Direct numerical simulation of open-channel flow over smooth-to-rough and rough-to-smooth step changes

Abstract

Direct numerical simulations (DNS) are reported for open-channel flow over streamwise-alternating patches of smooth and fully rough walls. The rough patch is a three-dimensional sinusoidal surface. Owing to the streamwise periodicity, the flow configuration consists of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 437 over the smooth patch to 704 over the rough patch. Through the fully resolved DNS dataset it is possible to explore many detailed aspects of this flow. Two aspects motivate this work. The first one is the equilibrium assumption that has been widely used in both experiments and computations. However, it is not clear where this assumption is valid. The detailed DNS data reveal a significant departure from equilibrium, in particular over the smooth patch. Over this patch, the mean velocity is recovered up to the beginning of the log layer after a fetch of five times the channel height. However, over the rough patch, the same recovery level is reached after a fetch of two times the channel height. This conclusion is arrived at by assuming that an error of up to 5 % is acceptable and the log layer, classically, starts from 30 wall units above the wall. The second aspect is the reported internal boundary-layer (IBL) growth rates in the literature, which are inconsistent with each other. This is conjectured to be partly caused by the diverse IBL definitions. Five common definitions are applied for the same DNS dataset. The resulting IBL thicknesses are different by 100 %, and their apparent power-law exponents are different by 50 %. The IBL concept, as a layer within which the flow feels the surface underneath, is taken as the basis to search for the proper definition. The definition based on the logarithmic slope of the velocity profile, as proposed by Elliot (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), yields better consistency with this concept based on turbulence characteristics.

Direct numerical simulation of turbulent flow through a ribbed square duct

“…2006; Scotti 2006; Bhaganagar 2008; Pinelli etal. 2010 a ; Lee, Sung & Krogstad 2011; Yuan& Piomelli 2014; Bhaganagar & Chau 2015; Rouhi, Chung & Hutchins 2019). As two popular methods, both BFM and IBM have advantages and disadvantages.…”

“…The IBM method started with Peskin (1972) and has been significantly developed since (Mittal & Iaccarino 2005;Griffith & Patankar 2020). The IBM method has been successfully applied to DNS and LES of turbulent flows over regular and irregular shaped roughness elements (Leonardi et al 2003;Orlandi et al 2006;Scotti 2006;Bhaganagar 2008;Pinelli et al 2010a;Lee, Sung & Krogstad 2011;Yuan & Piomelli 2014;Bhaganagar & Chau 2015;Rouhi, Chung & Hutchins 2019). As two popular methods, both BFM and IBM have advantages and disadvantages.…”

Recovery of wall-shear stress to equilibrium flow conditions after a rough-to-smooth step change in turbulent boundary layers

“…3.1), which is located below z + < 0.5 for the present case. Further details on the DNS database can be found in Rouhi et al (2019). Figure 6(b) presents the inner-normalised streamwise mean velocity U + from the DNS database at various locations downstream of the rough-to-smooth transition.…”

Roughness and Reynolds Number Effects on the Flow Past a Rough-to-Smooth Step Change

“…3a,d ) penetrates down to the viscous sublayer. We also quantify δ i using Elliott's [9] definition which we previously found to be more consistent with the IBL concept [8]. Considering the roughness origin effect (Fig.…”

“…The domain length is 12h, equally divided between the rough and smooth patches. With this length, the flow within the IBL is almost insensitive to the patch length and domain periodicity [8]. The flow was driven by the global Re τo ≡ u τo h/ν = 590 based on u τo averaged over time and the entire bottom surface.…”