0
Research Papers

# A Comparison of Approximate Versus Exact Geometrical Representations of Roughness for CFD Calculations of $cf$ and St

[+] Author and Article Information
J. P. Bons

Department of Mechanical Engineering,  Brigham Young University, Provo, UT 84602-4201jbons@byu.edu

S. T. McClain

Department of Mechanical Engineering,  University of Alabama-Birmingham, Birmingham, AL 35294-4461smcclain@eng.uab.edu

Z. J. Wang

Department of Aerospace Engineering,  Iowa State University, Ames, IA 50011-2271zjw@iastate.edu

X. Chi

Department of Aerospace Engineering,  Iowa State University, Ames, IA 50011-2271chixingk@egr.msu.edu

T. I. Shih

Department of Aerospace Engineering,  Iowa State University, Ames, IA 50011-2271tomshih@iastate.edu

J. Turbomach 130(2), 021024 (Mar 25, 2008) (10 pages) doi:10.1115/1.2752190 History: Received November 30, 2005; Revised March 16, 2006; Published March 25, 2008

## Abstract

Skin friction $(cf)$ and heat transfer (St) predictions were made for a turbulent boundary layer over randomly rough surfaces at Reynolds number of $1×106$. The rough surfaces are scaled models of actual gas turbine blade surfaces that have experienced degradation after service. Two different approximations are used to characterize the roughness in the computational model: the discrete element model and full 3D discretization of the surface. The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection on the flat part of the surface and the convection from each of the roughness elements. Correlations are used to model the roughness element drag and heat transfer, thus avoiding the complexity of gridding the irregular rough surface. The discrete element roughness representation was incorporated into a two-dimensional, finite difference boundary layer code with a mixing length turbulence model. The second prediction method employs a viscous adaptive Cartesian grid approach to fully resolve the three-dimensional roughness geometry. This significantly reduces the grid requirement compared to a structured grid. The flow prediction is made using a finite-volume Navier-Stokes solver capable of handling arbitrary grids with the Spalart-Allmaras $(S‐A)$ turbulence model. Comparisons are made to experimentally measured values of $cf$ and St for two unique roughness characterizations. The two methods predict $cf$ to within $±8%$ and St within $±17%$, the RANS code yielding slightly better agreement. In both cases, agreement with the experimental data is less favorable for the surface with larger roughness features. The RANS simulation requires a two to three order of magnitude increase in computational time compared to the DEM method and is not as readily adapted to a wide variety of roughness characterizations. The RANS simulation is capable of analyzing surfaces composed primarily of roughness valleys (rather than peaks), a feature that DEM does not have in its present formulation. Several basic assumptions employed by the discrete element model are evaluated using the 3D RANS flow predictions, namely: establishment of the midheight for application of the smooth wall boundary condition; $cD$ and Nu relations employed for roughness elements; and flow three dimensionality over and around roughness elements.

<>

## Figures

Figure 1

Schematic of flat plate wind tunnel at the Air Force Research Laboratory (shown for St measurement)

Figure 2

The discrete-element roughness model control volume schematic

Figure 3

Cutting planes showing the viscous adaptive Cartesian grids for the: (a) fuel deposit; and (b) erosion surfaces. Roughness regions are 240mm×120mm and 240mm×60mm, respectively. The two circles in (a) denote roughness peaks referred to in subsequent discussion.

Figure 4

Surface grid on the erosion surface showing grid refinement near leading edge

Figure 5

Comparison of % change in cf and St from experiment and computation: (3D RANS data from fine grid only)

Figure 6

Drag and heat flux distributions with elevation for isolated peaks on deposit surface. Both DEM and 3D RANS results shown: (a) Peak 1 and (b) Peak 2.

Figure 7

Flow streamlines around Peak 2 on deposit surface (from 3D RANS simulation): (a) top view—flow is left to right; and (b) view from upstream

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections