Corresponding author: Suhail Ahmad Khan (

Academic editor: Georgy Tikhomirov

The heat flux in a Light Water Reactor (

The power output of the reactor is limited by three dependent thermal and hydrodynamic variables: the

The general practice is to estimate the critical heat flux using empirical correlations that have been validated by extensive experimental testing. Most of these correlations are proprietary and only limited information is available in literature. A methodology to calculate the critical heat flux using the published W-3 (

The Indian Pressurized Water Reactor (_{th} with the targeted discharge burn up of 45 GWD/tU. Enriched uranium oxide is used as fuel and batch refueling scheme is adopted for fuel management and optimized to get a cycle length of 410 Full Power Days (

A brief description of the

The _{Th}/900 MW_{e}. The

The

Design Parameters of the

Rated Power MW_{th} |
2700 |

No. of fuel assemblies ( |
151 |

Hex | |

Average Linear Heat Generation rate in a pin kw/m | 15.96 |

Power density MW/m^{3} |
87.4 |

Core periphery dia m | 3.3 |

Core baffle dia m | 3.46 |

Material of the core baffle | SS + water |

System pressure MPa | 15.7 |

Active core height m | 3.6 |

Fuel Temperature °C | 625 |

Coolant inlet temperature °C | 292 |

Coolant outlet temperature °C | 323 |

Coolant Flow (m^{3}/hr) |
76700 |

Reactivity control | Soluble boron(H_{3}BO_{3} in water) |

Shutdown and Control | Rod clusters in fuel assembly |

Control rod material | B_{4}C and Dy_{2}O_{3}.TiO_{2} |

Equilibrium Core of

A lattice burnup code VISWAM has been developed to cater to the current and future requirements of reactor core design computations (

One model is based on a combination of 1-D multi group transport and 2-D few group diffusion theory. A typical fuel assembly cell consists of fuel pins of different enrichments and various heterogeneous cells like control rod, water rod or burnable absorber rod (_{ij}). The square or hexagonal cell boundary is cylindricalised to allow 1-D treatment of the Wigner-Seitz cell. Heterogeneities present in the fuel assembly are treated using appropriate 1-D supercell simulations. The pincell homogenized cross sections are collapsed to few groups using appropriate supercell spectra. For non-fuel cells, the few group cross sections are obtained from the respective supercell calculation of a given heterogeneity. The fuel assembly cell is treated by 2-D few group diffusion theory using centre-mesh finite difference method.

The second model uses interface current method based on 2D collision probability. In this model, a lattice cell may be a fuel pincell, water rod cell or an absorber rod cell. The geometry of the cell is not changed, i.e., the outermost region of the cell is retained as the square or hexagonal shape without cylindricalisation. The collision probabilities are calculated for single lattice cell in 2D geometry. For fuel assembly calculation, the lattice cells are linked using interface currents by using the double P2 (DP2) expansion of angular flux at the pincell boundary. In this method, the neutron transport equation for group ‘g’ (the group index ‘g’ is omitted for simplicity), when discretized over a region consisting of N_{V} zones and N_{S} surfaces reduces to linear flux and current equations (assuming flat flux approximation)

The summation over ν in above equations represents the order of expansion of angular flux at pincell boundary. Here _{i}_{si}V_{i}ϕ_{i}_{i}V_{i}_{si}_{i}

Here _{ji}^{ν}_{jα}^{ν}_{αi}^{νμ}_{αβ}

The fuel assembly cell calculation in VISWAM generates several parameters like the infinite multiplication factor ‘_{∞}, power distribution, homogenized and collapsed five or two group cross sections of the entire assembly cell, and kinetics parameters like delayed neutron fraction ‘β’ and prompt neutron mean life time ‘^{th} order Runge-Kutta method.

The results reported here have been obtained using the few group cross section lattice data generated using first model of 1D transport and 2D diffusion. This is because this model is computationally efficient and the few group lattice library with parametric variation of fuel temperature, coolant temperature, coolant density, Xenon and Samarium concentration is generated in reasonably small time.

TRIHEXFA is a 3D diffusion theory code developed indigenously for performing the full 3D core calculation with burnup. It has been extensively validated against the many benchmarks and experimental data (^{th} fuel mesh in axial direction is obtained as

_{c}_{c}

where Δ^{th} mesh is calculated using heat balance in the following expression.

where:

^{3}/hr)

_{p}

_{in}^{3}.

The fuel temperature for k^{th} fuel mesh is obtained as

_{f}_{c}_{rated}_{c}

where _{rated}

After calculating local parameters of the mesh, the cross section ratios for the mesh are obtained using interpolation for that parameter’s local value in the mesh. The perturbed cross section for a mesh is then obtained by multiplying the reference few group cross sections with the ratios for each type of perturbation, viz., fuel and coolant temperature, xenon and samarium loads.

A model to estimate reactivity coefficients using first order perturbation theory has been implemented in TRIHEXFA. This model is based on the method described in Stacey (

where the variables have their usual meaning. This method has been implemented in TRIHEX-_{eff}

Flow Chart of Neutronics and

For calculating

The W-3 correlation, developed at Westinghouse by Tong (

The uniform critical heat flux. (_{cr}) is computed with the W-3 correlation, using the local reactor conditions.

The non-uniform DNB heat flux
_{cr , n}) distribution is then obtained (assuming a flux shape similar to that of the reactor) by dividing
_{cr}

For a channel with axially uniform heat flux, the correlation, giving the uniform critical heat flux. (_{cr}), is given by the following equation (

_{cr}^{(18.177 − 0.5697p)xe}]

× [(0.1484 − 1.596_{e}_{e}_{e}

× [1.157 − 0.869_{e}^{−124.1Dℎ}]

× [0.8258 + 0.0003413(_{f}_{in}

where the symbols used and their valid ranges are as follows

_{cr}^{2}

_{e}

^{2}s (1356 to 6800)

_{h}

_{f}

_{in}

The enthalpy at DNB location is calculated using following expression (

where

_{c}

The coolant quality in axial mesh k is calculated using following expression

where _{fg}

The axially non-uniform heat flux (_{cr}_{,n}) is obtained by applying a corrective F factor to the uniform critical heat flux

where the factor F is given by

Here _{cr} model and C is an experimental coefficient given by

The OKB-Gidropress correlation was obtained on the basis of results of experimental studies of DNB in the rod bundles for the conditions of _{cr}_{,n}) is determined by the following correlation:

_{cr}_{,n} = _{cr}_{,unif}

where _{cr}_{,unif} is the uniform critical heat flux distribution and is given by

_{cr}_{,unif} = 0.795(1 − _{e}^{0.105p−0.5} × ^{0.184−0.311xe} × (1 − 0.0185

and the factor F is given by

where _{h}^{*} = 22.1 Mpa is the critical pressure and ^{*} is the critical temperature at ^{*}.

The 3D

Where

_{cr}_{,n} = Critical heat flux calculated as described above in each axial mesh (in kW/m^{2})

^{2}).

The minimum

In order to evaluate the

Typical Axial Fuel Temperature Profile.

Typical Axial Coolant Temperature Profile.

Fig.

Variation of

The

Axial Variation of

Radial Power Distribution at

As seen from Figs

The variation of minimum

The first author is thankful to Dr. V. Jagannathan and Arvind Mathur (Both Ex RPDD, BARC) for codeveloping and valuable discussions. The authors are thankful to Shri Gopal Mapdar of RPDD, BARC for plotting some figures appearing in the present paper.