Computational Characterization of Fluid Flow and Heat Transfer in the Pressure Tube of CANDU 6 Nuclear Reactor with Supercritical CO 2

Flow and Heat Transfer in the Pressure Tube of CANDU 6 Nuclear Reactor with Supercritical CO2 Lakshmana Kishore.T , Dr. Kiran Chaudhari , Dr. G. Ranga Janardhana #3 Assistant Professor of Mechanical Engineering, JNTUK University College of Engineering, Vizianagaram *2 Professor of Mechanical Engineering, MCT's Rajiv Gandhi Insitute of Technology, Mumbai #3 Professor of Mechanical Engineering, JNTUA University college of Engineering, Anantapuramu kishore.me@jntukucev.ac.in mkiran02@rediffmail.com ranga.janardhana@gmail.com


I. INTRODUCTION
The CANDU 6 Nuclear Reactor is using Heavy Water as the working fluid.In this paper the pressure tube of the Nuclear Reactor is studied using Supercritical Carbon-dioxide as the working fluid.The dimensions of the pressure tube taken, are same as that of the CANDU 6 Nuclear Reactor.

A. CANDU 6 Nuclear Reactor Pressure Tube
CANDU 6 is the Generation III, 600 MW class heavy-water moderated and cooled pressure tube reactor.Heavy water (D 2 O) is a natural form of water that is used as a moderator to slow down the neutrons in the reactor, enabling the use of natural uranium as fuel.Same D 2 O is used as the working liquid, responsible for transportation of heat.The dimensions used in the analysis is taken from [1] and [2].
Concept of nuclear reactors with water at supercritical pressures were studied as early as the 1950s and 1960s in the USA and Russia.Similar to the CANDU design, the CANDU-SCWR is moderated with Heavy water.The coolant used is light water at 25 Mpa pressure and with an inlet temperature of 350°C.With SCF's as a coolant the efficiency increased to over 40% [9].

B. Supercritical Fluid
Supercritical fluid is any substance at a pressure and temperature above its critical point, where distinct liquid and gas phases do not exist.Supercritical fluids combine useful properties of gas and liquid phases.Their behaviour is near gas from some aspects and near liquid in terms of different features.A supercritical fluids provides a gas like characteristic when it fills a container and it takes the shape of container.The motion of molecules are quite similar to gas molecules.On the other hand, a supercritical fluid behaves like a liquid because its density property is near liquid and, thus supercritical fluid shows a similarity to liquid in terms of dissolving effect.The formation of a supercritical fluid is the result of dynamic equilibrium.
When a material is heated until its specific critical temperature in a closed system, which means at constant pressure, a dynamic equilibrium is generated.This equilibrium includes the same number of molecules coming out of liquid phase to gas phase by gaining energy and going into liquid phase from gas phase by losing energy.
At this particular point, the phase curve between liquid and gas phases disappear and supercritical material appears.In the phase diagram, the field above critical temperature and critical pressure values is defined as supercritical region.The characteristic properties of a supercritical fluid are density, diffusivity and viscosity.Supercritical values for these features take place between liquids and gases II.MODELLING OF THE PRESSURE TUBE From [1] the dimensions of the pressure tube of the CANDU 6 Nuclear Reactor is modelled using CATIA V5.The pressure tube contains 12 fuel bundles and each fuel bundle contains 37 fuel rods.The modelled fuel bundle is shown in the figure There are total of 380 such pressure tubes forming the core of a nuclear reactor, through which heat addition takes place.The modelled pressure tube is imported to ANSYS-CFX for the analysis using different fluids.

III. VALIDATION OF THE PROBLEM
The pressure tube imported is solved in ANSYS-CFX using Heavy Water as the working fluid and compared with the existing results [3].The property values of the Heavy Water are taken from [4] & [5], the boundary conditions applied are taken from [1] and their values are given in table 1 and 2 respectively.The ANSYS-CFX result using Heavy Water matches well with the existing results.The comparison and the error percentage is given in table 3.  The model is solved using UPWIND Scheme.

V. RESULTS
After the completion of the analysis for the convergence criteria of 1e-05, the results obtained using carbondioxide as the working fluid are analysed by plotting different contours and different property parameters are compared with the results of the analysis using D 2 O as the working fluid.

A. Contours
Various contours have been drawn at the cross-section of the fuel bundle and between the fuel bundles 1) Contours at the fuel bundle:  2) Contours at the gap between fuel bundles:

B. Graphs
Various graphs are drawn comparing the results of the analysis of the pressure tube with Carbon-dioxide and Heavy water as the working fluids.
1) For one fuel bundle (12 th bundle): 2) For the total pressure tube:      With reference to the analysis using Supercritical Carbon-dioxide as the working fluid, more amount of heat transport is done when compared to Heavy Water as the working fluid.In effect the capacity of the Nuclear Reactor can be increased for more power generation.From the fig 18 we can observe that density at outlet of the pressure tube is reducing greatly in case of Carbon-dioxide.Because of this, the mass flow rate is reduced which in turn reduces the size of pump.
Even though more pressure to be controlled using Supercritical Carbon-dioxide when compared to Heavy Water, mass flow rate of the working fluid is getting reduced for the same inlet velocity.So Supercritical fluids show a vast scope of research in future nuclear reactors.

Fig 1 :
Fig 1: Pressure Vs Temperature for a supercritical fluid

Fig 4 :
Fig 4: Pressure contours at the fuel bundle

Fig 7 :
Fig 7: Velocity contours at the fuel bundle

Fig 16 :Fig 17 :
Fig 16: Graph between Temperature Vs Length for the total pressure tube

Fig 18 :
Fig 18: Graph between Density Vs Length for the total pressure tube

Fig 19 :
Fig 19: Graph between Pressure Vs Velocity for the total pressure tubeC.Variation of different properties for the pressure tube using Supercritical Carbon-dioxideVariation of some of the other properties with respect to the length of the pressure tube are plotted below.

Fig 20 :
Fig 20: Graph between Specific heat Vs Length for the total pressure tube

Fig 21 :
Fig 21: Graph between Reynolds number Vs Length for the total pressure tube

Fig 24 :
Fig 24: Graph between Nusselt number Vs Length for the total pressure tube VI.CONCLUSION The model of the pressure tube of CANDU 6 Nuclear Reactor created in CATIA V5 is validated with very less error percentage.With reference to the analysis using Supercritical Carbon-dioxide as the working fluid, more amount of heat transport is done when compared to Heavy Water as the working fluid.In effect the capacity of the Nuclear Reactor can be increased for more power generation.From the fig18 we can observe that density at outlet of the pressure tube is reducing greatly in case of Carbon-dioxide.Because of this, the mass flow rate is reduced which in turn reduces the size of pump.

TABLE I .
Properties of Heavy Water

TABLE 2 .
Boundary conditions for the pressure tube using Heavy Water

TABLE 3 .
[4]parison of outlet parameters for validationWith reference to the above table present model is considered to be validated.IV.ANALYSIS USING SUPERCRITICAL CARBON-DIOXIDEThe validated model of the pressure tube is now used to do the analysis using Supercritical Carbon-dioxide as the working fluid.The property values of the Supercritical Carbon-dioxide are taken from[4]&[5].The property values which are given as input in ANSYS-CFX is represented in table 4.

TABLE 4 .
Properties of Supercritical Carbon-dioxide

TABLE 5 .
Boundary conditions for the pressure tube using Supercritical Carbon-dioxide