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Research Papers: Fundamental Issues and Canonical Flows

Transient Growth and Receptivity of Steady Disturbances to Irregular Rough Walls

[+] Author and Article Information
Xiaofei Liu

State Key Laboratory of Clean Energy Utilization,
College of Energy Engineering,
Zhejiang University,
38 Zheda Road,
Hangzhou 310027, China
e-mail: lxf1095@zju.edu.cn

Kun Luo

State Key Laboratory of Clean Energy Utilization,
College of Energy Engineering,
Zhejiang University,
38 Zheda Road,
Hangzhou 310027, China
e-mail: zjulk@zju.edu.cn

Jianren Fan

State Key Laboratory of Clean Energy Utilization,
College of Energy Engineering,
Zhejiang University,
38 Zheda Road,
Hangzhou 310027, China
e-mail: fanjr@zju.edu.cn

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 7, 2015; final manuscript received February 15, 2017; published online April 24, 2017. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 139(7), 071202 (Apr 24, 2017) (8 pages) Paper No: FE-15-1637; doi: 10.1115/1.4036163 History: Received September 07, 2015; Revised February 15, 2017

Direct numerical simulations (DNS) are performed to investigate the transient growth of a steady disturbance induced by a numerically generated Gaussian rough wall in a laminar boundary layer. In the calculation of the interaction between the rough wall and the fluid, the multiple direct force and immersed boundary method (MDF/IBM) are adopted. The evolution of the streak structures and the energy of the disturbances generated by the rough wall are presented. A similar evolution into an almost sinusoidal modulation for the cylindrical roughness element is found for the current irregular rough wall, and the disturbance energy also undergoes the classical transient growth mode. Moreover, the influences of the skewness, kurtosis, and correlation length on the evolution of spanwise harmonics are also analyzed. The results show that the effects of skewness and kurtosis are on the distribution of energy among the wavelengths and the subsequent growth processes, while the wavelengths of the harmonics are linked to both the streamwise and spanwise correlation lengths of the rough wall.

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Figures

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Fig. 1

Numerical representation of the Gaussian rough wall colored by the normal height (case 1)

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Fig. 2

The histogram of HDF for the Gaussian rough wall (case 1)

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Fig. 3

The streamwise velocity deviation for case 1 at y/δin = 0.5

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Fig. 4

The local 3D view of instantaneous streamwise velocity deviation for case 1 at y/δin = 0.5

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Fig. 5

The evolutions of the streamwise velocity and perturbations

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Fig. 6

Perturbation profiles in the normal direction at different streamwise locations

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Fig. 7

The evolution of boundary layer thickness along the x direction for different rough walls

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Fig. 8

Streamwise evolution of spanwise maximum perturbation and the PSD profiles: (a) x/δin = 40.0, (b) x/δin = 48.5, and (c) x/δin = 97.0

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Fig. 9

The streamwise evolution of the perturbation energy for different spanwise harmonics

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Fig. 10

The PSD of disturbance for cases 1 and 2 at x/δin = 40.0

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Fig. 11

The streamwise evolution of the perturbation energy for two cases. Solid- and dashed-lines represent cases 1 and 2, respectively. The symbols are same as those in Fig. 7.

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Fig. 12

The PSD of disturbance for cases 1 and 3 at x/δin = 40.0

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Fig. 13

The PSD of disturbance for cases 1 and 4 at x/δin = 40.0

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