Abstract
The laminar flow in channels and tubes with compliant walls is destabilised by a variety of mechanisms, especially at moderate and low Reynolds number. There have been two types of classification schemes used for these instabilities. The first is the classification, adopted from boundary layer flow past compliant panels, into the Tollmien-Schlichting modes (Class A), the traveling-wave flutter (Class B) and the static divergence (Class C). The second is based on the Reynolds number regime, the flow structure, the scaling of the critical Reynolds number (ρVR/μ) with the dimensionless parameter Σ = (ρGR 2 /μ2 ), and the mechanism that destabilises the flow. Here, p and μ are the fluid density and viscosity, G is the shear modulus of the wall material, R is the cross-stream length scale and V is the maximum velocity. Linear stability analyses based on both of these classification schemes are discussed, with focus on flows which do not admit Tollmien-Schlichting waves, such as the Couette flow in a channel and the Poiseuille flow in a tube. The weakly non-linear studies carried out so far are briefly summarised.
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Kumaran, V. (2003). Hydrodynamic Stability of Flow Through Compliant Channels and Tubes. In: Carpenter, P.W., Pedley, T.J. (eds) Flow Past Highly Compliant Boundaries and in Collapsible Tubes. Fluid Mechanics and Its Applications, vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0415-1_5
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DOI: https://doi.org/10.1007/978-94-017-0415-1_5
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