Direct and Large-Eddy Simulation II pp 1-10 | Cite as

# Direct Numerical Simulations of the Free, Unsteady, Round, Unforced Jet at Low Reynolds Numbers

- 2 Citations
- 327 Downloads

## Abstract

Three-dimensional direct numerical simulations of unforced, incompressible, free, spatially evolving round jets are used to investigate the onset of instability at low diametral Reynolds numbers (Re ≤ 500). Compact, coherent structures are identified by means of iso-surfaces of vorticity and pressure fields. The Reynolds number proves to be the decisive parameter for the selection of the most amplified unstable mode once the inflow velocity profile is given. (A ‘top-hat’ profile is used). At the upper limit of the investigated range of Reynolds numbers, the present simulations are consistent with the widely accepted scenario of the space and time development of a round jet instability. For lower Reynolds numbers, a superposition of symmetry-breaking (helical) modes is shown to characterize the instability of the round jet. The Fourier decomposition of the fluctuating flow field allows to extract the helical modes and to identify them as the modes predicted already by Batchelor as possible linearly unstable modes in an axisymmetric parallel and inviscid jet. The dynamics of the unstable axisymmetric jet present some particular features that might be characteristic of axisymmetric flows in general: absence of a limit cycle and sensitivity of the asymptotic state to initial conditions.

## Keywords

Reynolds Number Direct Numerical Simulation Unstable Mode Spectral Element Momentum Thickness## Preview

Unable to display preview. Download preview PDF.

## References

- Batchelor, G. K., Gill, A. E. (1962) Analysis of the stability of axisymmetric jets,
*J. Fluid Mech*.**Vol. 14**, pp. 529–551CrossRefzbMATHMathSciNetADSGoogle Scholar - Becker, H. A., Massaro, T. A. (1968) Vortex evolution in a round jet,
*J. Fluid Mech*.**Vol. 31**, pp. 435–448CrossRefADSGoogle Scholar - Buelle, J. C., Huerre, P. (1988) Inflow/outflow boundary conditions and global dynamics of spatial mixing layers,
*Summer Programm***Rep. No**.**CTR-S88**, pp. 19–27Google Scholar - Carte, G., Dušek, J. & Fraunié, Ph., (1995) A Spectral Time Discretization for Flows with Dominant Periodicity,
*J. Comp. Phys*.**Vol. 120**, pp. 171–183CrossRefzbMATHADSGoogle Scholar - Crow, S. C., Champagne, F. H. (1971) Orderly structure in jet turbulence,
*J. Fluid Mech*.**Vol. 48**, pp. 547–591CrossRefADSGoogle Scholar - Dusek, J., Fraunie, Ph., Le Gal, P (1994) A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake,
*J. Fluid Mech*.**Vol. 264**, pp. 59–80CrossRefzbMATHMathSciNetADSGoogle Scholar - Dusek, J. (1996) Spatial structure of the Bénard — von Kármán instability,
*European Journal of Mechanics, B/Fluids*.,**Vol. 15**, No. 3Google Scholar - Gutmark, G., Ho, C. M. (1983) Preferred modes and the spreading rates of jets,
*Phys. Fluids***Vol. 26**no.**10**, pp. 2932–2938CrossRefADSGoogle Scholar - Ho, C. M., Huerre, P. (1984) Perturbed free shear layers,
*Ann. Rev. Fluid Mech*.**Vol. 16**, pp. 365–424CrossRefADSGoogle Scholar - Ho, C. M., Huang, L. S. (1982) Subharmonics and vortex merging in mixing layers,
*J. of Fluid Mech*.**Vol. 118**, pp. 443–473CrossRefADSGoogle Scholar - Huerre, P., Monkewitz, P. A. (1985) Absolute and convective instabilities in free shear flows,
*J. Fluid Mech*.**Vol**. 159, pp. 151–168CrossRefzbMATHMathSciNetADSGoogle Scholar - Liepmann, D., Gharib, M. (1992) The role of streamwise vorticity in the near-field entrainment of round jets,
*J. Fluid Mech*.**Vol. 245**, pp. 643–668CrossRefADSGoogle Scholar - Mattingly, G. E., Chang, C. C. (1974) Unstable waves on a axisymmetric jet column,
*J. Fluid Mech*.**Vol. 65**, pp. 541–560CrossRefzbMATHADSGoogle Scholar - Martin, J. E., Meiburg, E. (1991) Numerical investigation of the three-dimension ally evolving jets subject to axisymmetric and azimutal perturbations,
*J. Fluid Mech*.**Vol. 230**, pp. 271–318CrossRefzbMATHADSGoogle Scholar - Michalke, A. (1965) On spatially growing disturbances in an inviscid shear layer,
*J. Fluid Mech*.**Vol. 23**, pp. 521–544CrossRefMathSciNetADSGoogle Scholar - Mollendorf, J. C., Gebhart, B. (1973) An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without buoyancy for symmetric and asymmetric disturbance,
*J. Fluid Mech*.**Vol. 61**, pp. 367–399CrossRefzbMATHADSGoogle Scholar - Morris, P. J. (1976) The spatial viscous instability of axisymmetric jets,
*J. Fluid Mech*.**Vol. 77**, pp. 511–529CrossRefzbMATHADSGoogle Scholar - Neitzel, G. P., Kirkconnell, C. S., Little L. J.(1995) Transient, nonaxisymmetric modes in the instability of unsteady circular Couette flow. Laboratory and numerical experiments,
*Phys. Fluids***Vol. 7 no**.**2**, pp. 324–334CrossRefADSGoogle Scholar - Reynolds, A. J. (1962) Observation of a liquid-into-liquid jet,
*J. Fluid Mech*.**Vol. 14**, pp. 552–556CrossRefzbMATHADSGoogle Scholar - Yule, A. J. (1978) Large structures in the mixing layer of a round jet,
*J. Fluid Mech*.**Vol. 89**, pp. 413–443CrossRefADSGoogle Scholar