THE RESEARCH ON FLOW PATTERN OF
CYLINDER ISLAND IN THE SHALLOW WATER LAYER*

Li Ling, Li Yuliang and Chen Jiafan

Department of Hydraulic Engineering, Tsinghua University,

BeiJing 100084, China

Tel.: +86-010-62771011, Facsimile +86-010-62785699,

E-mail: hyd.llg@mail.tsinghua.edu.cn

Abstract：A series of experiments and calculation have been made to investigate shallow-water flow patterns in the wakes of cylinder island with 1.27m diameter. Measurements of flow patterns have been made in the laboratory using a digital particle image velocimetry (DPIV) system. This produces whole-field velocity vector maps of the wake flow and shows the characteristics of the wake flow. A “wake stability parameter” S has been used to classify the island wake into three types of patterns: for small values of S (S<0.2) vortex shedding is organized and vigorous in the wakes. For large values of S (0.2<S<0.45) vortex shedding is found to cease and unsteady flow appears. For great values of S (S>0.45) unsteady flow turns into steady flow. Depth-averaged Reynolds equations with k-e turbulent model based on RNG method has been solved to simulate the experimental flows. The calculating results are good agreement with experimental results.

Keywords: shallow-water wake flow, cylinder island, DPIV, numerical simulation, k-e turbulent model based on RNG method

1  INTRODUCTION

In coastal and estuarial regions, large-scale eddies can occur because of separation-like effects caused by flow past a headland or island. Such wakes with bed friction, namely shallow-water wakes are of considerable concern in a range of environmental engineering problems. The shallow-water wakes are different from the deep-water wakes. The confinement, which occurs between the bed and free surface in the shallow water wakes, results in the following two important distinguishing characteristics, namely: 1) Flow structures with two distinct length scales are produced, large-scale recirculation zones and small-scale turbulence generated by bed friction. 2) The confinement is imposed on the wake flow by the shallow-water depth.

Few of research on the shallow-water wake is going on in home and overseas. Studies on the stabilizing influence of bed friction on shallow flows with transverse shear have been made by Chu et.al(1983). In the analysis, Chu et.al introduced a “bed-friction parameter” describing the ratio of horizontal shear to vertical shear for such flows. Chu (1987) manipulated the bed friction parameter into a form suitable for application to wake flows, producing the “wake stability parameter” S, given by , where = bottom friction coefficient, D = transverse dimension of body, H = water depth. Experiments conducted by Chen and Jirka (1995) using circular cylinders and flat plates showed unclear flow patterns due to experimental apparatus and conditions. But they suggest the existence of two approximately values of 0.2 and 0.5 that are critical values of flow transition. While S<0.2, the vortex street occurs in the wake flow; 0.2<S<0.5, the unsteady flow structure appears; S>0.5, the wake flow turns into steady state.

2  EXPERIMENTAL APPARATUS AND METHOD

The experimental apparatus consist of water pool, experimental model and DPIV system. Water pool (see Fig.1) with dimensions 30m´3.5m´1.2m is furnished with pipes for guiding water in the upstream and downstream. There are boards made of iron laid on the bottom. Cylinder whose diameter is 1.27m acts as experimental model. Water depth ranges between 1.9cm and 8.9cm. The total flow is between 0.5L/s and 14.57L/s. Thus, Reynolds number  based on water depth is in the range from 146 to 4163. Reynolds number  based on cylinder diameter is in the range from  to . The measurement of wake flow around cylinder is made in the experiment. The image is gathered with gathering zone of 1.06m´3.0m, resolving rate of 768pels´512pels and interrogating scope of 32pels´32pels. The interval is 0.4 second for co-correlation analysis between two frames of image. 138 frames of image are gathered in every experimental condition.

In the experiment, the measurement is made in the near-wake where the influence of water depth and flow velocity is taken into account. Experimental conditions see Table 1.

Table 1  Experimental condition of shallow wake flow around Cylinder Island

Fig. 1  Water pool.   (a) Platform;   (b) Side elevation.

3  CONTROLLING EQUATIONS AND NUMERICAL METHOD

Depth-averaged shallow-water equations with k-e turbulent model based on RNG method are solved to simulate the shallow-water wakes considering the influence of the bed friction on the flow. The turbulent model can put up flow anisotropism and simulate large-scale movement correlative of time, for example vortex shedding. It has been verified in the reference [4]. The controlling equations are dispersed with finite volume method in the arbitrary curvilinear coordinate. The unsteady flow fields are generated by time-stepping method.

The following are controlling equations in the orthogonal coordinate:

                                                                        (1)

The usual hydrostatic pressure assumption is used and the controlling equations are solved by SIMPLE method. Here, ， =water density，h= water depth，u= velocity of x direction，v＝velocity of  y direction，R is source item，f、G and R see Table 2， is bed shear stress，and ignoring surface wind stress .Here,

                                                           (2)

                                                                              (3)

                                                                                 (4)

                                                                         (5)

                                                                                (6)

                                                                          (7)

The parameters of turbulent model see Table 3.

Table 2  List of all variables in the equations

Table 3  The parameters of turbulent model

The model computations in this study were made with a 267×100 mesh and a time step of 0.1 second. The upstream mesh boundary is a distance of 10 times diameter of cylinder island from the center of cylinder island. The downstream mesh boundary is a distance of 30 times diameter of cylinder island from the center of cylinder island. The lateral mesh boundary is a distance of 10 times diameter of cylinder island from the center of cylinder island.

Fig. 2  Grid for calculation of wake flow around cylinder

4  RESULTS AND ANALYSIS

Experimental runs were performed with the value of the wake stability parameter below 0.1 to investigate the model island wakes with a relatively small bed friction influence. With experimental results presented, numerical simulation had been made to investigate the experimental wake flow by solving controlling equations. The flow patterns were prescribed to be convenient for comparison with experimental results.

Fig. 3(a) and 3(b) present an instantaneous surface streamline drawing, measured using the DPIV system and calculated by solving equations. For this case the mean velocity V=4.677cm/s and the water depth H=8.9cm, with the wake stability parameter S=0.0965. Note that the two plots are produced at a corresponding time in the vortex shedding cycle as a means of comparing the wake structure. The result is good agreement between the two with the vortex size and the position of the dominant vortex center with experimental result by comprising two figures. For such small values of S, the wakes observed in Fig. 3(a) and 3(b) appear qualitatively similar to the Karman vortex sheet observed behind a circular cylinder in the range of 100-300. However, the limited vertical dimension prevents vortex breakdown. The tendency of vortex shedding remains visible. To examine the effect of increasing bed friction on the model island wakes, experiment was conducted with S=0.266 to observe the transition from a vortex street to an unsteady wake. Lowing the flow depth thus acts to increase significantly the magnitude the wake stability parameter S. Fig. 4(a) and 4(b) present an instantaneous surface streamline drawing, measured using the DPIV system and calculated by solving equations. For this case the mean velocity V=1.006cm/s and the water depth H=5.24cm, with the wake stability parameter S=0.266. It has shown regular vortex shedding is still occurring although the rolled-up vortex contains lower velocities relative to the previous case. The change happens in the wake flow with stability parameter S increased.

Fig.3  Flow patterns of island wake (S=0.0965) (a) Experimental result; (b) Calculating result

Fig. 5(a) and 5(b) present an instantaneous surface streamline drawing, measured using the DPIV system and calculated by solving equations. For this case the mean velocity V=0.853cm/s and the water depth H=3.25cm, with the wake stability parameter S=0.457. Any form of well-organized vortex shedding has ceased to exist with the wake now appearing as an “unsteady bubble” flow. This consisted of a bubble region with two zones of opposite recirculation, which extend downstream along the wake centerline to a diameter distance. The stability parameter S=0.45 which marks the transition from vortex shedding to a recirculating bubble wake in this study, is in accordance with the value 0.5 proposed by Chen and Jirka(1995) for circular cylinders.

Fig.4  Flow patterns of island wake (S=0.266) (a) Experimental result; (b) Calculating result

Fig. 5  Flow patterns of island wake (S=0.457) (a) Experimental result; (b) Calculating result

Fig. 6  Flow patterns of island wake (S=0.792) (a) Experimental result; (b) Calculating result

The larger value of wake stability parameter S is chosen in the experiment. Fig. 6(a) and 6(b) present an instantaneous surface streamline drawing, measured using the DPIV system and calculated by solving equations. For this case the mean velocity V=0.752cm/s and the water depth H=1.94cm, with the wake stability parameter S=0.792. More steady bubble is formed in the wake. The bubble region comprises of two zones of opposite recirculation, which extend downstream along the wake centerline to the distance of a diameter and half.

5  CONCLUSION

In this paper, the experimental research and numerical simulation have been made to investigate the shallow-water wake flow around Cylinder Island. The results have shown the calculating results are agreement with experimental ones. The change has happened in the shallow-water flow duo to bed friction. Here, Reynolds number is no longer the parameter which determines flow patterns in the shallow-water wake. The research results have shown steady recirculating flow similar to the Karman vortex sheet observed in the deep-water in the Red range of 100-300 is occurring in the shallow-water wake flow around cylinder island under the condition of Reynolds number  above . Flow pattern of shallow wake around cylinder is determined by characteristic parameter S ( ). Under the condition of experiments described in this paper, experimental results have shown that value of 0.2 is critical point of transition from Vortex Street to unsteady flow and that value of 0.45 is critical point of transition from unsteady flow to steady flow. The results are consistent with others.

References

[1]  Ingram R. G., Chu V. H. (1987):“Flow around island in Rupert Bay: an investigation of the bottom friction effect”, Journal of Geophys Res, Vol.92, No.c13, pp.14521-14533.

[2]  Chu V. H.，Wu J. H.，Khayat R. E. (1983):“Stabilityof turbulent shear flows in shallow channel”, Proc.，20^th Congr. of  IAHR，Moscow，U.S.S.R.，Vol.3, pp.128-133.

[3]  Chen D., Jirka G. H. (1995):“Experimental study of plane turbulent wakes in a shallow water layer”, Fluid Dynamics Research, Vol.16, pp.11-14.

[4]  Li Ling, Li yuliang(2000):“Numerical simulation of turbulent flow around bluff bodies using RNG k-e turbulent model”, Progress of water science, Vol.11, No.4,pp.357-361.