Flow through a rapidly rotating conduit of arbitrary cross-section

Abstract

The problem of flow through rotating channels of almost arbitrary cross-section is considered. It is shown that when the ratio of the Rossby number and the Reynolds number is small (ε = Ro/Re [Lt ] 1) and when the Reynolds number is not too large (Re [Lt ] ε−1): (1) the viscous effects are important only in thin boundary layers along the channel walls; (2) the flow in the interior is geostrophic; and (3) the inertia effects may be neglected everywhere. Solutions for the geostrophic region and the boundary layers are obtained and are combined to give the complete velocity field. Experimental results for a circular conduit are presented which are in good agreement with the theory.

Flow in Rotating Straight Pipes of Circular Cross Section

“…Benton and Boyer [10] have shown that when the rotational speed is higher and the Reynolds number is small, the inertia effects can be neglected everywhere. If the terms in the left hand side of (16) are ignored, then we have in the frictionless core…”

“…A somewhat different approach to the problem has been adopted by Jones and Walters [9], but their results were only of qualitative nature, because the actual secondary flow was replaced by a uniform stream in the plane of cross section of the pipe. Recently Benton and Boyer [10] have analyzed the laminar flow in a rotating straight pipe based on the boundary layer concept, but their theory was confined to a range of high rotational speed and small Reynolds number. Very recently, independently of the authors, Mori and Nakayama [11] have studied the laminar convective heat transfer in a rotating straight pipe by assuming velocity and temperature boundary layers along the pipe wall.…”

Counterflow in rotating superfluid helium

“…The results for the normal fluid solution are qualitatively the same as for classical rotating pipe flow. 19 In such a case, an element of normal fluid executes a counterclockwise, spiral-like motion in the upper half of the channel and a clockwise spiral in the lower half of the channel. The profile of the x component of the normal fluid velocity appears to be parabolic, but is in fact somewhat flattened due to rotation.…”

“…By including the effects on the normal fluid, one obtains the separate pressure and temperature gradient contributions to Vbe. In the absence of vortex curvature, the equations of motion in the rotating coordinate system are dvs Ps--~ = -OSVP +psS VT-2p, f~ x v~ +F P (18) dr,., -P"Vp-ps$ VT-2p,~12xvn +n[V2v,, + 89 v.)]-F p,.,--~-= p where F is the mutual friction force given by (19) and o~ = t7 • Vs + 211. The equations have been written for a point on the axis of rotation, so that the centripetal acceleration is zero.…”

Modeling of Flow Burst, Flow Timing in Lab‐on‐a‐CD Systems and Its Application in Digital Chemical Analysis

“…Because of the existence of the two-body forces, centrifugal flows can become quite complex. Macroscale flows in rotating channels have been investigated experimentally by Benton and Boyer [17], and Ram [18], theoretically by Baura [19] and Benton [20], and numerically by Yang and Kim [21], and Lei and Hsu [22]. Lei and Hsu [22] defined two dimensionless numbers: the rotational Reynolds number, R x (= x a 2 /m, where x, a, and m are the angular velocity of rotation, the characteristic size of the channel and the kinematic viscosity of the fluid, respectively), and the reduced pressure gradient, G (= G * a 3 / q m 2 , where G * is the reduced pressure gradient and q is the Figure 1.…”