Martin D. Griffith

Steady inlet flow in stenotic geometries: convective and absolute instabilities

Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing.

Wake behaviour and instability of flow through a partially blocked channel

The two-dimensional flow through a constricted channel is studied. A semi-circular bump is located on one side of the channel and the extent of blockage is varied by adjusting the radius of the bump. The blockage is varied between 0.05 and 0.9 of the channel width and the upstream Reynolds number between 25 and 3000. The geometry presents a simplified blockage specified by a single parameter, serving as a starting point for investigations of other more complex blockage geometries. For blockage ratios in excess of 0.4, the variation of reattachment length with Reynolds number collapses to within approximately 15 %, while at lower ratios the behaviour differs. For the constrained two-dimensional flow, various phenomena are identified, such as multiple mini-recirculations contained within the main recirculation bubble and vortex shedding at higher Reynolds numbers. The stability of the flow to three-dimensional perturbations is analysed, revealing a transition to a three-dimensional state at a critical Reynolds number which decreases with higher blockage ratios. Separation lengths and the onset and structure of three-dimensional instability observed from the geometry of blockage ratio 0.5 resemble results taken from backward-facing step investigations. The question of the underlying mechanism behind the instability being either centrifugal or elliptic in nature and operating within the initial recirculation zone is analytically tested.

Pulsatile flow in stenotic geometries: flow behaviour and stability

Pulsatile inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted pulsatile flows. The Reynolds number is varied between 50 and 700 and the stenosis degree by area between 0.20 and 0.90. Numerically, a spectral element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. For low Reynolds numbers, the flow is characterized by a vortex ring which forms directly downstream of the stenosis, for which the strength and downstream propagation velocity vary with the stenosis degree. Linear stability analysis is performed on the simulated axisymmetric base flows, revealing a range of absolute instability modes. Comparisons are drawn between the numerical linear stability analysis and the observed instability in the experimental flows. The observed flows are less stable than the numerical analysis predicts, with convective shear layer instability present in the experimental flows. Evidence is found of Kelvin–Helmholtz-type shear layer roll-ups; nonetheless, the possibility of the numerically predicted absolute instability modes acting in the experimental flow is left open.

Convective instability in steady stenotic flow: optimal transient growth and experimental observation

An optimal transient growth analysis is compared with experimental observation for the steady flow through an abrupt, axisymmetric stenosis of varying stenosis degree. Across the stenosis range, a localized sinuous convective shear-layer instability type is predicted to dominate. A comparison of the shape and development of the optimal modes is made with experimental dye visualizations. The presence of the same sinuous-type disturbance immediately upstream of the highly chaotic region observed in the experimental flow is consistent with the optimal growth predictions. This, together with the fact that the flow is unstable globally only at much higher Reynolds numbers, suggests bypass transition.

Computational Fluid Dynamics Study of the Effect of Leg Position on Cyclist Aerodynamic Drag

An experimental and numerical analysis of cycling aerodynamics is presented. The cyclist is modeled experimentally by a mannequin at static crank angle; numerically, the cyclist is modeled using a computer aided design (CAD) reproduction of the geometry. Wind tunnel observation of the flow reveals a large variation of drag force and associated downstream flow structure with crank angle; at a crank angle of 15 deg, where the two thighs of the rider are aligned, a minimum in drag is observed. At a crank angle of 75 deg, where one leg is at full extension and the other is raised close to the torso, a maximum in drag is observed. Simulation of the flow using computational fluid dynamics (CFD) reproduces the observed variation of drag with crank angle, but underpredicts the experimental drag measurements by approximately 15%, probably at least partially due to simplification of the geometry of the cyclist and bicycle. Inspection of the wake flow for the two sets of results reveals a good match in the downstream flow structure. Numerical simulation also reveals the transient nature of the entire flow field in greater detail. In particular, it shows how the flow separates from the body of the cyclist, which can be related to changes in the overall drag.