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A new insight into understanding the Crow and Champagne preferred mode: a numerical study

Published online by Cambridge University Press:  25 April 2019

A. Boguslawski Open the ORCID record for A. Boguslawski [Opens in a new window] ,
K. Wawrzak Open the ORCID record for K. Wawrzak [Opens in a new window]  and
A. Tyliszczak Open the ORCID record for A. Tyliszczak [Opens in a new window]
A. Boguslawski*
Affiliation:
Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Institute of Thermal Machinery, Al. Armii Krajowej 21, 42-201 Czestochowa, Poland
K. Wawrzak
Affiliation:
Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Institute of Thermal Machinery, Al. Armii Krajowej 21, 42-201 Czestochowa, Poland
A. Tyliszczak
Affiliation:
Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Institute of Thermal Machinery, Al. Armii Krajowej 21, 42-201 Czestochowa, Poland
*
†Email address for correspondence: [email protected]
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Abstract

The paper presents a new insight into understanding a mechanism to trigger the Crow and Champagne preferred mode. It is shown on the basis of numerical simulations that the preferred mode is established as a result of nonlinear interactions of primary structures generated by the Kelvin–Helmholtz instability. These interactions form larger coherent vortices characterized with frequency equal to half of the frequency of the primary perturbation. The paper shows that the shear-layer thickness at the nozzle exit constitutes a key parameter that influences significantly the jet response to an external forcing. The simulations were performed for jets with different shear-layer thicknesses. For the thicker shear layer the classical Kelvin–Helmholtz instability is observed. In this case the jet response to an external varicose forcing seems to be very similar to the experimental results of Crow and Champagne. The results presented shed new light on the preferred mode and the frequency selection mechanism confirming the suggestion of Crow and Champagne that nonlinearity is responsible for the preferred frequency. Significantly different results were obtained for a jet characterized by a thin shear layer. In this case the jet could be introduced into a self-sustained regime. External forcing with a frequency equal to the frequency of the natural self-sustained mode or with its subharmonic has practically no effect on the jet dynamics. The jet response to the forcing with frequencies different from the natural one depends on the forcing amplitude. A weak forcing disturbs the self-sustained mode leading to an interaction of two different modes that is observed in spectra with many frequencies related to both the self-sustained mode and the oscillations triggered by forcing. A stronger forcing suppresses the self-sustained mode and only the frequency components related to the stimulation are observed in the spectra. A mechanism responsible for the jet response to an external forcing under the self-sustained regime has not been extensively studied so far and a full understanding of these phenomena needs further studies and careful analysis.

JFM classification

Wakes/Jets: Jets Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 385 - 416
Copyright
© 2019 Cambridge University Press 

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References

Batchelor, G. K. & Gill, A. E 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14 (4), 529–551.Google Scholar
Boguslawski, A., Tyliszczak, A., Drobniak, S. & Asendrych, D. 2013 Self-sustained oscillations in a homogeneous-density round jet. J. Turbul. 14 (4), 25–52.Google Scholar
Brown, G. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Burattini, P., Antonia, R. A., Rajagopalan, S. & Stephens, M. 2004 Effect of initial conditions on the near-field development of a round jet. Exp. Fluids 37, 56–64.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Carpenter, M. H., Gottlieb, D. & Abarbanel, S. 1993 The stability of numerical boundary treatments for compact high-order finite-difference schemes. J. Comput. Phys. 108, 272–295.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–691.Google Scholar
Danaila, I. & Boersma, B. J. 2000 Direct numerical simulation of bifurcating jets. Phys. Fluids 12 (5), 1255–1257.Google Scholar
Drobniak, S. & Klajny, R. 2002 Coherent structures of free acoustically stimulated jet. J. Turbul. 3, 1–30.Google Scholar
Ducros, F., Comte, P. & Lesieur, M. 1996 Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 326, 1–36.Google Scholar
Durao, D. G. F. & Pita, G. 1984 Coherent vortices in the near field of round jet. Exp. Fluids 2, 145–149.Google Scholar
Fletcher, C. A. J. 1991 Computational Techniques for Fluid Dynamics. Springer.Google Scholar
Freund, J. B. & Moin, P.1998 Mixing enhancement in jet exhaust using fluidic actuators: direct numerical simulations. ASME: FEDSM98-5235.Google Scholar
Freund, J. B. & Moin, P. 2000 Jet mixing enhancement by high amplitude fluidic actuation. AIAA J. 38 (10), 1863–1870.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25 (4), 683–704.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.Google Scholar
Geurts, B. J. 2003 Elements of Direct and Large-Eddy Simulation. Edwards Publishing.Google Scholar
Gohil, T. B., Saha, A. K. & Muralidhar, K. 2013 Direct numerical simulation of forced circular jets: effect of varicose perturbation. Intl J. Heat Fluid Flow 44, 524–541.Google Scholar
Gohil, T. B., Saha, A. K. & Muralidhar, K. 2015 Simulation of the blooming phenomenon in forced circular jets. J. Fluid Mech. 783, 567–604.Google Scholar
Hussain, A. & Zaman, K. 1981 The ‘preferred mode’ of the axisymmetric jet. J. Fluid Mech. 110, 39–71.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1980 Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics. J. Fluid Mech. 101, 493–544.Google Scholar
Kempf, A., Klein, M. & Janicka, J. 2005 Efficient generation of initial- and inflow-conditions for transient turbulent flows in arbitrary geometries. Flow Turbul. Combust. 74, 67–84.Google Scholar
Lee, M. & Reynolds, W. C.1985 Bifurcating and blooming jets. Tech. Rep. TF-22. Stanford University.Google Scholar
Lele, S. K. 1992 Compact finite difference with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Lesieur, M., Métais, O. & Comte, P. 2005 Large Eddy Simulation of Turbulence. Cambridge University Press.Google Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 2, 159–199.Google Scholar
Orszag, S. A. & Crow, S. C. 1970 Instability of a vortex sheet leaving a semi-infinite plate. Stud. Appl. Maths 49, 167–181.Google Scholar
Petersen, R. A. & Samet, M. M. 1988 On the preferred mode of jet instability. J. Fluid Mech. 194, 153–173.Google Scholar
Sadeghi, H. & Pollard, A. 2012 Effects of passive control rings positioned in the shear layer and potential core of a turbulent round jet. Phys. Fluids 24, 115103.Google Scholar
Sagaut, P. 2001 Large Eddy Simulation for Incompressible Flows. Springer.Google Scholar
da Silva2001 The role of coherent structures in the control and interscale interactions of round, plane and coaxial jets: a numerical study. PhD thesis, Institut National Polytechnique de Grenoble.Google Scholar
da Silva, C. B. & Métais, O. 2002 Vortex control of bifurcating jets: a numerical study. Phys. Fluids 14 (11), 3798–3819.Google Scholar
Tyliszczak, A. 2014 A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows. J. Comput. Phys. 276, 438–467.Google Scholar
Tyliszczak, A. 2015a LES-CMC study of an excited hydrogen flame. Combust. Flame 162, 3864–3883.Google Scholar
Tyliszczak, A. 2015b Multi-armed jets: a subset of the blooming jets. Phys. Fluids 27, 041703.Google Scholar
Tyliszczak, A. 2018 Parametric study of multi-armed jets. Intl J. Heat Fluid Flow 73, 82–100.Google Scholar
Tyliszczak, A. & Boguslawski, A. 2007 LES of variable density bifurcating jets. In Complex Effects in Large Eddy Simulations (ed. Iacarrino, G., Kassinos, S. C., Langer, C. A. & Moin, P.), Lecture Notes in Computational Science and Engineering, no. 56, pp. 273–288. Springer.Google Scholar
Tyliszczak, A., Boguslawski, A. & Drobniak, S. 2008 Quality of LES predictions of isothermal and hot round jet. In Quality and Reliability of Large Eddy Simulations (ed. Meyers, J., Geurts, B. J. & Sagaut, P.), ERCOFTAC Series, no. 12, pp. 259–270. Springer.Google Scholar
Tyliszczak, A. & Geurts, B. J. 2014 Parametric analysis of excited round jets: numerical study. Flow Turbul. Combust. 93, 221–247.Google Scholar
Urbin, G. & Métais, O. 1997 Large-eddy simulations of three-dimensional spatially developing round jets. In Direct and Large Eddy Simulations II (ed. Chollet, J. P., Voke, P. R. & Kleiser, L.), pp. 35–46. Kluwer Academic.Google Scholar
Wawrzak, K., Boguslawski, A. & Tyliszczak, A. 2015 LES predictions of self-sustained oscillations in homogeneous density round free jet. Flow Turbul. Combust. 95, 437–459.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.Google Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101, 449–491.Google Scholar