k- modeling using Modified Nodal Integral Method

The simulation of turbulent flows is an ongoing challenge. This is especially true for the flows in nuclear reactors. In order to save computational time and resource, accurate numerical schemes are required for such simulations. The encouraging results from the laminar flow simulations using Modified Nodal Integral Method (MNIM), serves as a motivation to use the method for turbulent flow simulations. The kmodel in this work has been implemented using the MNIM formulation. Two models, one for low Reynolds number and one for high Reynolds number, are implemented. The application of the model to relatively simple problems shows that results are good and similar to what one would expect from the kmodel implementation with any other numerical scheme. The results are compared with the DNS data from various sources in the literature. The difference between the DNS data and current implementation arises mainly from the assumption made in the kmodel rather than the choice of the numerical scheme in the present work. It is seen that very coarse grids can be used away from the walls for the present simulation. This is especially true for low Reynolds number model. However, away from the wall very few cells are needed. Hence, MNIM formulation for the kmodel promises to reduce the over all computational cost despite the fact that there will be relatively little gain in regions near the walls.