Directed energy deposition (DED) with laser and powder allows the manufacturing of multi-metallic near net shape structures, with control over the feedstock composition and intense liquid mixing of elements. To better understand the multi-physical aspects of the melt pool and strive toward local composition prediction, a 3D finite element model of the laser deposition of chromium on stainless steel has been developed. A modified v2-f model is implemented to investigate the effect of melt pool turbulence on heat, momentum, and mass transport. The model is formulated in the moving frame of the laser, which allows reducing the domain size and the computation time. Overlapping on previous tracks is included by updating the upstream face boundary conditions with the composition and free-surface shape of the calculated molten cross section. This allows for fast computation of the steady-state solution of the layer formation. Simulation results are compared to the composition analysis of a part containing an interface between chromium and stainless steel manufactured using a controlled atmosphere laser powder-DED system. The diffusive effects induced by turbulence are analyzed with regard to a laminar simulation and are found to have a significant impact on the maximum fluid velocity and temperature. Melt pool turbulence thickens the flow vortices and homogenizes the core of the melt pool, which is consistent with the experimental results. Chemical heterogeneities can be seen at the boundary with the substrate and are reviewed in light of the simulation results.