Experimental study on the interaction between turbulent boundary layer and wake behind various types of two-dimensional cylinders

doi:10.1016/j.jweia.2020.104250

Journal of Wind Engineering and Industrial Aerodynamics

Volume 204, September 2020, 104250

https://doi.org/10.1016/j.jweia.2020.104250 Get rights and content

Highlights

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The interaction between boundary layer and wake behind two-dimensional cylinders is examined.
•
The wake width is sustained in the streamwise direction within the boundary layer.
•
The advective momentum flux contributes to momentum budget in the wake flow.

Abstract

The interaction between the turbulent boundary layer and wake behind various types of two-dimensional cylinders is examined based on the velocity measurements by hot-wire anemometry and particle image velocimetry. Three types of cylinders, such as circular, square, and 1:5 rectangular cylinders, of two different diameters of 5 mm and 10 mm were employed in this study. The streamwise velocity distributions of the wake flow showed that its width is sustained in the streamwise direction within the boundary layer because of its interaction with the turbulent boundary layer flow. Interestingly, this phenomenon was observed regardless of the cylinder shapes. The momentum exchange in both spanwise and vertical directions showed that the advective momentum flux considerably contributes to momentum budget in the wake flow owing to the weak vertical flow formed within the boundary layer. Consequently, the spanwise width of the wake does not expand in the streamwise direction due to the alternation of the momentum budget. The results of this study can contribute to clarifying the effect of interaction between the wake and the turbulent boundary layer, as well as explain the sustaining mechanics of the low speed streaks formed within the turbulent boundary layer, even for different origins of the low-speed regions.

Introduction

Turbulent boundary layers and two-dimensional wake flows are some typical turbulent flow phenomena commonly observed in nature that are well studied. It is well known that the velocity profile within the turbulent boundary layer follows the universal scaling expressed by the linear law within the viscous sub-layer, logarithmic law in the inertial sub-layer, and the outer layer law (Davidson, 2004). These universal characteristics of the mean velocity have also been confirmed for the rough wall turbulent boundary layers (Nikuradse, 1933) and large-scale urban boundary layers (Inagaki and Kanda, 2008). Moreover, the two-dimensional wake flow is a phenomenon of the free turbulent shear layer in which the formed velocity shear only contributes to momentum exchange without any restriction of the flow by an obstacle. Because of such nature, the velocity deficit profile of the two-dimensional wake flow can be expressed by the Gaussian type profile with the self-similar shape as a function of the drag coefficient, width of the wake generator, and traveling distance from the generator (Davidson, 2004). Despite the complex phenomena due to the turbulence flow fields in such shear-layer or free-shear layer conditions, previous studies have revealed the existence of universality of each velocity profile.

Although such independent characteristics of the turbulent boundary layer and wake flow have been studied previously, most airflows in the wind engineering fields are combinations of these two phenomena interacting with each other. For example, the wake flow of wind turbines, high-rise buildings, and skyscraper are mainly generated within the turbulent boundary layer formed by the ground surface. Especially, understanding of the wake flow of high-rise buildings immersed in the low-rise building arrays are required for both wind environmental assessment (e.g. Abd Razak et al., 2013; Yoshie et al., 2007) and scalar dispersion prediction (e.g. Kawaminami et al., 2018).

A classical study dealing with the interaction of the wake flow of a two-dimensional obstacle immersed in a turbulent boundary layer was reported by Counihan et al. (1974). They derived the theoretical velocity profile of the wake flow by employing the simple gradient transport theory along with eddy diffusivity, which is determined by both of the boundary layer and wake flow. Consequently, Castro and Robins (1977) reported the turbulence of the approaching flow reduces the wake flow region behind a three-dimensional obstacle within the boundary layer, because the effective momentum exchange. Accordingly, Tachie and Balachandar (2001), Balachandar and Tachie (2001) conducted experiments to quantify the interaction between the wake of an obstacle and boundary layer. They concluded that the wake recovery process depends on the height within the turbulent boundary layer. Furthermore, Wang et al. (2006) focused on the effect of on downstream wake flow structures under the three conditions of boundary layer depth. They also showed that the difference of the approaching velocity profiles affects the wake flow formation.

From these experiments, it can be said that the interaction of wake and boundary layer flows probably alter the wake flow structures within the boundary layer, compared with the usual two-dimensional wake structure. This is possibly because the enhanced turbulence generated by the wall shear and weak vertical velocity within the boundary layer may cause the different momentum exchange phenomena of the wake flow within the boundary layer. However, these aspects are not clarified yet because of the following limitations of the previous studies: First, most studies employed similar boundary layer depths and obstacle widths (Balachandar and Tachie, 2001; Tachie and Balachandar, 2001; Wang et al., 2006); second, the conditions of measurement positions were limited to a single height within the boundary layer (Balachandar and Tachie, 2001; Tachie and Balachandar, 2001); third, the momentum exchange process of the wake within in the boundary layer were rarely discussed, although the velocity and turbulence intensities of the wakes were displayed previously; fourth, the conditions of the wake generator shapes were only limited to the plate type.

Therefore, this study investigates the interaction phenomena between the turbulent boundary layer flow and wake flow behind various types of two-dimensional cylinders based on the velocity measurements by hot-wire anemometry and particle image velocimetry. Three types of cylinders, such as circular, square, and 1:5 rectangular cylinders, of two different diameters of 5 mm and 10 mm are employed. Section 2 describes the experimental setup, Section 3 explains the mean velocity distribution of the wake within and outside the boundary layer, and Section 4 discusses the momentum budget in the wake within the boundary layer to clarify the interaction of the wake and turbulent boundary layer flows. Finally, Section 5 concludes the paper.

Section snippets

Wind tunnel setup

All the experiments were conducted in the Eiffel-type wind tunnel at the laboratory in the Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Japan. The size of the measurement section of the wind tunnel was 2.5 m in the streamwise and 0.3 m in the spanwise and vertical directions. The air was sucked from the downwind side of the tunnel through the honeycomb and wire meshes installed at the upwind side of the tunnel. The maximum streamwise velocity was approximately

Boundary layer flow

This section shows the mean velocity profile and streamwise development of the turbulent boundary layer depth without a cylinder, to describe the boundary layer flow. Fig. 3 shows the vertical profiles of the streamwise mean velocity $\bar{u}$ at $x = 900$ mm and the streamwise change in the 99% boundary layer depth $δ$ .

Fig. 3 (a) shows the mean velocity profile $U = \bar{u} / u_{r e f} .$ The reference wind speed $u_{r e f}$ was measured at $y = - 80$ and $z = 180$ of each streamwise position, where the side walls of the wind tunnel and

Spanwise mean and turbulent momentum fluxes

To clarify the sustaining mechanism of the wake flow behind the cylinders, this section examines the vertical and spanwise mean and turbulent momentum flux profiles based on the PIV measurement results of the flow for the case of C5 at four selected heights. Fig. 8 shows the spanwise profiles of the spanwise velocity $V = \bar{v} / u_{r e f}$ , the gradient of the streamwise velocity $\partial U / d η$ with respect to the spanwise distance $η = y / D$ , and the turbulent momentum flux $τ_{U V} = \bar{u^{’} v^{’}} / u_{r e f}^{2}$ . The spanwise velocity was

Conclusion

The interaction between the turbulent boundary layer flow and wake flow behind various types of two-dimensional cylinders were examined based on the velocity measurements by means of hot-wire anemometry and particle image velocimetry. Three types of cylinders of two diameters of 5 mm and 10 mm were employed: circular, square, and 1:5 rectangular cylinders. The streamwise velocity distributions of the wake flow within and out of the boundary layer showed an interesting phenomenon in terms of

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors are grateful to Dr. Tsuru (Assistant professor in Faculty of Engineering Sciences, Kyushu University) for assistance for PIV measurements. This work is supported by JSPS KAKENHI Grant Numbers JP17H04946, JP17KK0117.

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View full text

Experimental study on the interaction between turbulent boundary layer and wake behind various types of two-dimensional cylinders

Highlights

Abstract

Introduction

Section snippets

Wind tunnel setup

Boundary layer flow

Spanwise mean and turbulent momentum fluxes

Conclusion

Declaration of competing interest

Acknowledgement

Build. Environ.

Build. Environ.

J. Wind Eng. Ind. Aerod.

J. Wind Eng. Ind. Aerod.

Vortex organization in the outer region of the turbulent boundary laer

J. Fluid Mech.

A study of boundary layer-wake interaction in shallow open channel flows

Exp. Fluid

The flow around a surface-mounted cube in uniform and turbulent streams

J. Fluid Mech.

Structure of turbulent flow over regular arrays of cubical roughness

J. Fluid Mech.

Wakes behind two-dimensional surface obstacles in turbulent boundary layers

J. Fluid Mech.

Measurements of intensity and scale of wind-tunnel turbulence and their relation to the critical Reynolds number of spheres

NACA Rep.