M. Fujino*, H. Ishikawa** and S. Igarashi**
*Information Technology Center, **Department of Systems Engineering
Nippon Institute of Technology
Miyashiro, Minami-Saitama, Saitama, 345-8501, JAPAN
Tel., Fax: (0480) 33-7731, E-mail: mfujino@nit.ac.jp
Date: 14 June, 2002
Computer and operating system: Gateway G7-450(Pentium Ⅲ ), WindowsNT
Version of PHOENICS: 3.2
Abstract
Time dependent simulations on drag reduction of a square prism in turbulent water flow were carried out. A small cylindrical rod is inserted upstream of the prism to control the flow.
The Reynolds number is 1.36
× 10
4
. In the simulations, the RNG k ―ε turbulence model was employed.
Flow pattern changes shown in experiments were observed in the controlled flow field. As a result of the flow control, the wake width from the prism became extremely narrower. The pressure around the prism was proved to decrease and the Strouhal number increased as compared with that without a control rod.
1.
Introduction.
New methods
1,2,3) were proposed to decrease the drag coefficient or increase of the heat transfer of the body in the flow. One of them is to set up a control rod with a small radius in the upstream of the obstacle. Studies were carried out to prove these effects, however, these effects were checked only by experiments. The reasons for lack of numerical simulations are considered as the storage capacity and computation speed of digital computers, the accuracy of the turbulence model and so on.
In the present paper, two-dimensional turbulent water flow around a square prism in a rectangular duct was calculated as a first step of the study on the effects. Flow was simulated time dependently to predict instantaneous behavior of the controlled flow.
The RNG k ―ε model
4)
is actually used in industry and gives agreements with experiments in flows with large-scale motions, as in turbulent vortex shedding. This model was therefore employed in the simulations. Experimental data
5)
were also available to survey the accuracy of prediction.
1

2. Calculation Procedure
The configuration for the simulation is illustrated in arbitrary scale in Fig.1. This geometry is made considering the experiments carried out by Durao et al [5]. The figure depicts a flow domain, 2180mm × 156mm in which a 20 × 20mm(D × D) square prism is placed on the center line. The inlet velocity U
0
is horizontal and constant, U
0
=0.68m/s. The Reynolds number based on U
0
and D is 1.37
× 10 4 , with the fluid being 20 ℃ water. A small cylindrical rod is inserted in the upstream of the prism to control the turbulent flow. The diameter of the control rod, d is 6mm. The length L(=60mm) is d(6mm) plus distance between the center line of the rod and front face of the prism, (54mm).
Fig.1 Flow geometry (mm)
The rectangular and locally refined mesh used for the calculations is shown widely in the region around the prism in Fig.2. The total number of nodes involved in the present configuration is 28,080 (234×120). The minimum mesh spacing around the prism is
0.43mm×0.43mm. Time step was chosen to cover each cycle of vortex shedding with over
150 steps. The solution was found to be practically independent of time step and mesh spacing by time and mesh refinement tests.
Fig.2 Mesh structure around the control rod and prism
2

As for the RNG k ―ε model in this simulation, this model answers the dual requirements of accuracy and efficiency, and it gave satisfactory agreement with other experiments in the vortex shedding or rotary flow.
3. Vortex shedding without a control rod
The predicted flow shows an oscillatory behavior and a periodic state was reached after some time. Figures 3 and 4 show developed periodic time changes of horizontal velocity, u and pressure, p on the center line in the back region of the prism. The calculated position is
X/D=1.5 and Y/D=0, where X and Y are the horizontal and vertical distances from the center of front face of the prism respectively. The distance X is, therefore, positive in downstream of the prism and Y is plus in the upper part of the center line of the main domain. The frequency of the shedding f is found to be 4.60Hz as compared with the measured value, 4.69Hz. This frequency f was independent of a location around the prism. The vortex shedding frequency from a bluff body is a dominant factor of the flow field and is characterized by the Strouhal number S t which is defined as;
S t
 fD
U
0
The computed value of S t
was found to be 0.135, whereas the measured S t
was 0.138.
Fig.3 Time change of u in the downstream of the prism
(X/D=1.5, Y/D=0)
Fig.4 Time change of p in the downstream of the prism
(X/D=1.5, Y/D=0)
3

t/T
0
=0.5 t/T
0
=0.75
The velocity, u contours over one cycle T
0
=1/4.60=0.22s are shown in fig.5. A pressure contour at one instant is shown in fig.6. t/T
0
=0 t/T
0
=0.25 t/T
0
=1.0
Fig.5 Horizontal velocity u contours over one shedding period T
0
4

Fig.6 Instantaneous p contour
4. Flow pattern change by a control rod.
4
－
1 Simulation of flow pattern
It is known by measurements that the flow pattern changes significantly with the
Reynolds number, d and L in the turbulent flow field controlled by a cylindrical rod. Here, L and d were determined as 60mm and 6mm respectively as shown in fig.1 considering the critical conditions of pattern changes predicted by measurements.
Time changes of u and p in the downstream of the prism are shown in figs.7 and 8 respectively. The location (X/D=1.5, Y/D=0) is same as that without a rod shown in figs.3 and
4. In figs. 7 and 8, the predicted time responses are compared with those without a control rod ．
The averaged velocity of u (=0.77m/s) is almost same in both cases. On the other hand, the amplitude of the fluctuations of u extremely decreased from 0.1m/s to 0.006m/s. The averaged pressure at the back of the prism decreased by approximately 13Pa. The frequency of the shedding increased to 7.09Hz and the kinetic energy of turbulent flow was also found smaller around the prism by adding a control rod.
Fig.7 Time change of u at the back of the prism
(X/D=1.5, Y/D=0)
5

t/T
1
=0.25
t/T
1
=0.5
Fig.8 Time change of p at the back of the prism
(X/D=1.5, Y/D=0)
Horizontal velocity contours over one shedding period T
1
=1/7.09=0.14s are shown in Fig.9.
In the calculated results, the wake width was narrower and the vortex shedding from the rod was not observed in front of the prism. t/T
1
=0.0
6

t/T
1
=0.75 t/T
1
=1.0
Fig.9 Horizontal velocity u contours of the controlled flow over one shedding period T
1
It was also observed that the shear layers from the rod reattached on the front face of the prism, and consequently, quasi-stationary velocity patterns were performed between the rod and prism. The vortex formation region of the prism moved still more downstream. From the pressure contours, pressure around the prism was proved to decrease (fig.10).
Fig.10 Instantaneous p contour of the controlled flow
The fluctuations of u and p in front of the prism are shown in figs.11 and 12 respectively.
The location of the predictions is X/D=-0.92, Y/D=0. The amplitude of u extremely decreased and the time-averaged u is about 0m/s in the case of adding a rod.
7

Fig.11 Time change of u in front of the prism
(X/D=-0.92, Y/D=0)
Fig.12 Time change of p in front of the prism
(X/D=-0.92, Y/D=0)
The time averaged pressure decreased from –111Pa to –185Pa in fig.12. From the predictions of pressure, it was clear that the reduction of pressure in front of the prism was greater than that in the downstream of the prism.
4-2 Increase in the Strouhal number
The Strouhal number S t based on the frequency of the shedding f=7.09Hz increased from
0.14 to 0.21. This increase due to the flow pattern change was also observed by the experiments [3, 6].
5. Conclusions
The time dependent simulations of turbulent water flow on drag reduction of a bluff body were carried out.
The flow pattern change by setting a small circular rod in the upstream of the prism was confirmed by numerical simulations. As the result of the flow pattern change, the following results were observed.
1.
The wake width in downstream of the prism became narrower than that without the rod.
8

2.
The pressure around the prism decreased.
3.
The Strouhal number increased from 0.14 to 0.21.
References
1.
Tsutsui, T. and Igarashi, T., Drag Reduction of a Circular Cylinder, Trans. J. S. M. E. (in
Japanese), Vol. 61, No.586, pp. 2069-2075, 1995
2.
Tsutsui, T. and Igarashi, T., Enhancement of Heat Transfer and Reduction of Drag of a
Circular Cylinder, Trans. J. S. M. E. (in Japanese), Vol. 62, No.597, pp. 1802-1809, 1996
3.
Igarashi, T., Drag Reduction of a Square Prism by Flow Control Using a Small Rod,
J. Wind Eng. Ind. Aerodyn. Vol. 69-71, pp. 141-153, 1997
4. Yakhot, V., and Orszag, S. A., Renormalization Group Analysis of Turbulence-Basic
Theory, J. Scientific Computing, vol.1, pp.1-51., 1986
5. Durao, D. F. G., et al, A Laser Anemometry Study of Separated Flow Around a Square
Obstacle, Laser Anemometry in Fluid Mechanics, III Ed. by Adrian ， R.J. et al ，
Laaddooen-1ST ， Lisbon ， Portugal, 1986
6. Igarashi, T., Visualization of Flow Around A Bluff Body Controlled by A Rod Set Upstream,
8th International Symposium on Flow Visualization, 101.1-101.6, 1998
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