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.
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.
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.
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.
The authors are grateful to an anonymous referee for pointing out a simplification to the method. This work was supported by the Council for Scientific and Industrial Research (CSIR) on Thematic Type A Grant No. TA-2009-013.
Smith, L., Oxtoby, O., Malan, A. and Meyer, J. (2013), "An interactive boundary layer modelling methodology for aerodynamic flows", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 8, pp. 1373-1392. https://doi.org/10.1108/HFF-02-2012-0034
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