This paper discusses theoretical models and numerical methods to simulate turbulent thermal plasma flow transporting a nanopowder. In addition to a thermal plasma flow model, a sophisticated model is described mathematically for the nanopowder's collective growth by homogeneous nucleation, heterogeneous condensation, and coagulation among nanoparticles, and also transport by convection, diffusion, and thermophoresis, simultaneously. Demonstrative simulations show clearly that a suitable numerical method with high‐order accuracy should be used for long and robust simulation capturing multiscale eddies and steep gradients of temperature, which are the turbulent features of thermal plasma flows with locally variable density, transport properties and Mach numbers. Eddies are first generated at the interfacial region between the plasma jet and ambient nonionized gas by fluid‐dynamic instability. As a result of the eddies' generation–breakup process, the plasma flow entrains the ambient cold gas and deforms its shape traveling downstream. Numerous sub‐nanometer particles are generated by nucleation and condensation in the thin layers near the plasma jet. Those particles diffuse and increase their size, thus decreasing their number by coagulation. Cross‐correlation analysis suggests that the nanopowder distribution distant from a plasma jet can be controlled by controlling the temperature fluctuation at the upstream plasma fringe. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.