Theoretical and experimental thermal-hydraulic analysis of a new sodium cooled fast breeder reactor core

Nuclear Engineering and Design 118 (1990) 77-86 North-Holland

77

THEORETICAL AND EXPERIMENTAL THERMAL-HYDRAULIC ANALYSIS OF A NEW SODIUM COOLED FAST BREEDER REACTOR CORE H. B(3SE, P. R()I~, H. U N G E R a n d A. Z I E G L E R Ruhr-Universitiit Bochum, Lehrstuhl /'fir Nukleare und Neue Energiesysteme, Universitiitsstrasse 150, 4630 Bochum, Fed. Rep. Germany

Received: first version 15 July 1988, revised version 27 April 1989

This paper presents the experimental and theoretical results of the thermal-hydraulic design of a new fast breeder reactor core concept. The main feature of this concept is the omission of fuel element cans. The hydraulic function of these fuel element cans is substituted by a winding flow path through the radial blanket and a ring chamber without tubes. A computer code based on the quasi-continuum-theory and especially adapted to the features of the new core concept is developed for theoretical investigations. The pressure drop of the rod bundles is specified by a resistance tensor. The experimental investigations are realized in a test facility, where sodium is simulated by water. Pressures and velocities are measured. Theoretical and experimental results show good agreement. The aim of flattening of the coolant outlet temperature distribution can be reached with satisfying accuracy.

1. Introduction Worldwide the reactor core of liquid metal cooled fast breeder reactors consists of hexagonal fuel elements enclosed in fuel assembly cans. These cans have the following main functions: (1) They form coolant channels. Throttles located at the bottom of the cans allow an individual matching of the fluid flow depending on the fuel element power. (2) They are protecting against deformation or destruction during fuel element handling. (3) They limit the expansion of local power transient conditions on the local channel. But the fuel assembly cans increase the amount of neutron-absorbing material in the reactor core. This decreases the breeding ratio and a higher fuel enrichment is necessary. For this reason, the Institute of Energy Systems Engineering at the Ruhr-University Bochum is concerned with an improvement of the reactor core itself. The new core concept for fast breeder reactors was proposed by Ziegler [1] and [2]. The main feature of this new core concept is the omission of fuel-element-cans. Therefore, it is called the "open" reactor core concept.

Advantages of the open core concept are: (1) Neutronics calculations [3] show far better fast breeder chracteristics, i.e., fuel consumption, breeding ratio and doubling time. Ultra long life core constructions ~re possible. (2) By adding a ring chamber around the radial breeding blanket the entrance and outlet pressure drop of the reactor core is reduced significantly. Therefore, the required main pumping power is decreased and a higher efficiency is realized. (3) The new concept offers the possibility of cooling voided regions by radial coolant flow. The reduction of the void coefficients mitigates the progress of power transients. (4) Simplification of fuel element fabrication. The omission of the canning reduces the element's bending resistance by nearly 90%. To fulfil the requirements imposed by a homogeneous mechanical core structure, it was necessary to design and develop adapted control rods and a new shutdown system. It consists of flexible finger absorbers, a magneticjack control rod drive and a pneumatic scramming mechanism. As a result of experimental tests and theoretical investigations, very short scram times and high reliability of the shutdown system were found, which were operable even

0 0 2 9 - 5 4 9 3 / 9 0 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V.

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H. BOse et al. / N e w sodium cooled fast breeder reactor core

I 1 2 3 4 5

Core Upperaxial blanket Loweraxial blanket Radialblanket Rtngchamber without fuel elements 6 Fission gee plenum 7

Ductless fuel

9

Adjustable throttle Permeable

i

element 8 Solidblockage 10

blockage 11 Flowdirection

®

Fig. 1. Main features of the open reactor core concept.

in the case of severe accidents like earthquake and deformation of the core structure [4]. In consequence of the omission of the hexagonal fuel cans, new spacers are required, too. They have to fulfil three purposes: (1) Transfer of forces between neighbouring fuel elements. (2) Guarantee of the positions of each fuel pin. (3) Most important, handling of the neutron induced void swelling of the structural materials without changing the outer cross-dimensions of the subassembly and keeping mechanical loads well within the structural material strength limits of spacers and fuel pins. Helically wired grid spacers could potentially meet the above mentioned requirements. They would consist of a hexagonally shaped peripheral steel bandage and groups of crosswise arranged steel wires between the pins [5]. A main problem of the new concept is the coolant temperature and flow path through the reactor core; it will now be discussed extensively. Figure 1 shows the main features of the open reactor core concept concerning the special design for the flow path through this core. The fission zone is radially surrounded by the breeding zone. The power distribution in this structure is radially decreasing and changing during operation. Therefore, it is necessary to adjust the coolant flow rate through the different zones of heat generation on this power distribution to achieve a radially flattened coolant outlet temperature. In the fast breeder reactors under construction or operating this flow adjustment is realized with throttles located at the

bottom of the fuel element cans. This way it is possible to adjust the mass flow rate for each coolant channel. The open reactor core concept needs a new design for the adjustment of the coolant flow rate. In the ductless fuel assemblies throttles at the bottom would be ineffective for shaping the flow pattern. Therefore, the breeding zone in the open rector core is radially surrounded by a flow region without any rod bundle geometry called the ring chamber. The ring chamber is subdivided by horizontal baffles. In the blanket these baffles are continued by partially permeable blockages in form of special spacers forcing the main coolant flow in radial direction. This design leads the coolant to a winding or meandering flow path through the reactor core. In this way the coolant flow rate through the blanket is reduced and the way of sodium from inlet to outlet is lengthened. During reactor operation the power distribution changes because of the breeding effect. To adjust the coolant flow rate through the blanket concerning this fact additional, adjustable throttles are located at the middle baffle in the ring chamber. These throttles can be opened during reactor operation depending on the power distribution and allowing an increased mass flow rate through the blanket. A computer code is developed for theoretical investigations. Experimental investigations are realized in a water test facility (scale 1:1) measuring the pressure distribution.

2. Theoretical investigations The thermal-hydraulic design requires the calculation of the flow and temperature distribution. A special feature of the new core concept is the inclined coolant flow - especially in the radial blanket - caused by the flow blockages. The mathematical formulation of the thermalhydraulic problem is based on the solution of the twodimensional incompressible unsteady Navier-Stokes and continuity equation to calculate the velocities and the pressure field. The solution of the energy equation gives the temperature distribution in the core. Fluid flow and heat transfer in the reactor core are complex. The complication arises from the fact that the flow region contains a rod bundle geometry, the fluid is flowing turbulently between the fuel rods and especially in the breeding zone the flow is inclined. The cost of a detailed thermal-hydraulic analysis with explicit treatment of these facts is prohibitive, if not impossible. The

79

H. Bi~se et al. / New sodium cooled fast breeder reactor core

limiting parameters are the computation times and the small core memories of the computer. It has therefore been decided to cover the essential features of the system and to express the flow and temperature field in terms of global quantities while sacrificing some of the details. This means that the reactor core is represented by a quasi-continuum-formulation with a flow region containing dispersed, but fixed heat generating solids. The porous media formulation takes advantage of the local volume averaging technique and modifies the governing equations, i.e., conservation of mass, momentum and energy. It uses the concept of volume porosity, surface permeabilities, distributed resistance, and heat source. Distributed resistance alone is normally used to characterize anisotropy of a porous medium. However, when local flow area changes abruptly, and high resolution of local temperature and velocity distribution is needed, additional delineation of the anisotropic characteristics of the medium is necessary. The concept of surface permeability facilitates the modeling of anisotropic effect of a medium [6]. In order to reach a comparability, the ductless rector core is based on the dimensions of the SNR-300 in Kalkar [7] by using the same fuel to sodium ratio and equal positions of the fuel elements. The most important geometrical parameters of the core design are given in table 1. During the averaging process for the quasi-continuum formulation the parameter R in the momentum equation represents the resistance force exerted on the fluid by the dispersed solid per unit volume of the fluid: ~--~( y p w ) + div(ypww) = y p g - g r a d ( y p ) + R. y w g p

= = = =

volume porosity [-], coolant velocity vector [m/s], gravity acceleration [ m / s 2 ], static pressure [ N / m 2],

,y

\

00, x\

p---,0.°, NX@

~p~y

Fig. 2. Directions of the pressure gradient and the velocity.

R = resistance force tensor of the rod cluster [Pa/m], p = fluid density [ k g / m 3]. The resistance force tensor R is defined as: P R= -~lwl~w,

where, for two-dimensional geometry

~xy The matrix values of the resistance tensor has to be calculated by empirical formulas on the basis of experimental results. The numerous experimental investigations (see for example B~ttgenbach [8] and Hollenhorst [9]) show a significant dependence of the matrix elements upon the flow angle between the direction of the mass flow and the fuel rod centerline. It was found that the resulting pressure gradient deflates from the velocity direction as shown in fig. 2. Hollenhorst [9] described the tensor with:

t=

(~x._ : . ) / . ( 0 )

~.

•

The diagonal elements ~'~x and ~yy represent the well known resistance values for parallel- and crossflow tube arrangements. The functions f x y ( O ) a n d fy,,(O) depend on the flow angle 0

Table 1 Main geometrical parameters

Rod diameter Pitch Hydraulic diameter Ratio pitch/diameter Volume porosity

,,

Fission zone

Radial blanket

[mm] [mm]

6.38 8.60

12.34 13.72

[mm]

6.40

4.48

[-] [-]

1.348 0.500

1.112 0.266

sin 0 cos 0 A~, B~ + sin20

~x(0)

sin 0 cos 0

A,

The definition of 0 is also given by fig. 2.

In this manner it is possible to evaluate resistance values for inclined flow directions. For example, the

H. BSse et a L / New sodium cooled fast breeder reactor core

80

investigations for the angle-dependence of the resistance coefficient parallel to the rod centerline (y-direction) are shown here:

R,(o)=- lwl sin0cos 0 A X

ByU2+coS20

u y

1

le~+~yylvleyj,

where the parameters Ay and By depend on the tube arrangement. They are calculated with a computer program, which gives the pressure gradients for all experimentally investigated flow angles in dependence of the eligible parameters Ay and By. For the extreme cases 0 = 0 ° and 0 = 90 °, R is a scalar function. Then it is possible to take the drag coefficients ~, for example, from the VDI-WS_rmeatlas [10], or other publications. In any case, the eligible parameters Ax, Bx, Ay and By have to be calculated in such a way that the difference between computed and experimentally investigated pressure gradients is minimal. Hollenhorst [9] denotes for the sector of dial 30 ° ~<~ ~<75 ° in a triangular tube arrangement with a rod diameter of d = 20

mm and a pitch-to-diameter ratio ing values

Ax=4.000 Ay =0.038

and

Bx = 5 . 0 ,

and

By=0.056.

s/d =

1.32 the follow-

The evaluation of the above equation is shown in fig. 3 for triangular (fig. 3a) and square tube arrangement (fig. 3b). Only a small dependence on the Reynolds number can be seen, but a significant increase of the resistance coefficient with flow angle increase. A maximum is reached near a = 80 °, followed by a steep decrease to zero. The coefficients for parallel- and cross flow are calculated with the correlations of [10]. Because the tube bundle geometry and the Reynolds number range is similar, the flow angle dependend values of the resistance tensor measured by [9] are used in the computer code. With these resistance coefficients it is now possible to evaluate all terms of R, depending upon flow angle and Reynolds number for each flow components. The numerical treatment of the governing equations is based on a modified MARKER-AND-CELL (MAC) method and adapted from the SOLA-code [11]. The momentum equations in this code are treated explicitly

s l d = 1.20

7

Re = 50000~ - - ~

2/.

Re= 50000~ Re = 7 5 0 0 0 ~ Z0" Re = 1 0 0 0 0 0 ~ ~EE Re=125000~

2.0 Re =I00000-~-~

,

~

'E ..,.,,:" 'L6" t2-

1.2'

0.8.

0.8"

0/-.

0A

0.0

o°

lb*

z~° 3'oo io o ~'o° ~oo ~b °

8'o* 90 °

Yaw angle 8

Fig. 3a. Pressure drop in tube direction (y-direction) in a triangular rod array [9].

ao oo ~b° 2'0° 3~o ~'o° ~o io° ?ha do° 90 ° Yaw angle

8

Fig. 35. Pressure drop in the tube direction (y-direction) in a square rod array [8].

1t. BSse et al. / New sodium cooled fast breeder reactor core

81

853.3/.

752.15

RADIUS

Fig. 4a. Temperature distribution in the open reactor core without blockages.

while the continuity equation is solved implicitly-in-time by successive-overrelaxation (SOR) which upgrades the pressure field until the divergence of the velocity field becomes negligible. The equations are finite-differenced in a staggered-

mesh system. The pressure (p), temperature (T), density (p), resistance terms (R) and volume porosity (-/) are defined at cell centers. The velocities are located at cell surfaces. The steady state calculation begins with the evalua-

862.53

;96.$2

RADI US

Fig. 4b. Temperature distribution in the open reactor core with blockages.

82

H. BOse et al.

/ N e w sodium cooled fast breeder reactor core

tion of the hydraulic configuration. Having reached steady state conditions, the calculation of the temperature distribution follows. Because the fluid density is not constant, it is necessary to correct the velocity field. This procedure is repeated until the required accuracies for the velocity-, pressure- and temperature fields are achieved. In this manner it is now possible to calculate the thermal-hydraulic configuration for the new reactor core. The aim to flatten the temperature distribution at the top of the reactor core can now be reached by varying the following parameters: (1) the distance of the impermeable flow blockages, (2) the permeability of the blanket flow blockages, (3) the size of the opening of the throttles in the ring chamber. Figure 4 shows a typical two-dimensional temperature distribution in the reactor core and blanket. This figure shows the case with (fig. 4a) and without any additional measures for flow conduction (fig. 4b). A significant radial drop of the outlet temperature in the radial blanket and the ring chamber can be seen in the latter case. The calculation does not consider the terms of heat diffusion and the mixing effect in the ring chamber. It can be expected that the flattening would

Flow direction

50%

80% 100%

Fig. 5. Winding flow path in the open reactor core.

[K] O 1000

3 SHORT BLOCKAGES • CURVE ~ (BEGIN OF CYCLE) 3 LONG BLOCKAGES , CURVE 2 (BEGIN OF CYCLE)

+ 3 LONG BLOCKAGES

• RING CHAMBERTHROTTLE

OPENED , CURVE 3 (END OF CYCLE)

950

BOO 850 800 750 700 650 SO0

' 10

-2:0

, 30

, ":0

, 50

, SO

, 70

, 80

, 90

, , t_00 1t.0

,[S> R [ ~ ] 120

CORE RADIUS

Fig. 6. Coolant outlet temperature distribution.

be much better if this features were implemented in the computer program. Figure 5 shows the flow field in the reactor core presented by streamlines. The flow blockages in the ring chamber and the radial blanket produce a winding flow path through the core. The design of the flow blockages and throttles has a significant influence on the flow field and the temperature distribution. Figure 6 shows the outlet coolant temperature distribution versus the core radius. Curve 1 shows the distribution in the case of minimal flow blockage achieved by omitting the partially permeable flow blockages, located in the radial blanket, completely. The result is a strong radial outlet temperature decrease in the radial blanket. An extreme case is given by Curve 2. All blockages are impermeable and the ring chamber and the radial blanket is totally blocked. The impermeable blockages are simulated by boundary conditions. A substantial flattening of the radial coolant outlet temperature distribution is achieved. The position of the throttles is also important during and at the end of the fuel cycle. At this time the power generation in the blanket is higher than at the begin of the cycle. Therefore, it is necessary to gradually increase the mass flow rate through the blanket during operation. A bypass valve has to be opened completely at the end of the operation period. Curve 3 shows the temperature distribution in this case. It is even somewhat flatter than those achieved for the begin of the cycle. This way a suitable concept for the thermal-hydraulic design of the new fast breeder reactor core has been worked out and lead to a substantial flattening of the outlet temperature distribution.

H. BOse et al.

/ N e w sodium cooled fast breeder reactor core

3. Experimental investigations

83

The fluid gets into a lower plenum beneath the tube assembly after passing a 90 ° bend with an outer diameter of 350 mm. The upper plenum, located on the top of the fuel element dummies, has an outlet flange mounted 400 mm above the ring chamber. The flow rate is regulated by a bypass loop and the maximum reachable mass flow through the test section is 660 kg/s. The temperature as well as the pressure of the circulating fluid is controled in a range of 0.1 K and 100 Pa during the time of each measuring cycle.

The intention of the experimental set-up is to check the correctness of the resistance tensor mentioned before (see fig. 3). But no acceptable way to measure simultaneously the pressure distribution and the distribution of the volumetric averaged velocity w within the narrow flow channels between the fuel rods has been found yet. Therefore, only the pressure distribution inside the core is examined for the extreme cases of a closed and totally opened throttle in the ring chamber.

5. Test section

4. Water mock-up

The test section is built up with 32 complete and 7 half fuel element dummies, shown in fig. 7. Next to the radial breeding blanket the ring chamber can be seen. The circle in the middle of fig. 7 indicates the position of the 90 ° bend, which conducts the fluid into the lower plenum. The fuel elements dummies are constructed of PVC tubes with an outer diameter of 30 mm in the breeding blanket and 15 mm in the fission zone. This is nearly two times the tube dimensions used at S N R 300 in Kalkar (FRG) [7]. The tube height is 2500 mm. The geometric dimensions of the dummy construction is shown in table 2. The spacer blockage factor in table 2 is defined as the ratio of the cross sectional area of the spacer to the fluid filled area in the tube assembly without spacers. The meandering flow path of the coolant through the radial breeding blanket is received by the sum of all the totally impermeable spacer grids in the breeding zone, which will have the same effect as one baffle plate, and

A water test facility is built up to investigate the patterns of fluid flow in the reactor core. The kinematic viscosity v of water at 60 ° C is equal to that of sodium at 460 * C. Therefore, the dimensionless Reynolds number: Re = w d / v , where d = tube diameter, w = volumetric averaged velocity, = kinematic viscosity, characterizing the hydraulic situation, is equal for water and sodium for identical geometrical dimensions. The test section, consisting of a 30 0 reactor core sector, is mounted vertically in a tank, which is designed for an excess pressure of 0.3 MPa. The tank has a height of 5.48 m and a diameter of L45 m. The complete flow loop is constructed of stainle~ steel and the fluid used is demineralized water circulaWA by a 160 kW pump.

TEST SECTION bes

ooo~

with

")P-qq"

DOOO<

o

me0suring

oc~&~

DO000

,

- -

cells

c ~ ( o,

Fig. 7. Test section tube assembly.

•

"

•

~0000("~-

~ o

)

~

.,t,

• • •

84

11. BiJse et al. / New sodium cooled fast breeder reactor core

Table 2 Geometric dimensions of test facility fuel element dummies

Number of dummies Tubes per dement Tube pitch [ram] Pitch/diameter Hydraulic diameter [mm] Volume porosity Element pitch [ram] Spacers per element Spacer blockage factor

Fission zone

Radial blanket

20+4x0.5 37 20.59 1.373 16.16 0.51 124.5 4 0.198

12+3x0.5 10 + 4 x 0.5 35.94 1.198 17.48 0.368 124.5 3 1.0

produce uncertainties up to this range. Furthermore, the porosity of the hollow cylinder will damp the pressure fluctuations existing inside the test section. The measured pressure inside the porous cells is conducted via flexible plastic tubes to a system of magnetic valves, which leads the pressure of selected measuring positions computer controlled to 10 difference pressure transducers, having a measuring range up to 10000 Pa. The medium distance from the porous measuring cells to the difference pressure transducers is 10 m.

7. Experimental results

by the middle blockage in the ring chamber constructed as an adjustable throttle. Hence, the throttle must be fully opened to get the winding flow. It has to be mentioned that the spacer grids in the breeding blanket are constructed to be totally impermeable for the water mock-up only. In a reactor assembly with power generation in the breeding blanket, the spacer grids will permit a defined axial mass flow to avoid local superheating.

6. Instrumentation

The test facility is equipped with a multi-position measuring device to investigate the pressure distribution inside the tube bundle assembly. 30 rods in the test section are prepared for pressure measurement• Each tube consists of 10 porous pressure measuring cells at different axial positions (fig. 7). These measuring cells are made of hollow cylinders of sintered bronze spheres with a medium diameter of 45/~m. The height of the cylinders is 10 mm, the outer diameter is the same as the diameter of the tubes and the wall thickness is 1.5 mm. Hence, the flow through the tube arrangement is not disturbed by any measuring device, only the surface roughness of the porous cells is different from that of the rods. But the main advantage of the porous cells is the independance of the pressure inside of the hollow cylinder of the flow direction relativ to the tube. At Reynolds Numbers of Re = 20000, the difference between the extreme values of the pressure distribution around a cylinder inside the tube bundle at crossflow can reach an amount up to 1500 Pa. Crossflow will appear in the test assembly above and beneath the flow blockages in the breeding region. Measurements with only one pressure hole at an unknown flow direction to the tubes will

The pressure field inside the test section is investigated as a function of the mass flow. Figure 8 shows the measured values for the maximum flow rate through the tube assembly with the adjustable throttle fully opened. The axial positions of the measuring cells can be read from fig. 8. The origin of the coordinate system is the entrance into the tube bundle axially and radially the first tube equipped with measuring cells in the fission zone at the tip of the test section. The first axial pressure measurement position is 50 mm downstream of the tube beginning, and the last position is 50 mm beneath the end of the tube assembly. The axial positions of the spacer grids in the breeding region are: 940 mm, 1420 mm and 1900 mm. The pressure decrease in

PRESSURE [.105 pQ ] 1.5 Gore radJus 1.1. 1.3 1.2 1.1 1.0

~0.

Flowdirection/ AXIAL POS. [drn]

Fig. 8. Measured pressure distribution.

H. BOse et aL / New sodium cooled fast breeder reactor core

0.6 Pressure drop[lOS Pal ==" calculated -e,- measured

0,5 0,4 O,3 0,2 0,1 0 0

500

. . . . . . .

10'o0 1500 ' 20'o 0 Flow rate [m3/h]

2500

1 Pressure drop in the breeding region 2 Pressure drop in the driver region

85

account for the presence of tubes and obstacles by the use of volume-based porosities and distributed resistances was shown for a turbulent flow through a tube bundle with a flow blockage by [12], the difference depends only on the correlation used for the crossflow pressure drop coefficient. The spread of the computed results is based on the extreme values of the correlations cited in the VDI-WArrneatlas [10]. The overprediction of the breeding region pressure drop at the maximum flow rate is 7.6%, respectively 31.1%, using the formula producing the greater pressure drop coefficients [13]. The comparison of measured and computed pressure distribution in an open reactor core shows generally an acceptable agreement, especially if it is taken in account that more actual pressure drop investigations tend to be at the lower range of crossflow friction factors [14].

Fig. 9. Computed and measured pressure drop versus flow.

8. Concluding remarks the center of a reactor core, here represented by the first radial measuring position ('symmetry-fine'), is a linear function of the tube length overlapped by the pressure decrease caused by the spacer grids, which are at the same axial position as those in the breeding region, but constructed of a sample honeycomb grid with a blockage factor of 0.198. The pressure drop at the opposite radial position, the 'ring chamber pressure drop' is marked by the total impermeable spacers in the breeding region. The spacers produce a strong decrease of the pressure values. At the axial position of the ring chamber throttle, the pressure drop nearly vanishes, because the throttle is fully opened. A local pressure maximum beneath the middle spacers in the breeding region indicates a flow separation into two directions. One part of the coolant flows through the breeding blanket. The other part is forced by the spacer blockage back into the driver zone. The abrupt radial pressure drop in the blanket behind the last blockage indicates a large wake region. Figure 9 shows the pressure drop across the tube assembly as well as computed results at two radial measurement positions dependent of the flow rate through the test section. The first measuring tube in the tip of the test section characterizes the pressure rise in the driver region (2) and the last tube close to the ring chamber marks the pressure drop in the breeding region (1). The calculated pressure drop matches the measured values at the 'symmetry-line' very well over the whole range of the flow rate. For the breeding region, however, the computed values are always greater than the measured ones. Because the validity of the porous media principles that

This report describes basic engineering development towards a new fast breeder reactor core. A thermal-hydraulic computer code, which is verified generally by experiments, is able to calculate for various geometrical properties the patterns of coolant flow inside the ductless reactor core with flow conducting blockages. The computed coolant outlet temperature distribution is flattened, hot streaming is avoided and a higher plant efficiency is reached. For further investigations and more detailed computation it is important to develop a three-dimensional computer code. Future experiments are needed to elaborate more exactly the values of the resistance tensor. In addition to the determination of the velocity distribution inside the reactor core, the heat diffusion through the fuel element bundles will be investigated. Because of the advantages mentioned it is desirable to continue the research and development of the fast breeder reactor core concept, which has been presented and discussed here.

Nomenclature A B d dh f g p

coefficient [-], coefficient [-], tube diameter [ram], hydraulic diameter [ram], correction function [-], gravity acceleration [ m / s 2], static pressure [N/m2],

86 R Re t w

H. Bbse et aL / New sodium cooled fast breeder reactor core

resistance force tensor of the rod cluster [ k g / m 3s], Reynolds number [-], time Is], coolant velocity vector [m/s].

G r e e k letters

volume porosity [-], fluid density [kg/m3], drag coefficient [ m - 1], angle between flow direction and rod bundle inclination [degrees], kinematic viscosity [m2/s]. Subscripts X

Y

refers to x-direction, refers to y-direction.

References [1] A. Ziegler, Strt~mungsfeld in Reaktoren mit offenen Brennelementen, Atomkernenergie (ATKE) Bd. 27 Lfg. 2 (1976) 120-124. [2] A. Ziegler, Ein neues Konzept t'dr den natriumgekiihlten Schnellen Briiter, Brennstoff-W~trme-Kraft 35 Nr. 1-2 (1983) 50-55. [3] W. Leer, Untersuchung eines Schnellen B~ter Kerns mit kastenlosen Elementen arthand einer neutronenphysikalischen Kemauslegungsrechnung und einer vergieichenden Bewertung der resultierenden Eigenschaften, Dissertation Ruhr-Universit~it Bochum 1983. [4] A. Willeke und A. Ziegler, Entwicklung eines Abschaltsystems ftir einen sclmellen Brutreaktor mit offenen Brennelementen, Kemtechnische Gesellschaft, Bonn: Bericht, Jahrestagung Kerntechnik May 1988, S. 507-510.

[5] E. Fischer und A. Ziegler, Ein neues Abstandshalterkonzept for einen Schnellbriiterkern mit kastenlosen Brennelementen, Kerntechnische Gesellschaft, Bonn: Bericht, Jahrestagung Kerntechnik May 1988, S. 489-492. [6] W.T. Shah and B.T. Chao, Local volume-averaged equations for single-phase flow in regions containing fixed dispersed heat generating solids, NUREG/CR-1969, Argonne National Laboratory, ANL-80-124 (April 1981). [7] Kernkraftwerk Kalkar, Anlagenbeschreibung mit Betriebs- und Auslegungsdaten, INB Internationale Natrium-Brutreaktor-Bau Gesellschaft mbH (September 1978). [8] H. B0ttgenbach, Messungen von Str/Smungsfeldern in engen Stabbiindein zur Oberpriifung einer anisotropen Str/Smungsfeldtheorie, Dissertation Ruhr-Universitiit Bochum (1977). [9] D. Hollenhorst, Experimentelle Bestimmung und Darsteilung des Widerstandstensors f'tir Strtimungen durch enge Stabgitter, Dissertation Ruhr-Universitiit Bochum (1983). [10] VDI-W~irmeatlas, Berechnungsbl~itter fiir den W~trmeiibergang (VDI-Verlag Diisseldorf, 1984). [11] C.W. Hirt, B.D. Nichols and N.C. Romero, SOLA - a numerical solution algorithm for transient fluid flows, Los Alamos Scientific Laboratory Report, Los Alamos, LA5652 (1975). [12] D.B. Rhodes, L.N. Carlucci, Predicted and measured velocity distributions in a model heat exchanger, AECL8271, Atomic Energy of Canada Limited, Chalk River, Ontario (January 1984). [13] D.B. Ebeling-Koning, Hydrodynamics of single and two phase flow in inclined rod arrays, PhD Thesis, Massachussetts Institute of Technology (1984). [14] D. Traub und K. Stephan, Einfluss yon Rohrreihenzahl und Anstr~mturbulenz auf die W~rmeleistung von querangestr~mten Rohrbiindeln, W~irme- und Stofftibertragung 21 (1987) 103-113.