The Oseen model for internal separated flows

✍ Scribed by S. V. Ramakrishnan; P. N. Shankar

• Book ID: 104617369
• Publisher: Springer
• Year: 1982
• Tongue: English
• Weight: 955 KB
• Volume: 16
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00037734

✦ Synopsis

The flow field studied in this paper is the viscous laminar, separated flow downstream of a sudden expansion in a two-dimensional duct. 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-Reynoldsnumber limit equation suggested by Kumar and Yajnik [6 ] is obtained. Next, the solution to the full equations is sought in terms of an eigenfunction-expansion procedure which leads to a non-standard eigenvalue problem. A detailed study is made of the latter and a number of expansion procedures are considered for the boundaryvalue problem. Specific calculations of the separated flow are presented for Reynolds numbers R = 10 n, n = 0-5. It is found that as R --, ** 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 x r scales with R as R -* ~.