Modelling Of Nuclear Reactor Channel Temperature Distributio

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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Modelling of Nuclear Reactor Channel Temperature Distribution at Steady-State Using LabVIEW Simulation Program F. M. BSEBSU*, and A. A. ESTUTI** * Tajoura Nuclear Research Centre P. O. Box 30878, Tajoura, Tripoli / Libya [email protected] ** Technical University of Budapest, H-1521 Budapest, Hungary Fax: +36 1 463-3272, *Phone + 36 1 463-2183

Abstract This paper shows the possibility to use graphical programming language (LabVIEW) to determine the axial temperature distribution of nuclear reactor channel, at steady state, and compare our results to Pascal program THERMAL and with safety report analysis of KFKI reactor fuel channel as a sample problem of the implementation. The use of LabVIEW environment as tool for above calculations was in good agreement with THERMAL code and KFKI safety report. . Finally, the results of this calculation are at equilibrium and starting core with maximum and average core loading. Nomenclature Tf1 = Reactor coolant inlet temperature, C q "i max = maximum heat flux rate , W/cm2

Cp. = coolant specific heat, J/Kg.K

Ki R

α= heat transfer coefficient, W/cm2 K Tm (z)= axial centre line fuel temperature, C Tf(z)= axial coolant temperature, C AAl+U= cross sectional area of Al and Uranium ring, cm2 AH2O= cross sectional area of water ring, cm2 λ= Thermal conductivity coefficient, W/cm.K

o

m i = coolant mass flow rate, Kg/sec

= wet and heated contours, cm = channel thermal resistance ,K/W

Z = axial distance, cm De = equivalent heated diameter, cm Tcl (z)= axial cladding surface temperature, C He = extrapolated length, cm

1. Introduction The main purposes of heat transfer analysis are accomplished by choosing the operating temperatures within the detailed and precise limits. The basic of the worldwide LWR safety research programmes is to develop computer codes to analyse the abnormal events. These codes are to be based on physical understanding, yet these codes have become so large and complex that few people understanding all of the models employed or the numerical tech-

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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niques. There are a lot of computer codes, but I’ll mentioned about:[1] • RELAP5 code is an advanced, one-dimensional, code based on a non-homogeneouse, non-equilibrium mode (Ransom et al, 1978). • TRAC-P1A (Pryor and Sicilian, 1978) embodies the current state of the art and features a nonhomogeneouse, multidimensional fluid dynamic treatment. For design engineers its less expensive and easier to use numerical simulation for studying the system and optimising its performance. By using simulation one can determine the axial temperature distribution in reactor coolant channel and parameters governing the heat transport rate at the channel wall. On anther hand, these parameters can then be used to choose materials and flow conditions that maximise heat transport in the channel. In the Western reactor design a channel with single passage is usually used (Fig.1). In the Eastern reactor design, however, a channel design with a multiple passage is common, usually, the later type is modelled as a single equivalent channel if the famous thermohydraulic computer programmes such as RELAP to be used. The error introduced by this can be avoided by taking the geometry into considerations. Therefore, it is desirable to have a programme suitable for the calculations of the thermohydraulic of a channel with multisections (Fig.2). In addition the use of big programmes is time consuming. In design and operation simple methods are desirable.

Fig. 1 Single Passage Fuel Channel Fig. 2 Multiple Passage Fuel Channel [1] SIMULATION Definitions In general the words ‘to simulate a system ‘mean to obtain the hypothetical operation of a system under given conditions. The main term ‘system’ refereed to here may be defined as a combination of several elements which all perform together for a particular purpose. For example, the reactor coolant channel is a

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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component of the reactor coolant system and at the same time is a system itself. This system can contain subsystems and these subsystems individually can be a system, which contain again subsystems and so on. A coolant channel of the nuclear reactor can be a thermal system because it responds thermally to environment excitations. Calculation of clad surface temperature is an example of system simulation, which is very important from safety point view to avoid surface boiling at any part of the cladding surface of the coolant channel Tools for simulation Once a mathematical model representing the system under study has been formulated, it has to be solved. For practical systems such mathematical models are usually complex and need to be solved by a computer. The researchers have several ways to accomplish this task: • Use one of high level programming languages such as FORTRAN, PASCAL, or C to solve the model. This method is tedious and time consuming. It should be avoided unless necessary. • Use general-purpose simulation programs such as LabVIEW, and many others. These languages provide for general mathematical functions and integration procedures in addition to instructions available in high-level languages. There is also facilitating the introduction of new model functions in the form of blocks with inputs and outputs. A system may be composing of such functions by connecting their inputs and outputs. Procedure for simulation Use of a computer is mandatory for system simulation in most cases. In general the procedure of system simulation may be broken down into the following steps: • Setting up system model based on: § Measured data or, § Physical knowledge about the examined system. • Preparing input data, •

Programming,

•

Execution of simulation, • Analysis of the result to modify the simulation model structure or parameters based on the simulation results. In the following we shall introduce the one of most useful tool for simulation LabVIEW LabVIEW [3] LabVIEW “Laboratory virtual instrument Engineering Workbench “ is a powerful and flexible instrumentation and analysis soft3

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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ware system where LabVIEW programs called virtual instrument (Vis). A VIs consists of a front panel and a block diagram. The front panel specifies the inputs and outputs and features the user interface for interactive operation. Behind the front panel is the block diagram, which is the actual executable program. The components of the block diagram, icons, represent lower-level instruments and program control structures. You ‘ wire ‘ the icons together to indicate data flow in the block diagram.

2. Mathematical model of Reactor Channel

[1,4]

The fuel channel can be divided into four hydraulic regions. The most inner channel is a tube, marked by “ A ”, followed by a channel with annulus cross section, marked by “ B ”. The outer wall of the next channel is hexagonal, while its inner wall is a circle. “C” marks this channel. The last region, marked by “ D ” is that part of the channel, which belongs both to the given assembly and its neighbouring assemblies. The starting point of the modelling is to simulate the system as presented before the axial temperature distribution along the channels “ A ” and “ D “ is given by:

Tf ( z ) = Tf 1 +

q′i′ K i H e i πc p m max

  πz     1 − cos H  e  

The axial temperature distribution of the cladding surface along both channels “A ” and “ D ” is given by:

Tcl ( z ) = Tf 1 +

q′i′ K i H e i πc p m max

   πz    πz   q′i′      1 − cos + sin   H  α  H    e  i   e  max

The axial temperature distribution of the centre of fuel meat is given by:

Tm ( z ) = Tf 1 +

q′i′ K i H e i πc p m max

   πz    πz      ′ ′   1 − cos + q K R sin  i i  H   H    e    e  max

The above algorithm is valid only for the two regions from our model as mentioned before “A” and “ D ” as shown in Fig.3. But, for another two regions: “ B ” and “ C ”. The temperature distribution along these channels is not the same as in channels “A” and “ D ” because each channel gets the heat from both sides. For example, The channel “ B ” gets the heat from the fuel element (1) and (2). The temperature distribution function is given by:

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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 (q′′ K + q′′ K )H  i i j j e  Tf ( z ) = Tf 1 +   i   πc p m j   max

max

  πz    1 − cos    H  e  

For engineering analysis, the difference between the wall temperature and the bulk flow temperature is obtained by defining the heat transfer coefficient ( α ) through the dimensionless Nusselt number [5] : µw α DH Nu = f (Re,Pr,Gr, )= µb λ The Nusselt number in both experiment and theory show that for almost all non-metallic fluids is given by the Seider and Tate equation [6] : Nu = 0.023 Re0.8 Pr0.4 (

µw ) µb

For more accurate calculations and for cases when µw = µb the Dittus-Boelter equation is the most universally used correlation in the reactor calculations [7]: Nu = 0.023 Re0.8 Pr0.4 For 0.710000, and L/D>60. All fluid properties are evaluated at the arithmetic mean bulk temperature. By transforming the above mathematical relations to 1.0 PASCAL computer programme (THERMAL), and 2.0 LabVIEW simulation programme. The main flow diagram as shown in figure 3[8]

VA

1

VB

2

VC

3

VD AL

U

AL

1

q

2 A q q D

B

3 r* 0 18.38 rAL 16.80

q C

q

3.0

q

5.5

8.5

5

11.0

14.18

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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∆ rU 0.7 0.7 ∆ rH2O 3.0 3.0 1.58 de 6.0 6.0 6.274 K 18.85 34.56 53.41 110.85 18.85 87.97 110.85 AAL+U 66.76 153.15 AH2O 28.27 131.90 174.1 * All dimensions are in mm and mm2

0.74

3.18 6.176 69.12

93.53 162.65

251.20

255.50

Fig. 3 The axial cross section of a channel

3. Sample Problem description

[8]

Using the Budapest research reactor (KFKI reactor) as a testing sample problem does the implementation of the computer programme. The Budapest Research Reactor is a tank type reactor, moderated and cooled by light water. The reactor is in a cylindrical reactor tank, made of a special aluminium alloy with a diameter of 2300 mm, and a height of 5685 mm. The heavy concrete reactorshielding block is situated in a rectangular semihermetically sealed reactor hall. The area of the reactor hall is approximately 600 m2. It is ventilated individually. The fuel of the research reactor is of the VVR-SM type (Russian product). It is an alloy of aluminium and uranium-aluminium eutectic with aluminium cladding. The uranium enrichment is 36 %, the average U235 content is 39 g/fuel element. The fuel element contains three fuel tubes, the outer tubes are of hexagonal shape, while the two inner ones are cylindrical. The active length of fuel elements is 600 mm. The equilibrium core consists of 223 fuel assemblies, with a lattice pitch of 35 mm. A solid beryllium reflector surrounds the core radially. The reactor is equipped with boron carbide safety and shim rods. There is a one stainless steel rod for the purpose of automatic power control [7].

AXIAL TEMPERATURE CALCULATION

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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INPUT DATA (Channel data)

Calculation the main Hydraulic parameters

Channel

B

Channel C Channel D

OUTPUT RES ULTS Fig. 4 The flow diagram of simulation processes [1] The axial cross-section of fuel channel of the KFKI reactor is shown in Fig. 3. The most important parameters of the ring shaped U-AL fuel, of the Aluminium cladding, and of the cooling channels (r, ∆r ). Moreover, the wet and heated contours (K), the equivalent diameter (de), cross-section area (A), and the heated surfaces are presented and the main geometrical data of the VVR-SM type assembly also are presented in Fig 3.

4. Calculation and Results The axial temperature and heat flux distribution along each channel of the [1] fuel element for both of calculations (THERMAL code, KFKI[8] group, and LabVIEW[3]) are shown in figures 5 - 10 respectively.

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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Fig. 5 Axial temperature distribution for KFKI fuel channel calculated by THERMAL code at equilibrium core with (Max. and average) loading [1].

Fig. 6 Axial temperature distribution for KFKI fuel channel calculated by calculated by THERMAL code at starting core with (Max. and average) loading [1]. 8

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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Fig. 7 Axial temperature distribution for KFKI fuel channel calculated by KFKI group at equilibrium core with (Max. and average) loading [8]

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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Fig. 8. Axial temperature distribution for KFKI fuel channel calculated by KFKI group at equilibrium core with (Max. and average) loading [8].

Fig.9 Axial temperature distribution for KFKI fuel channel calculated by LabVIEW at equilibrium core with (Max. and average) loading.

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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Fig.10 Axial temperature distribution for KFKI fuel channel calculated by LabVIEW at Starting core with (Max. and average) loading.

5. Conclusion In this paper, we have used a LabVIEW program environment to simulate reactor coolant channel axial temperature distribution, and compared the results of the this simulation by results of a simple computer programme THERMAL and KFKI reactor safety report analysis for channel as shown in Fig.3. The results of the above methods are given in the following table: Reactor State Equilibrium core Starting core

Loading Maximum Average Maximum Average

Maximum Clad Surface Temperature Results [C] [8] KFKI THERMAL[1] LabVIEW 97.72 100.50 98.56 70.84 71.13 67.50 97.03 101.9 105.88 79.90 81.21 79.60

From above table it is to be noted that there is a good agreement between the results of three calculation methods with error percentage less than (2%) if we take the KFKI safety report analysis results as a base of our comparing.

6. References [1] BSEBSU, F. M. and G. Bede, (1997), A Simple computer programmes for the calculations of reactor channel - Temperature distribution, Polytech TUB Hungary, under publishing. [2] A.A. ESTUEI [3] LabVIEW [4] BSEBSU, F. M. (1995), “ Physics and Thermal hydraulics reactor modelling “, M.Sc. Thesis, Technical University of Budapest, Hungary. [5] Neil Todreas and Mujid S. Kasimi, (1990), “ Thermal Hydraulic fundamental and elements of thermal hydraulic design “, Hemisphere publishing corporation, New York, USA. [6] Maurizio Cumo and Antonio Naviglio, (1988),”Thermal Hydraulics Vol. I”, CRC Press, Inc. USA. [7] J. M. Delhaye, M. Giot, and M. L. Riethmuller,(1980), “thermohydraulic of Two-Phase systems for industrial design and nuclear engineering”, McGraw-Hill Book Company, New York, USA.

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Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

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[8]KFKI - Atomic Energy Research Institute,(1994), “ The Budapest research reactor safety report analysis “, Budapest, Hungary..

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