FLOW AROUND A CYLINDER - istiarto

– 5.45 –
and surface profiles (see Fig. 5.10 to Fig. 5.14 and Fig. 5.16 to Fig. 5.19). In the two flow
cases, the comparisons show satisfactory agreements. It was found, however, that the
method of locating the surface boundary opted in the model became less accurate in
regions of strong pressure gradient. In the scoured channel bed simulation, comparison
was also done to the turbulent kinetic energy (see Fig. 5.20). It was shown that reasonable
results were obtained, showing a comparable pattern of the distribution of turbulent
kinetic energy obtained from the simulation and the measurements.
Conclusively, the numerical model developed in the present work can be considered as
being applicable and reliable to simulate flow around a cylinder. It can also be stipulated
that this model would also be applicable to other type of flow, such as flows in a channel
bend and in a compound channel.
5.8 Recommendations for future works
Judging that the major problem encountered in the simulation is the computation of the
surface boundary, below is a proposition to adopt another method that is feasible to be
incorporated in the present model.
The approach used in the present model to locate the surface boundary is by imposing a
known (zero) flux across the boundary. From the pressure computation, the SIMPLE
algorithm, non-zero pressures will be obtained at the surface boundary. Referring to Fig.
5.24a, the surface computation of the present model works as follows:
� Impose zero discharge, qt = 0, at the surface boundaries.
� Obtain the pressure at the cell centers, pP, from the SIMPLE algorithm.
� Extrapolate the pressure to the surface by assuming a hydrostatic distribution:
pt � pP � �gz�z t � zP�. � Move the surface according to the pressure: �h � p t �g z .
� Distribute the surface to get the coordinate of the cell vertices: �h 1 � 1
4
�hj is the surface of the four neighbors.
� �h j , where
The proposed alternative approach, on the other hand, imposes a zero pressure at the
surface. By assuming a hydrostatic distribution, the pressure at the cell center below the
surface can be obtained, pP � pt � �gz�z t � zP�. This pressure is not corrected in the
pressure computation of the SIMPLE algorithm. For cells just below the surface, the
pressure-correction, pc , is known (zero). The discharge across the surface, qt, becomes the
unknown. It can be incorporated in the pressure-correction equation (see Eq. 4.67 in
Chapter 4) by interchanging those two variables. The qt is brought to the left-hand side
and the pc is put to the source term on the right-hand side. Once the discharge, qt , is
obtained, the velocity at the surface can be computed and used to move the surface.
Introducing a surface function, � t � � x,y,t
� �, to denote the position of the surface and
differentiating that function with respect to time, one has: