Modelling spanwise heterogeneous roughness through a parametric forcing approach

Inhomogeneous rough surfaces in which strips of roughness alternate with smooth-wall strips are known to generate large-scale secondary motions. Those secondary motions are strongest if the strip width is of the order of the half-channel height and they generate a spatial wall shear stress distribution whose mean value can significantly exceed the area-averaged mean value of a homogeneously smooth and rough surface. In the present paper it is shown that a parametric forcing approach (Busse & Sandham, J. Fluid Mech., vol. 712, 2012, pp. 169–202; Forooghi et al., Intl J. Heat Fluid Flow, vol. 71, 2018, pp. 200–209), calibrated with data from turbulent channel flows over homogeneous roughness, can capture the topological features of the secondary motion over protruding and recessed roughness strips (Stroh et al., J. Fluid Mech., vol. 885, 2020, R5). However, the results suggest that the parametric forcing approach roughness model induces a slightly larger wall offset when applied to the present heterogeneous rough-wall conditions. Contrary to roughness-resolving simulations, where a significantly higher resolution is required to capture roughness geometry, the parametric forcing approach can be applied with usual smooth-wall direct numerical simulation resolution resulting in less computationally expensive simulations for the study of localized roughness effects. Such roughness model simulations are employed to systematically investigate the effect of the relative roughness protrusion on the physical mechanism of secondary flow formation and the related drag increase. It is found that strong secondary motions present over spanwise heterogeneous roughness with geometrical height difference generally lead to a drag increase. However, the physical mechanism guiding the secondary flow formation, and the resulting secondary flow topology, is different for protruding roughness strips and recessed roughness strips separated by protruding smooth surface strips.

PIV measurements in a turbulent boundary layer overlying a spanwise heterogeneous roughness

In nature and engineering applications, wall-bounded flow often encounter a heterogeneous surface condition, such as the atmosphere boundary layer at the urban boundary and flow over riveted aircraft surfaces. In a particular scenario, when the surface heterogeneity is predominantly in the spanwise direction of the flow, this roughness heterogeneity can generate secondary flow in cross flow plane which is very different from smooth-wall or homogeneous rough-wall boundary layers.

Flow in a Simulated Turbine Blade Cooling Channel With Spatially Varying Roughness Caused by Additive Manufacturing Orientation

Because of the effects of gravity acting on the melt region created during the laser sintering process, additively manufactured surfaces that are pointed upward have been shown to exhibit roughness characteristics different from those seen on surfaces that point downward. For this investigation, the roughness internal flow tunnel (RIFT) and computational fluid dynamics models were used to investigate flow in channels with different roughness on opposing walls of the channel. Three rough surfaces were employed for the investigation. Two of the surfaces were created using scaled, structured-light scans of the upskin and downskin surfaces of an Inconel 718 component which was created at a 45 deg angle to the printing surface and documented by Snyder et al. (2015). A third rough surface was created for the RIFT investigation using a structured-light scan of a surface similar to the Inconel 718 downskin surface, but a different scaling was used to provide larger roughness elements in the RIFT. The resulting roughness dimensions (Rq/Dh) of the three surfaces used were 0.0064, 0.0156, and 0.0405. The friction coefficients were measured over the range of 10,000 < ReDh < 70,000 for each surface opposed by a smooth wall and opposed by each of the other rough walls. At multiple ReDh values, x-array hot-film anemometry was used to characterize the velocity and turbulence profiles for each roughness combination. The friction factor variations for each rough wall opposed by a smooth wall approached complete turbulence. However, when rough surfaces were opposed, the surfaces did not reach complete turbulence over the Reynolds number range investigated. The results of inner variable analysis demonstrate that the roughness function (ΔU+) becomes independent of the roughness condition of the opposing wall providing evidence that Townsend’s hypothesis holds for the relative roughness values expected for additively manufactured turbine blade cooling passages.