Modification of SIMPLE algorithm to handle supercritical natural circulation in a loop

The conventional SIMPLE algorithm for the pressure-velocity coupling has been adopted by many commercial CFD codes. Since it encounters convergence problem when it is used for numerical analysis of a two-dimensional unsteady natural convection flow in a rectangular cavity with zero-isothermal compressibility, the modification of SIMPLE algorithm has been proposed for such a fluid. In this paper, differences between solutions for a one dimensional natural circulation of a super-critical carbon dioxide in a loop with a horizontal heater and a horizontal cooler configuration obtained by using the conventional SIMPLE algorithm and the modified version of the algorithm are investigated. The modification of the algorithm includes updating the density at each time step based on its value at the previous time step to satisfy the mass conservation. The differences of the velocity and temperature are relatively small comparing with the two-dimensional natural convection case. As an example of utilizing the modified SIMPLE algorithm, characteristics of the unsteady natural circulation of super-critical carbon dioxide in a rectangular loop are revealed.