Ian Sobey

Bio: Ian Sobey is an academic researcher from University of Oxford. The author has contributed to research in topics: Reynolds number & Vortex. The author has an hindex of 19, co-authored 44 publications receiving 1576 citations. Previous affiliations of Ian Sobey include University of Cambridge & University of Bristol.

On flow through furrowed channels. Part 1. Calculated flow patterns

Abstract: Bellhouse et al. (1973) have developed a high-efficiency membrane oxygenator which utilizes pulsatile flow through furrowed channels to achieve high mass transfer rates. We present numerical solutions of the time-dependent two-dimensional Navier–Stokes equations in order to show the structure of the flow. Experimental observations which support this work are presented in a companion paper (Stephanoff, Sobey & Bellhouse 1980). Steady flow through a furrowed channel will separate provided the Reynolds number is sufficiently large. The effect of varying the Reynolds number and the geometric parameters is given and comparisons with solutions calculated using the modern boundary-layer theory of Smith (1976) show excellent agreement. Unsteady flow solutions are given as the physical and geometric parameters are varied. The structure of the flow patterns leads to an explanation of the high efficiency of the devices of Bellhouse.

Bifurcations of two-dimensional channel flows

Abstract: In this paper we study some instabilities and bifurcations of two-dimensional channel flows. We use analytical, numerical and experimental methods. We start by recapitulating some basic results in linear and nonlinear stability and drawing a connection with bifurcation theory. We then examine Jeffery–Hamel flows and discover new results about the stability of such flows. Next we consider two-dimensional indented channels and their symmetric and asymmetric flows. We demonstrate that the unique symmetric flow which exists at small Reynolds number is not stable at larger Reynolds number, there being a pitchfork bifurcation so that two stable asymmetric steady flows occur. At larger Reynolds number we find as many as eight asymmetric stable steady solutions, and infer the existence of another seven unstable solutions. When the Reynolds number is sufficiently large we find time-periodic solutions and deduce the existence of a Hopf bifurcation. These results show a rich and unexpected structure to solutions of the Navier–Stokes equations at Reynolds numbers of less than a few hundred.

Observation of waves during oscillatory channel flow

Abstract: We have observed steady and oscillatory flow through a two-dimensional channel expansion. The experimental results are supported by numerical solutions of the unsteady Navier–Stokes equations. This work was prompted by the recent discovery of vortex waves during steady flow past a moving indentation in a channel wall. Our work deals with both asymmetric channels, in which we show that vortex waves are observed during oscillatory flow with rigid walls, and with symmetric channels, in which a vortex street is observed. We believe that the vortex street is not a vortex wave, but the result of a shear-layer instability.

On flow through furrowed channels. Part 2. Observed flow patterns

Abstract: Observations of flow in furrowed channels support the calculations of part 1 (Sobey 1980). If the mainstream flow is steady there is a critical Reynolds number below which separation does not occur. Above that Reynolds number vortices form and fill the furrow. When the mainstream is oscillatory, the flow may separate during the acceleration to form strong vortices. During the deceleration the vortices grow to fill the furrow and channel. As the mainstream reverses the vortices are ejected from the furrows as the fluid flows between the wall and the vortex. Photographs show that this pattern occurs for sinusoidally varying walls, furrows that are arcs of circles and rectangular hollows.

On the stability of Poiseuille flow of a Bingham fluid

Abstract: The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

Abstract: Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

An analytical study of transport, mixing and chaos in an unsteady vortical flow

Abstract: We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. In the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Abstract: The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Methods Employed for Control of Fouling in MF and UF Membranes: A Comprehensive Review

Abstract: Membrane‐based processes are very susceptible to flux decline due to concentration polarization and fouling problems and the concept of fouling control via process optimization, membrane surface modification, and cleaning have been the focus of research in wastewater and water treatment. MF and UF membranes are utilized in many areas of industry. The main sector of application includes water and wastewater. There has been emphasis on the various methods used to reduce and, where possible, eliminate fouling. This review is a comprehensive insight into the wide range of techniques used in the control of fouling in both MF and UF membranes. It also addresses the amount of research that has gone into the various techniques used and the results achieved after experimental work.