On the Singular Role of Viscosity in the Theory of Thin Airfoils.
Abstract
The general problem of a lifting incompressible viscous thin airfoil is formulated and the viscous counterpart of the classical thin airfoil equation is derived. For any Reynolds number, however large, it is shown that the Cauchy singularity in the kernel is replaced by a logarithmic singularity and the resulting kernel does not have upstream/downstream symmetry. The downstream influence decays algebraically, while upstream influence decays exponentially with distance away from the singularity. A moment solution of the viscous airfoil equation is developed in the limit of high Reynolds number. The classical steady state 'Kutta Condition' is derived in the limit and the Reynolds number correction is found to be of order (1/1n Re), much greater than inviscid boundary layer thickness effects. For Reynolds numbers between one and ten million there is a 20% reduction in the lift curve slope that offsets the increase due to geometric thickness. The correction correlates reasonably well with experiment for a large variety of thin airfoils. The unsteady viscous thin airfoil equation is derived and the singularities of the kernel are discussed in the light of recent experimental work on oscillating airfoils.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1977
- Accession Number
- ADA069067
Entities
People
- John E. Yates