Semester of Graduation

Spring, 2024


Master of Science (MS)


Mechanical and Industrial Engineering

Document Type



This report presents a numerical transient analysis of Close Contact Melting (CCM), intended to help in accurate prediction of melt rate and interface configuration, which is to be utilized for a prospective frozen propellant based propulsion system. Three different substrate shapes namely- Flat, Cylindrical and Wedge, are chosen for the study. The domain discretization is based on generation of boundary fitted mesh and the time varying physical domain is transformed to a fixed computational domain, wherein the associated governing equations are solved. Apart from the conventional linear system solvers, an algebraic multigrid based solver is implemented. A non-iterative implicit/explicit melt interface tracking method is utilized, for determining the interface position at increasing time points. The problem is studied on materials of three different Prandlt number, in order to understand the advective and convective effects. Both Dirichlet and Neumann boundary conditions are utilized for the study. A seperate analytical analysis is conducted for the steady state solutions, for all the three different substrate shapes.

For high Prandlt number materials, the steady state solution obtained as a limit of the transient analysis compares well with the simplified analytical solution, for all the substrate conditions. For low Prandlt number materials, the advective effects are to be included to get an accurate prediction of melt parameters. Accordingly, a closed form solution for a simplified system of momentum equations, including the transverse advective effects, is developed for flat plate substrate. For the cylindrical and wedge shaped substrate, a simplified iterative procedure is developed for accurate prediction of the melt parameters, with the inclusion of the advective effects. The steady state solution of low Prandlt number material based on the above procedure, has a close agreement to the steady state solution obtained as a limit of the numerical transient analysis. Even for a transient analysis (with no expected steady state), which includes the effect of undercooling in the solid phase, it is observed that the melt rates reach a quasi steady state. By the inclusion of gradients from the solid phase numerical results, in the interfacial heat balance, it is observed that the steady solution, at a particular time point, obtained by a simplified procedure has a good agreement to the results of a complete transient analysis. A separate parametric data fitting is carried out for the numerical results corresponding to the tested input values.



Committee Chair

Adam Baran

Available for download on Thursday, April 17, 2025