Upward Normal Drag Prediction in Distributed Element Roughness Modeling

Distributed Element Roughness Modeling (DERM) is a volumetric surface roughness model-

ing approach, that provides better generality than equivalent sand grain height (ks) based Reynolds-

Averaged Navier-Stokes (RANS) modeling, while retaining the cost-effectiveness of RANS. DERM

models are based on the Double Averaged Navier-Stokes (DANS) equations. To ensure the accu-

racy of the DERM model, it is crucial to consistently model the interfacial drag term, spatial

dispersion term, and Reynolds Stress term, which emerge in the DANS equation after volumet-

ric and time averaging of the Navier-Stokes equations. Traditionally, the drag term in DANS has

been modeled using a convective drag law, which only accounts for pressure/form drag. However,

this approach has limitations when capturing drag in flows over high-packing density arrays. The

streamwise drag force from the roughness element can be partitioned into pressure force on the

windward and leeward faces of the roughness element (τxx), the viscous drag on the side faces of

the roughness element (τxy), and the viscous drag on the top faces of the roughness element (τxz ).

The first two components can be combined into flow sheltering drag (fP ) and the remaining com-

ponent, here termed upward normal drag (fT ), can be modeled separately. In this work, we develop

an upward normal drag model by considering DNS data of flow over cube arrays, sinusoidal rough

surfaces, and quasi-random additively manufactured rough surfaces. We calibrate this viscous drag

based on several geometric roughness morphology statistics. Significant improvements in predic-

tive capability are demonstrated for all three classes of roughness compared to other methods that

have appeared.