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Research Papers: Flows in Complex Systems

Energy Redistribution Between the Mean and Pulsating Flow Field in a Separated Flow Region

[+] Author and Article Information
Sharul S. Dol

Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB, T2N 1N4, Canada
e-mail: sharulsham@curtin.edu.my

M. Mehdi Salek, Robert J. Martinuzzi

Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB, T2N 1N4, Canada

1Corresponding author. Present address: Department of Mechanical Engineering, Curtin University, Sarawak Campus CDT 250, 98009 Miri, Sarawak, Malaysia.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 2, 2013; final manuscript received February 17, 2014; published online September 4, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 136(11), 111105 (Sep 04, 2014) (9 pages) Paper No: FE-13-1406; doi: 10.1115/1.4026923 History: Received July 02, 2013; Revised February 17, 2014

One of the main features of the backward-facing step (BFS) low frequency pulsatile flow is the unsteadiness due to the convection of vortical (coherent) structures, which characterize the flow dynamics in the shear layer. The physics of the flow field is analyzed by looking at energy redistribution between the mean and pulsating flow field obtained via a particle image velocimeter (PIV) using the concept of a triple decomposition. The total fluctuating kinetic budget is calculated and discussed for a mean Reynolds number of 100 and for 0.035 ≤ St ≤ 2.19. The effects that these coherent structures have on the fluctuating kinetic energy production, dissipation, and transport mechanism are examined. The results provide insight into the physics of the flow and suggest reasons for vortex growth and decay. Fluctuating kinetic energy is generally produced at the separated shear layers and transported towards the core flow and then to the upper and lower walls where viscosity dissipates the energy. The remaining energy is transported streamwise and decays as it is convected downstream (St = 0.4 and 1 cases). It was also found that the pressure-velocity correlation diffusion plays a significant role in the transport of kinetic energy and Reynolds stresses, especially in the separated shear layer. More energy was dissipated at the walls for the high Strouhal number case St = 2.19 due to the transverse pressure diffusion term being increasingly dominant. This could be the reason why the convected primary vortices were much smaller in size and weaker with no upper wall vortices formed at this pulsation Strouhal number. The shear production for St = 0.035 was very minimal; thus, the vortices died down quickly even before the shedding could happen. Finally, the pressure-strain correlation term was found to be significant in redistributing the kinetic energy from u-component to v-component.

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Figures

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Fig. 1

Fluctuating kinetic energy budget for St = 0.4 at x/S = 0.5: (a) total budget and (b) production by shear and normal stresses

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Fig. 2

Fluctuating kinetic energy budget for St = 0.4 at x/S = 3: (a) total budget and (b) production by shear and normal stresses

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Fig. 3

Fluctuating kinetic energy budget for St = 0.4 at x/S = 6: (a) total budget and (b) production by shear and normal stresses

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Fig. 4

Variation of trajectory of the vortex centroids with St (Re = 100)

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Fig. 5

Fluctuating kinetic energy budget for St = 1 at x/S = 0.5: (a) total budget and (b) production by shear and normal stresses

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Fig. 6

Fluctuating kinetic energy budget for St = 1 at x/S = 3: (a) total budget and (b) production by shear and normal stresses

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Fig. 7

Fluctuating kinetic energy budget for St = 2.19 at x/S = 0.5: (a) total budget and (b) production by shear and normal stresses

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Fig. 8

Fluctuating kinetic energy budget for St = 2.19 at x/S = 3: (a) total budget and (b) production by shear and normal stresses

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Fig. 9

Variation of transverse pressure diffusion ϕ=(1/ρ)(v∂p/∂y¯) with St at x/S = 0.2

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Fig. 10

Fluctuating kinetic energy budget for St = 0.035 at x/S = 0.5: (a) total budget and (b) production by shear and normal stresses

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Fig. 11

Fluctuating kinetic energy budget for St = 0.035 at x/S = 3: (a) total budget and (b) production by shear and normal stresses

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Fig. 12

Production of u2¯ and v2¯ at x/S = 1 for St = 0.4

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Fig. 13

Pressure-strain correlation and diffusion terms at x/S = 1 for St = 0.4: (a) u2¯ balance and (b) v2¯ balance

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