Unsteady Forces on a Slender Body of Revolution in a Tube. (Effect of Tube and/or Body Deformation).

The problem under consideration is the axisymmetric unsteady potential flow past a slender body of revolution capable of arbitrary radial deformations in a tube which also performs wavy deformation, where the mean radius of the tube wall is the same order as that of the body. In the analysis, the Stokes stream function is introduced and the method of matched asymptotic expansions is used. The flow is examined for two different time parameters. As a result, unsteady contributions to the flow generated by a deformable slender body and tube are obtained up to the second-order approximation, and effects of various parameters on the axial force coefficients are examined in two cases.