A Distributed Element Roughness Model for Deterministic Roughness Morphologies using the Double Averaged Navier Stokes Equations

Design for cooling effectiveness in internal flow systems relies on accurate models for dynamic losses and heat transfer. In these systems (e.g., gas turbine blades, intercoolers), thousands of individual passages of varying configuration and roughness morphology can be present, and this can render roughness-element resolved CFD methods impractical. Alternatively, a volumetric roughness modeling approach, such as distributed element roughness modeling (DERM) has a computational cost orders of magnitude lower.

In this approach, which draws on elements of Eulerian two-fluid modeling, the detailed geometry of the roughness is not resolved, and the surface is represented by volume fraction and volume fraction gradient distributions. Attendant forces due to interfacial drag and spatial dispersion are imparted on the flow to represent the roughness field.  

In this work, a DERM model based on the Double Averaged Navier-Stokes (DANS) equations is presented. Unique to this formulation of DERM is the specific treatment of the spatially averaged Reynolds stresses, the treatment of wall normal facing surfaces, and the spatially varying DERM sectional drag coefficient. Comparisons between this DERM model and resolved CFD are shown for a suite of academic roughness configurations.