Abstract :
In this paper, obtaining the characteristics of unsteady three-dimensional
incompressible flows with heat transfer along with artificial compressibility of
Chorin is investigated. At first, compatibility equations and pseudo
characteristics for three-dimensional flows are derived from five governing
equations (continuity equation, momentum equations in three directions, and
energy equation) and then results are simplified to two-dimensional flows.
Pseudo Mach hyper-cone (four-dimensional cone) is found, and its cross-section
with physical axis is calculated numerically. Unlike compressible flow, this is
not a sphere. It is found that the pseudo-acoustic speed within the incompressible
flow is a function of the artificial compressibility parameter and the directions.
In two-dimensional flow, Pseudo Mach cone is obtained by numerical solution
of characteristic equations. Unlike compressible flow, the cross-section of Mach
cone with the x-y plane is not a circle. This shape is not oval, too. The influence
of artificial compressibility parameter on convergence history and accuracy is
surveyed by simulation of cavity flow as a benchmark.
Keywords :
Three-dimensional characteristics , Incompressible flow , Artificial compressibility , Convergence history , Energy equation
