EMBEDDING AN EXPONENTIAL FUNCTION IN A TWO-BOUNDARY GRID GENERATION TECHNIQUE FOR THE TURBULENT HEAT TRANSFER IN A PISTON-CYLINDER SYSTEM

Abstract

An algorithm for a multidimensional numerical solution is developed to calculate the turbulent flow field and heat flux in a piston-cylinder system. The two-boundary grid generation technique is used to transfer a rectangular computational plane into the physical domain of a piston-cylinder system for each simulation time step with a connecting function, which may be a linear function or a cubic polynomial with/without an exponential function embedded. Hence, the Jacobian matrix can be obtained by direct analytic differentiation, and less computation time is required for the solution. It is found that the technique of embedding an exponential function in a cubic polynomial function is the most efficient of the four generation techniques mentioned above. Comparison is made between the present results and other earlier results. The computational algorithm in the present study can successfully calculate the turbulent flow field and wall heat flux in a piston-cylinder system on a commercial personal computer.