Abstract
Surface roughness in turbulent channel flow is effectively modelled using a modified version of the Parametric Forcing Approach introduced by Busse and Sandham (2012). In this modified approach, the model functions are determined based on the surface geometry and two model constants, whose value can be fine tuned. In addition to a quadratic forcing term, accounting for the effect of form drag due to roughness, a linear forcing term, analogous to the Darcy term in the context of porous media, is employed in order to represent the viscous drag. Comparison of the results with full-geometry resolved Direct Numerical Simulation (DNS) data for the case of dense roughness (frontal solidity ≅0.4) shows a satisfactory prediction of mean velocity profile, and hence the friction factor, by the model. The model is found to be able to reproduce the trends of friction factor with morphological properties of surface such as skewness of the surface height probability density function and coefficient of variation of the peak heights.
Highlights
Study of turbulent flows over rough surfaces finds application in several engineering – e.g. turbomachinery, marine transportation and ice accretion on aircrafts – and geophysical – e.g. wind flow over plant and urban canopies – problems
It can be shown that an increase in the roughness function ΔU+ corresponds to an increase in friction factor (Jimenez, 2004; Flack and Schultz, 2010)
The present work aims at a modified version of Parametric Forcing Approach (PFA), in which – apart from the tunable scalar model constants – the forcing amplitude can be determined a priori for a desired roughness geometry, so that the mean flow profile and, the ‘friction factor’ can be predicted correctly
Summary
Study of turbulent flows over rough surfaces finds application in several engineering – e.g. turbomachinery, marine transportation and ice accretion on aircrafts – and geophysical – e.g. wind flow over plant and urban canopies – problems. A way to avoid such difficulties is using a modified version of the Navier–Stokes equation near the wall, in which roughness is ‘effectively’ modelled These models, clearly, do not process the degree of fidelity that full-surface resolved DNS provides, require careful verification. Cui et al (2003) suggested an approach in which an arbitrary rough surface is decomposed into two parts: resolved scale and sub-grid scale roughness, for the former immersed boundary method and for the latter a random body-force model is used. The present work aims at a modified version of PFA, in which – apart from the tunable scalar model constants – the forcing amplitude can be determined a priori for a desired roughness geometry, so that the mean flow profile and, the ‘friction factor’ can be predicted correctly. Full-geometry resolved DNS data from Forooghi et al (2017) is used to evaluate the model and its capability to follow the physical trends
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