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Research Papers: Fundamental Issues and Canonical Flows

# Large Eddy Simulation of a Free Circular Jet

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

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

Arun K. Saha

Department of Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208 016, India
e-mail: aksaha@iitk.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 20, 2013; final manuscript received January 14, 2014; published online March 17, 2014. Assoc. Editor: Meng Wang.

J. Fluids Eng 136(5), 051205 (Mar 17, 2014) (14 pages) Paper No: FE-13-1101; doi: 10.1115/1.4026563 History: Received February 20, 2013; Revised January 14, 2014

## Abstract

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components $u'u'¯$, $v'v'¯$, and $u'v'¯$ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

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## Figures

Fig. 1

Description of the computational domain

Fig. 2

Grid distribution on the orthogonal planes: (a) xy-plane, and (b) yz-plane; the main flow direction is from left to right on the xy-plane. The jet is contained mainly in the axial region of high grid density.

Fig. 3

Dimensionless power spectra of velocity along the jet centerline at selected axial locations

Fig. 4

Isosurfaces of the Q-function (top) and the contour plot of the z-component of the vorticity on the x-y plane of a circular jet (bottom). In the near field, laminar vortex rings are visible; however, far downstream, a very complex flow field represents the turbulent state.

Fig. 6

Axial location of various vortex rings versus time. Vortex pairing processes are visible. Respective convective velocities are also indicated near the positions.

Fig. 7

Location of twelve cross-sectional planes in the streamwise direction and the respective structures shown as isosurfaces of vortical structures at a time t = 16 units

Fig. 8

Contour plots of the modulus of vorticity on the cross-sectional plane at various streamwise locations, time t = 16 units

Fig. 9

Streamwise vortex filaments: Isosurfaces of the Q-function (red) and streamwise vorticity (blue for ωx=-1 and green for ωx=1). Vortex rings in the red color are visible and streamwise filaments develop over it.

Fig. 5

Isosurfaces of the Q-function revealing various pairing processes

Fig. 5

(Continued)

Fig. 10

Variation of (a) the time-averaged streamwise velocity and (b) the jet half-width and vorticity thickness along the jet centerline. Zaman: Zaman and Hussain [33]; Crow: Crow and Champagne [1].

Fig. 11

Radial variation of the time-averaged streamwise velocity profiles at various x/D locations. The velocity profiles show self-similarity until the end of the computational domain.

Fig. 12

Variation of (a) the normalized flux profile along the jet centerline and (b) the normal turbulent stress along the jet centerline and their comparison with the experimental data reported in the literature

Fig. 13

Radial variation of the Reynolds stress components

Fig. 14

Variation of various turbulent Reynolds stress components (a) streamwise normal stress u'u'¯, (b) transverse normal stress v'v'¯, and (c) shear stress u'v'¯

Fig. 15

Variation of various quantities in the turbulent kinetic energy budget: (a) TKE, (b) production of TKE, and (c) convection of TKE

Fig. 16

Radial variation of the components of the triple-moment tensor

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