Fast Burst Reactors (FBRs) are important subjects for criticality safety analysis research. They are characterized by irregular geometry, strong transient processes, tight multi-physics coupling, and complex feedback characteristics. This paper introduces an OpenFOAM based multi-physics nuclear criticality safety analysis code named INSL-UniFoam. It integrates discrete ordinate neutron transport solver, heat transfer and stress-strain solvers to detailly model the prompt super-critical burst pulse of FBRs. The UniFoam is first verified in the Godiva-I benchmark under both the steady-state condition and several transient scenarios. The results demonstrate that the program aligns well with the reference solution in terms of K_eff calculation, peak power, and fission yield. Furthermore, it is capable of comprehensively outputting the distributions of power, temperature, and stress-strain throughout the pulse process.