FLOW AROUND A CYLINDER - istiarto

– 5.48 –
� Distribute the surface to get the coordinate of the cell vertices, for example by using a
simple relation (see Fig. 5.24c): � t,ne � 1 4 � t,e � � t,n � � t,1 � � t,2
� �.
The cost of the proposed approach, compared to the present one, is the additional
equation to be solved at each time step. The iterative matrix solver, similar to the existing
matrix solver of the present model but written for a 2D case, can be used to solve Eq. 5.6.
References
Graf, W. H., and Yulistiyanto, B. (1998). “Experiments on flow around a cylinder; the
velocity and vorticity fields.” IAHR, J. Hydr. Res., 36(4), 637-653.
Hurther, D., Lemmin, U., and Arditi, M. (1996). “Using an annular curved array
transducer for bistatic ADVP application.” Rapport Annuel, Laboratoire de
recherches hydrauliques, EPFL, 1996, B.201.1-B.201.19.
Lhermitte, R., and Lemmin, U. (1994). “Open-channel flow and turbulence measurement
by high-resolution Doppler sonar.” J. Atm. Ocean. Tech., 11, 1295-1308.
Versteeg, H. K., and Malalasekera, W. (1995). An Introduction to Computational Fluid
Dynamics: The Finite Volume Method., Longman Group, Essex, England.
Yulistiyanto, B. (1997). Flow around a cylinder installed in a fixed-bed open channel.,
Doctoral Dissertation, No. 1631, EPFL, Lausanne, Switzerland.
Notations
anb [m2 /s] variable coefficients of the surface function equation.
b [m3 /s] source term of the surface function equation.
p
anb [m3 /s/Pa] variable coefficients of the pressure-correction equation.
b p [m3 /s] source term of the pressure-correction equation.
c� [–] k-� model constant.
Dp [m] diameter of cylinder.
d50 [m] mean diameter of sediment.
G [m2 /s3 ] production of turbulent kinetic energy.
g [m/s2 ] gravitational acceleration.
h, h∞ [m] flow depth, uniform-flow depth.
k [m2 /s2 ] turbulent kinetic energy.
ks [m] equivalent roughness.
n [–] normal direction.
p, pc [Pa] pressure, pressure correction.
Q [m3 /s] discharge.
q [m2 /s] discharge per unit width.
Re [–] Reynolds number.
r [m] radial direction.