Developing flow in a rotating duct

by Hui, Tze-mei

(Uncorrected OCR) Abstract of thesis entitled

"Developing flow i.n a rotati.ng duct"

submi tted by HITI Tze Mei

for the degree of ~ter of Philosophy

at the University of Hong Kong in June, 1919

Incompressible developing flow in a rotating rectangular

radial duct is investigated. Experimental measurements of the crossstream reduced pressure difference .~ P between two points Dps apart

of the water flow through a rotating duct of 4 inch width x 1 inch height and 16 inch length were made at selected distances along the duct, with the angular velocity ~ varied from 6.07 rad/s to 11.5 rad/s.

Eased on the hydraulic diameter ~ and the bulk mean velocity U, the rotation number Ro = tu ~ ranged from 1.44 to 4.61 and the Reynolds number Re = P uDhl..u. ranged from 3,400 to 1,400. From the experimental

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results? it was verified that 6. P = 2 rw U Dps' This relationship is

equivalent to that derived theoretically by Moore (1969) for A P

between the side walls of the duct. The relationship is assumed to

be applicable for values of the variables outside the test range, and

is used in the development of a mathematical model for the prediction

of the incompressible turbulent developing flow in the centre-plane of

a rotating rectangular radial duct from the entrance to a distance

close to the exit of the duct.

The Navier-Stokes equations are simplified with the following

assumptions: the mean flow is steady; there is a predominant direction

of flow which is along the rotating duct, when viewed from a rota.ting

ooordinate system; uniform eddy viscosity as a function of the Roand

the Re,fcrmulated from Ito and Nanbu's (1971) experimental data on

pipe flow, is used to close the equations of motion; and, the effect

of the wall layers is approximated by slip velocities. The resulting

mathematical equations are a parabolic partial differential equation

ii

for the predominant flow along the duct, and a hyperbolic partial differential equation for the secondary cross-stream flow. The verified relationship for the reduced cross-stream pressure difference is used in the latter equation to eliminate the pressure term. For calculation of the cross-stream velocities, the viscous effects are taken into account using a postulated accelerated bulk mean velocity. The equation of continuity is also required for the solution. With a uniform velocity profile and a linear cross-stream reduced pressure distribution at the entrance to the duct, the governing equations

are solved by a finite difference marching scheme. The method is not applicable if flow separation occurs.

Predicted centre-plane predominant and secondary velocities and centre-plane cross-stream reduced pressure distributions were obtained for Wagner and Velkoff's (1972) rotating air duct and compared with their published experimental data for rotation numbers Ro from 0.045 to O.l~ and a Reynolds number He of 66,000. Their corresponding angular velocity range was 10.5 rad/s to 31.4 rad/s. General agreement in the predominant velocities, the secondary velocities, and the reduced pressure distributions at a representative section in the second half of their duct was obtained. Numerical calculations with the prediction scheme indicate that the predominant velocity profiles are skewed towards the pressure-side wall as the predominant velocities decrease near the suction-side wall with increasing rotational speed. This phenomenon closely resembles that occurring in the flow within

a centrifugal impeller channel.