The Oseen model for internal separated flows

The viscous laminar, separated flowfield downstream of a sudden expansion in a two-dimensional duct is studied. The flow is modelled by the Oseen equations and a solution is sought for the downstream flow given the conditions at the sudden expansion. First, the exact solution to a high-Reynolds-number limit equation suggested by Kumar and Yajnik (1980) is obtained. Next, the solution to the full equations is sought in terms of an eigenfunction-expansion procedure which leads to a nonstandard eigenvalue problem. A detailed study is made of the latter and a number of expansion procedures are considered for the boundary-value problem. Specific calculations of the separated flow are presented for Reynolds number between 1-100,000. It is found that as the Reynolds number approaches the solution of the full equation does indeed agree with the solution of the high-Reynolds-number limit equation. In particular it is found that the length of the recirculating region scales with R as the Reynolds number infinit