In this paper, a novel nodalized reduced order model (NROM) has been developed to analyze the linear stability in a heated channel using supercritical water (SCW) as a coolant. The presented reduced order model is developed based on the two-phase flow system approach. The model is much simplified, which reduced the requirement of computational efforts and resources. In the heated channel, the SCW’s density shows a dramatic downfall near the pseudo-critical temperature, based on which it has been divided into n number of nodes. The one-dimension partial differentiation conservation equations of energy, mass and momentum are used and have been linearized by a small perturbation applied on its steady-state solution. These PDEs are converted into the corresponding time-dependent, nonlinear ordinary differential equations (ODEs) by using weighted residual method applied under some appropriate assumptions and approximations. These sets of ODEs (n+1 equations) are then solved analytically by using a state space approach to capture the stability boundary (SB) in terms of trans-pseudo-critical phase change number ( N tpc ), pseudo-subcooling number ( N spc ) by applying a constant external pressure drop (Δ P tpc ) condition across the channel. The NROM results are found to be in good agreement with the methodology and have been verified by numerical simulation. To extend this as a nonlinear stability analysis, the different types of the Hopf Bifurcation regime are also reported.

To reduce computational time for simulation of natural convection in open cavities, it is quite common to use a domain restricted to the cavity with approximate boundary conditions at the cavity opening. It had been shown that such approach leads to quite accurate solutions for high Rayleigh number (Ra) flows. Such approach has been extended to flows involving radiative heat transfer as well. However, it is important to note that the effect of radiation on the accuracy of restricted domain approach has not been evaluated. In the present work, a comparison of Nusselt numbers is obtained by restricted domain approach with those obtained by using extended domain approach. The convective as well as radiative Nusselt numbers are considered for comparison for various values of Ra and radiation conduction parameter (N r ) . It is observed that the accuracy of the restricted domain approach varies with the radiation conduction parameter as well and the approach is found to be quite accurate for high values of N r .

The recently developed lattice Boltzmann equation (LBE) framework [1] for radiation transport is extended to solve time-dependent nonequilibrium neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling the radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE equations are obtained for corresponding radiative or neutron transport in constant source and reactor criticality search problems. Furthermore, a two-dimensional D 2 Q 8 & D 2 Q 16 LBEs are proposed for solving the time-dependent neutron transport equation in a heterogenous media (e.g., a checkerboard lattice with pure scattering and absorbing cells). The results obtained with LBE are in good agreement with the existing discrete ordinate method results for the benchmark problem.

Safety evaluation is one of the most important aspects of the nuclear reactors. Here some safety studies have been carried out on High Temperature Gas cooled Reactors (HTGR) with fuel in the form of pebbles. This is one of the six types of GEN IV reactors that are being developed internationally with emphasis on features like inherent safety, nuclear proliferation resistance and high thermal to electric conversion efficiency. This work pertains to the dynamic simulation of the reactor with, as well as without reactivity feedback. It involves the solution of point kinetics equations with reactivity feedback arising from the power rise. First, the reactivity feedback arising from the power rise is calculated in the form of power coefficient of reactivity. The steady state temperatures are calculated at two different steady state power levels of the reactor using the heat balance between the fission power produced in the reactor and the heat removed by the coolant. A simplified model of the reactor and lumped model of heat transfer is developed and used. The temperature rise in going from one power level to other power level is calculated. This is multiplied by typical value of the temperature coefficient of reactivity available in the literature. The reactivity changes divided by the power rise provides the power coefficient of reactivity. For performing dynamic analysis of the reactor, the kinetics equations along with feedback are solved. The methodology is verified against the analytical expressions available. Simulations are carried out for the case of raising the power of the reactor from low power to high power and transients at full power and shutting down of the reactor by reactor SCRAM. It is observed that for raising the power of the reactor, the reactivity addition beyond 20pcm/second may not be acceptable as the higher reactivity addition rates result in lower instantaneous reactor period resulting in SCRAM of the reactor. This information is useful in designing the short term and long term decay heat power removal system. Moreover, it provides insight on the determination of the maximum permissible reactivity addition rates in the reactor and optimization of the reactivity feedback due to rise in power.

Very High Temperature Reactor (VHTR) is one of the six reactor concepts selected for further consideration by Generation IV International Forum (GIF) members. Adequate heat removal under steady-state and transient condition is important for the safe operation of VHTR. In one of the proposed designs for reactor cavity cooling system, under off normal conditions, coolant comes down through a downcomer and is then distributed into riser channels. The purpose of this design is to enhance heat transfer rates. The heat transfer characteristics in such a cavity are modeled by natural convection in a square cavity with plate. The plate divides the cavity into channels. The cavity is open at the top and the left side wall is isothermal. The plate is parallel to the side walls. The plate is isothermal and is maintained at a lower temperature than the left wall. The plate is shorter than the height of the cavity so that flow down in one channel turns up in the next channel. The right wall has a temperature lower than the plate, and bottom of the cavity is adiabatic. The flow in the cavity is simulated by recently developed Modified Nodal Integral Method (MNIM). Simulations are done for two different heights of the plate. The cavity without plate is also studied for comparison purposes. The numerical investigation is done for Rayleigh numbers of 10 3 , 10 4 and 10 5 . Nusselt numbers at hot wall and volumetric flow rate into the cavity are reported for all nine cases. Results show that there is significant enhancement in heat transfer in the presence of a plate for higher Rayleigh numbers.