Research Papers: Fundamental Issues and Canonical Flows

Direct Numerical Simulation of Naturally Evolving Free Circular Jet

[+] Author and Article Information
Trushar B. Gohil, Arun K. Saha, K. Muralidhar

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India

J. Fluids Eng 133(11), 111203 (Oct 27, 2011) (11 pages) doi:10.1115/1.4005199 History: Received July 29, 2010; Revised September 23, 2011; Published October 27, 2011; Online October 27, 2011

Direct numerical simulation (DNS) of incompressible, spatially developing circular jets at a moderate Reynolds number of 1030 is performed to understand the details of the evolution of the flow field. The axisymmetric shear layer rolls up in the near field of the jet forming vortex rings. The rings tilt as they convect downstream before becoming turbulent in the far field. The evolution of vortical structures reveals the presence of a helical structure in the flow field along with the occurrence of vortex pairing. The time-averaged streamwise velocity distribution shows self-similarity in the far field. The cross-streamwise distribution of the Reynolds stresses also shows weak self-similarity downstream as the flow is not fully developed within the streamwise length of the computational domain. A detailed comparison with experiments is carried out and the computed time-averaged as well as statistical data shows excellent match with the experimental results. Numerical simulation also reveals various transitions during flow evolution in the streamwise direction.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Description of the computational domain

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Figure 2

Iso-surfaces of vortical structures for three different grids – coarse, medium and fine

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Figure 3

(left) Decay of the time-averaged axial velocity on the centerline and (right) radial/transverse variation of time-averaged axial velocity at x/D = 10

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Figure 4

Iso-surfaces of vortical structures. The dominance of the helical mode is apparent before transition to the turbulent states.

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Figure 5

Iso-surfaces of vortical structures at six time instants within the preferred mode cycle, (a) t = t0 (arbitrary), (b) t = t0  + 0.3, (c) t = t0  + 0.6, (d) t = t0  + 0.9, (e) t = t0  + 1.2, (f) t = t0  + 1.5. Vortex paring phenomenon between two consecutive inclined cortex rings V2 and V3 has been captured. Highlighted square region shows vortex rings that experience pairing process and are used for a detailed explanation in Fig. 6.

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Figure 6

Iso-surfaces of vortical structures for the highlighted square region (Fig. 5) representing detailed pairing phenomenon. The sequence of vortex evolution is first top to bottom and then left to right.

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Figure 7

Instantaneous contours of vorticity modulus on the mid x-z plane

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Figure 8

Velocity signals and spectra at three x/D locations inside the shear layer along y/D = 0.5. At a far downstream location (x/D = 10), the spectrum is shown on a logarithmic scale.

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Figure 9

Variation of the dimensionless jet half-width scaled by the initial momentum thickness and the vorticity thickness scaled by the nozzle diameter along the streamwise direction

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Figure 10

Variation of axial velocity decay and jet half-width in the near-orifice region (2≤x/D≤5, left) and far-orifice region (10≤x/D≤12.0, right) for a Reynolds number of 1030

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Figure 11

Radial/transverse variation of time-averaged velocity profile in the near-orifice region (2≤x/D≤5, left) and far-orifice region (10≤x/D≤12.0, right) for a Reynolds number of 1030

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Figure 12

Contours of time-mean streamwise velocity (u¯/Uinlet) on the mid x-y plane

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Figure 13

Contours of the time-averaged streamwise velocity having a magnitude of one half of the local centerline velocity at various x/D locations. The inner most contour is for x/D = 2 while the outer most is for x/D = 12.

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Figure 14

Centerline variation of (left) rms fluctuating axial and radial velocity, (right) turbulent intensity of axial and radial component of velocity

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Figure 15

Transverse variation of (a) streamwise normal stress, (b) transverse normal stress, and (c) Reynolds stress components at the far-orifice region for a Reynolds number of 1030

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Figure 16

Contour plots of stress components: (a) u'u'¯, (b) v'v'¯ and (c) u'v'¯on the mid x-y plane



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