The Axi-symmetric Laminar Flow in an Arbitrarily Shaped Narrow Gap : 1st Report, Theoretical Analysis for the Inlet Region

抄録

A theoretical analysis is presented for the inlet region of the laminar, meridional flow in an arbitrarily shaped narrow gap between two axi-symmetrically formed walls. A series expansion method is used and the most general form of the exact solutions of the boundary layer equations is obtained. As an example, numerical calculations have been made for the radial flow in a gap formed by two parallel discs, by which the following important conclusions are confirmed. Separation of flow from the wall occurs, the separation point moving in downstream direction as the Reynolds number decreases. When the Reynolds number further decreases, reaching a value below a certain small finite value, separation does not occur. A result which is very important from the theoretical standpoint is that the separation point calculated in this work is not a mathematical singularity. This is the first theoretical example verifying actually the existance of a non-singular separation, which has already been predicted by S. Goldstein, K. Stewartson and others.