Simulation of reactivity transients in a miniature neutron source reactor core

Nuclear Engineering and Design 213 (2002) 31 – 42 www.elsevier.com/locate/nucengdes

Simulation of reactivity transients in a miniature neutron source reactor core E.H.K. Akaho *, B.T. Maakuu Department of Nuclear Engineering, National Nuclear Research Institute, Ghana Atomic Energy Commission, P.O. Box LG 80, Legon-Accra, Ghana Received 6 November 2000; received in revised form 27 July 2001; accepted 19 October 2001

Abstract Computer simulation was carried out for reactivity induced transients in a HEU core of a tank-in-pool reactor, a miniature neutron source reactor (MNSR). The reactivity transients without scram at initial power of 3 W were studied. From the low power level, the power steadily increased with time and then rose sharply to higher peak values followed by a gradual decrease in value due to temperature feedback effects. The trends of theoretical results were found to be similar to measured values and the peak powers agreed well with experimental results. For ramp reactivity equivalent of clean core cold excess reactivity of 4 mk (4 ×10 − 3 Dk/k), the predicted peak power of 100.8 kW agrees favourably with the experimental value of 100.2 kW. The measured outlet temperature of 72.6 °C is also in agreement with the calculated value of 72.9 °C for the release of the core excess reactivity. Theoretical results for the postulated accidents due to fresh fuel replacement of reactivity worth 6.71 mk and addition of incorrect thickness of Be plates resulting in 9 mk reactivity insertion were 187.23 and 254.3 kW, respectively. For these high peak powers associated with these reactivity insertions, it is expected that nucleate boiling will occur within the flow channels of the reactor core. © 2002 Published by Elsevier Science B.V.

1. Introduction For normal reactor operating conditions, it is expected that the rate of heat generation in the fuel will be the same as the rate of removal of heat by the coolant. Any imbalance in this state is likely to bring about a perturbation, which can lead to an accident. Transients induced by reactivity insertions will put the reactor in a super-critical state causing its power to rise suddenly to * Corresponding author. Tel./fax: + 233-21-400398. E-mail address: [email protected] (E.H.K. Akaho).

levels beyond the capabilities of the reactor to remove heat. The transient behaviour depends on the design features of the reactor, the rate and magnitude of the reactivity inserted and the operating condition before the initiation of the excursion. In order to demonstrate the inherent safety characteristics of Ghana research reactor-1 (GHARR-1), a commercial version of the Chinese miniature neutron source reactor (MNSR), dynamic experiments were performed by Akaho et al. (1996) by inserting step reactivity of 2.1 mk (2.1× 10 − 3 Dk/k) and ramp reactivity of the cold

0029-5493/02/$ - see front matter © 2002 Published by Elsevier Science B.V. PII: S 0 0 2 9 - 5 4 9 3 ( 0 1 ) 0 0 4 5 7 - 5

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clean core excess reactivity of 4 mk. The reactor powers rose to peak values of 37.5 and 100.2 kW, respectively. If procedures are not correctly followed for some abnormal operations such as the installation of a new core, then a maximum of 6.71 mk could be inserted (SAR, 1995). Due to human error, the reactivity that could be inserted during the addition of the incorrect thickness of top Be plates in the Al tray located on top of the core is estimated to be 9 mk (SAR, 1995). These large reactivity insertions could lead to very high powers. Transient analysis for these two abnormal operations is needed for the safety assessment of the reactor and to update the Safety Analysis Report. The reactor GHARR-1 is a 30 kW tank-inpool reactor, which uses 90.2% enriched uranium–Al alloy as fuel. The diameter of the fuel meat is 4.3 mm and the thickness of the aluminium cladding material is 0.6 mm. The total length of the element is 248 mm and the active length is 230 mm. The percentage of U in the UAl4 dispersed in Al is 27.5% and the loading of U-235 in the core with 344 fuel elements is 990.72 g. In order to reduce the thermal resistance between fuel pellet and the cladding tube, after the fuel meat has been loaded into the cladding tube, the cladding is drawn to obtain mechanical close attachment between the cladding and the fuel meat. The clearance between pellet and end plug is 0.5 mm, which is allowed for the thermal expansion of the pellets. To ensure fuel element stability in the core, the lower end of the fuel rod is designed to have a tapered structure which enables a self-lock fit between the fuel end and the lower grid plate and thus the fuel rods and dummy elements are tightly locked to the lower grid plate while its upper end is free in the lattice of the upper grid plate. The reactor is designed to be compact and safe and it is used mainly for neutron activation analysis, production of short-lived radioisotopes and for education and training. The maximum thermal neutron flux at its inner irradiation site is 1×1012 ncm − 2 s − 1. It is cooled and moderated with light water, and light water and beryllium act as reflectors. The fuel cage consisting of 344

fuel pins, four tie and six dummy rods are concentrically arranged in 10 rings. The core has a central guide tube through which a Cd control rod cladded in stainless steel moves to cover the active length of 230 mm of the core. The single control rod is used for regulation of power, compensation of reactivity and for reactor shutdown during normal and abnormal operations. The fuel cage is placed on a 50 mm thick Be reflector of diameter 290 mm and it is surrounded by another 100 mm thick metallic Be reflector of height 238.5 mm. The bottom beryllium plate and the side Be annular form the inlet orifice and the supporting plate and the side beryllium annular form the outlet orifice. On top of the core is placed an Al tray which may contain certain thickness of Be plates required for adjustment of core excess reactivity for compensation of fuel depletion and Sm poisoning. The reactor core is located in the lower section of a sealed aluminium alloy vessel of diameter 0.6 m which is hanged on a frame across a stainless steel lined water pool of diameter 2.7 m and depth 6.5 m. The heat generated by fission is transferred in an upward direction and the hot water, which moves to the upper section of the reactor tank, is transferred to the water in the pool. The core is cooled by natural convection and under normal operational conditions, the flow regime is single phase but nucleate boiling is expected under abnormal condition when power excursion occurs due to large reactivity insertions. There are two pairs of NiCr–NiAl thermocouples, which are fixed in the inlet and outlet of the core coolant for measuring the temperature difference between the inlet and outlet of the coolant. A platinum resistance thermometer is used for measuring the inlet temperature of the coolant The reactor which is undermoderated with atomic ratio of H/U-235 as 197 possesses the non-sufficient natural circulation feature. Due to the suction, part of the hot outlet coolant is taken into the core by the coolant near the inlet orifice as shown in Fig. 1. Guo Chengzhan (1990) reported that hydraulic feedback experiments showed that the hot coolant recirculation speeds up the increase of the inlet coolant temperature, which increased

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the average temperature of the water in the core and thus shortened the time of temperature feedback. It was noticed that the higher the reactivity inserted with higher reactor power, the shorter the coupling action. Since the core is undermoderated, any mechanism which will cause a decrease in the number of moderating nuclei in the reactor core will lead to a decrease in system reactivity. The mechanisms that may affect the system reactivity are the fuel and moderator expansion by heating, void production by boiling, etc. In order to predict quantitatively the consequences of the reactivity accidents due to fresh core replacement and addition of Be plates, the coupled thermal– hydraulics and neutronic effects were evaluated for the reactor. The present study aims at providing a simulation and analysis of reactivity induced transients that were carried out at initial power of 3 W and without scram conditions for the present HEU core. The temperature-reactivity feedback characteristics of the reactor as related to safety are discussed.

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2. Theory The transient, driven by reactivity z(t), is caused by several mechanisms. The net effect can be written in the form: z(t)= z0(t)+ zfb(t)+ zc(t)+ zsd(t)

(1)

where z0(t), reactivity inserted by an initiating event; zfb(t), reactivity due to feedback from thermal –hydraulics effect; zc(t), reactivity due to reactor control system; zsd(t), shut down or trip reactivity. Prompt and inherent reactivity feedback are important for research reactor safety and because of the inherent safety features provided by the design of MNSR and SLOWPOKE reactors, only reactivities due to initiation events and thermal– hydraulic effects are considered in this work. The total reactivities inserted were varied to study the effect of these characteristics of z0(t) on power and temperatures in the system. The feedback reactivity is considered to be zero at the low power of 3 W and that only reactivity is due to

Fig. 1. A schematic diagram of the coolant flow pattern.

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feedback effects as the power increases. Therefore, the reactivity due to the temperature feedback can be expressed in the form: z(t) =z0(t)+ hmDTm(t) + hfmDTfm(t)

(2)

where hm and hfm are the moderator and fuel temperature coefficients, respectively and DTm and DTfm are the deviations of the spatially averaged moderator and fuel temperatures from its equilibrium temperatures, respectively. For coolant flow pattern shown in Fig. 1, the partial differential equations for diffusion of heat within each fuel element in the reactor core region is written as:





(T 1 ( ( cpfmzfm (r,t) = k r T(r,t) +qv(r,t) (t r (r fm (r (3) and for cladding region, it is expressed in the form: cpczc





(T 1 ( ( (r,t) = k r T(r,t) (t r (r c (r

(4)

The heat capacity for the fuel meat is cpfm and that of the cladding is cpc. The cladding surface temperature is Tc and kc and kfm are the thermal conductivities of the cladding and fuel meat, respectively. From steady-state thermal– hydraulics analysis, it has been demonstrated that due to the fact that the fuel element possesses low power density and high thermal conductivity the temperature difference between the meat at the centre and the outside of the cladding is 1 °C for nominal power of 30 kW (Shi Shuankai, 1990; Akaho and Dagadu, 1999). Due to the fact that there is a close attachment of the thin cladding with the fuel meat without any gas gap, in order to avoid any thermal resistance between meat and cladding (Quian Shunfa, 1990), we assumed that at any power level attained during transient the temperature at the fuel and cladding regions will be almost the same: Tc(t)=Tfm(t)

(5)

Thus, the simplified equation based on the lump parameter technique using Eqs. (3) and (4) becomes:

dTc = P(t)− Qf(t) dt

(mfmcpfm + mccpc)

(6)

The total mass of the Al cladding of density 2.7 g cm − 3 is mc and the mass of fuel mfm is: mfm =

Nfyd 2fmhzfm 4

(7)

where Nf is the number of fuel elements, dfm is the diameter of the fuel meat and the active height of the fuel rod is h. The density of the fuel element is zfm which is calculated using the expression (Quian Shunfa, 1990): zfm =

3.3596(1−m) 1.2443−X

(8)

with m as the porosity (3%) and X is the percentage of weight of uranium in the U–Al alloy (27.5%). The heat transferred to the coolant at time t, Qf(t), is expressed in the form: Qf(t)= Ash(Tc(t)− T( f(t))

(9)

where T( f(t)= 1/2[T3(t)+ T1(t)] is the average (bulk) water temperature. Substitution of Eq. (9) into Eq. (6) gives the relationship: dTc = P(t)− Ash(Tc(t)− T( f(t)) dt (10)

(mfmcpfm + mccpc)

The heat transfer coefficient h(t) which varies with power and therefore time, is determined from full scale simulation experiment and correlated in the form (Zhang Yongji, 1993): h(t)=

kf(t) n(Grf(t) · Prf(t))m deq

(11)

where the constant n and exponent m only valid for the MNSR core are: n=

!

0.68 0.174

m=

!

1/4 1/3

GrfPrf B 6×106 laminar GrfPrf \ 6×106 turbulent

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If the power excursion is of sufficient magnitude, large fuel element surface heat fluxes will be generated and temperatures will rise to the saturation temperature of the water moderator and subcooled boiling will commence. In order to determine whether or not the heat flux leading to nucleate boiling reaches or exceeds the condition of Onset of Nucleate Boiling (ONB) along the channel, the temperature of the cladding surface is computed using the correlating equation (VDIVerlag, 1984): Ts = Tsat +(4.31 −0.11Tsat)q 0.3

(12)

where q is the heat flux (MW m − 2). Voids formed during boiling expel moderator and thereby further decreased system reactivity. The Bankoff variable density model (Bankoff, 1959) for bubble flow as reported by Hewitt (1978) which assumes no local slip between the two phases was used to estimate the void fraction across the flow channels: h=

KBzlex zv − ex(zv −zl)

(13)

where KB is a parameter which has a value of 0.89 (Hewitt, 1978) using experimental data for steam–water systems. The ex is the thermodynamic equilibrium quality at any power, which is calculated using the relationship derived, based on energy balance on the reactor core: ex =

P Dh − i mhfg hfg

(14)

where Dhi is the enthalpy of subcooling and hfg is the enthalpy of vaporisation. The nucleate boiling heat transfer coefficient hb, is determined using the correlation of Mikheev (1954): hb = 3.0q 0.7p 0.15

(15)

where p is the system pressure (bar) and q is the heat flux (MW m − 2). The conservation of momentum equation for the reactor coolant water is written as: −





(p (U(t) (U 1 fr x =z¯ f + z¯ fU + + z¯ U 2(t) (z (t (z 2 deq Dz f +zfg

(16)

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The skin friction, fr and the drag coefficient x are dependent on the flow regime. The flow velocity is U and the equivalent diameter of the flow channel is deq and the density of the fluid is zf. With the earlier assumption that there is no thermal resistance between fuel meat and cladding and therefore Tfm(t)# Tc(t) at any power level attained during the transient, the conservation of energy equation is expressed in the form: cpfzf

(Tf(t) (T (t) A h + cpfzfU(t) f = s (Tc(t)− T( f(t)) (t (z AF (17)

and simplified to the form: Hcpfz¯ f

dT( f AshH = (Tc(t)− T( f(t)) dt AF − cpfU(t)z¯ f(T2(t)− T1(t))

(18)

where As is the heated surface area and AF is the flow area. The active height of the core is H. The core inlet temperature at any time is T1(t) and the outlet temperature is determined using the correlation between reactor power and the inlet– outlet temperature and height of inlet orifice channel H1 (Shi Shuankai, 1990): T2(t)− T1(t) 2.674 = (5.725+ 147.6H − )P(t)(0.59 + 0.0019T1(t)) 1

(19)

It must be pointed out that Eq. (19) is valid only for the MNSR core which is cooled under natural convection condition. Based on the thermal –hydraulic design consideration, the height of the core inlet orifice channel for the MNSR core is chosen in order to control the coolant flow within the core in order to achieve large temperature difference between inlet and outlet temperatures and thereby enhance the negative moderator temperature effect. For the upper part of the reactor vessel (Region 3) the heat transfer equation is written as: m3cpf3

dT3 =AupcpfU(t)(zf2T2(t)− zf3T3(t))−Q0 dt (20)

The mass of water in the upper part of the reactor vessel is m3 and Q0 is the heat transfer to

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Table 1 Kinetic and thermal–hydraulics parameters

The relevant heat transfer equation for the water pool region is simply written as:

hm = 2.6445E-05 Moderator temperature − 3.4752E-06Tm coefficient (mk °C−1) Fuel temperature coefficient (mk hfm = 7.73E-06 °C−1) − 2.90E-07 Tfm+1.09T 2fm Void coefficient (mk per %) −4.78 Prompt neutron generation 8.1E-05 time, \ (s) Total effective delayed fraction, 8.03E-03 ieff Decay constant, u (s−1) 9.62E-02

m0cpf

the pool and the coolant temperature for the region is T3 with fluid density of the region represented as zf3. For the annular down-comer region (Region 4) the heat transfer equation is: m4cpf

dT4(t) = AdccpfU(t)(zf3T3(t) − zf4T4(t))− Q4 dt +QB

(21)

The mass of coolant for the region is designated m4 and the time dependent temperature of the coolant is T4(t) with its associated coolant density zf4, respectively. The flow area of the downcomer region is Adc. The quantity of heat transferred from the downcomer region to the pool is Q4 and that heat transferred from the annular beryllium reflector to the downcomer region is QB. Experimental evidence (Zhang Yongji, 1993) under steady-state condition and hydraulic feedback experiments using prototype MNSR (Guo Chengzhan, 1990) showed that the temperature at the downcomer region is almost the same as the inlet temperature into the core. Hence T4(t)# T1(t). Eq. (21) is rewritten as: m4cpf

dT1(t) = AdccpfU(t)(zf3T3(t) − zf4T1(t))− Q4 dt +QB

(22)

Since the pool water has a large heat capacity, it is assumed that the heat transfer in the pool is isothermal to the ambient and the heat released from the core is totally absorbed by the water.

dT0(t) = Q 0 + Q4 dt

(23)

The different quantities of heat transferred to the pool Q0 and from the downcomer region Q4 are computed using heat transfer equations for natural convection. Various parameters are needed for the transient analysis. The kinetic and thermal– hydraulic parameters such as hfm, hm, u, \, i and void coefficient, for the core are listed in Table 1 (Akaho and Maakuu, 1996). In order to eliminate the possibility of prompt criticality occurring in the reactor, the cold clean core excess reactivity of the reactor is limited to the value zex 5 1/2i. Thus, for the i value of 8.03 mk, the cold clean core excess reactivity is 4 mk. The heat capacities and thermal conductivities of the fuel meat and cladding (IAEA, 1992) and the fluid properties (VDI-Verlag, 1984) were evaluated as functions of temperature. Appropriate expressions could not be obtained for drag coefficient x for laminar and turbulent flows in rod bundle geometry for the estimation of flow velocity U(t) using Eq. (16). Instead, the flow velocity at any time U(t) was calculated using the definition of Stanton number as a function of time St(t): St(t)=

h(t) A DTc(t) = F z¯ fU(t)cpf As DTf(t)

(24)

where DTc(t)= Tc(t)− T1(t) and DTf(t)= T2(t)− T1(t). The flow velocity at any time t is estimated from initial operating conditions using the expression: h(t) z¯ f0 DTf(t) DTc(0) U(t)= U(0) h(0) z¯ f DTf(0) DTc(t)

(25)

The initial flow velocity U(0), at low power 3 W was calculated based on steady-state thermal–hydraulic analysis of the core (Akaho and Dagadu, 1999). It was ensured that the total pressure losses including the entrance, exit and over all the segments and virtual chimney are equal to the hydrostatic pressure drop across the coolant channel height.

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The first order differential equations for which numerical solution is provided to determine time dependent thermal– hydraulic parameters of the core are listed as follows: (26)

dQ i = P(t) − uQ(t) dt L

(27)

dTc(t) P(t) = dt (mfmcpfm +mccpc) Ash Tc(t) (mfmcpfm +mccpc)

+

Ash T( f(t) mfmcpfm +mccpc

(28)

dT( f(t) Ash Ash U(t)T1(t) = T( (t) + T (t) − dt (cpfzfAF) c cpfzfAF f H −

U(t)T2(t) H

(29)

dT3(t) Aupcpf2zf2U(t)T2(t) Aupz3(t)U(t)T3(t) = − dt m3cpf3 m3cpf3 −

Q0 m3cpf3

(30)

dT4(t) Adccpfzf3U(t) A c z U(t) = T3(t) − dc pf f4 T4(t) dt m4cpf m4cpf −

(QB −Q4) m4cpf

(31)

dT1(t) Adccpf3zf3U(t) = T3(t) dt m4cpf −

Adccpf4zf4U(t) (QB −Q4) T1(t) − m4cpf m4cpf

thermal–hydraulics equations that describe the transient behaviour of the GHARR-1 core.

3. Results and discussions

dP z(t)− i = P(t) + uQ(t) dt L

−

37

(32)

The Eqs. (26)– (29), (31) and (32) are expressed in the form of a matrix and the numerical solution was based on exponential transformation method (Hansen et al., 1965). A computer code TEMPFED is written in FORTRAN77 programming language (Akaho and Maakuu, 1998) to solve the above listed neutronic and

The equations and models used in the code were tested by comparing the simulation results to the transient experimental data for the demonstration of the inherent safety of the reactor GHARR-1. All simulations were carried out for unprotected transients (without scram) with the central control rod completely out of the core. To make it possible for these transient experiments to be carried out, the scram system incorporated in the control and protection system for abnormality during reactor operation if the temperature difference or reactor power exceeds its rated value by 20% was first disabled. The transients were initiated from low power of 3 W at ambient temperature of 30 °C with very low coolant flows. Fig. 2 illustrates the comparison between the calculations using the code TEMPFED and experimental measurements for ramp reactivity equivalent of core excess reactivity of 4 mk. From this plot, one notices that the reactor power slowly begins to increase as compared with the development of convective flow through the reactor core until hot recirculating water is drawn into the inlet of the core. Once the peak power is reached, the reactor power decreases slowly due to reactivity feedback caused by thermal effects due to moderator heating. The reactor power attains a peak value (: 100 kW) when the feedback effect caused by moderator expansion has accommodated the initial reactivity inserted. This clearly suggests that there is an efficient energy removal from the core by natural circulation resulting into a much lower rates of reactivity feedback and build-up of fission product poisons. It can be observed that the trends of calculated results and measured data are in good agreement. The peak power of 100.8 kW predicted is almost the same as the experimental value of 100.2 kW. The effect of the transient on temperatures of the fuel meat or the cladding temperature and the outlet

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temperature is shown in Fig. 3. It can be observed that after the initiation of the reactivity insertion, the core temperatures increase very slowly at first and then rapidly until the peak power is reached. The convection flow, which develops after the peak power is formed removes significant quantities of energy from the core hence core temperatures tend to stabilise. The measured maximum outlet temperatures of 72.6 °C corresponded with the predicted value of 72.9 °C.

The results of the various transient experiments are listed in Table 2 showing the reactor peak powers and core outlet temperatures for different reactivity insertions. One notices that the peak powers and coolant temperatures increase with reactivity insertion. However, there is a discrepancy in the periods for the occurrence of the peak powers for the excursion which can be at tributed to the fact that the numerical solution provided by the present version of the TEMPFED

Fig. 2. Power excursion for ramp insertion of 4 mk.

Fig. 3. Temperatures for ramp insertion of 4 mk.

Ramp 2.0 Step 2.1 Ramp 2.92 Ramp 4.0

Reactivity inserted (mk)

33.8 36.0 58.2 100.2

34.4 36.7 58.7 –

34.8 36.8 63.2 100.8

TEMPFED

570 555 361 380

Experimental

Calculated

RELAP

Experimental

Calculated

Time (s)

Power (kW)

Table 2 Experimental and calculated peak powers and outlet temperatures

640 610 370 –

RELAP

Calculated

355 352 350 353

TEMPFED

Calculated

46.7 47.1 59.8 72.9

Experimental

48.4 48.7 56.4 –

RELAP

Calculated

Outlet temperature (°C)

55.7 56.4 63.4 72.6

TEMPFED

Calculated

E.H.K. Akaho, B.T. Maakuu / Nuclear Engineering and Design 213 (2002) 31–42 39

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E.H.K. Akaho, B.T. Maakuu / Nuclear Engineering and Design 213 (2002) 31–42

Fig. 4. Power excursion for ramp insertion of 6.71 mk.

Fig. 5. Temperatures for ramp insertion of 6.71 mk.

code was not expressed as an exponential function in time modified by a correction function of time as suggested by Nakamura (1977). Comparisons between calculated and experimental values of power as reported in Table 2 also show that all predicted peak powers using RELAP-4 by Guo Chengzhan et al. (1985), a sophisticated code and the simple code TEMPFED are in good agreement. Furthermore, the code was used to simulate experimental results of SLOWPOKE-1 reactor. The peak power of 186 kW obtained experimentally for reactivity insertion of 6.48 mk compared favourably with the value of 181.5 kW predicted using the code.

Based on the successful validation of the code in predicting peak powers, it was used to simulate the rapid reactivity insertions of 6.71 and 9 mk associated with safety analysis of fresh core replacement and addition of incorrect thickness of Be plates in the tray, respectively. Figs. 4 and 5 are plots for the variation of reactor power and temperature, respectively, with increase in time when a reactivity of 6.71 mk is inserted due to fresh fuel replacement accident. The computed results of simulation of reactivity insertion of 9 mk for incorrect selection of thickness of Be shims follow similar trends. The peak powers predicted

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are 187.2 and 254.3 kW for 6.71 and 9 mk, respectively. For both cases, large surface heat fluxes will be generated and saturation temperature would be reached. Subcooled nucleate boiling is expected to occur within the flow channels of the reactor for these reactivity insertions. The results of the various transients investigated are plotted in Figs. 6 and 7 for peak powers and peak core outlet temperatures as functions of reactivity insertion. The peak powers increase lin-

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early with the size of the reactivity insertion and the peak outlet temperatures generally increase with the value of the reactivity inserted, which is eventually limited by boiling.

4. Conclusion The numerical scheme based on exponential transformation method was used to develop a

Fig. 6. Peak power vs. reactivity.

Fig. 7. Peak outlet temperature vs. reactivity.

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computer code TEMPFED for PC. The code solves the neutronics and thermal– hydraulics equations describing the dynamic behaviour of a tank-inpool reactor, MNSR. The code was validated against experimental values using the reactor for reactivity insertions from low power levels and those computed using a more sophisticated code. Simulations of reactivity transients without scram for postulated accident scenarios characterised by large reactivity insertions for the malfunctioning of MNSR using the present HEU fuel were also predicted. It can be concluded from this study that due to the reactivity feedback effect due to moderator heating significant fraction of the heat generated in the core has been removed from the core by natural convection. This clearly demonstrates the inherent safety characteristics of MNSR. In general, the values of peak powers and outlet temperatures attained during various excursions increase with the magnitude of the reactivity inserted. Postulated accidents due to insertion of large reactivities during fresh fuel replacement and addition of incorrect thickness of Be shims show that large amounts of heat will be generated suggesting that subcooled nucleate boiling may take place at those times.

Acknowledgements The authors acknowledge with gratitude the financial support of International Atomic Energy Agency, Vienna for the award of Research Contract No. 8789/RB. We particularly thank Dr K.M. Akhtar, Dr V. Dimic and Professor B. Dodd for the stimulating interest shown in this project.

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