PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 2000 REACTOR CORE

Transcription

1 PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 000 REACTOR CORE Efrizon Umar Center for Research and Development of Nuclear Techniques (P3TkN) ABSTRACT PREDICTION OF MASS FLOW RATE AND PRESSURE DROP IN THE COOLANT CHANNEL OF THE TRIGA 000 REACTOR CORE Prediction of the mass flow rate and pressure drop in the coolant channel of the TRIGA 000 reactor core have been carried out and the value of mass flow rate and pressure drop for the maximum and average powered fuel rod have been also obtained After calculating the steady state condition at an operating power of 000 kw, the total pressure drop is 138 Pa for the maximum powered fuel rod and 645 Pa for the average powered fuel rod This result corresponds to the mass flow rate of 0113 and 0085 kg/s, respectively key words : mass flow rate, pressure drop, buoyant force, natural convection INTRODUCTION With the increasing demand of radioisotopes, the TRIGA Mark II reactor was upgraded into 000 kw and reached its first criticality on May 13, 000 In the upgrading activity, modification of core and cooling system were performed to accommodate the power increase [1] The TRIGA 000 reactor upgrade include a redesign of the core structures to allow adequate cooling of the core at the 000 kw power rating This design consists of new reactor core subassembly which fits within the existing reflector assembly (Figure 1) The fuel elements used in the upgraded TRIGA core have the same shape and size as the fuel elements in the previous core The heat generated by fission in the fuel elements is transported to the coolant by natural convection and the pool water is drawn through the coolant pump and forced through the heat exchanger The core configuration is a hexagonal grid plate surrounded by a graphite reflector The existing top and bottom grid plates assure adequate performance for operation at 000 kw which include the following features []: a Constant triangular pitch The plates have a hole pattern which locates all the fuel rods on a constant triangular pitch of cm (Figure ) b Redesigned hole configuration All fuel element holes for the grid plate have been redesigned to allow a greater coolant flow The holes have also been tapered to assure that there is no problems with the natural circulation flow 67

2 The cooling requirement for the 000 kw TRIGA reactor is based on the ability of the TRIGA core to establish adequate natural convection cooling Thermal-hydraulic analysis for TRIGA 000 reactor is needed to evaluate a capability of the natural convection cooling in the reactor core In the present study, the analysis will be conducted to evaluate the mass flow rate and pressure drop in the coolant channel of the TRIGA 000 reactor core The target mission is to verify the mass flow rate and pressure drop in the coolant channel by comparing analysis results calculated by General Atomic using STAT computer code This analysis is apart to the thermal hydraulic analysis of the Bandung TRIGA 000 reactor and an average powered fuel rod and a maximum powered fuel rod were analyzed METHODOLOGY Assumption The main assumptions pertaining to the mass flow rate and pressure drop analysis in the coolant channel of the TRIGA 000 reactor core are taken to be the same in the safety analysis report of the upgrade of TRIGA Mark II reactor, as follows : 1 The evaluation is made for a TRIGA system operating with cooling from natural convection water flow around the fuel rods The steady state thermal-hydraulic performance of TRIGA core is determined for the reactor operating at 000 kw and water inlet temperature of 3 o C The coolant saturation temperature in the core channel is 114 o C 3 The radial peak-to-average ratio is assumed to be 19 for initial core condition 4 The initial core condition of TRIGA analyzed has 116 fuel elements 5 If boiling would occur in the core, the influence of void fraction to the driving force is negligible Cases The cases calculated in the present study are summarized as follows : 1 Mass flow rate in the coolant channel for a maximum powered fuel Mass flow rate in the coolant channel for an average powered fuel 3 Pressure drop in the coolant channel for a maximum powered fuel 4 Pressure drop in the coolant channel for an averag e powered fuel 68

3 ANALYSIS To determine the flow through the core of TRIGA 000 reactor, the buoyant forces were equated to the friction losses, form losses, and acceleration losses in the channel as shown in the expression : ÄP + b = ÄPfriction+ ÄPformentrance + ÄPformexit ÄPaccelerati on (1) The buoyant forces are given by where : P : fluid density (kg/m 3 ) g : gravity (m/ s ), b = g ( 0 L dl) ( 0 L 0 L0 L f L ), () Pb = g 1 0, 1 : the entrance, exit, and mean fluid densities, respectively (kg/m 3 ) L : the effective length of the channel ( L = L 0 + L f + L ) (m) L 0, L f, L : the length of the channel adjacent to the bottom end reflector, fuel, and top end reflector, respectively (m) a Friction losses The frictional pressure losses result from wall friction and turbulence in channel of uniform cross section such as those between fuel rods in a core of TRIGA reactor These losses are normally calculated as follows [3] : ÄP friction = 4 K V ref (3) V ref : the velocity at reference cross section ( A ref ) (m/s) The frictional pressure drop coefficient (K) is, however, conveniently taken to be proportional to the length of the flow channel and inversely proportional to the channel diameter, so the pressure drop is, in practice, given by : ref (4) friction Li = i V ÄP 4 fi i De L = 4 i m Pfriction fi i De i Aref (5) 69

4 where : i = the summation is over the lower unheated length, the heated length, and the upper unheated length f i = dimensionless friction factor L i = channel length (m) = equivalent diameter of channel (m) D e m = mass flow rate (kg/s) i = density (kg/m 3 ) A ref = the flow area through the core per element (m ) When a fluid is forced to flow at a rather low velocity in a heated channel, the selection of the proper value of the friction factor depends on the dominant flow regime in the loop One of three regimes may exist : forced convection, mixed convection and natural convection Several dimensionless groups have been proposed to characterize the flow regime boundaries [4] Metais and Eckerd have proposed Re and GrPr The higher the Re number, the higher is the value of GrPr number needed to reach a purely natural convection flow regime [4,5] The dimensionless friction factor associated with natural convection in small tube experiments has also been observed and the transition between laminar and turbulent flow was observed to occur around Re = 1500, similar to forced convection flow condition [4 ] In the present study, to provide the friction factor as a function of mass flow rate, the laminar friction factors for fully developed laminar flow in a triangular array are adopted from Sparrow and Loeffler [6] A complete set of laminar results are available from Rehmi [7,8] By neglecting channel (rods) near reactor core wall, these results have been fit by Cheng and Todreas [9] with polynomial for each sub-channel The polynomials have the form : C fil = a + b 1 (P/D 1) + b (P/D 1) (6) f il C = m D µ A fil e ref n il Table 1 presents the coefficients a, b1 and b for the sub-channel of hexagonal arrays For the turbulent flow situation, Rehme [10] also proposed a method for solving the turbulent flow case in the actual geometry Cheng and Todreas [9] fitted results of this method with the polynomials : CfiT = a + b1(p/d 1) + b(p/d 1) (7) 70 f it C = m D µ A fit e ref n it

5 where : n f il f it C fi P/D = correlation exponent of the Reynolds number (10 for laminar flow and 018 for turbulent flow) = friction factor for laminar flow = friction factor for turbulent flow = sub-channel friction factor constants = pitch-to-diameter ratio b Entrance and exit pressure losses The pressure loss due to an abrupt change in flow direction and/or geometry is usually called a form loss The pressure loss due to form losses is, in practic e, related to the kinetic pressure, so the pressure loss is given by : P form = K V ref (8) = K m Pform Aref (9) For incompressible fluids and steady state flow, the velocity varies inversely to the flow area, thus : K K A T ref T = i = i K A i i A Ki Ai ref (10) (11) The relation in equation (11) allows all the partial pressure losses to be referred to the velocity at some reference cross section ( A ref ) where : entrance Tentrance m P = K (1) exi exit 1A ref 0 Aref m P t = K (13) K T entrance = form losses coefficient for channel entrance K T exit = form losses coefficient for channel exit 71

6 c Acceleration losses The increase in coolant velocity along the coolant channel yields a component of pressure drop not present in a system with constant coolant density This component is due to the increase in kinetic energy of the gradual increase in fluid momentum [3] and is called the acceleration pressure drop The acceleration pressure drop is equal to the change in momentum of the coolant between channel inlet and channel outlet Pacc = iv (14) m P = (15) P acc ia ref 1 = 1 m acc 1 0 A ref (16) RESULTS AND DISCUSSIONS The first step on the determination of the mass flow rate and pressure drop in the coolant channel is achieved via a parametric study of the coolant channel and the grid plate (top and bottom grid plate) of the TRIGA 000 core As mentioned before, the plates have a hole pattern which locates all the fuel rods on a constant triangular pitch of cm All fuel element holes of the grid plate have been redesigned to allow a greater coolant flow The holes have also been tapered to assure that there is no problems with the natural circulation flow (Figure 3 and 4) The cooling water flows through the hole of the bottom grid plate, pass a lower unheated region of the element, pass the heated region, pass an upper unheated region, through the hole of the top grid plate and trough a real chimney The minimum diameter of the top and bottom grid hole are 387 and 3175 cm, respectively Figure 5 illustrates schematically the natural convection system established by the fuel element bounding one flow channel in the core The system shown is general and does not represent any specific configuration The actual calculations for the TRIGA 000 core were based on a hexagonal array of fuel elements (Figure ) Determination of KT entrance and K T exit As mentioned before, the partial pressure losses to be referred to the velocity at some reference cross section ( A ref ) The form losses coefficient for channel entrance (KT entrance ) is determined from equation 17 7

7 A K = ref Tentrance Ko (17) Ao where : K o = inlet losses coefficient for sharp-edged entrance to coolant channel A ref = reference cross section, (m ) A o = the flow area between fuel element and bottom grid hole, (m ) By using the data in Figure 3, the flow area between fuel element and bottom grid hole (A o ) can be calculated A o = A hole - A fuel (18) Finally, the form losses coefficient for channel entrance (KT entrance ) is 031 Because the flow area between fuel element and bottom grid hole (Ao) is bigger than the reference cross section (Aref), the form losses coefficient in the entrance channel of TRIGA 000 core is lower than in any pipe entrance from a plenum The form losses coefficient for channel exit (KT exit) is determined from equation 19 A K = ref Texit K1 A1 (19) where : K 1 = exit losses coefficient A ref = reference cross section, (m ) A 1 = the minimum flow area between fuel element and top grid hole, (m ) By using the data in Figure 4, the flow area between fuel element and top grid hole (A 1 ) can be calculated A 1 = A hole - A fuel (0) Finally, the form losses coefficient for channel exit (K T exit ) is 195 Because the flow area between fuel element and top grid hole (A1) is smaller than the reference cross section (Aref), the form losses coefficient in the exit channel of TRIGA 000 core is higher than in any pipe exit to a plenum The results of the parametric study of the coolant channel and grid plate of TRIGA 000 core are shown in Table The mass flow rate equation The transcendental equation for the determination of mass flow rate in the coolant channel is obtained by introducing the solutions given by 73

8 equations (5), (1), (13), (16) together with the definition of friction factor (6), (7) into the pressure drop equation (1) and the buoyant force equation () By using the data shown in Table and expanding the right hand side of equation 1and utilizing the buoyant forces (equation ), we get the mass flow rate equations : m and : µ m = = o o µ m µ µ m µ m µ The first equation (1) is applied for laminar flow and the second equation () for turbulent flow It is easily seen that to solve the mass flow rate equation and obtain the maximum flow velocity in the sub-channel, the density ( ) and viscosity (µ ) of the fluid must be specified A higher degree of the exit temper ature is necessary to increase the mass flow rate in the sub-channel For a higher exit temperature, the driving force supplied by the buoyancy of the heated water in the reactor core will cause a higher mass flow rate in the sub-channel The steady state thermal-hydraulics performance of the TRIGA 000 core was determined for the maximum power at MW and a water inlet temperature of 3 0 C Figure 6 shows the relationship of mass flow rate and exit channel temperature for the inlet temperature of 3 0 C For a fixed value of the inlet temperature, the curve represents the variation of mass flow rate as a function of the exit channel temperature and the mass flow rate was found to increase with exit channel temperature By neglecting the energy terms due to the pressure gradient and friction dissipation, at steady state the energy equation in a channel with constant axial flow area (Figure 5) reduces to : d, m hm = q ( z) (3) dz h m = enthalpy (J/kg) q' = linear heat generation rate (J/s) m (1) 1) () + 74

9 For single-phase flow, equation 3 can be integrated over the axial length : or : where : q, total m C p q, m C p total = T (z) m Cp (T = power / fuel element (W) = mass flow rate (kg/s) = specific heat (J/kg 0 C) T m inlet dt = q, total exit T inlet ) (4) (5) By using Figure 6 and equation 5, for a fixed value of the inlet temperature (3 o C), we can calculate a total power per fuel element Figure 7 represents the relationship of power per fuel element and mass flow rate in the subchannel for the inlet temperature of 3 0 C The curve represents the variation of mass flow rate as a function of the power of fuel element and the mass flow rate was found to increase with power The minimum power of fuel element to produce the turbulent flow in the coolant channel is 17 kw The relationship of a maximum flow velocity in the sub-channel and the power per fuel element is shown in Figure 8 and the minimum velocity to produce the turbulent flow in the coolant channel is 007 m/s a A maximum powered fuel rod The radial peak-to-average power ratio is assumed to be 19 [] for initial core condition and a maximum powered fuel rod was obtained about 331 kw From Figure 7, mass flow rate for the maximum powered fuel rod of 331 kw is 0113 kg/s and corresponds to the temperature at the exit of the coolant channel of 10 o C (Figure 6) The saturation temperature at the exit of the channel is reached at the fuel element power of 409 kw This result corresponds to the thermal power of,471 kw The total pressure drop in the coolant channel of the TRIGA 000 reactor core is 138 Pa for the maximum powered fuel rod b An average powered fuel rod An average powered fuel rod for initial core condition (116 elements) is 17 kw From Figure 7, mass flow rate for the average powered fuel rod of 17 kw is 0085 kg/s and corresponds to the temperature at the exit of the coolant channel of 80 o C (Figure 6) The total pressure drop in the coolant channel of the TRIGA 000 reactor core is 645 Pa for the average 75

10 powered fuel rod A summary of the calculation results for the average and maximum powered fuel is given in Table 3 Table 4 shows calculation results of mass flow rate and pressure drop for the maximum powered fuel rod of TRIGA 000 core In the table, calculation results by STAT code are also shown for a comparison The mass flow rate and total pressure drop in the present study is a little bit lower than that calculated by STAT code This difference is due to the sub-cooled boiling region in the end of the sub-channel are considered in the STAT code Meanwhile, the main assumption in the present study, if boiling would occur in the core, the influence of void fraction to the driving force is negligible In Table 4, the exit coolant temperature in the present study is a little bit higher than that calculated by STAT code This difference is due to the two phase flow in the end of sub-channel are considered in STAT code, so that a small fraction of the heat generated in fuel element is used to evaporate the coolant water Meanwhile, in the present study, only a single phase flow is considered in sub-channel and all of the heat generated in the fuel element is used to increase the coolant temperature CONCLUSIONS The following conclusions can be drawn from the results : 1 The pressure drop in the coolant channel of the TRIGA 000 reactor core is 138 Pa for the maximum powered fuel rod and 645 Pa for the average powered fuel rod These results correspond to the mass flow rate of 0113 and 0085 kg/s Further analysis is needed to calculate the heat transfer coefficient for the maximum and average powered fuel rod REFERENCES 1 Anonymous, "Bid Invitation of Specification of upgrade of TRIGA Mark II reactor", CNTR-BATAN, Bandung, (1995) Anonymous, "Safety analysis report for upgrade of TRIGA Mark II reactor", General Atomic, June (1996) 3 HWGRAVES, "Nuclear Fuel Management, John Wiley & Sons", New York, (1979) 4 NETODREAS, "Elements of Thermal Hydraulics Design Nuclear Systems II", Hemisphere Publishing Corporation, New York, (1990) 5 BMETAIS, E ECKERT, "Forced, mixed and free convection regimes", Journal of Heat Transfer, (1964) 76

11 6 EM SPARROW, AL LOEFFLER, "Longitudinal laminar flow between cylinders arranged in regular array", AIChE, J, 5 :35, (1959) 7 K REHME, "Laminar stromung in stabbundden", ChemIngenieur Technik, 43:17, (1971) 8 NETODREAS, "Thermal Hydraulics Fundamental Nuclear Systems I", Hemisphere Publishing Corporation, New York, (1990) 9 SKCHENG, NETODREAS, "Hydrodynamics and correlation for wirewrapped LMFBR bundles and sub-channel friction factors and mixing parameters", Nucl Eng Design, 9:7 (1985) 10 K REHME, "Simple method of predicting friction factors of turbulent flow in non-circular channels", Int J Heat Mass Transfer, (1973) 77

12 Table 1 Coefficients in equation 6 and 7 for sub-channel friction factor constants (C fi ) in hexagonal array [6] Sub-channel A b 1 b Laminar flow Turbulent flow Table Input data Form losses coeffic ient for channel entrance, K T entrance 031 Form losses coefficient for channel exit, K T exit 195 Pitch-to-diameter ratio, P/D 116 Inlet losses coefficient for sharp-edged entrance, K o 05 Exit losses coefficient, K 1 10 Thermal power (kw) 000 Number of fuel elements 116 Flow area (mm /element), A ref 539 Wetted perimeter (mm/element), S 1177 Hydraulic diameter (mm) 183 Fuel element heated length (mm), L f 381 Fuel element lower unheated length L o 94 cm Fuel element upper unheated length L ' 165 cm Fuel element diameter (mm), D 375 Fuel element surface area (mm ) 449 x 10 4 Table 3 The steady state results for one flow channel for TRIGA 000 operating at 000 kw Parameters Maximum powered fuel Average powered fuel Natural convection mass flow rate 0113 kg/s 0085 kg/s Exit coolant flow temperature 10 0 C 80 0 C Maximum flow velocity 019 m/s 016 m/s Form losses pressure drop 366 Pa 05 Pa Frictional pressure drop 951 Pa 434 Pa Acceleration pressure drop 11 Pa 06 Pa Total pressure drop 138 Pa 645 Pa 78

13 Table 4 Comparison of calculation results between calculation in the present study and STAT computer code [] for a maximum powered fuel rod Parameters Calculatio n results in the present study Calculation results STAD computer code % Difference Mass flow rate (kg/s) Form losses pressure drop (Pa) Frictional pressure drop (Pa) Acceleration pressure drop (Pa) Total pressure drop (Pa) Maximum flow velocity (cm/s) Exit coolant flow temperature ( 0 C)

14 80 Figure 1 Reactor core subassembly elevation

15 37465 cm A ref Elemental coolant flow section cm Figure Basic cell data FUEL ELEMENT A ref A fuel = 774 cm A o = cm BOTTOM GRID 3175 cm 54 cm D = 3175 cm 0 Figure 3 Position of fuel element in bottom grid hole 81

16 0 TOP GRID 3175 cm A1 FUEL ELEMENT A ref Figure 4 Position of fuel element in top grid hole T exit ṁ Top grid plate Fuel element A ref Bottom grid plate T inlet ṁ Figure 5 General system configuration 8

17 Mass flow rate (kg/s 0,14 0,1 0,1 0,08 0,06 0,04 0,0 Inlet temperature = 3 o C Turbulent flow regime Laminar flow regime Exit temperature ( o C) Figure 6 The relationship of mass flow rate and exit channel temperature o Inlet temperature = 3 C Mass flow rate (kg/s Turbulent flow region Laminar flow region Power/element (W) Figure 7 The relationship of power element and mass flow rate in the sub-channel 83

18 05 o Inlet temperature = 3 C Turbulent flow region Maximum velocity (m/s) Laminar flow region Power/element (W) Figure 8 The relationship of a maximum flow velocity and the power per fuel element 84