Finite Element Simulation of Two-Phase flows with Heat and Mass Transfer Through a Decoupled Mesh Method
Congress: ENCIT
ABSTRACT:
In this work, a description of heat and mass transfer in two phase flows is presented, using a Lagrangian-Eulerian decoupled mesh method, similar to that of front tracking methods. The “one fluid” formulation for the incompressible Navier-Stokes equations for two-phase flows is solved through the Finite Element Method, coupled with the energy equation for a fluid without viscous dissipation and heat source. Two distinct meshes are used, one fixed mesh representing both fluid phases, and a mesh representing the fluid interface. The mini element is utilized in order to respect the Ladyzenskaja-Babuska-Brezzi condition in the fluid, thereby avoiding artificial stabilization schemes. The advective terms of the momentum and energy equation are discretized using a semi-Lagrangian method. The mass transfer will be accounted through an added term to the conservation of mass equation, updated at each time step. The fluid phases are identified through the use of a Heaviside function anchored at the interface. This same function is used to smooth fluid properties over the interface, reducing the property gradient and avoiding possible numerical instability. The inter- face curvature is calculated through the Laplace-Beltrami operator, and the surface tension force derived from it. The methodology is tested by simulating the bubble growing in superheated fluid test case and comparing it to existing data.