Application of a Distributed Element Roughness Model to Additively Manufactured Internal Cooling Channels

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Abstract 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, heat exchangers), thousands of individual passages of varying configuration and roughness morphology can be present. In recent years, additive manufacturing (AM) has further expanded the design space, but can give rise to large-scale roughness features, whose sizes are comparable to the channel height. The range of roughness length scales in these systems makes CFD of the resolved rough surfaces impractical at a design level. Alternately, volumetric roughness modeling approaches, such as distributed element roughness models (DERM) can be leveraged, as they have computational costs orders of magnitude lower. In this work, a DERM model based on the Double Averaged Navier-Stokes (DANS) equations is presented and applied to additively manufactured rough channels, representative of gas turbine blade cooling passages. Unique to this formulation of DERM is the specific treatment of the DERM drag coefficient and the spatially averaged Reynolds stresses. This generalized formulation of the drag coefficient allows for improved model accuracy across a wider array of potential roughness fields, without having to rely on calibration for each morphology. A novel two-layer approach to modeling the spatially averaged Reynolds stress is also proposed. Three different AM rough surfaces documented by McClain et al. [1] were configured opposite smooth walls as well as each other to create a total of six channel configurations. Across the six cases, th roughness trough to peak size ranges from 0.15δ to 0.66δ, where δ is the channel half-width, and the roughness Reynolds number ranges from Rek = 60 to Rek = 300. DERM predictions for spatially and temporally averaged mean flow quantities are compared to previously reported DNS results. Specifically, we observe good agreement in the mean velocity profiles, stress balances and drag partitions across the case matrix. While DERM models are typically calibrated to specific deterministic roughness shape families at comparatively small roughness Reynolds numbers, these results demonstrate a wider range of applicability for the present, more generalized formulation. It is demonstrated that the proposed model can accommodate random roughness of large scale, typical of AM.