A Distributed Element Roughness Model Based on the Double Averaged Navier-Stokes Equations
Open Access
- Author:
- Altland, Samuel
- Graduate Program:
- Mechanical Engineering (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 11, 2022
- Committee Members:
- Sven Schmitz, Outside Unit & Field Member
Robert Kunz, Chair & Dissertation Advisor
Stephen Lynch, Major Field Member
Xiang Yang, Major Field Member
Daniel Haworth, Professor in Charge/Director of Graduate Studies - Keywords:
- DERM
Surface Roughness
CFD
Roughness Modeling - Abstract:
- Surface roughness presents a fundamental challenge across a wide array of engineering applications. For example, dynamic losses and heat transfer for gas turbine blade cooling systems are directly affected by surface roughness. In these systems, thousands of individual passages of varying configuration and roughness morphology can be present. The combination of both large-scale deterministic surface features, as well as the smaller more random elements due to manufacturing gives rise to macroscopic performance characteristics, such augmented drag and heat transfer, which fall well outside of our ability to predict using classical correlations. These systems are even challenging to assess using Computational Fluid Dynamics (CFD). Even RANS modeling requires sublayer resolution, due to the comparatively low Reynolds numbers present and the small geometric scales of the explicitly resolved deterministic roughness elements, such as turbulators or fins. This leads to mesh requirements that would be impractical for most designers. Using surface parameterization methods, such as sand-grain roughness (SGR) models within the context of CFD is considerably easier to implement and requires far less resolution. However, these methods suffer from many deficiencies, such as ambiguity in determining the appropriate representative roughness length scale, and their limitations at correctly predicting both friction and heat transfer simultaneously. In order to leverage CFD as an engineering design tool, a Distributed Element Roughness Method (DERM) is proposed as a compromise between direct resolution and surface parameterization methods. In this approach, which draws on Eulerian two-fluid modeling, and is akin to Immersed Boundary Methods, the detailed geometry of roughness elements is not resolved, but rather the morphology is represented by volume fraction and volume fraction gradient distributions. Attendant forces due to drag are imparted on the flow to simulate the presence of the unresolved roughness field. In this work, a DERM model based on the Double Averaged Navier-Stokes (DANS) equations is developed. This formulation presents a complete and unique treatment of the three essential modeling components of DERM. For closure of the roughness induced drag sink, this work proposes the use of a spatially varying sectional drag coefficient which is determined by invoking so called "sheltering theory". 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 detailed calibration for every morphology. In addition, this work is the first to decouple the viscous drag as the result of wall normal facing surfaces in the context of DERM. To accommodate dispersive stresses, this work demonstrates the utility of a data-based approach, and a feedforward neural network is employed to model the DERM dispersion. Finally, this work proposes a new treatment of the spatially averaged Reynolds stresses below the height of the roughness occupied layer in order to better approximate a wider array of roughness topologies than legacy models. As part of this work, roughness resolving DNS and RANS simulations were conducted on a host of different academic roughness shapes, in order to provide calibration data for DERM, and to provide insight into the significance of the various spatially fluctuating quantities that are required for model closure. Resolved CFD statistics are interpreted and applied to validate the DERM model for each of the morphologies studied. Specifically, this work interrogates additively manufactured surfaces, sinusoidal rough surfaces, and cube array roughness. Arrays of cubes are of particular interest in this work, as they exhibit special limit behaviors, a unique feature that most DERM models are not equipped to handle.