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An interactive boundary layer modelling methodology for aerodynamic flows

An interactive boundary layer modelling methodology for aerodynamic flows Purpose – The purpose of this paper is to introduce a unique technique to couple the two‐integral boundary layer solutions to a generic inviscid solver in an iterative fashion. Design/methodology/approach – The boundary layer solution is obtained using the two‐integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh‐based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness. Findings – The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code. Originality/value – A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

An interactive boundary layer modelling methodology for aerodynamic flows

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Publisher
Emerald Publishing
Copyright
Copyright © 2013 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/HFF-02-2012-0034
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to introduce a unique technique to couple the two‐integral boundary layer solutions to a generic inviscid solver in an iterative fashion. Design/methodology/approach – The boundary layer solution is obtained using the two‐integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh‐based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness. Findings – The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code. Originality/value – A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Oct 25, 2013

Keywords: Boundary‐layer modelling; Goldstein singularity; Viscid‐inviscid interaction methods

References