In this study, the overall performance enhancement and the solution to the excessively high heat flux problem in the fore-end chamber of a dual-vortical-flow (DVF) hybrid rocket engine is investigated by employing a design concept of tri-propellant combustion. Numerical investigation is conducted in the present study, which is serving as a guideline for experimental validation tests that will follow. A Navier-Stokes solution method suitable for all speed regimes with unstructured-mesh discretization approach is employed in this study. This flow solver also features a very-large-eddy simulation turbulence model based on an extended two-equation turbulence model, a finite-rate chemistry model with real-fluid thermodynamics properties, solid propellant surface thermal balance model, and a gray-gas radiative transfer model. The baseline dual-vortical-flow hybrid rocket engine design can use N2O/HTPB, N2O/HDPE, H2O2/HTPB or H2O2/HDPE propellant combinations. Gaseous hydrogen is proposed to be added to the baseline system in the present tripropellant combustion applications. Performance enhancement of the present tri-propellant design is revealed in the numerical solutions and the fore-end chamber solid propellant surface is suitably protected against the high heat flux in the central-port region.