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Thermal hydraulic investigations of intermediate heat exchanger in a pool-type fast breeder reactor
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Nuclear Engineering and Design 238 (2008) 1577–1591
Thermal hydraulic investigations of intermediate heat exchanger in a pool-type fast breeder reactor R. Gajapathy a,∗ , K. Velusamy a , P. Selvaraj a , P. Chellapandi a , S.C. Chetal a , T. Sundararajan b a
Nuclear Engineering Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India b Department of Mechanical Engineering, Indian Institute of Technology-Madras, Chennai 600036, India Received 6 July 2007; received in revised form 20 November 2007; accepted 9 January 2008
Abstract Intermediate heat exchanger (IHX) in a pool-type liquid metal cooled fast breeder reactor is an important heat exchanging component as it forms an intermediate boundary between the radioactive primary sodium in the pool and the non-radioactive secondary sodium in the steam generator (SG). The thermal loads during steady state and transient conditions impose thermal stresses on the heat exchanger tubes and on the shells which hold the tube bundle. Estimation of these thermal loads and achieving uniform temperature distribution in the tubes and shells by having uniform flow distributions are the major tasks of thermal hydraulic investigations of IHX. Through multi-dimensional thermal hydraulic investigations performed using commercially available computer codes such as PHOENICS, the flow and temperature distributions in the tubes and shells and in its secondary sodium inlet and outlet headers are obtained with and with out provisions of flow distribution devices. The effectiveness of these devices in achieving acceptably uniform flow and temperature distributions has been assessed and thermal loads on the tubes and shells for thermo mechanical analysis of the IHX have been defined. The predictions of the computational studies have been validated against simulated experiments. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In India, a 500-MW(e), pool type, liquid sodium cooled prototype fast breeder reactor (PFBR) is under construction (Chetal et al., 1995). PFBR has three systems of heat transfer in series, viz. (i) the primary sodium system, (ii) the secondary sodium system and (iii) the steam–water system, as depicted in Fig. 1. In the primary sodium system, the nuclear heat generated in the core is removed by primary sodium circulated by primary pumps. The hot primary sodium emerging from the core mixes with a hot sodium pool and penetrates the intermediate heat ∗
Corresponding author at: Nuclear Engineering Group, Indira Gandhi Centre for Atomic Research, Thermal hydraulic Section, Room No. 251, CDO Building, IGCAR, Kalpakkam 603 102, India. Tel.: +91 44 27480106; fax: +91 44 27480104. E-mail address: [email protected] (R. Gajapathy). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.01.005
exchanger (IHX) through its inlet window (Fig. 2). In the secondary sodium system, the primary sodium flowing in the shell side of the IHX exchanges heat with the secondary sodium flowing in the tube side. The cool primary sodium comes out of the IHX through the outlet window and mixes with cold sodium pool. The sodium temperature of 544 ◦ C in the hot plenum is reduced to 394 ◦ C after the heat exchange. The secondary sodium enters the IHX at the top and flows downwards through a central pipe (Fig. 3) at a temperature of 355 ◦ C. On reaching the bottom, the secondary flow is reversed upwards through the tubes. After the bundle, the hot secondary sodium at 525 ◦ C is collected in an annular pipe which leaves the IHX through a lateral outlet nozzle. In the steam–water system, the secondary sodium exchanges heat with water in a once through steam generator (SG), to produce superheated steam for power generation. Thus, the IHX acts as an intermediate boundary between the highly radioactive primary sodium circulating through the
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Fig. 1. Heat transport flowsheet.
reactor core and the non-radioactive secondary sodium. Also, the IHX must keep its leak-tightness in case of a sodium–water reaction occurring in SG. The IHX is supported on the roof slab (Fig. 2), which is maintained at 100 ◦ C and is freely hanging from the top. The lower part of the IHX is in the cold sodium pool of the reactor vessel. The top of the IHX is surrounded by complementary shielding. So, in these situations, the IHX experiences thermo mechanical loads in the tube bundle related to heat exchange and also in the shell that encloses the tubes during normal as well plant transients. Also, the IHX has to be highly reliable, since removal of it for repair leads to stopping of the plant operation for a long period. Hence, it is very important to investigate the thermal mechanical loads on IHX, to ensure safe and reliable operation of IHX and the reactor as well. This paper focuses the thermal hydraulic investigations, viz. (i) primary and secondary sodium flow and temperature distributions carried out by 2D axi-symmetric porous body models for the tube bundle, (ii) secondary flow distribution in the inlet header and the effectiveness of the flow distribution device, (iii) secondary sodium mixing in the outlet header of the IHX and the effectiveness of the mixing device, (iv) transient thermal hydraulic analysis of the tube bundle during the event of loss of feed water flow to SG and (v) comparison of the predictions against simulated experiments.
2. Main characteristics of IHX The total thermal power generated in the reactor core is exchanged by four IHXs in the reactor vessel. IHX is a straight tube heat exchanger of counter current shell and tube type (Fig. 3). The tubes are arranged in circumferential rows around the secondary sodium down comer between the top and bottom tube sheets.
Total thermal power of reactor Thermal capacity of each IHX Primary sodium inlet flow Primary sodium inlet temperature Primary sodium outlet temperature T between primary sodium inlet and outlet Secondary sodium inlet flow Secondary sodium inlet temperature Secondary sodium outlet temperature T between secondary sodium inlet and outlet Inlet and outlet windows height Heat exchanging tubes OD and thickness Total number of tubes Number of rows Radial pitch of the rows Circumferential pitch Heat transfer length Overall diameter of IHX Overall height of IHX
1250 MW(t) 315 MW(t) 1649 kg/s 544 ◦ C 394 ◦ C 150 ◦ C 1450 kg/s 355 ◦ C 525 ◦ C 170 ◦ C 0.9 m 19 and 0.8 mm 3600 25 25 mm 28 mm 7.5 m 2m 7m
3. Thermal hydraulics and structural assessment of IHX The IHX is subjected to pressure loading due to primary and secondary sodium. Due to this pressure loading, the inner rows of the tube bundle are under compression. In other words, these tubes are subjected to buckling risk between the top and bottom tube sheets. The outer rows of the tube bundle are under tension. In other words, the tubes try to pullout from the tube sheets. The tubes will fail if the buckling and pullout loads exceed the acceptable limits. If the inner rows of tubes are cooler, the thermal load reduces the pressure load and reduces the buckling load on the inner tubes. If the outer rows of tubes are hotter, the thermal load reduces the pressure load, which results in reduced pullout load on the outer rows of tubes. If the inner and outer tubes are hotter and colder respectively, the thermal loads increase the buckling and pullout loads on the tubes.
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Fig. 2. PFBR reactor assembly vertical section. (01) Main vessel, (02) core support structure, (03) core catcher, (04) grid plate, (05) core, (06) inner vessel, (07) roof slab, (08) large rotatable plug, (09) small rotatable plug, (10) control plug, (11) control and safety rod mechanism, (12) in-vessel transfer machine, (13) intermediate heat exchanger, (14) primary sodium pump, (15) safety vessel and (16) reactor vault.
As the primary sodium enters the shell side of IHX radially through the inlet windows, the flow takes place across the tube bundle. Due to the cluster arrangement of the tubes, the tube bundle offers high resistance to the radial flow. Due to that, the radial flow takes turn and start flowing downwards. The flow is higher in the outer rows; it gradually reduces as it penetrates through the bundle and is the least in the inner rows. Near the inlet region, the outer rows of tubes experience higher primary sodium temperature compared to the tubes in the inner rows. Due to this, the outer rows of tubes will become hotter and the inner rows will become cooler. Hence, in this situation, the thermal loads help in reducing the buckling and pullout loads on the tubes. The thermal loads for IHX tubes are based on acceptable
temperature difference (T) between the heat exchange tubes during steady state and transient conditions. In order to estimate temperatures of the tubes and the thermal loads and how far this thermal load helps in reducing the buckling and pullout loads, the temperature distribution in the tube bundle needs to be evaluated. For this purpose, a 2D thermal hydraulic analysis of the tube bundle is carried out. From this analysis, the primary and secondary sodium temperature distributions are computed. The results of this analysis are discussed in Section 4. In order to have lower thermal loads, the T between the tubes must be low. This calls for uniform temperature distribution in the tube bundle. Since, the primary sodium flow in the shell side takes place by gravity, there is little control over its
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ature distribution in the bundle for this condition are presented in Section 6. Using the tube bundle temperature distribution during steady state and transient conditions, thermal loads are estimated and thermo mechanical analysis is carried to compute the thermal stresses developed. From the thermal stress analysis, the design stress limits are met and the adequacy of tube diameter, thickness and the height of the bundle are evaluated. In spite of the efforts to make the tube bundle temperature uniform, the secondary sodium outlet temperature coming out of the tube bundle will be less uniform. This will impose thermal load on the inner and outer shells of the secondary sodium outlet plenum. Hence, a mixing device is introduced to mix the hot and cold secondary sodium that comes out of the inner and outer rows of the tube bundle and reduce the T further. To assess the efficiency of the mixing device and compute the temperature difference between the shells of the outlet plenum, a 3D thermal hydraulic analysis has been carried out, which is discussed in Section 7. Using the inner and the outer shell temperature distribution, stress analysis is carried out to find out the stresses developed in the weld joints of the shells and the design requirement for the bellows are arrived at. 4. 2D thermal hydraulic analysis of the tube bundle 4.1. Mathematical modeling Fig. 3. Schematic of IHX.
distribution. It shall be highlighted, that in the case of PFBR, no attempt has been made to incorporate any baffle at the primary sodium inlet to alter the flow distribution. This is to have a minimum pressure drop in the primary side and hence minimum load on the inner vessel which separates the sodium pool into hot pool and cold pool. Hence, the only way is to alter the secondary sodium flow distribution inside the tubes. To achieve the desired secondary flow distribution, a flow distributing device (FDD) is developed and located at the bottom of the tube bundle. Theoretical and experimental investigations are carried out to find out secondary sodium inlet flow distribution to the tubes such that the temperature distributions in the primary and secondary side are uniform. The results of the flow distribution are discussed in Section 5. During the event of loss of feed water flow to the SG, the secondary sodium pumps trip which results in loss of heat removal from IHX. Consequently, the primary side of IHX is filled with hot sodium, from top to bottom. Afterwards, reactor scram actuated by high core outlet temperature. As a result of this, cold sodium enters the hot pool and the cold front of sodium moves gradually upwards and reaches lower edge of IHX primary inlet windows. Then, this low temperature primary sodium enters outer rows of tubes, while the temperature of tubes in the inner rows remains hot. The temperature difference across the tube bundle will be higher during this case. This condition is analyzed using the same 2D computational model developed for the steady state analysis of the tube bundle. The results of temper-
In IHX, the tubes are arranged in rows and they are symmetrical in the circumferential directions. Hence, a 2D axi-symmetric analysis of the tube bundle is carried out using the Computational Fluid dynamics code PHOENICS 2.2.1 (CHAM, 1991). In this computer code, the Navier–Stokes equations for mass, momentum and energy equation derived for an elemental control volume are solved to obtain pressure, velocity and temperature using finite volume approach which uses control volume based discretisation method (Patankar, 1980). The governing equations can be represented by the following single general equation for constant property viscous flow in vector form as follows (Launder and Spalding, 1974; Hughes and Gaylord, 1964): ∂ (βV ρΦ) + ∇(βS ρ uΦ) = ∇(βS ΓΦ ∇Φ) + βV SΦ ∂t where, is the divergence operator, Γ Φ is the diffusion coefficient, u is the velocity field, SΦ is the source term, βV is the volumetric porosity, βS is the surface permeability and Φ takes the following values, each of which gives rise to a particular conservation equation: Φ=1
gives the continuity equation
Φ = u gives the axial direction momentum equation Φ=v Φ = cp T
gives the radial direction momentum equation and gives the energy equation
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The above equations are solved iteratively. The SIMPLEST algorithm resolves the pressure–velocity coupling. To evaluate the convective and diffusive fluxes at the interfaces, the HYBRID scheme is used. In the code PHOENICS, only the shell side of IHX is modeled and the pressure, velocity and temperature distributions of primary sodium flow over the bundle is solved iteratively. The secondary sodium is modeled as heat sink in the energy equation of the primary sodium. The tube bundle is modeled by porous body formulations. The radial and axial surface permeability’s and volumetric porosities of the tube bundle are calculated and fed as input to the code. The inlet flow of primary sodium from the hot pool into the IHX is specified in terms of velocity and temperature distributions at the IHX primary inlet window. The outlet is specified at the bottom of the IHX. The schematic of computational model and boundary conditions is presented in Fig. 4. It may be highlighted that it is difficult to model each and every tube in the simulation for large equipment like IHX, which comprises of 3600 tubes in a tight pitch. To circumvent this difficulty, porous body formulation with large mesh size has been adopted. The effect of the tube bundle is to offer pressure drop for the sodium flow and absorb heat from the primary sodium. These effects are externally accounted by incorporating momentum and heat sinks in the governing equations. No turbulence model is used in the simulation. The pressure drop and heat transfer coefficient required for the porous body model in the turbulent regime are evaluated from the correlations discussed in the following section.
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4.2. Pressure drop correlations As already explained the primary sodium flow on the shell side of the tube bundle takes place due to the level difference between the hot and cold pools, by gravity. Hence, the primary sodium pressure drop through the IHX imposes this level difference. From the considerations of reducing the power of primary pumps as well load on the inner vessel, this pressure drop must be as low as possible. For the primary flow, the Reynolds number in the bundle is about 82,500. Experimental correlations to evaluate pressure loss coefficients are reported in open literature (Zukauskas and Ulinskas, 1983; Idelchik, 1966), as function of bundle geometry and Reynolds number, both for cross flow as well as parallel flow. 4.2.1. Resistance coefficient for cross flow The flow resistance coefficient ‘K’ for turbulent cross flow over bundle of smooth-wall staggered tubes is given by (Idelchik, 1966), P =
KρU 2 2
where K = A Re−0.27 (Z + 1) A = 3.2 + (4.6 − 2.7 ((S1 − d)/(S2 − d))) (2.0 − S1/d) S2 = (0.25 S12 + S22 )0.5 P, pressure drop (Pa) ρ, density of sodium (850 kg/m3 ) ν, Kinematic viscosity of sodium (3.3 × 10−7 m/s2 ) U, primary sodium velocity at the inlet window (m/s) Re, Reynolds number Z, half the number of tubes d, tube outer diameter (m) S1, S2 and S2 , circumferential, radial and transverse pitch distance between the tubes, respectively. 4.2.2. Resistance coefficient for axial flow For the axial flow, the friction factor, ‘f’ is calculated from (Idelchik, 1966), ΔP =
ρfLV 2 (2Deq )
where f = 0.11((ε/d) + (68/Re))0.25 f, friction coefficient ε, roughness of tubes (m) d, tube OD (m) L, axial mesh size (m) V, axial velocity (m/s) Deq , equivalent diameter of the shell side of IHX (m). 4.3. Heat transfer correlations
Fig. 4. Boundary conditions for IHX tube bundle analysis.
For heat transfer from primary sodium to secondary sodium, both the cross flow and axial flow of primary sodium over the
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bundle is taken into account in the estimation of effective heat transfer coefficient. The following heat transfer correlations are taken from (Marcellin and Guidez, 1984): Tubes : Nu = 4.82 + 0.0185Pe0.827 Shell : Nu = 6.0 + 0.006Pe Cross flow : Nu = 4.03 + 0.228Pe0.67 where Nu and Pe are Nusselt and Peclet numbers, respectively. If hc is cross flow heat transfer coefficient and ha is the axial flow heat transfer coefficient from the above correlations, then the effective shell side heat transfer coefficient hp , given by ((U 2 / h2c ) + (V 2 / h2a )) 1 = h2p (U 2 + V 2 ) where U and V are cross flow and axial flow velocities, respectively. 4.4. Estimation of heat sink From the velocity values, the film heat transfer coefficients on both the sides of the tube are calculated. The overall heat transfer coefficient is calculated as follows taking into account the conduction resistance offered by the tubes. ho =
1 [(1/ hp ) + (do /2k) ln(do /di ) + (1/ hs )(do /di )]
where ho , overall heat transfer coefficient (W/m2 K) hp , effective heat transfer coefficient in the primary side (W/m2 K) hs , heat transfer coefficient in the secondary side (W/m2 K) k, conductivity of tube material (W/m K) do /di , tube outer and inner diameter (m) The rise in temperature of secondary sodium from its initial value is calculated, by equating the heat transferred from primary to secondary sodium. Then, the heat gained by the secondary sodium in each control volume is calculated and applied as heat sink in the energy equation for primary side. The process is repeated until convergence takes place. 4.5. Results and discussion The analysis of primary sodium flow and temperature in the tube bundle has been carried out, first for a theoretical case of uniform secondary sodium inlet flow distribution. Then, the secondary flow distribution that results in acceptable tube bundle temperature distribution is determined by a parametric study. The secondary outlet temperature distribution obtained for various secondary sodium inlet flow distributions are shown in Fig. 5. For uniform flow case, it is found that there is sharp temperature gradient near the inner rows. This is due to the fact that near the primary sodium inlet region, the outer rows of tubes experience higher primary sodium temperature compared to the tubes in the inner rows. The outer rows of tubes are hotter while
Fig. 5. Secondary sodium temperature distribution at the outlet of the tube bundle.
the inner rows are cooler. Hence, in this case the secondary sodium outlet T between the outer and inner rows of the tube bundle is 47 ◦ C, which is very high. In the case of secondary flow distribution without any distributor, the temperature at the inner rows remains the same but the temperature at the outer rows gets reduced. The T in this case is 37 ◦ C, which is better than the theoretical case of uniform flow. Hence, to reduce the temperature gradient further, the secondary sodium flow at the outer rows of the tube should be higher compared to that at the inner rows to reduce the T. For this, the flow in the inner rows should be reduced and correspondingly the flow in the outer rows should to be increased. This is possible by providing a FDD, which can divert more flow towards outer rows. Towards designing a FDD, a parametric study of secondary sodium flow distribution (keeping the total flow constant) has been carried out. It was found that when the tubes in the outer six rows receive 1.5 times the secondary flow of the other tubes, the value of secondary sodium outlet T got reduced to 16 ◦ C as shown in Fig. 5, which is acceptable from thermal stress consideration (discussed in the following section). For this case, the primary sodium flow and temperature distributions are presented in Figs. 6 and 7. 4.6. Thermal loads for stress analysis From the results of thermal hydraulic analysis of the tube bundle, the temperature distribution of the tubes are obtained and used as input for carrying out thermal stress analysis. From the heat sink distribution and the heat transfer coefficients, which are position dependent, the tube wall temperature of each row in the computational mesh is calculated. The average temperature of each tube is calculated by averaging the tube wall temperature along the height of the tube. The average temperature of the entire tube bundle (Ta ) is calculated by averaging tube temperature in the bundle. By comparing each tube temperature with
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the bundle average, the hottest tube temperature (Th ) and coldest tube temperature (Tc ) are found out. The hottest tube tries to expand more than the rest of the tube bundle. As the tube sheets resist this undue thermal expansion, the hottest tube is subjected to compressive stress. Hence, the governing T from the consideration of buckling of the tube is (T )b = (Th − Ta ). The coldest tube tries to expand less compared to rest of the tube bundle. As the tube sheets resist this, the tube-to-tube sheet weld joint of the coldest tube is subjected to pull out. Hence, the governing T from pull out strength consideration is (T )p = (Tc − Ta ). For uniform flow through the secondary sodium inlet, the temperature difference between the shells of the outlet header is exceeding the limits from thermal stress consideration. For flow through the secondary sodium inlet without any distribution device, the net stresses are not meeting the corresponding limits of bucking of the tubes. It has been found that for 50% more flow in the outer 6 rows, the induced stresses are much less than that in the case without FDD and uniform flow. 5. Flow distribution device at IHX bottom header
Fig. 6. Velocity field in IHX tube bundle during normal operating conditions.
To achieve the acceptable secondary sodium flow distribution discussed in the Section 4.5, a FDD is provided at the bottom header of IHX (Fig. 8). The FDD is a perforated plate, consisting of holes in line with the tube sheet holes. The diameter of the holes is equal to the inner diameter of the tubes. To divert more flow to the outer rows ring baffles are provided below the perforated plate. An end piece is welded to the perforated plate at the edge preventing flow from the sides into the region enclosed by the tube sheet and the perforated plate. A theoretical investigation of secondary sodium flow in the IHX bottom header is carried out using the code PHOENICS. The computational fluid dynamic study comprises of a boundary fitted mesh and standard high Reynolds number k–ε turbulence model. In the present 2D axi-symmetric study, equivalent cross sectional flow area for each of the 25 rings has been used. The resistance characteristics of the annular slots were made to represent that of the 3D tube bundle. Favorable comparison of flow distribution predicted by this model with the experiments carried out on 1/2 scale model with all the 3600 tubes validates the model. The study was carried out with and without FDD and the flow distribution at the inlet of the tube bundle has been found out. 5.1. Theoretical estimation of secondary sodium flow distribution
Fig. 7. Temperature field in IHX tube bundle during normal operating conditions.
The ratio of secondary sodium velocity at the inlet of each tube to that of at the entry of the bottom header (Vt /Vd ) versus tube rows is presented in Fig. 9, for the case without FDD. It is seen that the flow is higher at the inner and outer rows and is minimum in the middle rows. The reason for this can be found by observing the velocity pattern shown in Fig. 10. The fluid
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Fig. 8. Flow distributing device at the inlet of tube bundle in secondary sodium inlet header.
flow follows the contour of the dished head and enters the outer rows of tubes axially. Because of the re-circulation, the flow is radial near the bottom tube sheet and the middle rows of the tubes get less flow. Near the inner rows, the radial momentum is destroyed due to the presence of down-comer tube and there is a consequent increase in pressure. This increases the flow in the inner rows. The velocity–vector plot for the case with FDD is shown in Fig. 11. Comparing with Fig. 10, it can be seen that near the bottom tube sheet, the flow becomes more axial. The velocity ratio (Vt /Vd ) versus tube rows is presented in Fig. 12. The ideal flow distribution determined from the tube bundle thermal hydraulic analysis (Section 4) is also presented in the same figure. It can be seen that the FDD is able to provide the required flow distribution.
5.2. Experimental validation of FDD In order to validate the computational results, an experiment has been carried out for the secondary flow distribution inside the tubes. The flow inside the tubes is in the forced convection regime with Richardson number (0.05) far less than 1. Hence, it is judged that the flow experiments using air (without heat transfer) is alright. The scale of the model is 1:2 and the working fluid is air (Fig. 13). All the 3600 tubes have been simulated and the Reynolds number of air flow in the model was maintained well in the turbulent regime, at 1 × 106 . Care was taken that the Mach number of flow is less than 0.3, thus avoiding any compressibility effects. A 2 mm ellipsoidal nose, NPL type Pitot static tube was used to measure the velocities downstream of tubes. Air velocity was measured in each row of tubes. In this large scale engineering experiments, no turbulent kinetic energy has been measured. More details about the experimental setup and procedure can be found elsewhere (Padmakumar et al., 2003). Experiments have been carried out for the cases with and without FDD. Measured velocity distribution among the various rows of tubes, normalized with respect to the downcomer velocity, is depicted in Fig. 9, for the case without FDD. Similar measured distribution with FDD is depicted in Fig. 12. It is clear that the computational results match satisfactorily with the measurements, validating the computational model. 6. Assessment of tube bundle temperature during normal operation and transient conditions 6.1. Initial conditions of the transient event
Fig. 9. Flow distribution without FDD.
During normal operation of IHX, the primary and secondary sodium inlet temperatures are 817 and 628 K. The flows are
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Fig. 10. Velocity field at the secondary sodium inlet header without any distribution device.
100% nominal (i.e. 1650 and 1460 kg/s, respectively). During the event of loss of feed water flow to SG, the secondary sodium inlet temperature increases steeply from 628 to 785 K in 60 s after loss of feed water. Afterwards, it increases slowly to 800 K in about 300 s. There is no heat removal in the SG following this event. When the IHX primary outlet temperature increases, the reactor inlet as well as the outlet temperatures also increase. Once, the core outlet temperature crosses the set point, reactor scram takes place. Due to this, core outlet temperature rapidly drops. The evolution of the primary sodium temperature has been obtained by detailed plant dynamics studies, which considers the SG dynamics also. It is computed that the temperature drops sharply from 850 to 727 K in 60 s and then it increases to 750 K to stabilize at that value, as depicted in Fig. 14. The core flow and secondary sodium flow are reduced to below 25% of their nominal values. When the core outlet temperature drops due to scram, the cold front sodium from core top moves upwards in the hot pool. A moment comes when cold sodium reaches the lower edge of IHX primary inlet window. Then, low temperature (727 K) sodium enters outer rows of tubes, while temperatures of tubes in inner rows remain at a higher level of 817 K. The primary sodium T at the entry to the inlet window, thus reaches 90 K, which may not be acceptable from buckling of the tubes and tube-to-tube sheet weld strength considerations.
6.2. Simulation of cold sodium entry into IHX The objective of this analysis is only to estimate the maximum possible T in the IHX tubes during these events. Based on the transient history of the plant (Fig. 14), it is clear that the maximum T is expected at 60 s after the event. Hence, only a steady state analysis has been carried out, corresponding to the conditions at 60 s. It is known that during these events, the cold sodium front moves up gradually in the hot pool. IHX would be fed by hot sodium till the cold front reaches the window. When this happens, the bottom part of the window is fed by cold sodium and the top part of the window is fed by hot sodium. But the fraction of the window that feeds hot/cold sodium is not precisely known and it varies with time. Hence, the window height fed by cold sodium is varied as a parameter to get the maximum possible T. 6.3. Results and discussion 6.3.1. Normal operation The tube average temperature at different rows for various fractions of window that feeds cold sodium flow (c.f.) into IHX, is presented in Fig. 15. During normal operation, the tube temperature is minimum at the outer row and maximum at the 19th
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Fig. 11. Velocity field at the secondary sodium inlet header with distribution device.
row. During loss of feed water flow event, the tube temperatures are maximum at the inner rows. They are minimum at the outer rows for c.f. < 1/2. But for c.f. > 1/2, the maximum occurs at the 19th row. It is found that during normal operation, the hottest tube prevails at 19th row of tubes and the maximum value of Tb is 11 K. The coldest tube prevails at the outer row of tubes and the value of Tp is −22 K. The inner row is at 723 K compared to the average bundle temperature of 738 K.
6.3.2. Loss of feed water flow event The temperature contours for various values of c.f. are presented in Fig. 16. It is seen that the hottest tube prevails in the inner row of tubes and the maximum value of Tb is 24 K when the IHX inlet window is fully flowing with cold primary sodium. It is also seen that the coldest tube prevails in the outer rows and the value Tp is equal to −23 K, when 1/3rd of IHX inlet window is flowing with cold primary sodium. It is clear that even though, a large axial T of 90 K prevails in the primary inlet sodium, the maximum values of Tb and Tp are only 24 and 23 K, respectively, which is acceptable from thermal stress considerations.
7. Thermal hydraulic analysis of secondary sodium outlet plenum
Fig. 12. Flow distribution with FDD.
The outlet plenum is formed by inner and outer shells, which are welded to the top tube sheet and at their top end, as shown in Fig. 3. The secondary sodium leaves the tube bundle at the top tube sheet and enters the outlet plenum as jets (corresponding to the different rows of the tube bundle) with different velocities and temperatures. Because of jet effect, the secondary sodium at the outlet plenum move vertically upward with limited mixing. Due to this, the inner and outer shells remain nearly at the same temperatures of the sodium jets adjacent to them. This leads to
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large temperature difference (T) between them. Due to this, the weld joints of the shells may be subjected to differential thermal expansion. This may lead to failure of the shells and junctions of the hot outlet plenum due to creep and fatigue during normal operation and transient conditions respectively. This type of failure has been observed in the IHX of PHENIX reactor (Vial et al., 1978). To alleviate this problem, a mixing device (Fig. 17) is designed to reduce the T between the shells by ensuring good mixing of hot and cold jets. The details of this thermal hydraulic analysis are described below. 7.1. Modeling details
Fig. 13. Experimental setup for testing FDD with air.
Fig. 14. Temperature evolution of core outlet, primary sodium pool and IHX outlet during loss of feed water flow event.
The various rows of tubes in the top tube sheet are modeled as concentric openings in the azimuthal direction of equivalent flow area. Thus, there are 25 annular concentric jets of sodium, corresponding to 25 rows of tube bundle, emanating from the top tube sheet. The mixing device consists of an array of 12 pipes, which are joined to an annular shell concentric to the inner shell (Fig. 17). The pipes are inclined by 50◦ to horizontal. However, the bottom end of the pipes is vertical to the tube sheet in order to receive the incoming sodium jets. A portion of the hot jets flows into the pipes provided just above the jets. The flow is then directed through the inclined portion of the pipes and discharged into the annular shell. Then the flow passes through this vertical annular gap and comes out at the top of the shell. Thus, the hot sodium jets are made to mix with the cold sodium jets, which are flowing adjacent to the inner shell. To enhance this, holes have been provided at the bottom of the annular gap to allow colder jets to enter the annular shell and mix with the hotter jets. The pipe of the mixing device is simplified into a rectangular channel of equivalent area of flow. The rectangular channel simulates the flow direction and the pressure drop of the circular channel. A
Fig. 15. IHX tube temperature at different rows of the tube bundle for various fractions of cold primary sodium flow during loss of feed water flow event.
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Fig. 16. Transient temperature contours for various primary sodium inlet conditions during loss of feed water flow event.
3D 15◦ sector of the outlet plenum is considered for the study (Fig. 18), employing a boundary fitted grid and high Reynolds number k–ε model. To assess the effectiveness of the mixing device two cases have been studied; one with mixing device and the other without mixing device. 7.2. Boundary conditions The schematic showing the boundary conditions is presented in Fig. 18. At the inlet, both the velocity and temperature conditions are prescribed. The inner shell of the plenum is separated from the down-comer pipe by argon gap. In this gap, heat transfer is by conduction, natural convection and radiation. The equivalent conductivity of this gap was calculated and found to be negligible. Hence, inner shell is assumed as adiabatic. The outer
shell of the plenum is facing the hot sodium pool at 820 K for a height of 1.18 m from the top tube sheet with a heat transfer coefficient of 8000 W/m2 K (for sodium flow over a vertical cylinder). Above the height of 1.18 m, the outer shell is facing the argon cover gas, which is at a mean temperature of 703 K. The heat transfer from the outer shell to cover gas is by combined natural convection and radiation. For this, the equivalent heat transfer coefficient is calculated as 22 W/m2 K. 7.3. Results and discussion 7.3.1. Without mixing device From the flow and temperature distributions presented in Fig. 19, it is seen that the incoming sodium jets flow up in the outlet plenum without much mixing. Also, at the conical portion
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Fig. 17. Mixing device at the secondary sodium outlet header.
Fig. 18. Boundary conditions for the analysis of secondary sodium outlet plenum.
of the outer shell they are flowing parallel to the outer shell due to the smooth inclination of the conical shell. Because of these, the inner and outer jets influence each other to a lesser extent. The effect of this can be seen clearly from the isotherms, that the temperature contours adjacent to the shells continue to prevail from the bottom to top of the plenum.
The temperature profiles of the inner and outer shells at various elevations of the plenum are presented in Fig. 20. It is seen that the temperature of the outer shell is uniform at 817 K up to a height of 1.2 m as the IHX is surrounded by sodium pool up to this elevation. Then it drops sharply, in the cover gas region. Above 1.4 m elevation, it remains fairly constant at 798 K due to
Fig. 19. Flow and temperature fields in IHX outlet plenum without mixing device.
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Fig. 20. Variation of IHX shells temperature with and without mixing device.
adiabatic conditions. On the other hand, the inner shell temperature increases from 782 to 790 K up to the elevation of conical outer shell due to conduction heat transfer from the hot outer jets to cold inner jets. Then, it increases sharply to 795 K due to mixing of sodium jets in the reduced area above the elevation of conical outer shell. The mean T between the shells averaged over the height of the plenum is found to be 14 K. It is seen that the T between the shells is higher at the bottom of the shells and reduces along the shell height. 7.3.2. With mixing device From the flow and temperature distributions presented in Fig. 21, it is seen that incoming sodium jets just below the open-
ing of the mixing device enter into the device, takes a turn inside the inclined pipe and enter into the annular shell adjacent to the inner shell. From the annular shell, the flow exits at the conical portion of the outlet plenum. Hence, due to the provision of mixing device, a part of the outer jets now mixes with the inner jets. Through this, the outer hotter jets heat up the inner shell. As the hotter jets heat up the inner shell, the T between the shells reduces. The bottom of the annular shell stops the colder jets from going up by the side of the inner shell. Thus, it reduces the T between the shells. This can be observed from the isotherms presented in Fig. 21. The hot jets of 803 K at the 15th–17th rows prevail below the mixing device inlet pipe. The 800 K isothermal contour prevails just above the inclined pipe of the mixing device and also up to 4 m height of the inner shell. It can be seen from Fig. 20, the temperature profile of the outer shell is not influenced by the mixing device, while the inner shell temperature is altered considerably. The inner shell is at 782 K (up to the height of the bottom of the annular shell (0.7 m)). Then, it increases sharply to 801 K as the hot jets brought by the mixing device heat the inner shell. Afterwards, it slowly reduces to 800 K. From the inner shell temperature profile, it can be clearly seen that the mixing device heats up the inner shell. The mean T between the shells averaged over the height of the plenum is found to be negligible (4 K). This results in negligible creep damage in the shells and junctions of the hot outlet plenum during normal operation. Also, comfortable margin exists for the fatigue damage, which occurs during transient conditions. The increase in pressure drop due to mixing device is also negligible (200 Pa) compared to the total pressure drop of 2500 Pa in the outlet plenum.
Fig. 21. Flow and temperature fields in IHX outlet plenum with mixing device.
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8. Conclusions • Thermal hydraulic investigations of IHX carried out using PHOENICS code have helped to ratify various design provisions of IHX and assure structural integrity of IHX tubes and shells. • The cross flow heat transfer at the primary sodium entrance demands flow zoning at the secondary sodium inlet of the tube bundle with 50% more flow in six outer rows of tubes from thermo-mechanical considerations. FDD employed at the entrance of the tube bundle is found to achieve the required flow zoning. • Steady-state analysis of the IHX tube bundle has been carried out with the optimized flow zoning to obtain tube temperatures and secondary sodium outlet flow and temperature distributions to define thermal loads on the heat exchanging tubes and shells. • The transient problem of slow entry of cold primary sodium into the inlet window of IHX during loss of feed water flow event, subjecting the heat exchanger tubes to large temperature variations leading to buckling and pull out loads has been analyzed by a conservative quasi-static model. • By evaluating the temperature difference between the hottest/coldest tube and the tube bundle average temperatures for normal operation and transient conditions, it is found that the Ts for buckling and pull out design of IHX tubes are within ±25 K. • From the 3D analysis of mixing of sodium jets in IHX secondary sodium outlet plenum, it is found that there is poor mixing. Enhanced mixing is observed with a mixing device.
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It is seen that due to the mixing device, there is rise in the inner shell temperature. This greatly reduces the T and differential thermal expansion between the shells of the plenum. • The mean temperature difference between the shells averaged over the length of the plenum reduces from 14 K (without mixing device) to 4 K with mixing device. References Chetal, S.C., et al., 1995. Conceptual design of heat transport system and components of PFBR-NSSS. In: Proceeding, Conceptual Design of Advanced Fast Reactors, IAEA Tech. Committee Meeting, IAEA-TECDOC-907, Kalpakkam, pp. 117–132. CHAM Development Team, 1991. The PHOENICS reference manual, CHAM REF:CHAM/TR200. CHAM Ltd., Wimbledon, London. Hughes, W.F., Gaylord, E.W., 1964. Basic equations of engineering science. In: Schaum’s Outline Series. McGraw-Hill, New York. Idelchik, I.E., 1966. Handbook of Hydraulic Resistances, AEC-TR-6630. Launder, B.E., Spalding, D.B., 1974. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3, 269–289. Marcellin, C., Guidez, J., 1984. Hydrodynamic Behaviour of Intermediate Heat Exchangers in a Pool-type Fast Breeder Reactor. Liquid Metal Engg & Tech., BNES, London, pp. 211–214. Padmakumar, G., et al., 2003. Flow distribution device for PFBR IHX. In: Proceedings of 11th International Conference on Nuclear Engineering, Tokyo, Japan. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. McGraw-Hill, New York. Vial, et al., 1978. Le Circuit Primarie de Phenix e Superphenix. IAEA SM225/11, Bologna. Zukauskas, A., Ulinskas, R., 1983. Heat Exchanger Design Hand Book. Hemisphere Publishing Corporation (Chapter 2.2.4).
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Thermal hydraulic investigations of intermediate heat exchanger in a pool-type fast breeder reactor R. Gajapathy a,∗ , K. Velusamy a , P. Selvaraj a , P. Chellapandi a , S.C. Chetal a , T. Sundararajan b a
Nuclear Engineering Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India b Department of Mechanical Engineering, Indian Institute of Technology-Madras, Chennai 600036, India Received 6 July 2007; received in revised form 20 November 2007; accepted 9 January 2008
Abstract Intermediate heat exchanger (IHX) in a pool-type liquid metal cooled fast breeder reactor is an important heat exchanging component as it forms an intermediate boundary between the radioactive primary sodium in the pool and the non-radioactive secondary sodium in the steam generator (SG). The thermal loads during steady state and transient conditions impose thermal stresses on the heat exchanger tubes and on the shells which hold the tube bundle. Estimation of these thermal loads and achieving uniform temperature distribution in the tubes and shells by having uniform flow distributions are the major tasks of thermal hydraulic investigations of IHX. Through multi-dimensional thermal hydraulic investigations performed using commercially available computer codes such as PHOENICS, the flow and temperature distributions in the tubes and shells and in its secondary sodium inlet and outlet headers are obtained with and with out provisions of flow distribution devices. The effectiveness of these devices in achieving acceptably uniform flow and temperature distributions has been assessed and thermal loads on the tubes and shells for thermo mechanical analysis of the IHX have been defined. The predictions of the computational studies have been validated against simulated experiments. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In India, a 500-MW(e), pool type, liquid sodium cooled prototype fast breeder reactor (PFBR) is under construction (Chetal et al., 1995). PFBR has three systems of heat transfer in series, viz. (i) the primary sodium system, (ii) the secondary sodium system and (iii) the steam–water system, as depicted in Fig. 1. In the primary sodium system, the nuclear heat generated in the core is removed by primary sodium circulated by primary pumps. The hot primary sodium emerging from the core mixes with a hot sodium pool and penetrates the intermediate heat ∗
Corresponding author at: Nuclear Engineering Group, Indira Gandhi Centre for Atomic Research, Thermal hydraulic Section, Room No. 251, CDO Building, IGCAR, Kalpakkam 603 102, India. Tel.: +91 44 27480106; fax: +91 44 27480104. E-mail address: [email protected] (R. Gajapathy). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.01.005
exchanger (IHX) through its inlet window (Fig. 2). In the secondary sodium system, the primary sodium flowing in the shell side of the IHX exchanges heat with the secondary sodium flowing in the tube side. The cool primary sodium comes out of the IHX through the outlet window and mixes with cold sodium pool. The sodium temperature of 544 ◦ C in the hot plenum is reduced to 394 ◦ C after the heat exchange. The secondary sodium enters the IHX at the top and flows downwards through a central pipe (Fig. 3) at a temperature of 355 ◦ C. On reaching the bottom, the secondary flow is reversed upwards through the tubes. After the bundle, the hot secondary sodium at 525 ◦ C is collected in an annular pipe which leaves the IHX through a lateral outlet nozzle. In the steam–water system, the secondary sodium exchanges heat with water in a once through steam generator (SG), to produce superheated steam for power generation. Thus, the IHX acts as an intermediate boundary between the highly radioactive primary sodium circulating through the
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Fig. 1. Heat transport flowsheet.
reactor core and the non-radioactive secondary sodium. Also, the IHX must keep its leak-tightness in case of a sodium–water reaction occurring in SG. The IHX is supported on the roof slab (Fig. 2), which is maintained at 100 ◦ C and is freely hanging from the top. The lower part of the IHX is in the cold sodium pool of the reactor vessel. The top of the IHX is surrounded by complementary shielding. So, in these situations, the IHX experiences thermo mechanical loads in the tube bundle related to heat exchange and also in the shell that encloses the tubes during normal as well plant transients. Also, the IHX has to be highly reliable, since removal of it for repair leads to stopping of the plant operation for a long period. Hence, it is very important to investigate the thermal mechanical loads on IHX, to ensure safe and reliable operation of IHX and the reactor as well. This paper focuses the thermal hydraulic investigations, viz. (i) primary and secondary sodium flow and temperature distributions carried out by 2D axi-symmetric porous body models for the tube bundle, (ii) secondary flow distribution in the inlet header and the effectiveness of the flow distribution device, (iii) secondary sodium mixing in the outlet header of the IHX and the effectiveness of the mixing device, (iv) transient thermal hydraulic analysis of the tube bundle during the event of loss of feed water flow to SG and (v) comparison of the predictions against simulated experiments.
2. Main characteristics of IHX The total thermal power generated in the reactor core is exchanged by four IHXs in the reactor vessel. IHX is a straight tube heat exchanger of counter current shell and tube type (Fig. 3). The tubes are arranged in circumferential rows around the secondary sodium down comer between the top and bottom tube sheets.
Total thermal power of reactor Thermal capacity of each IHX Primary sodium inlet flow Primary sodium inlet temperature Primary sodium outlet temperature T between primary sodium inlet and outlet Secondary sodium inlet flow Secondary sodium inlet temperature Secondary sodium outlet temperature T between secondary sodium inlet and outlet Inlet and outlet windows height Heat exchanging tubes OD and thickness Total number of tubes Number of rows Radial pitch of the rows Circumferential pitch Heat transfer length Overall diameter of IHX Overall height of IHX
1250 MW(t) 315 MW(t) 1649 kg/s 544 ◦ C 394 ◦ C 150 ◦ C 1450 kg/s 355 ◦ C 525 ◦ C 170 ◦ C 0.9 m 19 and 0.8 mm 3600 25 25 mm 28 mm 7.5 m 2m 7m
3. Thermal hydraulics and structural assessment of IHX The IHX is subjected to pressure loading due to primary and secondary sodium. Due to this pressure loading, the inner rows of the tube bundle are under compression. In other words, these tubes are subjected to buckling risk between the top and bottom tube sheets. The outer rows of the tube bundle are under tension. In other words, the tubes try to pullout from the tube sheets. The tubes will fail if the buckling and pullout loads exceed the acceptable limits. If the inner rows of tubes are cooler, the thermal load reduces the pressure load and reduces the buckling load on the inner tubes. If the outer rows of tubes are hotter, the thermal load reduces the pressure load, which results in reduced pullout load on the outer rows of tubes. If the inner and outer tubes are hotter and colder respectively, the thermal loads increase the buckling and pullout loads on the tubes.
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Fig. 2. PFBR reactor assembly vertical section. (01) Main vessel, (02) core support structure, (03) core catcher, (04) grid plate, (05) core, (06) inner vessel, (07) roof slab, (08) large rotatable plug, (09) small rotatable plug, (10) control plug, (11) control and safety rod mechanism, (12) in-vessel transfer machine, (13) intermediate heat exchanger, (14) primary sodium pump, (15) safety vessel and (16) reactor vault.
As the primary sodium enters the shell side of IHX radially through the inlet windows, the flow takes place across the tube bundle. Due to the cluster arrangement of the tubes, the tube bundle offers high resistance to the radial flow. Due to that, the radial flow takes turn and start flowing downwards. The flow is higher in the outer rows; it gradually reduces as it penetrates through the bundle and is the least in the inner rows. Near the inlet region, the outer rows of tubes experience higher primary sodium temperature compared to the tubes in the inner rows. Due to this, the outer rows of tubes will become hotter and the inner rows will become cooler. Hence, in this situation, the thermal loads help in reducing the buckling and pullout loads on the tubes. The thermal loads for IHX tubes are based on acceptable
temperature difference (T) between the heat exchange tubes during steady state and transient conditions. In order to estimate temperatures of the tubes and the thermal loads and how far this thermal load helps in reducing the buckling and pullout loads, the temperature distribution in the tube bundle needs to be evaluated. For this purpose, a 2D thermal hydraulic analysis of the tube bundle is carried out. From this analysis, the primary and secondary sodium temperature distributions are computed. The results of this analysis are discussed in Section 4. In order to have lower thermal loads, the T between the tubes must be low. This calls for uniform temperature distribution in the tube bundle. Since, the primary sodium flow in the shell side takes place by gravity, there is little control over its
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ature distribution in the bundle for this condition are presented in Section 6. Using the tube bundle temperature distribution during steady state and transient conditions, thermal loads are estimated and thermo mechanical analysis is carried to compute the thermal stresses developed. From the thermal stress analysis, the design stress limits are met and the adequacy of tube diameter, thickness and the height of the bundle are evaluated. In spite of the efforts to make the tube bundle temperature uniform, the secondary sodium outlet temperature coming out of the tube bundle will be less uniform. This will impose thermal load on the inner and outer shells of the secondary sodium outlet plenum. Hence, a mixing device is introduced to mix the hot and cold secondary sodium that comes out of the inner and outer rows of the tube bundle and reduce the T further. To assess the efficiency of the mixing device and compute the temperature difference between the shells of the outlet plenum, a 3D thermal hydraulic analysis has been carried out, which is discussed in Section 7. Using the inner and the outer shell temperature distribution, stress analysis is carried out to find out the stresses developed in the weld joints of the shells and the design requirement for the bellows are arrived at. 4. 2D thermal hydraulic analysis of the tube bundle 4.1. Mathematical modeling Fig. 3. Schematic of IHX.
distribution. It shall be highlighted, that in the case of PFBR, no attempt has been made to incorporate any baffle at the primary sodium inlet to alter the flow distribution. This is to have a minimum pressure drop in the primary side and hence minimum load on the inner vessel which separates the sodium pool into hot pool and cold pool. Hence, the only way is to alter the secondary sodium flow distribution inside the tubes. To achieve the desired secondary flow distribution, a flow distributing device (FDD) is developed and located at the bottom of the tube bundle. Theoretical and experimental investigations are carried out to find out secondary sodium inlet flow distribution to the tubes such that the temperature distributions in the primary and secondary side are uniform. The results of the flow distribution are discussed in Section 5. During the event of loss of feed water flow to the SG, the secondary sodium pumps trip which results in loss of heat removal from IHX. Consequently, the primary side of IHX is filled with hot sodium, from top to bottom. Afterwards, reactor scram actuated by high core outlet temperature. As a result of this, cold sodium enters the hot pool and the cold front of sodium moves gradually upwards and reaches lower edge of IHX primary inlet windows. Then, this low temperature primary sodium enters outer rows of tubes, while the temperature of tubes in the inner rows remains hot. The temperature difference across the tube bundle will be higher during this case. This condition is analyzed using the same 2D computational model developed for the steady state analysis of the tube bundle. The results of temper-
In IHX, the tubes are arranged in rows and they are symmetrical in the circumferential directions. Hence, a 2D axi-symmetric analysis of the tube bundle is carried out using the Computational Fluid dynamics code PHOENICS 2.2.1 (CHAM, 1991). In this computer code, the Navier–Stokes equations for mass, momentum and energy equation derived for an elemental control volume are solved to obtain pressure, velocity and temperature using finite volume approach which uses control volume based discretisation method (Patankar, 1980). The governing equations can be represented by the following single general equation for constant property viscous flow in vector form as follows (Launder and Spalding, 1974; Hughes and Gaylord, 1964): ∂ (βV ρΦ) + ∇(βS ρ uΦ) = ∇(βS ΓΦ ∇Φ) + βV SΦ ∂t where, is the divergence operator, Γ Φ is the diffusion coefficient, u is the velocity field, SΦ is the source term, βV is the volumetric porosity, βS is the surface permeability and Φ takes the following values, each of which gives rise to a particular conservation equation: Φ=1
gives the continuity equation
Φ = u gives the axial direction momentum equation Φ=v Φ = cp T
gives the radial direction momentum equation and gives the energy equation
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The above equations are solved iteratively. The SIMPLEST algorithm resolves the pressure–velocity coupling. To evaluate the convective and diffusive fluxes at the interfaces, the HYBRID scheme is used. In the code PHOENICS, only the shell side of IHX is modeled and the pressure, velocity and temperature distributions of primary sodium flow over the bundle is solved iteratively. The secondary sodium is modeled as heat sink in the energy equation of the primary sodium. The tube bundle is modeled by porous body formulations. The radial and axial surface permeability’s and volumetric porosities of the tube bundle are calculated and fed as input to the code. The inlet flow of primary sodium from the hot pool into the IHX is specified in terms of velocity and temperature distributions at the IHX primary inlet window. The outlet is specified at the bottom of the IHX. The schematic of computational model and boundary conditions is presented in Fig. 4. It may be highlighted that it is difficult to model each and every tube in the simulation for large equipment like IHX, which comprises of 3600 tubes in a tight pitch. To circumvent this difficulty, porous body formulation with large mesh size has been adopted. The effect of the tube bundle is to offer pressure drop for the sodium flow and absorb heat from the primary sodium. These effects are externally accounted by incorporating momentum and heat sinks in the governing equations. No turbulence model is used in the simulation. The pressure drop and heat transfer coefficient required for the porous body model in the turbulent regime are evaluated from the correlations discussed in the following section.
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4.2. Pressure drop correlations As already explained the primary sodium flow on the shell side of the tube bundle takes place due to the level difference between the hot and cold pools, by gravity. Hence, the primary sodium pressure drop through the IHX imposes this level difference. From the considerations of reducing the power of primary pumps as well load on the inner vessel, this pressure drop must be as low as possible. For the primary flow, the Reynolds number in the bundle is about 82,500. Experimental correlations to evaluate pressure loss coefficients are reported in open literature (Zukauskas and Ulinskas, 1983; Idelchik, 1966), as function of bundle geometry and Reynolds number, both for cross flow as well as parallel flow. 4.2.1. Resistance coefficient for cross flow The flow resistance coefficient ‘K’ for turbulent cross flow over bundle of smooth-wall staggered tubes is given by (Idelchik, 1966), P =
KρU 2 2
where K = A Re−0.27 (Z + 1) A = 3.2 + (4.6 − 2.7 ((S1 − d)/(S2 − d))) (2.0 − S1/d) S2 = (0.25 S12 + S22 )0.5 P, pressure drop (Pa) ρ, density of sodium (850 kg/m3 ) ν, Kinematic viscosity of sodium (3.3 × 10−7 m/s2 ) U, primary sodium velocity at the inlet window (m/s) Re, Reynolds number Z, half the number of tubes d, tube outer diameter (m) S1, S2 and S2 , circumferential, radial and transverse pitch distance between the tubes, respectively. 4.2.2. Resistance coefficient for axial flow For the axial flow, the friction factor, ‘f’ is calculated from (Idelchik, 1966), ΔP =
ρfLV 2 (2Deq )
where f = 0.11((ε/d) + (68/Re))0.25 f, friction coefficient ε, roughness of tubes (m) d, tube OD (m) L, axial mesh size (m) V, axial velocity (m/s) Deq , equivalent diameter of the shell side of IHX (m). 4.3. Heat transfer correlations
Fig. 4. Boundary conditions for IHX tube bundle analysis.
For heat transfer from primary sodium to secondary sodium, both the cross flow and axial flow of primary sodium over the
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bundle is taken into account in the estimation of effective heat transfer coefficient. The following heat transfer correlations are taken from (Marcellin and Guidez, 1984): Tubes : Nu = 4.82 + 0.0185Pe0.827 Shell : Nu = 6.0 + 0.006Pe Cross flow : Nu = 4.03 + 0.228Pe0.67 where Nu and Pe are Nusselt and Peclet numbers, respectively. If hc is cross flow heat transfer coefficient and ha is the axial flow heat transfer coefficient from the above correlations, then the effective shell side heat transfer coefficient hp , given by ((U 2 / h2c ) + (V 2 / h2a )) 1 = h2p (U 2 + V 2 ) where U and V are cross flow and axial flow velocities, respectively. 4.4. Estimation of heat sink From the velocity values, the film heat transfer coefficients on both the sides of the tube are calculated. The overall heat transfer coefficient is calculated as follows taking into account the conduction resistance offered by the tubes. ho =
1 [(1/ hp ) + (do /2k) ln(do /di ) + (1/ hs )(do /di )]
where ho , overall heat transfer coefficient (W/m2 K) hp , effective heat transfer coefficient in the primary side (W/m2 K) hs , heat transfer coefficient in the secondary side (W/m2 K) k, conductivity of tube material (W/m K) do /di , tube outer and inner diameter (m) The rise in temperature of secondary sodium from its initial value is calculated, by equating the heat transferred from primary to secondary sodium. Then, the heat gained by the secondary sodium in each control volume is calculated and applied as heat sink in the energy equation for primary side. The process is repeated until convergence takes place. 4.5. Results and discussion The analysis of primary sodium flow and temperature in the tube bundle has been carried out, first for a theoretical case of uniform secondary sodium inlet flow distribution. Then, the secondary flow distribution that results in acceptable tube bundle temperature distribution is determined by a parametric study. The secondary outlet temperature distribution obtained for various secondary sodium inlet flow distributions are shown in Fig. 5. For uniform flow case, it is found that there is sharp temperature gradient near the inner rows. This is due to the fact that near the primary sodium inlet region, the outer rows of tubes experience higher primary sodium temperature compared to the tubes in the inner rows. The outer rows of tubes are hotter while
Fig. 5. Secondary sodium temperature distribution at the outlet of the tube bundle.
the inner rows are cooler. Hence, in this case the secondary sodium outlet T between the outer and inner rows of the tube bundle is 47 ◦ C, which is very high. In the case of secondary flow distribution without any distributor, the temperature at the inner rows remains the same but the temperature at the outer rows gets reduced. The T in this case is 37 ◦ C, which is better than the theoretical case of uniform flow. Hence, to reduce the temperature gradient further, the secondary sodium flow at the outer rows of the tube should be higher compared to that at the inner rows to reduce the T. For this, the flow in the inner rows should be reduced and correspondingly the flow in the outer rows should to be increased. This is possible by providing a FDD, which can divert more flow towards outer rows. Towards designing a FDD, a parametric study of secondary sodium flow distribution (keeping the total flow constant) has been carried out. It was found that when the tubes in the outer six rows receive 1.5 times the secondary flow of the other tubes, the value of secondary sodium outlet T got reduced to 16 ◦ C as shown in Fig. 5, which is acceptable from thermal stress consideration (discussed in the following section). For this case, the primary sodium flow and temperature distributions are presented in Figs. 6 and 7. 4.6. Thermal loads for stress analysis From the results of thermal hydraulic analysis of the tube bundle, the temperature distribution of the tubes are obtained and used as input for carrying out thermal stress analysis. From the heat sink distribution and the heat transfer coefficients, which are position dependent, the tube wall temperature of each row in the computational mesh is calculated. The average temperature of each tube is calculated by averaging the tube wall temperature along the height of the tube. The average temperature of the entire tube bundle (Ta ) is calculated by averaging tube temperature in the bundle. By comparing each tube temperature with
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the bundle average, the hottest tube temperature (Th ) and coldest tube temperature (Tc ) are found out. The hottest tube tries to expand more than the rest of the tube bundle. As the tube sheets resist this undue thermal expansion, the hottest tube is subjected to compressive stress. Hence, the governing T from the consideration of buckling of the tube is (T )b = (Th − Ta ). The coldest tube tries to expand less compared to rest of the tube bundle. As the tube sheets resist this, the tube-to-tube sheet weld joint of the coldest tube is subjected to pull out. Hence, the governing T from pull out strength consideration is (T )p = (Tc − Ta ). For uniform flow through the secondary sodium inlet, the temperature difference between the shells of the outlet header is exceeding the limits from thermal stress consideration. For flow through the secondary sodium inlet without any distribution device, the net stresses are not meeting the corresponding limits of bucking of the tubes. It has been found that for 50% more flow in the outer 6 rows, the induced stresses are much less than that in the case without FDD and uniform flow. 5. Flow distribution device at IHX bottom header
Fig. 6. Velocity field in IHX tube bundle during normal operating conditions.
To achieve the acceptable secondary sodium flow distribution discussed in the Section 4.5, a FDD is provided at the bottom header of IHX (Fig. 8). The FDD is a perforated plate, consisting of holes in line with the tube sheet holes. The diameter of the holes is equal to the inner diameter of the tubes. To divert more flow to the outer rows ring baffles are provided below the perforated plate. An end piece is welded to the perforated plate at the edge preventing flow from the sides into the region enclosed by the tube sheet and the perforated plate. A theoretical investigation of secondary sodium flow in the IHX bottom header is carried out using the code PHOENICS. The computational fluid dynamic study comprises of a boundary fitted mesh and standard high Reynolds number k–ε turbulence model. In the present 2D axi-symmetric study, equivalent cross sectional flow area for each of the 25 rings has been used. The resistance characteristics of the annular slots were made to represent that of the 3D tube bundle. Favorable comparison of flow distribution predicted by this model with the experiments carried out on 1/2 scale model with all the 3600 tubes validates the model. The study was carried out with and without FDD and the flow distribution at the inlet of the tube bundle has been found out. 5.1. Theoretical estimation of secondary sodium flow distribution
Fig. 7. Temperature field in IHX tube bundle during normal operating conditions.
The ratio of secondary sodium velocity at the inlet of each tube to that of at the entry of the bottom header (Vt /Vd ) versus tube rows is presented in Fig. 9, for the case without FDD. It is seen that the flow is higher at the inner and outer rows and is minimum in the middle rows. The reason for this can be found by observing the velocity pattern shown in Fig. 10. The fluid
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Fig. 8. Flow distributing device at the inlet of tube bundle in secondary sodium inlet header.
flow follows the contour of the dished head and enters the outer rows of tubes axially. Because of the re-circulation, the flow is radial near the bottom tube sheet and the middle rows of the tubes get less flow. Near the inner rows, the radial momentum is destroyed due to the presence of down-comer tube and there is a consequent increase in pressure. This increases the flow in the inner rows. The velocity–vector plot for the case with FDD is shown in Fig. 11. Comparing with Fig. 10, it can be seen that near the bottom tube sheet, the flow becomes more axial. The velocity ratio (Vt /Vd ) versus tube rows is presented in Fig. 12. The ideal flow distribution determined from the tube bundle thermal hydraulic analysis (Section 4) is also presented in the same figure. It can be seen that the FDD is able to provide the required flow distribution.
5.2. Experimental validation of FDD In order to validate the computational results, an experiment has been carried out for the secondary flow distribution inside the tubes. The flow inside the tubes is in the forced convection regime with Richardson number (0.05) far less than 1. Hence, it is judged that the flow experiments using air (without heat transfer) is alright. The scale of the model is 1:2 and the working fluid is air (Fig. 13). All the 3600 tubes have been simulated and the Reynolds number of air flow in the model was maintained well in the turbulent regime, at 1 × 106 . Care was taken that the Mach number of flow is less than 0.3, thus avoiding any compressibility effects. A 2 mm ellipsoidal nose, NPL type Pitot static tube was used to measure the velocities downstream of tubes. Air velocity was measured in each row of tubes. In this large scale engineering experiments, no turbulent kinetic energy has been measured. More details about the experimental setup and procedure can be found elsewhere (Padmakumar et al., 2003). Experiments have been carried out for the cases with and without FDD. Measured velocity distribution among the various rows of tubes, normalized with respect to the downcomer velocity, is depicted in Fig. 9, for the case without FDD. Similar measured distribution with FDD is depicted in Fig. 12. It is clear that the computational results match satisfactorily with the measurements, validating the computational model. 6. Assessment of tube bundle temperature during normal operation and transient conditions 6.1. Initial conditions of the transient event
Fig. 9. Flow distribution without FDD.
During normal operation of IHX, the primary and secondary sodium inlet temperatures are 817 and 628 K. The flows are
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Fig. 10. Velocity field at the secondary sodium inlet header without any distribution device.
100% nominal (i.e. 1650 and 1460 kg/s, respectively). During the event of loss of feed water flow to SG, the secondary sodium inlet temperature increases steeply from 628 to 785 K in 60 s after loss of feed water. Afterwards, it increases slowly to 800 K in about 300 s. There is no heat removal in the SG following this event. When the IHX primary outlet temperature increases, the reactor inlet as well as the outlet temperatures also increase. Once, the core outlet temperature crosses the set point, reactor scram takes place. Due to this, core outlet temperature rapidly drops. The evolution of the primary sodium temperature has been obtained by detailed plant dynamics studies, which considers the SG dynamics also. It is computed that the temperature drops sharply from 850 to 727 K in 60 s and then it increases to 750 K to stabilize at that value, as depicted in Fig. 14. The core flow and secondary sodium flow are reduced to below 25% of their nominal values. When the core outlet temperature drops due to scram, the cold front sodium from core top moves upwards in the hot pool. A moment comes when cold sodium reaches the lower edge of IHX primary inlet window. Then, low temperature (727 K) sodium enters outer rows of tubes, while temperatures of tubes in inner rows remain at a higher level of 817 K. The primary sodium T at the entry to the inlet window, thus reaches 90 K, which may not be acceptable from buckling of the tubes and tube-to-tube sheet weld strength considerations.
6.2. Simulation of cold sodium entry into IHX The objective of this analysis is only to estimate the maximum possible T in the IHX tubes during these events. Based on the transient history of the plant (Fig. 14), it is clear that the maximum T is expected at 60 s after the event. Hence, only a steady state analysis has been carried out, corresponding to the conditions at 60 s. It is known that during these events, the cold sodium front moves up gradually in the hot pool. IHX would be fed by hot sodium till the cold front reaches the window. When this happens, the bottom part of the window is fed by cold sodium and the top part of the window is fed by hot sodium. But the fraction of the window that feeds hot/cold sodium is not precisely known and it varies with time. Hence, the window height fed by cold sodium is varied as a parameter to get the maximum possible T. 6.3. Results and discussion 6.3.1. Normal operation The tube average temperature at different rows for various fractions of window that feeds cold sodium flow (c.f.) into IHX, is presented in Fig. 15. During normal operation, the tube temperature is minimum at the outer row and maximum at the 19th
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Fig. 11. Velocity field at the secondary sodium inlet header with distribution device.
row. During loss of feed water flow event, the tube temperatures are maximum at the inner rows. They are minimum at the outer rows for c.f. < 1/2. But for c.f. > 1/2, the maximum occurs at the 19th row. It is found that during normal operation, the hottest tube prevails at 19th row of tubes and the maximum value of Tb is 11 K. The coldest tube prevails at the outer row of tubes and the value of Tp is −22 K. The inner row is at 723 K compared to the average bundle temperature of 738 K.
6.3.2. Loss of feed water flow event The temperature contours for various values of c.f. are presented in Fig. 16. It is seen that the hottest tube prevails in the inner row of tubes and the maximum value of Tb is 24 K when the IHX inlet window is fully flowing with cold primary sodium. It is also seen that the coldest tube prevails in the outer rows and the value Tp is equal to −23 K, when 1/3rd of IHX inlet window is flowing with cold primary sodium. It is clear that even though, a large axial T of 90 K prevails in the primary inlet sodium, the maximum values of Tb and Tp are only 24 and 23 K, respectively, which is acceptable from thermal stress considerations.
7. Thermal hydraulic analysis of secondary sodium outlet plenum
Fig. 12. Flow distribution with FDD.
The outlet plenum is formed by inner and outer shells, which are welded to the top tube sheet and at their top end, as shown in Fig. 3. The secondary sodium leaves the tube bundle at the top tube sheet and enters the outlet plenum as jets (corresponding to the different rows of the tube bundle) with different velocities and temperatures. Because of jet effect, the secondary sodium at the outlet plenum move vertically upward with limited mixing. Due to this, the inner and outer shells remain nearly at the same temperatures of the sodium jets adjacent to them. This leads to
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large temperature difference (T) between them. Due to this, the weld joints of the shells may be subjected to differential thermal expansion. This may lead to failure of the shells and junctions of the hot outlet plenum due to creep and fatigue during normal operation and transient conditions respectively. This type of failure has been observed in the IHX of PHENIX reactor (Vial et al., 1978). To alleviate this problem, a mixing device (Fig. 17) is designed to reduce the T between the shells by ensuring good mixing of hot and cold jets. The details of this thermal hydraulic analysis are described below. 7.1. Modeling details
Fig. 13. Experimental setup for testing FDD with air.
Fig. 14. Temperature evolution of core outlet, primary sodium pool and IHX outlet during loss of feed water flow event.
The various rows of tubes in the top tube sheet are modeled as concentric openings in the azimuthal direction of equivalent flow area. Thus, there are 25 annular concentric jets of sodium, corresponding to 25 rows of tube bundle, emanating from the top tube sheet. The mixing device consists of an array of 12 pipes, which are joined to an annular shell concentric to the inner shell (Fig. 17). The pipes are inclined by 50◦ to horizontal. However, the bottom end of the pipes is vertical to the tube sheet in order to receive the incoming sodium jets. A portion of the hot jets flows into the pipes provided just above the jets. The flow is then directed through the inclined portion of the pipes and discharged into the annular shell. Then the flow passes through this vertical annular gap and comes out at the top of the shell. Thus, the hot sodium jets are made to mix with the cold sodium jets, which are flowing adjacent to the inner shell. To enhance this, holes have been provided at the bottom of the annular gap to allow colder jets to enter the annular shell and mix with the hotter jets. The pipe of the mixing device is simplified into a rectangular channel of equivalent area of flow. The rectangular channel simulates the flow direction and the pressure drop of the circular channel. A
Fig. 15. IHX tube temperature at different rows of the tube bundle for various fractions of cold primary sodium flow during loss of feed water flow event.
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Fig. 16. Transient temperature contours for various primary sodium inlet conditions during loss of feed water flow event.
3D 15◦ sector of the outlet plenum is considered for the study (Fig. 18), employing a boundary fitted grid and high Reynolds number k–ε model. To assess the effectiveness of the mixing device two cases have been studied; one with mixing device and the other without mixing device. 7.2. Boundary conditions The schematic showing the boundary conditions is presented in Fig. 18. At the inlet, both the velocity and temperature conditions are prescribed. The inner shell of the plenum is separated from the down-comer pipe by argon gap. In this gap, heat transfer is by conduction, natural convection and radiation. The equivalent conductivity of this gap was calculated and found to be negligible. Hence, inner shell is assumed as adiabatic. The outer
shell of the plenum is facing the hot sodium pool at 820 K for a height of 1.18 m from the top tube sheet with a heat transfer coefficient of 8000 W/m2 K (for sodium flow over a vertical cylinder). Above the height of 1.18 m, the outer shell is facing the argon cover gas, which is at a mean temperature of 703 K. The heat transfer from the outer shell to cover gas is by combined natural convection and radiation. For this, the equivalent heat transfer coefficient is calculated as 22 W/m2 K. 7.3. Results and discussion 7.3.1. Without mixing device From the flow and temperature distributions presented in Fig. 19, it is seen that the incoming sodium jets flow up in the outlet plenum without much mixing. Also, at the conical portion
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Fig. 17. Mixing device at the secondary sodium outlet header.
Fig. 18. Boundary conditions for the analysis of secondary sodium outlet plenum.
of the outer shell they are flowing parallel to the outer shell due to the smooth inclination of the conical shell. Because of these, the inner and outer jets influence each other to a lesser extent. The effect of this can be seen clearly from the isotherms, that the temperature contours adjacent to the shells continue to prevail from the bottom to top of the plenum.
The temperature profiles of the inner and outer shells at various elevations of the plenum are presented in Fig. 20. It is seen that the temperature of the outer shell is uniform at 817 K up to a height of 1.2 m as the IHX is surrounded by sodium pool up to this elevation. Then it drops sharply, in the cover gas region. Above 1.4 m elevation, it remains fairly constant at 798 K due to
Fig. 19. Flow and temperature fields in IHX outlet plenum without mixing device.
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Fig. 20. Variation of IHX shells temperature with and without mixing device.
adiabatic conditions. On the other hand, the inner shell temperature increases from 782 to 790 K up to the elevation of conical outer shell due to conduction heat transfer from the hot outer jets to cold inner jets. Then, it increases sharply to 795 K due to mixing of sodium jets in the reduced area above the elevation of conical outer shell. The mean T between the shells averaged over the height of the plenum is found to be 14 K. It is seen that the T between the shells is higher at the bottom of the shells and reduces along the shell height. 7.3.2. With mixing device From the flow and temperature distributions presented in Fig. 21, it is seen that incoming sodium jets just below the open-
ing of the mixing device enter into the device, takes a turn inside the inclined pipe and enter into the annular shell adjacent to the inner shell. From the annular shell, the flow exits at the conical portion of the outlet plenum. Hence, due to the provision of mixing device, a part of the outer jets now mixes with the inner jets. Through this, the outer hotter jets heat up the inner shell. As the hotter jets heat up the inner shell, the T between the shells reduces. The bottom of the annular shell stops the colder jets from going up by the side of the inner shell. Thus, it reduces the T between the shells. This can be observed from the isotherms presented in Fig. 21. The hot jets of 803 K at the 15th–17th rows prevail below the mixing device inlet pipe. The 800 K isothermal contour prevails just above the inclined pipe of the mixing device and also up to 4 m height of the inner shell. It can be seen from Fig. 20, the temperature profile of the outer shell is not influenced by the mixing device, while the inner shell temperature is altered considerably. The inner shell is at 782 K (up to the height of the bottom of the annular shell (0.7 m)). Then, it increases sharply to 801 K as the hot jets brought by the mixing device heat the inner shell. Afterwards, it slowly reduces to 800 K. From the inner shell temperature profile, it can be clearly seen that the mixing device heats up the inner shell. The mean T between the shells averaged over the height of the plenum is found to be negligible (4 K). This results in negligible creep damage in the shells and junctions of the hot outlet plenum during normal operation. Also, comfortable margin exists for the fatigue damage, which occurs during transient conditions. The increase in pressure drop due to mixing device is also negligible (200 Pa) compared to the total pressure drop of 2500 Pa in the outlet plenum.
Fig. 21. Flow and temperature fields in IHX outlet plenum with mixing device.
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8. Conclusions • Thermal hydraulic investigations of IHX carried out using PHOENICS code have helped to ratify various design provisions of IHX and assure structural integrity of IHX tubes and shells. • The cross flow heat transfer at the primary sodium entrance demands flow zoning at the secondary sodium inlet of the tube bundle with 50% more flow in six outer rows of tubes from thermo-mechanical considerations. FDD employed at the entrance of the tube bundle is found to achieve the required flow zoning. • Steady-state analysis of the IHX tube bundle has been carried out with the optimized flow zoning to obtain tube temperatures and secondary sodium outlet flow and temperature distributions to define thermal loads on the heat exchanging tubes and shells. • The transient problem of slow entry of cold primary sodium into the inlet window of IHX during loss of feed water flow event, subjecting the heat exchanger tubes to large temperature variations leading to buckling and pull out loads has been analyzed by a conservative quasi-static model. • By evaluating the temperature difference between the hottest/coldest tube and the tube bundle average temperatures for normal operation and transient conditions, it is found that the Ts for buckling and pull out design of IHX tubes are within ±25 K. • From the 3D analysis of mixing of sodium jets in IHX secondary sodium outlet plenum, it is found that there is poor mixing. Enhanced mixing is observed with a mixing device.
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It is seen that due to the mixing device, there is rise in the inner shell temperature. This greatly reduces the T and differential thermal expansion between the shells of the plenum. • The mean temperature difference between the shells averaged over the length of the plenum reduces from 14 K (without mixing device) to 4 K with mixing device. References Chetal, S.C., et al., 1995. Conceptual design of heat transport system and components of PFBR-NSSS. In: Proceeding, Conceptual Design of Advanced Fast Reactors, IAEA Tech. Committee Meeting, IAEA-TECDOC-907, Kalpakkam, pp. 117–132. CHAM Development Team, 1991. The PHOENICS reference manual, CHAM REF:CHAM/TR200. CHAM Ltd., Wimbledon, London. Hughes, W.F., Gaylord, E.W., 1964. Basic equations of engineering science. In: Schaum’s Outline Series. McGraw-Hill, New York. Idelchik, I.E., 1966. Handbook of Hydraulic Resistances, AEC-TR-6630. Launder, B.E., Spalding, D.B., 1974. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3, 269–289. Marcellin, C., Guidez, J., 1984. Hydrodynamic Behaviour of Intermediate Heat Exchangers in a Pool-type Fast Breeder Reactor. Liquid Metal Engg & Tech., BNES, London, pp. 211–214. Padmakumar, G., et al., 2003. Flow distribution device for PFBR IHX. In: Proceedings of 11th International Conference on Nuclear Engineering, Tokyo, Japan. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. McGraw-Hill, New York. Vial, et al., 1978. Le Circuit Primarie de Phenix e Superphenix. IAEA SM225/11, Bologna. Zukauskas, A., Ulinskas, R., 1983. Heat Exchanger Design Hand Book. Hemisphere Publishing Corporation (Chapter 2.2.4).