Developing flow in a rotating duct
"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

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 centreplane of
a rotating rectangular radial duct from the entrance to a distance
close to the exit of the duct.
The NavierStokes 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 crossstream flow. The verified relationship for the reduced crossstream pressure difference is used in the latter equation to eliminate the pressure term. For calculation of the crossstream 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 crossstream 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 centreplane predominant and secondary velocities and centreplane crossstream 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 pressureside wall as the predominant velocities decrease near the suctionside wall with increasing rotational speed. This phenomenon closely resembles that occurring in the flow within
a centrifugal impeller channel.
Advisor:
School:The University of Hong Kong
School Location:China  Hong Kong SAR
Source Type:Master's Thesis
Keywords:fluid dynamics hydraulics
ISBN:
Date of Publication:01/01/1979