Application of Asymptotic Expansion Procedures to Low Reynolds Number Flows about Infinite Bodies

Citation

Hunter, Herbert Erwin (1960) Application of Asymptotic Expansion Procedures to Low Reynolds Number Flows about Infinite Bodies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5PBX-0J36. https://resolver.caltech.edu/CaltechETD:etd-12092005-134820

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Several limiting cases for viscous incompressible flow are considered for two examples. The first example considered is that of the flow past an expanding infinite cylinder at an angle of attack. The time dependence of the radius of the cylinder is given by the power law R = [...]. The second example considered is the flow past a semi-infinite power law body of revolution (i. e. R = [...]) at zero angle of attack. Both examples are considered for the limiting case of small Reynolds number. The Reynolds number is based on a characteristic length obtained from the parameters in the expression for the radius. The second example is also considered for the limiting case of the flow far down stream. Asymptotic expansions of the solution valid for the limiting cases considered (i. e, low Reynolds number or flow far down stream) are obtained by applying singular perturbation procedures. These expansions are obtained for 0 <= n < 1 for the first example and for 0 <= n <= 1/2 for the second example. For the second example the terms in the low Reynolds number expansion are not obtained in closed form, except for n = 1/2. For n < 1/2 the low Reynolds number expansion of the Navier-Stokes equations is expressed in terms of the solution of the corresponding Stokes flow problem. The expansions obtained for the flow far down stream on the power law body of revolution have the character of a very viscous flow although they are valid for any fixed Reynolds number.

Thesis Files