TY - THES
AU - DeGiuli, Eric
PY - 2009
TI - Turbulent flow in geophysical channels
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - The problem of turbulent
ow in a rough pipe of arbitrary shape is considered.
The classical Izakson-Millikan argument for a logarithmic velocity
profile is presented, and matched asymptotic expansions are introduced.
Scaled, dimensionless equations are produced and simplified. A simple mixing
length turbulence model is presented, which closes the problem. To calibrate
the model, the mechanical problem is solved in the case of a circular
pipe. Excellent agreement with engineering relations is obtained. The mechanical
problem for a non-circular pipe is posed, and the boundary layer
problem is solved. This leaves unknown the wall stress, which is sought
through approximate methods of solution in the outer region. These are
presented and the approximate solutions thus obtained are compared to full
numerical solutions and data for a square, elliptical, and semi-elliptical pipe.
The approximations are vindicated, but agreement between the numerical
solutions and data is only moderate. Discrepancies are explained in terms
of the neglected secondary
ow.
The thermal problem is posed, with scalings taken for intended application
in glaciology. The problem is solved for a circular pipe. Heat transfer
results are presented and compared with empirical relations. The general
problem for a non-circular pipe is posed, and approximate methods of solution
are motivated, in analogy to those used for the mechanical problem.
These are used to obtain approximate solutions, which are compared with
numerical solutions, to good agreement. Possible applications of these solutions
are discussed.
N2 - The problem of turbulent
ow in a rough pipe of arbitrary shape is considered.
The classical Izakson-Millikan argument for a logarithmic velocity
profile is presented, and matched asymptotic expansions are introduced.
Scaled, dimensionless equations are produced and simplified. A simple mixing
length turbulence model is presented, which closes the problem. To calibrate
the model, the mechanical problem is solved in the case of a circular
pipe. Excellent agreement with engineering relations is obtained. The mechanical
problem for a non-circular pipe is posed, and the boundary layer
problem is solved. This leaves unknown the wall stress, which is sought
through approximate methods of solution in the outer region. These are
presented and the approximate solutions thus obtained are compared to full
numerical solutions and data for a square, elliptical, and semi-elliptical pipe.
The approximations are vindicated, but agreement between the numerical
solutions and data is only moderate. Discrepancies are explained in terms
of the neglected secondary
ow.
The thermal problem is posed, with scalings taken for intended application
in glaciology. The problem is solved for a circular pipe. Heat transfer
results are presented and compared with empirical relations. The general
problem for a non-circular pipe is posed, and approximate methods of solution
are motivated, in analogy to those used for the mechanical problem.
These are used to obtain approximate solutions, which are compared with
numerical solutions, to good agreement. Possible applications of these solutions
are discussed.
UR - https://open.library.ubc.ca/collections/24/items/1.0052882
ER - End of Reference