Second-Order Theory on Wall Effect in Cavitating Flow past a Thin Jet-Flapped foil

Abstract

This paper presents a short survey of the more analytical development of the second-order theory which was formulated in the previous paper (Ref. 1). The method of matched asymptotic expansions is applied to the integro-differential equation for the case of the small jet momentum coefficient C_j, which was previously derived in the first-order theory on a twodimensional supercavitating jet-flapped foil between two parallel solid walls. The lift slopes are found as series expansions in powers of δ and logδ valid for δ≤1, where the small parameter δ is proportional to C_j. Expressions of the lift slopes which are found to the third order expansions for δ agree closely with the numerical results obtained by earlier study (Ref.1), even near δ=1.