass in the core. Cpf2 , Specific heat capacity of coolant at the core exit. Guv ; Glv , Water mass in the upper and lower part of the vessel, respectively. Cpuv ; Cplv , Water specific heat capacity in the upper and lower part of the vessel, respectively. Kuv ; Flv , Overall heat transfer coefficient of vessel wall at the upper and lower part, respectively. Fuvi ; Flvi , Internal surface area of vessel wall at the upper and lower part, respectively. Tgr , Ground temperature. Fup ; Flp , Internal surface area of the pool wall at the upper and lower part, respectively.
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Gup ; Glp , Water mass in the upper and lower part of the pool, respectively. Cpup ; Cplp , Water specific heat capacity in the upper and lower part of the pool, respectively. Klpgr ; Kupgr , Overall heat transfer coefficient of pool wall at the upper and lower part, respectively. hex , The height of the core outlet and exit orifice. H, The effective height of the core. xi ; Wi , Local pressure loss factors and coolant velocities for the parts of coolant flow i. fwj ; Wj , Friction pressure loss factors and coolant velocities in the parts of coolant flow j. Lj , Length of the parts j of coolant flow. rfi ; rfj , Coolant density in the parts i and j of coolant flow, respectively. Ai ; Aj , The cross-section areas for the parts i and j of coolant flow, respectively.
References Akaho, E.H.K., Maakuu, B.T., 2002. Simulation of reactivity transients in a miniature neutron source reactor core. Nuclear Engineering and Design 213, 31e42. El-Wakil, M.M., 1962. Nuclear Power Engineering. McGraw-Hill, Inc., New York. IAEA-TECDOC-384, Technology and Use of Low Power Research Reactors, 1986. IAEA, Vienna, pp. 89e98. Incropera, F.P., De Witt, D.P., 1981. Fundamentals of Heat Transfer. John Wiley Sons, Inc., New York. Khamis, I., et al., 2000. Dynamic simulator for the miniature neutron source reactor. Progress in Nuclear Energy 36 (4), 379e385. Rust, J.H., 1979. Nuclear Power Plant Engineering. Haralson Publishing Company, Buchanan, Georgia. Shi Shuangkai, 1993. MNSR Thermal Hydraulics. MNSR Training Materials. China Institute of Atomic Energy, Beijing, China. The Syrian Safety Analysis Report (SAR) for MNSR, 1992 (internal report). Wolf, H., 1984. Heat Transfer. Harper & Row, Publishers, New York.
Assessment of cooling effects on extending the maximum operating time for the Syrian miniature neutron source reactor I. Khamis*, W. Alhalabi Department of Nuclear Engineering, Atomic Energy Commission of Syria, P.O. Box 6091, Damascus, Syria
Abstract Various schemes of cooling have been investigated for the purpose of assessing potential benefits on the operational characteristics of the Syrian MNSR reactor. A detailed thermal hydraulic model for the analysis of MNSR has been developed. The analysis shows that an auxiliary cooling system, installed in the pool which surrounds the lower section of the reactor vessel, will significantly offset the consumption of excess reactivity due to the negative reactivity temperature coefficient. Hence, the maximum operating time of the reactor is extended. Compared with experimental data, the suggested model proves to be valid for the analysis of MNSR behavior under both steady state and transient conditions. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: MNSR; Time extension; Assessment; Cooling effect; Thermal hydraulic
1. Introduction Very similar in all aspects to the Canadian SLOWPOKE reactors (IAEA, 1986), the miniature neutron source reactor (MNSR) has a maximum thermal neutron flux of 1 1012 n cm2 s1 in each one of the five inner irradiation sites. The main utilizations of MNSR are neutron activation analysis, production of short-lived radioisotopes, and training. It is a tank-in-pool reactor which uses 89.87% enriched uraniumeAl alloy as fuel, beryllium as a reflector, and water as moderator and coolant. The reactor is designed to be compact with no direct access to the core which is cooled through natural circulation. Normal daily operation at nominal power (30 kW) involves withdrawal of the solely controlled rod, which has a reactivity worth of about 3e4 mk, to compensate for temperature and poison effects. Long-term reactivity adjustment is handled, almost every two years of operation, through the addition of beryllium-reflector shim plate to the top reflector. The principal feature of the MNSR design is its inherent safety resulting from limited initial excess reactivity on one hand, and the reduced ratio of hydrogen to uranium in fuel rod lattice, i.e. large degree of core under moderation which is capable at suppression power excursions on the other hand (SAR, 1992). The operating limiting conditions of MNSR restricts the available cold excess reactivity in the core to less than 4 mk.
* Corresponding author. Tel.: þ963 11 2132580; fax: þ963 11 6112289. E-mail address: [email protected] (I. Khamis). 0149-1970/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.pnucene.2007.01.003
I. Khamis, W. Alhalabi / Progress in Nuclear Energy 49 (2007) 253e261
254
One of the main disadvantages of the Chinese MNSR is its short time of operation at nominal power (about 2.5 h) (SAR, 1992). At very low power, e.g. 5 kW, the MNSR can operate for a very long time. Whereas if the reactor operates at the nominal value, i.e. 30 kW, the moderator temperature increases, hence, the excess reactivity available for operation is reduced. Therefore, the time available for continuing operation is limited. In fact, it becomes rather cumbersome to make good use of the thermal neutron flux available at nominal power during the analysis of medium or long-lived radionuclides which require relatively longer time of irradiation. In MNSRs, the two most excess reactivity-consuming processes are the increase in moderator temperature due to operation and buildup of xenon poison (IAEA, 1986). Nearly half of the cold excess reactivity is lost due to the temperature effect, hence, hot excess reactivity is relatively small. Furthermore, a small share of this hot excess reactivity will be used to compensate xenon poisoning. The average isothermal reactivity coefficient of moderator in MNSR is 0.092 103 Dk/k/ C, i.e. 0.092 mk/ C (SAR, 1992). After 2 h of operation at nominal power, the average core-coolant temperature rises about 20 C, and the excess reactivity drops from 3.9 mk to 1.1 mk (SAR, 1992). Consequently, the temperature effect is approximately equal to 2.8 mk. As a result, the overall average temperature coefficient is about 0.14 mk/ C (including moderator temperature, flow, and power coefficients). In this paper, focus will be made on developing the thermal hydraulic model of MNSR and improving operational characteristics of the MNSR through various cooling schemes being investigated and presented. 2. Theory The present thermal hydraulic model of MNSR was developed to enable quantitative and qualitative assessments for the benefit of having an auxiliary cooling system capable to overcome the temperature rise in the reactor vessel. Basically, the effectiveness of such cooling system will be demonstrated through detailed analysis of the core parameters, and core temperatures versus operating time. The model considers not only natural circulation and heat transfer across the core, but also the physical coupling between reactor power and rise in coolant temperature on one side and heat transfer to coolant in the reactor vessel and finally towards the pool. The schematic representation of both heat transfer and coolant flow, elaborated in the model, is presented in Fig. 1. Formulation of the mathematical model is based on the lumped parameter model and complete mixing approximations. Based on the actual distribution of fuel elements, dummy-fuel elements, and tie rods on 10 circles with varying pitch in the core, the model calculates the overall coolant flow area in the core, average hydraulic diameter, fuelcoolant and coolant-reflector heat transfer areas. In addition, calculation includes flow areas, hydraulic diameters, and heat transfer areas for the lower and upper parts of the reactor vessel and the pool. The MNSR model considers both steady state and transient conditions using an empirical function for the overshoot and periodicity of thermal power generated in the core. Based on the real reactor startup of the Syrian MNSR, time-related multiplier f(t) is introduced in the value of the reactor operating power during time of operation. Fitting the real experimental data, we found that the reactor power, P, can be expressed as P ¼ f ðtÞPss
ð1Þ
where f ðtÞ ¼ 1 expð0:091745tÞcosð0:055036tÞ and Pss is the reactor power at steady state. f ðtÞ will assume the value 1 when steady state prevails. Heat generated in the core will be partially absorbed by the core constituents, small part transferred to reactor components (according to their masses) as gamma radiation, and the rest transferred from the fuel to the coolant inside the core (El-Wakil, 1962). The latter will contribute to core-coolant heating, heat transfer across the reflector QcB (see Fig. 1) and temperature rise of coolant leaving the core. Heat transported outside the core will result in heating the water bulk present in the upper and lower parts of the reactor vessel. In the upper part, heat will dissipate partially across the vessel wall to the pool Quv and the rest will be transported back downward to the lower part of the vessel. Similarly, heat in the lower part will partially result in an increase of temperature of the coolant at the entrance to the core, and the rest will be transferred to the pool Qlv . Since heating of both the reflector and reactor vessel wall was found to be trivial, an assumption was made to neglect such heating during calculations (Akaho and Maakuu, 2002). Thermal hydraulic model is formulated applying power balance equations for all the considered volumes, Bernoulli and mass conserve equations (Rust, 1979), conduction and natural convection heat transfer equations (Incropera and De Witt, 1981; Wolf, 1984). The model consists of a number of deferential equations with respect to time which
I. Khamis, W. Alhalabi / Progress in Nuclear Energy 49 (2007) 253e261
255
Fig. 1. Schematic representation of coolant flow and heat transfer in MNSR.
describe the physical phenomena of thermal and hydraulic aspects (Akaho and Maakuu, 2002; Shi Shuangkai, 1993). The state variables are the average temperature of fuel Tc and coolant Tf in the core, coolant mass flow and velocity, vessel water temperatures in the lower and upper part Tlv ; Tuv , pool water temperatures in the lower and upper part Tlp ; Tup , consequently, the average Tp , as functions of time. dTc ¼ 0:92P Fc ac Tc Tf dt
ð2Þ
dTf _ pf 2 Tf Tin ¼ Fc ac Tc Tf KB FBi Tf Tin mC dt
ð3Þ
ðGUAl Cpu þ GAl CpAl Þ Gf Cpf
Guv Cpuv
dTuv _ f2 Cpuv mT _ uv Kuv Fuvi Tuv Tup ¼ Cpf2 mT dt
ð4Þ
Glv Cplv
dTlv _ puv Tuv mC _ plv Tlv Klv Flvi Tlv Tlp þ KB FBi Tf Tin ¼ mC dt
ð5Þ
Gup Cpup
dTup ¼ Kuv Fuvi Tuv Tup Fup Kupgr Tup Tgr dt
ð6Þ
Glp Cplp
dTlp ¼ Klv Flvi Tlv Tlp Flp Klpgr Tlp Tgr dt
ð7Þ
hp ¼ h l
ð8Þ
Eq. (2) represents the change of average fuel elements’ temperature Tc considering that the fuel meat and cladding have the same temperature because of small heat flux and good conductivity. In this equation, the term Fc ac ðTc Tf Þ
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is the power transferred to the coolant with average temperature Tf in the core and about 8% of the reactor power is considered absorbed gamma power by reactor component. Eq. (3) represents the change of average coolant temperature in the core Tf considering the transferred power from the core across the side reflector QcB ¼ KB FBi ðTf Tin Þ and the transferred power to the coolant from the fuel _ pf 2ðTf Tin Þ. elements mC Eq. (4) represents the change of average water temperature Tuv in the upper section of the vessel considering the _ f2 , the transported power from this volume transported power by the coolant with temperature Tf2 from the core Cpf2 mT _ uv and the transferred power to the reactor pool water Quv ¼ Kuv Fuvi to the lower section of the vessel Cpuv mT ðTuv Tup Þ. Eq. (5) represents the change of average water temperature Tlv in the lower section of the vessel considering the _ plvw Tlvw Qlv ¼ Klv Flvi ðTlv Tlp Þ: transported and transferred power mC Eqs. (6) and (7) represent the change of average water temperatures Tup in the upper and Tlp in the lower section of the pool. The terms Flp Klpgr ðTlp Tgr Þ and Fup Kupgr ðTup Tgr Þ are the transferred powers to the ambient across the side wall in the lower and upper sections of the pool, respectively. Due to natural circulation, Bernoulli Eq. (8) represents balancing the total pressure losses hl for coolant flow (i.e. local and friction pressure losses) against the density head hp produced due to coolant density difference, consequently, the average flow velocity can be evaluated. The density pressure head consist of two components as follows Z H hp ¼ g rf1 rf2 hex þ g rf1 rfz dz ð9Þ 0
The first component is related to the coolant density at the core exit, whereas the second one represents the variance in density due to coolant temperature distribution across the core. Both components can be evaluated once the density is evaluated as a function of temperature as rf ðTÞ ¼ A þ BT þ CT 2 , hence, integration can be carried out considering Tfz ¼ Tf1 þ ð2ðTf Tin Þ=HÞf ðzÞ: The total pressure losses hl consist of local and friction losses. It can be evaluated as follows (Rust, 1979): hl ¼
X
fwj
X Lj 1 1 rfj Wj2 þ xi rfi Wi2 2 dhj 2 i
ð10Þ
fwj
Lj 1 m_ 2 X 1 m_ 2 þ xi 2rfi A2i dhj 2rfj A2j i
ð11Þ
j
or hl ¼
X j
All the symbols are explained in Appendix. The model is able to simulate the following schemes of cooling (see Fig. 2). External chiller with a heat exchanger to be installed in the upper part of pool M.1 having a capacity Qp : External chiller with a heat exchanger to be installed in the upper part of the reactor vessel M.2 having a capacity Qv : External chiller with sprayers (spargers) to be installed in the pool and surround the reactor vessel at the lower section M.3 with cooling water temperature Tcw : For method M.1 Eq. (6) in the model should be modified as follows: Cpup Gup
dTup ¼ Kuv Fuvi Tuv Tup QP Fup Kupgr Tup Tgr dt
ð12Þ
For M.2 Eq. (4) should be modified as follows: Cpuv Guv
dTuv _ f2 Cpuv mT _ uv Kuv Fuvi Tuv Tup QV ¼ Cpf2 mT dt
ð13Þ
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Fig. 2. Simulated cooling schemes.
For M.3, the pool water in the lower section is considered constant because of the balance between the cooling capacity and the removed power from the lower section of the vessel and the large heat capacity for pool water, and the temperature of vessel wall in the lower section is equal to cooling water Tcw. Consumption of excess reactivity due to moderator temperature is given as: dRT ¼ aT dTf
ð14Þ
The moderator reactivity factor, aT , is a function of the average coolant temperature Tf K as follows: aT ¼ 0:00034752Tf 0:0026445 mk=K
ð15Þ
IntegratingR Eq. (14) as coolant temperature increases from T0 to Tf , the consumption of excess reactivity, T i.e. RTf T0 ¼ T0 aT dTf is given as: ! Tf2 T02 ð16Þ RTf T0 ¼ 0:00034752 0:0026445 Tf T0 mk 2 During operation, consumption of the excess reactivity due to xenon poison effect Rxe is considered as a function of time and power of the reactor (SAR, 1992) as seen in Fig. 3. Finally, the change of excess reactivity as a function of operation time, ER, is determined as: ER ¼ ER293 ERT0 293 RTf T0 Rxe
ð17Þ
Where, ER293 is the excess reactivity available in the core at 293 K, and RT0 293 is the reduced reactivity when the initial temperature T0 is different from 293 K. The maximum operation time of the reactor tmax can be calculated when ER ¼ 0 for defined power and initial temperature values.
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1.6 1.4
Rxe { mk }
1.2
P = 30 kW
1
25 20
0.8
15
0.6
10
0.4
5 0.2 0 1
0
3
2
5
4
6
7
8
9
10
Operation Time { hr } Fig. 3. Xenon poison effect as a function of time and power. 49 Experimental Calculated
Coolant temperature { °C }
44
Tf ,without cooling Tf ,with cooling
39
Tin ,without cooling
34
Tin ,with cooling 29
24
19 0
0.5
1
2
1.5
2.5
Operation time { hr } Fig. 4. Average and inlet coolant temperatures for real operation.
Average Coolant Temperature { °C }
57
Shutdown points for ER293 = 3.7 T0 = 22 °C
52
Without cooling
47
M.1 42
M.3
37
M.2
32 27 22 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Oeration Time { hr } Fig. 5. Average coolant temperature vs. operation time during various cooling modes.
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Table 1 Comparison between real and calculated shutdown time of MNSRs without any cooling Reactor
T0 ½ C
ERT0 ½mk
tmax ½h experimental
tmax ½h calculated
Syrian Chinese Chinese
21.2 20 20
3.71 3.9 3.7
6.05 7.25 6.8
6.3 7.47 6.7
3. Results and discussions Having both a dynamic simulator (Khamis et al., 2000) and experimental data for the real operation of MNSR already established, validation of the thermal hydraulic model was easily made through comparison of results obtained by the model, applying modified Euler method, against the real data as in Fig. 4. Because real data on the reactor console involve only measurement of inlet temperature Tin and temperature difference across the core; hence, core average temperature Tf , Fig. 3 presents these two variables without cooling and with cooling using M.3 having cooling water temperature Tcw ¼ T0 8. Agreement between real and simulated results is rather clear. In order to select the most suitable cooling scheme in the MNSR, the mode of typical operational characteristics was firstly simulated but with an extension of the operating time. The normal operating time is 2.5 h at nominal power. After that, the core average temperature usually increases and almost half of the available excess reactivity is consumed. However, if cooling was to be implemented, the operating time should be extended beyond 2.5 h possibly to about 10e15 h, i.e. long-time operation. Therefore, actual operational characteristics without cooling should be established first. The following calculation is based on a typical operation of MNSR having 30 kW, as a nominal power when the initial condition of temperature for all components is set to T0 ¼ 22 C. Simulation results of the currently developed model of the MNSR, typical operational characteristics without additional cooling are presented in Fig. 5. After 15 h, the average core-coolant temperature reaches about 53 C. Of course such rise in temperature will definitely override the available excess reactivity since the moderator reactivity coefficient in the MNSR is about 0.1 mk/ C. Thus, it is clear as shown in Fig. 5 that the shutdown point after 6 h for ER293 ¼ 3:7 mk. Fig. 5 shows also a comparison of various cooling schemes, i.e. M.1, M.2, and M.3 with specific condition, i.e. the maximum possible cooling capacity. Such capacity is limited to 27 kW for the vessel or pool water cooling system ðQv ; Qp Þ. Whereas, it is 7:5 kW for the sprayers system assuming that the temperature of cooling water to be sprayed on the vessel wall, having a height of 30 cm, is Tcw ¼ T0 8. It can be seen from Fig. 5 that the vessel cooling system, M.2, is the best and its effect begins immediately after the startup of operation. Despite its small cooling capacity, the sprayer system, M.3, is better than the pool cooling system, M.1. It can also be noticed that the shutdown points in Fig. 5 are achieved when all excess reactivity is consumed. In this case, the maximum operation time is 14.5 h, and belongs to the cooling scheme M.2. Verification of calculations was made first for the cold and clean core. Table 1 presents a comparison between the real and calculated shutdown time tmax of the reactor without cooling for three MNSRs, involving the Syrian MNSR and two Chinese reactors having different conditions. From Table 1, one may conclude that the suggested model predicts rather accurately the maximum time of operation taking into consideration coolant temperature changes during the period of reactor operation with and without cooling. The M.3 system, having preferable advantages over all other suggested cooling systems due to easy of installation and being more effective, was selected for further analysis. The model was then utilized for the evaluation of the currently installed cooling system, M.3, with Tcw ¼ T0 8 in the Syrian MNSR for a specified testing case where the total excess reactivity has been reduced from 3:7 mk to 3 mk. Table 2 presents the effect of cooling on maximum operation time and the expected maximum operation time for cold and clean reactor.
Table 2 Effects of M.3 cooling system ER293 ½mk
T0 ½ C
tmax ½h without cooling
tmax ½h with cooling M:3
3 3.7
20 20
3.8 6.7
6.77 10
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Maximum Operation Time { hr }
260
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
M. 2
M. 3
M. 1
Without cooling
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Initial Temperature { °C } Fig. 6. Maximum operation time without and with cooling for ER293 ¼ 3:7 mk:
Finally, Fig. 6 shows the relationship of the maximum operation time with the initial temperature for excess reactivity ER293 ¼ 3:7 mk. Again, one may see that the sprayers M.3 (despite its small capacity) and the vessel cooling systems M.2 are more efficient than pool cooling system M.1 for the complete range being considered for the initial temperatures 20e33 C. However, the pool cooling system M.1 is not much effective for high initial temperature and converges to M.3 system for low initial temperature. The vessel cooling system M.2 without doubt is the best and is capable to guarantee a maximum operation time of 15 h for T0 ¼ 20 C. Acknowledgements The authors are grateful to Prof. Dr. I. Othman, Director General of the Atomic Energy Commission of Syria, for his keen interest and support. Appendix Fc , Surface area of fuel elements. ac , Heat transfer coefficient of fuel elements. GUAl , Fuel meat mass. GAl , Mass of cladding, guide tube and link rods in the core. CpUAl ; CpAl , Specific heat capacity of fuel meat and aluminum. FBi , Internal surface area of side reflector. KB , Overall heat transfer coefficient of side reflector. Tin , Inlet coolant temperature. _ Coolant flow rate. m, Cpf , Average coolant specific heat capacity in the core. Gf , Coolant mass in the core. Cpf2 , Specific heat capacity of coolant at the core exit. Guv ; Glv , Water mass in the upper and lower part of the vessel, respectively. Cpuv ; Cplv , Water specific heat capacity in the upper and lower part of the vessel, respectively. Kuv ; Flv , Overall heat transfer coefficient of vessel wall at the upper and lower part, respectively. Fuvi ; Flvi , Internal surface area of vessel wall at the upper and lower part, respectively. Tgr , Ground temperature. Fup ; Flp , Internal surface area of the pool wall at the upper and lower part, respectively.
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Gup ; Glp , Water mass in the upper and lower part of the pool, respectively. Cpup ; Cplp , Water specific heat capacity in the upper and lower part of the pool, respectively. Klpgr ; Kupgr , Overall heat transfer coefficient of pool wall at the upper and lower part, respectively. hex , The height of the core outlet and exit orifice. H, The effective height of the core. xi ; Wi , Local pressure loss factors and coolant velocities for the parts of coolant flow i. fwj ; Wj , Friction pressure loss factors and coolant velocities in the parts of coolant flow j. Lj , Length of the parts j of coolant flow. rfi ; rfj , Coolant density in the parts i and j of coolant flow, respectively. Ai ; Aj , The cross-section areas for the parts i and j of coolant flow, respectively.
References Akaho, E.H.K., Maakuu, B.T., 2002. Simulation of reactivity transients in a miniature neutron source reactor core. Nuclear Engineering and Design 213, 31e42. El-Wakil, M.M., 1962. Nuclear Power Engineering. McGraw-Hill, Inc., New York. IAEA-TECDOC-384, Technology and Use of Low Power Research Reactors, 1986. IAEA, Vienna, pp. 89e98. Incropera, F.P., De Witt, D.P., 1981. Fundamentals of Heat Transfer. John Wiley Sons, Inc., New York. Khamis, I., et al., 2000. Dynamic simulator for the miniature neutron source reactor. Progress in Nuclear Energy 36 (4), 379e385. Rust, J.H., 1979. Nuclear Power Plant Engineering. Haralson Publishing Company, Buchanan, Georgia. Shi Shuangkai, 1993. MNSR Thermal Hydraulics. MNSR Training Materials. China Institute of Atomic Energy, Beijing, China. The Syrian Safety Analysis Report (SAR) for MNSR, 1992 (internal report). Wolf, H., 1984. Heat Transfer. Harper & Row, Publishers, New York.