Channel Flow Past A Near-Wall Body

• Published in: Quarterly journal of mechanics and applied mathematics 2019-08, Vol.72 (3), p.359-385
• Main Authors: Smith, F T, Servini, P
• Format: Article
• Language: English
• ISSN: 0033-5614; 1464-3855
• DOI: 10.1093/qjmam/hbz009

Near-wall behaviour arising when a finite sized body moves in a channel flow is investigated for high flow rates. This is over the interactive-flow length scale that admits considerable upstream influence. The focus is first on quasi-steady two-dimensional flow past a thin body in the outer reaches of one of the viscous wall layers. The jump conditions near the front of the body play an important part in the whole solution which involves an unusual multi-structured flow due to the presence of the body: flows above, below, ahead of and behind the body interact fully. Analytical solutions are presented and the repercussions for shorter and longer bodies are then examined. Second, implications are followed through for the movement of a free body in a dynamic fluid–body interaction. Particular key findings are that instability persists for all body lengths, the growth rate decreases like the $1/4$ power of distance as the body approaches the wall, and lift production on the body is dominated by high pressures from an unexpected flow region emerging on the front of the body.