Flow along a long thin cylinder

Two different approaches have been used to calculate turblent flow along a long thin culinder where the flow is aligned with the cylinder. A boundary-layer code is used to predict the mean flow for very long cylinders (length to ratio of up to O(106)), with the effects of the turbulence estimated through a turbulence model. Detailed comparison with experimental results shows that the mean properties of the flow are predicted within experimental accuracy. The boundary-layer model predicts that, sufficiently far downstream, the surface shear stress will be (almost) constant. This is consistent with experimental results from long cylinders in the form of sonar arrays. A periodic Navier-Stokes problem is formulated, and solutions generated for the boundary-layer model and experiments. Strongly turbulent flow occurs only near the surface of the cylinder, with relatively weak turbulence over most of the boundary layer. For a thick boundary layer with the boundary-layer thickness much larger than the cylinder radius, the mean flow is effectively constant near the surface, in both temporal and spatial frameworks, while the outer flow continues to develop in time or space. Calculations of the circumferentially averaged surface pressure spectrum sho that, in physical terms, as the radius of the cylinder decreases, the surface noise from the turbulence increases, with the maximum noise at a Reynolds number of O(103). An increase in noise with a decrease in radius (Reynolds number) is consistent with experimental results

High Reynolds number flow in collapsible pipes and channels

Imperial Users onl

Boundary layer flow on a long thin cylinder

The development of the boundary layer along a long thin cylinder aligned with the flow is considered. Numerical solutions are presented and compared with previous asymptotic results. Very near the leading edge the flow is given by the Blasius solution for a flat plate. However, there is soon a significant deviation from Blasius flow, with a thinner boundary layer and higher wall shear stress. Linear normal mode stability of the flow is investigated. It is found that for Reynolds numbers less than a critical value of 1060 the flow is unconditionally stable. Also, axisymmetric modes are only the fourth least stable modes for this problem, with the first three three-dimensional modes all having a lower critical Reynolds number. Further, for Reynolds numbers above the critical value, the flow is unstable only for a finite distance, and returns to stability sufficiently far downstream