0
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.

<>
Your Session has timed out. Please sign back in to continue.

References

Crow, S. C., and Champagne, F. H., 1971, “Orderly Structure in Jet Turbulence,” J. Fluid Mech., 48, pp. 547–591.
Petersen, R. A., 1978, “Influence of Wave Dispersion on Vortex Pairing in a Jet,” J. Fluid Mech., 89(3), pp. 469–495.
Yule, A. J., 1978, “Large-Scale Structure in the Mixing Layer of a Round Jet,” J. Fluid Mech., 89, pp. 413–432.
Lau, J. C., and Fisher, M. J., 1975, “The Vortex Sheet Structure of Turbulent Jets,” J. Fluid Mech., 67(1), pp. 299–377.
Davis, M. R., and Davies, P. O. A. L., 1979, “Shear Fluctuations in a Turbulent Jet Shear Layer,” J. Fluid Mech., 93, pp. 281–303.
Liepmann, D., and Gharib, M., 1992, “The Role of Streamwise Vorticity in the Near-Field Entrainment of Round Jets,” J. Fluid Mech., 245, pp. 643–668.
Hussein, H. J., Capp, S. P., and George, W. K., 1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75.
Wygnanski, I., and Fiedler, H., 1969, “Some Measurements in the Self-Preserving Jet,” J. Fluid Mech., 38(3), pp. 577–612.
Pope, S. B., 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Townsend, A. A., 1956, The Structure of Turbulent Shear Flow, Cambridge University Press, New York.
Kim, J., and Choi, H., 2009, “Large Eddy Simulation of a Circular Jet: Effect of Inflow Conditions on the Near Field,” J. Fluid Mech., 620, pp. 383–411.
Boersma, B. J., 2005, “Large Eddy Simulation of the Sound Field of a Round Turbulent Jet,” Theor. Comput. Fluid Dyn., 19, pp. 161–170.
Bogey, C., and Bailly, C., 2006, “Large Eddy Simulations of Round Free Jets Using Explicit Filtering With/Without Dynamic Smagorinsky Model,” Int. J Heat Fluid Flow, 27, pp. 603–610.
Ranga Dinesh, K. K. J., Savill, A. M., Jenkins, K. W., and Kirkpatrick, M. P., 2010, “LES of Intermittency in a Turbulent Round Jet With Different Inlet Conditions,” Comput. Fluids, 39, pp. 1685–1695.
Gohil, T. B., Saha, A. K., and Muralidhar, K., 2012, “Numerical Study of Instability Mechanisms in a Circular Jet at Low Reynolds Numbers,” Comput. Fluids, 64, pp. 1–18.
Lesieur, M., Metais, O., and Comte, P., 2005, Large Eddy Simulations of Turbulence, Cambridge University Press, Cambridge, UK.
Harlow, F. H., and Welch, J. E., 1966, “Numerical Study of Large-Amplitude Free-Surface Motions,” Phys. Fluids, 9, pp. 842–851.
Gohil, T. B., Saha, A. K., and Muralidhar, K., 2011, “Direct Numerical Simulation of Naturally Evolving Free Circular Jet,” ASME J. Fluids Eng., 133, p. 111203.
Michalke, A., and Hermann, G., 1982, “On the Inviscid Instability of a Circular Jets With External Flow,” J. Fluid Mech., 114, pp. 343–359.
Orlanski, I., 1976, “A Simple Boundary Condition for Unbounded Flows,” J. Comput. Phys., 21, pp. 251–269.
Rogallo, R. S., and Moin, P., 1984, “Numerical Simulation of Turbulent Flows,” Annu. Rev. Fluid Mech., 16, pp. 99–137.
Lilly, D. K., 1967, “The Representation of Small Scale Turbulence in Numerical Simulation Experiments,” IBM Scientific Computing Symposium on Environmental Sciences, White Plains, New York, pp. 195–209.
Moin, P., and Kim, J., 1982, “Numerical Investigation of Turbulent Channel Flow,” J. Fluid Mech., 118, pp. 341–377.
Piomelli, U., and Zang, T. A., 1991, “Large-Eddy Simulation of Transitional Channel Flow,” Comput. Phys. Commun., 65, pp. 224–230.
Lévêque, E., Toschi, F., Shao, L., and Bertoglio, J. P., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502.
Toschi, F., Lévêque, E., and Ruiz-Chavarria, G., 2000, “Shear Effects in Non Homogeneous Turbulence,” Phys. Rev. Lett., 85, pp. 1436–1439. [PubMed]
Cahuzac, A., Boudet, J., Borgnat, P., and Lévêque, E., 2010, “Smoothing Algorithms for Mean-Flow Extraction in Large-Eddy Simulation of Complex Flows,” Phys. Fluids, 22, p.125104.
Hunt, J. C. R., Wray, A. A., and Moin, P., 1988, “Eddies, Stream, and Convergence Zones in Turbulent Flows,” Center For Turbulence Research, Report No. CTR-S88.
Gutmark, E., and Ho, C. M., 1983, “Preferred Modes and the Spreading Rates of Jets,” Phys. Fluids, 26, pp. 2932–2938.
Hussain, A. K. M. F., 1986, “Coherent Structures and Turbulence,” J. Fluid Mech., 173, pp. 303–356.
Hernan, M. A., and Jimenez, J., 1982, “Computer Analysis of a High-Speed Film of the Plane Turbulent Mixing Layer,” J. Fluid Mech., 119, pp. 323–345.
Hussain, A. K. M. F., and Clark, A. R., 1981, “On the Coherent Structure of the Axisymmetric Mixing Layer: A Flow-Visualization Study,” J. Fluid Mech., 104, pp. 263–294.
Zaman, K. B. M. Q., and Hussain, A. K. M. F., 1980, “Vortex Pairing in a Circular Jet Under Controlled Excitation. Part 1. General Jet Response,” J. Fluid Mech., 101, pp. 449–544.
Cohen, J., and Wygnanski, I., 1987, “The Evolution of Instabilities in the Axisymmetric Jet. Part 1.The Linear Growth of Disturbances Near the Nozzle,” J. Fluid Mech., 176, pp. 191–219.
Panchapakesan, N. R., and Lumley, J. L., 1993, “Turbulence Measurements in Axisymmetric Jets of Air and Helium. 1. Air Jet,” J. Fluid Mech., 246, pp. 197–223.

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. 16

Radial variation of the components of the triple-moment tensor

Fig. 15

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

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. 13

Radial variation of the Reynolds stress components

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. 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.

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections