Residual-based stabilization methods remain predominant in Variational Multiscale formulations due to their intrinsic consistency property. An important aspect of these formulations is the large number of stabilization terms from the inner product of the spatial adjoint and finite element residual operators. An alternative to the residual-based methods is term-by-term formulations that consider only stabilizing terms of quadratic structure, which, from the stability point of view, are the only ones required by Galerkin to ensure stability \cite{Castillo}. In non-residual-based formulations, orthogonal projections have been successfully applied in non-Newtonian and dispersed multiphase flows to ensure optimal convergence error orders in high-order elements (of order two or more) \cite{González,Gravenkamp}. This work proposes an orthogonal and dynamic term-by-term stabilization to approximate numerically liquid-solid phase change flows, including macrosegregation scenarios \cite{Cabrales}. In addition to presenting numerical results related to the problem under study, the presentation emphasizes implementation aspects for the computation of orthogonal projections, highlighting iterative and explicit forms (conditionally and unconditionally stable).