Edward R. Benton

Bio: Edward R. Benton is an academic researcher from National Center for Atmospheric Research. The author has contributed to research in topics: Boundary layer & Boundary layer thickness. The author has an hindex of 5, co-authored 7 publications receiving 394 citations.

On the flow due to a rotating disk

Abstract: The von Karman (1921) rotating disk problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution. Exact representations of the non-steady velocity field and pressure are given by suitable power-series expansions in the angle of rotation, Ωt, with coefficients that are functions of a similarity variable. The first four equations for velocity coefficient functions are solved exactly in closed form, and the next six by numerical integration. This gives four terms in the series for the primary flow and three terms in each series for the secondary flow.The results indicate that the asymptotic steady state is approached after about 2 radians of the disk's motion and that it can be approximately obtained from the initial-value, time-dependent analysis. Furthermore, the non-steady flow has three phases, the first two of which are accurately and fully described with the terms computed. During the first-half radian (phase 1), the velocity field is essentially similar in time, with boundary-layer thickening the only significant effect. For 0·5 [lsim ] Ωt [lsim ] 1·5 (phase 2), boundary-layer growth continues at a slower rate, but simultaneously the velocity profiles adjust towards the shape of the ultimate steady-state profiles. At about Ωt = 1·5, some flow quantities overshoot the steady-state values by small amounts. In analogy with the ‘Greenspan-Howard problem’ (1963) it is believed that the third phase (Ωt > 1·5) consists of a small amplitude decaying oscillation about the steady-state solution.

A composite Ekman boundary layer problem

Abstract: The steady, axially symmetric, viscous, incompressible flow induced by an infinite rotating disk in the presence of a stationary coaxial disk is studied numerically for the complete laminar range of a Taylor number, R . Emphasis is placed on qualitative interpretation of the numerical solutions. The asymptotic state for large R is shown to consist of two well-known special Ekman boundary layers on the disks which are linked by a Taylor column, with Ekman layer suction into one layer just balanced by axial outflow from the other layer. DOI: 10.1111/j.2153-3490.1968.tb00409.x

On the flow due to a rotating disk

Abstract: The von Karman (1921) rotating disk problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution. Exact representations of the non-steady velocity field and pressure are given by suitable power-series expansions in the angle of rotation, Ωt, with coefficients that are functions of a similarity variable. The first four equations for velocity coefficient functions are solved exactly in closed form, and the next six by numerical integration. This gives four terms in the series for the primary flow and three terms in each series for the secondary flow.The results indicate that the asymptotic steady state is approached after about 2 radians of the disk's motion and that it can be approximately obtained from the initial-value, time-dependent analysis. Furthermore, the non-steady flow has three phases, the first two of which are accurately and fully described with the terms computed. During the first-half radian (phase 1), the velocity field is essentially similar in time, with boundary-layer thickening the only significant effect. For 0·5 [lsim ] Ωt [lsim ] 1·5 (phase 2), boundary-layer growth continues at a slower rate, but simultaneously the velocity profiles adjust towards the shape of the ultimate steady-state profiles. At about Ωt = 1·5, some flow quantities overshoot the steady-state values by small amounts. In analogy with the ‘Greenspan-Howard problem’ (1963) it is believed that the third phase (Ωt > 1·5) consists of a small amplitude decaying oscillation about the steady-state solution.

Laminar boundary layer on an impulsively started rotating sphere

Abstract: The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time The calculations have been carried out on the assumption that the Reynolds number is very large The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers