عنوان مقاله [English]
In this study, a numerical approach and a reduced order model based on POD method are developed for simulation of the fluid flow and mass transfer. The flow field is under the effects of temperature gradients associated with contaminant transport. For this purpose, unsteady incompressible Navier-Stokes equations with terms of effects of buoyancy forces, unsteady heat transfer, and
concentrations transport equations were solved simultaneously using numerical method. In order to discreatize the spatial terms, the second-order central difference method was used and the time integration was performed using Runge-Kutta fourth-order approach. The required snapshots for reconstruction of dynamical system were calculated using the numerical simulation data. Firstly, the CFD model was incorporated for simulation of a classic fluid mechanics problem, such as cavity flow, for validating its accuracy. Then, the developed computer code was applied for simulation of natural convection and mass transfer in a bounded domain under specified boundary conditions. In order to construct the reduced order model, based on the concept of dynamical system and projection approach, momentum and concentration transport equations were projected along POD modes. Moreover, for modeling the dynamics of flow field, velocity field and concentration transport dynamical system equations were solved for related modal coefficients variations. For simulation of heat transfer, temperature field modes were computed according to the modal coefficients of concentration field. The special achievement of this research would be reduction in the number of equations required to simulate the dynamic of the flow field. Based on POD modes energy level results in a higher level of captured kinetic energy of flow field when using a smaller number of modes. This means that by the described method a reduced order model can be obtained. The proposed model has the ability to simulate the flow and contaminant transport with higher speed of computations. The results of the reduced model were compared with the data obtained from numerical model and the accuracy and the ability of the developed model have been validated.