Interactive flow around a circular cylinder controlled by a small rod

. In this paper, a unique flow control method using a small rod, called the forced reattachment method, is proposed for the control of the flow around a bluff body. As described in previous papers, the forced reattachment method is a type of separated shear layer control that reduces drag and generates lift, and it can only occur under certain conditions. The forced reattachment phenomenon occurs as a result of an interactive flow between a circular cylinder and a small rod. This phenomenon is characterized by many special features, such as a large stagnant region behind the circular cylinder and the reattachment flow, which adheres to the rear face of the circular cylinder. It is also interesting how it reduces the total drag, including that of the small rod. The aim of this study was to elucidate the details of the stagnant region, the properties of the reattachment flow, and the reduction of the total drag.


Introduction
The use of the forced reattachment phenomenon as a unique flow control method has been reported in previous papers [ 1 -6 ].In this method, which can be categorized as a shear layer control method, a small rod is placed near a circular cylinder, dividing the separated shear layer from the circular cylinder into upper and lower components.The upper shear layer is elongated, and the lower shear layer reattaches and adheres to the rear face of the circular cylinder, forming a large stagnant region behind the circular cylinder.As a result, the drag of the circular cylinder is reduced by 20 % to 30 %, and a lift with a lift coefficient of CL = 1.0 is generated.Recently, we have reported formulas describing the features of this phenomenon and the optimal conditions of the rod size and position [6].
The forced reattachment phenomenon occurs as a result of an interactive flow between the circular cylinder and the small rod.Figures 1(a) and (b) respectively show a flow visualization photograph and a schematic demonstrating the phenomenon.This phenomenon is characterized by several features for example, a large stagnant region and the adhered flow on the rear face of the cylinder.When this flow control method is used in engineering applications, the total drag reduction, including that of the small rod, must be known.
In this study, we describe several features of the forced reattachment phenomenon and the total drag reduction including that of the small rod.(

Experimental device and methods
The coordinate systems and notation used in the present study are shown in Figure 2. The diameter of the circular cylinder was D = 40 mm, and the diameter d of the small rod was 2 mm.The width G of the gap between the circular cylinder and the small rod was 6 mm.The angular position α of the small rod was varied from 90°t o 180°.
Experiments were carried out in a low-speed wind tunnel, the working section of which has a height of 1,000 mm, a width of 150 mm, and a length of 1,200 mm.The free-stream velocity U was 16 m / s, and the turbulence intensity was approximately 0.4 % in this velocity.The Reynolds number Re based on D was 4.2 × 10 4 .
In experiment, the surface pressure on the circular cylinder and the small rod were measured, and the drag and lift coefficients were obtained by integrating the pressure distribution.The time-averaged velocity in the wake and the gap were measured with an I-type hot wire anemometer.

Forced reattchment
Figure 3(a) and (b) shows the contours of the timeaveraged velocity u behind the circular cylinder with and without the small rod, respectively.In Fig. 3(a), a wide low speed region ( u / U ≤ 0.4) formed behind the circular cylinder, and a very low speed region (u / U ≤ 0.1) formed just behind the reattachment flow, this latter region is completely stagnant.A high-speed flow appeared in the gap between the cylinder and the small rod.This is the lower component of the divided shear layer, and it reattached and adhered to the rear face of the circular cylinder.The maximum velocity of this reattachment flow was u / U = 1.6.The reattachment flow decreased gradually along the rear face of the circular cylinder.A comparison of the forced reattachment case in Fig. 3 (a) with the case with no small rod in Fig. 3 (b) indicates that the stagnant region and the high-speed reattachment flow are characteristic of the forced reattachment phenomenon.

Total drag reduction
Typical flow patterns at different angular positions α are shown in Figures 4 and 5, which are already described in a previous paper [6].
To assess the total drag, including that of the small rod, the pressure distribution around the small rod was measured for various values of α, and the results are shown in Figure 6.At α = 115 °, the small rod is outside of the shear layer separated from the circular cylinder.The base pressure coefficient Cpbr was approximately − 2.5, which is considerably lower than that of the small rod alone, and the pressure coefficient at the front stagnant point was Cp = 1.1, which is greater than 1.0.Because the approaching velocity to the small rod was equal to the velocity of the separated shear layer from the circular cylinder Us = U 1 − Cp .
At α = 121 °, the forced reattachment phenomenon occurred.The front stagnant point was located at φ = 20 °, and Cpbr increased to − 0.7.Because the shear layer separated from the circular cylinder impinged on the front face of the small rod, a large stagnant region formed behind the small rod.
At α = 124 °, the small rod is located just inside the separated shear layer.The forced reattachment phenomenon did not occur in this case, but the separated shear layer was elongated by the support of the small rod.The entirety of the small rod was in the stagnant region, causing the pressure coefficient distribution to take a negative value.
At α = 130 °, the small rod is completely buried in the stagnant region.The pressure coefficient had a nearly flat distribution this position.Cp took a constant value of − 1.1.
Figure 7 shows the drag coefficients of the circular cylinder and small rod and the total drag coefficient.The total drag coefficient CDT is given by CDT = CD + CDr, where CDr is the drag coefficient of the small rod and CDr is the additional drag coefficient.The additional drag coefficient is less than 5 % for 90 ° ≤ α ≤ 121 °, and for 121 ° ＜ α ≤ 180 °, the small rod has no effect on the drag coefficient.The total drag coefficient CDT in the case of the forced reattachment phenomenon is approximately 25 % less than that in the case of the circular cylinder without the small rod.The velocity distributions at φ = 121 ° and 130 °exhibit a low velocity near the rear face of the circular cylinder because of the separation bubble [1].The velocity distributions gradually developed with increasing angle of φ.
The velocity profiles for the reattachment flow and a turbulent wall jet are shown in Figure 9 for comparison.The data for the velocity distributions at the φ = 121 °, 130 °, and 140 ° sections are omitted because they were not fully developed.The velocity profile of the reattachment flow is plotted along with two other velocity profiles in the figure.Shabayek [7] has reported that the velocity profile was off to up and down from the classical wall jet profile [8] increase in roughness.In this study, the same tendency was observed.
It was thus concluded that the reattachment flow has the same properties as the turbulent wall jet.

Conclusions
Flow control by the forced reattachment phenomenon was considered in this study.The features of this phenomenon, for example the details of the stagnant region, the properties of the reattachment flow, and the reduction in the total drag reduction, were discussed.
A wide low speed region ( u / U ≤ 0.4) formed behind the circular cylinder, and a very low speed region ( u / U ≤ 0.1) formed just behind the reattachment flow.
The total drag coefficient CDT was approximately 25 % less than that of the circular cylinder without the small rod.
The properties of the reattachment flow are similar to those of a turbulent wall jet.

F ig. 2 .
Coordinate system and notation.

Fig. 3 .
Fig. 3. Contours of the time-averaged velocity behind the circular cylinder.

,Figure 8
Figure8shows the distributions of the time-averaged velocity of the reattachment flow along on the rear face of the circular cylinder at different angular positions φ.The velocity distributions at φ = 121 ° and 130 °exhibit a low velocity near the rear face of the circular cylinder because of the separation bubble[1].The velocity distributions gradually developed with increasing angle of φ.The velocity profiles for the reattachment flow and a turbulent wall jet are shown in Figure9for comparison.The data for the velocity distributions at the φ = 121 °, 130 °, and 140 ° sections are omitted because they were not fully developed.The velocity profile of the reattachment flow is plotted along with two other velocity profiles in the figure.Shabayek[7] has reported that the velocity profile was off to up and down from the classical wall jet profile[8] increase in roughness.In this study, the same tendency was observed.It was thus concluded that the reattachment flow has the same properties as the turbulent wall jet. )