This work presents direct numerical simulations (DNS) of a circular turbulent jet impinging on rough plates. The roughness is once resolved through an immersed boundary method (IBM) and once modeled through a parametric forcing approach (PFA) which accounts for surface roughness effects by applying a forcing term into the Navier-Stokes equations within a thin layer in the near-wall region. The DNS with the IBM setup is validated using optical flow field measurements over a smooth and a rough plate with similar statistical surface properties. In the study, IBM-resolved cases are used to show that the PFA is capable of reproducing mean flow features well at large wall-normal distances, while less accurate predictions are observed in the near-wall region. The demarcation between these two regions is approximately identified with the mean wall height k m of the surface roughness distribution. Based on the observed differences in the results between IBM-and PFA-resolved cases, plausible future improvements of the PFA are suggested.

The heat transfer between an impinging circular jet and a flat plate is studied by means of direct numerical simulations (DNS) for different Prandtl numbers of the fluid. The thermal field is resolved for Pr = 1, 0.72, 0.025, and 0.01. The flow is incompressible and the temperature is treated as a passive scalar field. The jet originates from a fully developed turbulent pipe flow and impinges perpendicularly on a smooth solid heated plate placed at two pipe diameters distance from the jet exit section. The values of Reynolds numbers based on the pipe diameter and bulk mean velocity in the pipe are set to Re = 5300 and Re = 10000. Inflow boundary conditions are enforced using a precursor simulation. Heat transfer at the wall is addressed through the Nusselt number distribution and main flow field statistics. At fixed Reynolds number it is shown that the Prandtl number influences the intensity of the Nusselt number at a given radial location, and that the Nusselt number distribution along the plate exhibit similar features at different Prandtl numbers. The characteristic secondary peak in the Nusselt number distribution is found for both Reynolds numbers for Pr = 0.025 and Pr = 0.01. All the simulations presented in this study were performed with the high order spectral element code Nek5000. Generated flow field statistics are available in the open access repository KITOpen.

The study reports direct numerical simulations of a turbulent jet impinging onto smooth and rough surfaces at Reynolds number Re = 10,000 (based on the jet mean bulk velocity and diameter). Surface roughness is included in the simulations using an immersed boundary method. The deflection of the flow after jet impingement generates a radial wall-jet that develops parallel to the mean plate surface. The wall-jet is structured into an inner and an outer layer that, in the limit of infinite local Reynolds number, resemble a turbulent boundary layer and a free-shear flow. The investigation assesses the self-similar character of the mean radial velocity and Reynolds stresses profiles scaled by inner and outer layer units for varying size of the roughness topography. Namely the usual viscous units $$u_\tau$$ u τ and $$\delta _\nu$$ δ ν are used as inner layer scales, while the maximum radial velocity $$u_m$$ u m and its wall-normal location $$z_m$$ z m are used as outer layer scales. It is shown that the self-similarity of the mean radial velocity profiles scaled by outer layer units is marginally affected by the span of roughness topographies investigated, as outer layer velocity and length reference scales do not show a significantly modified behavior when surface roughness is considered. On the other hand, the mean radial velocity profiles scaled by inner layer units show a considerable scatter, as the roughness sub-layer determined by the considered roughness topographies extends up to the outer layer of the wall-jet. Nevertheless, the similar character of the velocity profiles appears to be conserved despite the profound impact of surface roughness.