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Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

Abstract

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.

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Acknowledgments

This research was undertaken with the assistance of resources provided at the NCI NF through the National Computational Merit Allocation Scheme supported by the Australian Government. Computer time was also provided by SNIC (Swedish National Infrastructure for Computing). The authors also acknowledge the financial support of the Australian Research Council as well as the Lundeqvist foundation.

Author information

Correspondence to Cheng Chin.

Appendix

Appendix

The smoothing function (χ) used to implement the LEBU is as shown below in Fig. 13. Inside the blue region where the LEBU is located, χ = 0. Within the yellow region are functions consisting of a cosine smoothing equation as indicated by the equation numbers.

$$ \begin{array}{l} \chi=1 \left\{ \begin{array}{c} x \le X_{c} + 0.5 L_{LEBU} \\ x \ge X_{c} - 0.5 L_{LEBU} \\ y \le Y_{c} + 0.5 T_{LEBU} \\ y \ge Y_{c} - 0.5 T_{LEBU} \end{array} \right. \end{array} $$
(7)
$$ \begin{array}{l} \chi=0 \left\{ \begin{array}{c} x \le X_{c} - (0.5 L_{LEBU} +0.2) \\ x \ge X_{c} + (0.5 L_{LEBU} +0.2) \\ y \le Y_{c} - (0.5 T_{LEBU} +0.2) \\ y \ge Y_{c} + (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(8)
$$ \begin{array}{l} \chi=-{\cos} \left( \frac{ y-Y_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5 \left\{ \begin{array}{c} x \le X_{c} + (0.5 L_{LEBU} ) \\ x \ge X_{c} - (0.5 L_{LEBU} ) \\ y \le Y_{c} - (0.5 T_{LEBU} ) \\ y \ge Y_{c} - (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(9)
$$ \begin{array}{l} \chi={\cos} \left( \frac{ y-Y_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5 \left\{ \begin{array}{c} x \le X_{c} + (0.5 L_{LEBU} ) \\ x \ge X_{c} - (0.5 L_{LEBU} ) \\ y \ge Y_{c} + (0.5 T_{LEBU} ) \\ y \le Y_{c} + (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(10)
$$ \begin{array}{l} \chi=-{\cos} \left( \frac{ x-X_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5 \left\{ \begin{array}{c} x \le X_{c} - (0.5 L_{LEBU} ) \\ x \ge X_{c} - (0.5 L_{LEBU}+0.2 ) \\ y \le Y_{c} + (0.5 T_{LEBU} ) \\ y \ge Y_{c} - (0.5 T_{LEBU} ) \end{array} \right. \end{array} $$
(11)
$$ \begin{array}{l} \chi={\cos} \left( \frac{ x-X_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5 \left\{ \begin{array}{c} x \ge X_{c} + (0.5 L_{LEBU} ) \\ x \le X_{c} + (0.5 L_{LEBU}+0.2 ) \\ y \le Y_{c} + (0.5 T_{LEBU} ) \\ y \ge Y_{c} - (0.5 T_{LEBU} ) \end{array} \right. \end{array} $$
(12)
$$ \begin{array}{l} \chi= \left[ -{\cos} \left( \frac{ y-Y_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5\right]. \left[ -{\cos} \left( \frac{ x-X_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5 \right] \\ \hspace{50mm} \left\{ \begin{array}{c} x \le X_{c} - (0.5 L_{LEBU} ) \\ x \ge X_{c} - (0.5 L_{LEBU}+0.2 ) \\ y \le Y_{c} - (0.5 T_{LEBU} ) \\ y \ge Y_{c} - (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(13)
$$ \begin{array}{l} \chi= \left[ -{\cos} \left( \frac{ y-Y_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5\right] . \left[{\cos} \left( \frac{ x-X_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5 \right] \\ \hspace{50mm} \left\{ \begin{array}{c} x \ge X_{c} + (0.5 L_{LEBU} ) \\ x \le X_{c} + (0.5 L_{LEBU}+0.2 ) \\ y \le Y_{c} - (0.5 T_{LEBU} ) \\ y \ge Y_{c} - (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(14)
$$ \begin{array}{l} \chi= \left[ {\cos} \left( \frac{ y-Y_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5\right] . \left[ -{\cos} \left( \frac{ x-X_{c}+0.5T_{LEBU}+0.2}{0.2}\pi \right)+0.5 \right] \\ \hspace{50mm} \left\{ \begin{array}{c} x \le X_{c} - (0.5 L_{LEBU} ) \\ x \ge X_{c} - (0.5 L_{LEBU}+0.2 ) \\ y \ge Y_{c} + (0.5 T_{LEBU} ) \\ y \le Y_{c} + (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(15)
$$ \begin{array}{l} \chi= \left[ {\cos} \left( \frac{ y-Y_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5\right] . \left[{\cos} \left( \frac{ x-X_{c}-0.5T_{LEBU}}{0.2}\pi \right)+0.5 \right] \\ \hspace{50mm} \left\{ \begin{array}{c} x \ge X_{c} + (0.5 L_{LEBU} ) \\ x \le X_{c} + (0.5 L_{LEBU}+0.2 ) \\ y \ge Y_{c} + (0.5 T_{LEBU} ) \\ y \le Y_{c} + (0.5 T_{LEBU} +0.2) \end{array} \right. \end{array} $$
(16)

where X c and Y c are the x,y location of the centroid of the LEBU, T L E B U and L L E B U are the thickness and length of the LEBU respectively.

Fig. 13
figure13

The forcing function (χ) around the LEBU. Blue region denotes the LEBU where χ = 1. The yellow region consists of smoothing function denoted by the equation numbers. Outside of the yellow region, χ = 0

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Chin, C., Örlü, R., Monty, J. et al. Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer. Flow Turbulence Combust 98, 445–460 (2017). https://doi.org/10.1007/s10494-016-9757-y

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Keywords

  • Boundary layer
  • Large eddy simulation
  • Wall turbulence
  • Large-eddy-break-up device
  • Drag reduction