Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T05:14:56.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence, entrainment and low-order description of a transitional variable-density jet

Published online by Cambridge University Press:  18 December 2017

B. Viggiano Open the ORCID record for B. Viggiano [Opens in a new window] ,
T. Dib ,
N. Ali Open the ORCID record for N. Ali [Opens in a new window] ,
L. G. Mastin ,
R. B. Cal  and
S. A. Solovitz Open the ORCID record for S. A. Solovitz [Opens in a new window]
B. Viggiano
Affiliation:
Department of Mechanical and Materials Engineering, Maseeh College of Engineering and Computer Sciences, Portland State University, Portland, OR 97201, USA
T. Dib
Affiliation:
Department of Mechanical and Materials Engineering, Maseeh College of Engineering and Computer Sciences, Portland State University, Portland, OR 97201, USA
N. Ali
Affiliation:
Department of Mechanical and Materials Engineering, Maseeh College of Engineering and Computer Sciences, Portland State University, Portland, OR 97201, USA
L. G. Mastin
Affiliation:
United States Geological Survey, Cascades Volcano Observatory, Vancouver, WA 98683, USA
R. B. Cal
Affiliation:
Department of Mechanical and Materials Engineering, Maseeh College of Engineering and Computer Sciences, Portland State University, Portland, OR 97201, USA
S. A. Solovitz*
Affiliation:
School of Engineering and Computer Science, Washington State University Vancouver, Vancouver, WA 98686, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Geophysical flows occur over a large range of scales, with Reynolds numbers and Richardson numbers varying over several orders of magnitude. For this study, jets of different densities were ejected vertically into a large ambient region, considering conditions relevant to some geophysical phenomena. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air – specifically helium, air and argon. Measurements focused on both the jet core and the entrained ambient. Experiments considered relatively low Reynolds numbers from approximately 1500 to 10 000 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably a nearly laminar jet, turbulent jets and a transitioning jet in between. Several features were studied, including the jet development, the local entrainment ratio, the turbulent Reynolds stresses and the eddy strength. Compared to a fully turbulent jet, the transitioning jet showed up to 50 % higher local entrainment and more significant turbulent fluctuations. For this condition, the eddies were non-axisymmetric and larger than the exit radius. For turbulent jets, the eddies were initially smaller and axisymmetric while growing with the shear layer. At lower turbulent Reynolds number, the turbulent stresses were more than 50 % higher than at higher turbulent Reynolds number. In either case, the low-density jet developed faster than a comparable non-buoyant jet. Quadrant analysis and proper orthogonal decomposition were also utilized for insight into the entrainment of the jet, as well as to assess the energy distribution with respect to the number of eigenmodes. Reynolds shear stresses were dominant in Q1 and Q3 and exhibited negligible contributions from the remaining two quadrants. Both analysis techniques showed that the development of stresses downstream was dependent on the Reynolds number while the spanwise location of the stresses depended on the Richardson number.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Wakes/Jets: Jets Wakes/Jets: Wakes/Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 1009 - 1049
Check for updates
Copyright
© Cambridge University Press 2017. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29 (3), 275–290.CrossRefGoogle Scholar
Agrawal, A. & Prasad, A. K. 2003 Integral solution for the mean flow profiles of turbulent jets, plumes, and wakes. Trans. ASME J. Fluids Engng 125 (5), 813–822.Google Scholar
Amielh, M., Djeridane, T., Anselmet, F. & Fulachier, L. 1996 Velocity near-field of variable density turbulent jets. Intl J. Heat Mass Transfer 39 (10), 2149–2164.CrossRefGoogle Scholar
Arndt, R. E. A., Long, D. F. & Glauser, M. N. 1997 The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 1–33.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Caraballo, E., Samimy, M., Scott, J., Narayanan, S. & Debonis, J. 2003 Application of proper orthogonal decomposition to a supersonic axisymmetric jet. AIAA J. 41 (5), 866–877.Google Scholar
Chen, C. J. & Rodi, W.1980 Vertical turbulent buoyant jets: a review of experimental data. NASA STI/Recon Tech. Rep. A 80.Google Scholar
Chojnicki, K. N., Clarke, A. B., Adrian, R. J. & Phillips, J. C. 2014 The flow structure of jets from transient sources and implications for modeling short-duration explosive volcanic eruptions. Geochem. Geophys. Geosyst. 15 (12), 4831–4845.Google Scholar
Costa, A., Suzuki, Y. J., Cerminara, M., Devenish, B. J., Esposti Ongaro, T., Herzog, M., Van Eaton, A. R., Denby, L. C., Bursik, M., de’Michieli Vitturi, M. et al. 2016 Results of the eruptive column model inter-comparison study. J. Volcanol. Geotherm. Res. 326, 2–25.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Djeridane, T., Amielh, M., Anselmet, F. & Fulachier, L. 1996 Velocity turbulence properties in the near-field region of axisymmetric variable density jets. Phys. Fluids 8 (6), 1614–1630.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability, Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press.Google Scholar
Dunn, J. R. 1953 The origin of the deposits of tufa in Mono Lake. J. Sedim. Res. 23 (1), 18–23.CrossRefGoogle Scholar
Falcone, A. M. & Cataldo, J. C. 2003 Entrainment velocity in an axisymmetric turbulent jet. Trans. ASME J. Fluids Engng 125 (4), 620–627.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Gerashchenko, S. & Prestridge, K. 2015 Density and velocity statistics in variable density turbulent mixing. J. Turbul. 16 (11), 1011–1035.Google Scholar
Gharbi, A., Amielh, M. & Anselmet, F. 1995 Experimental investigation of turbulence properties in the interface region of variable density jets. Phys. Fluids 7 (10), 2444–2454.Google Scholar
Ginster, U., Mottl, M. J. & Von Herzen, R. P. 1994 Heat flux from black smokers on the endeavour and cleft segments, Juan de Fuca ridge. J. Geophys. Res. 99 (B3), 4937–4950.Google Scholar
Hamilton, N., Kang, H. S., Meneveau, C. & Cal, R. B. 2012 Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer. J. Renew. Sustainable Energy 4 (6), 063105.Google Scholar
Han, D.2001 Study of turbulent nonpremixed jet flames using simultaneous measurements of velocity and CH distribution. PhD thesis, Stanford University.Google Scholar
Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75.Google Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.Google Scholar
Katul, G., Poggi, D., Cava, D. & Finnigan, J. 2006 The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Boundary-Layer Meteorol. 120 (3), 367–375.Google Scholar
Kays, W. M. & Crawford, M. E. 1993 Convective Heat and Mass Transfer, 2nd edn. McGraw-Hill.Google Scholar
Kotsovinos, N. E. 1976 A note on the spreading rate and virtual origin of a plane turbulent jet. J. Fluid Mech. 77 (2), 305–311.Google Scholar
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017 Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222–250.Google Scholar
Kwon, S. J. & Seo, I. W. 2005 Reynolds number effects on the behavior of a non-buoyant round jet. Exp. Fluids 38 (6), 801–812.Google Scholar
Kyle, D. M. & Sreenivasan, K. R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.CrossRefGoogle Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation, pp. 166–178. Nauka.Google Scholar
Mastin, L. G 2007 A user-friendly one-dimensional model for wet volcanic plumes. Geochem. Geophys. Geosyst. 8 (3), Q03014.CrossRefGoogle Scholar
Mi, J. B., Kalt, P., Nathan, G. J. & Wong, C. Y. 2007 PIV measurements of a turbulent jet issuing from round sharp-edged plate. Exp. Fluids 42 (4), 625–637.CrossRefGoogle Scholar
Monkewitz, P. A., Lehmann, B., Barsikow, B. & Bechert, D. W. 1989 The spreading of self-excited hot jets by side jets. Phys. Fluids A 1 (3), 446–448.Google Scholar
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Namer, I. & Ötügen, M. V. 1988 Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers. Exp. Fluids 6 (6), 387–399.Google Scholar
Nolan, K. P., Walsh, E. J. & McEligot, D. M. 2010 Quadrant analysis of a transitional boundary layer subject to free-stream turbulence. J. Fluid Mech. 658, 310–335.Google Scholar
O’Neill, P., Soria, J. & Honnery, D. 2004 The stability of low Reynolds number round jets. Exp. Fluids 36 (3), 473–483.CrossRefGoogle Scholar
Örlü, R. & Alfredsson, P. H. 2008 An experimental study of the near-field mixing characteristics of a swirling jet. Flow Turbul. Combust. 80 (3), 323–350.Google Scholar
Paillat, S. & Kaminski, E. 2014 Second-order model of entrainment in planar turbulent jets at low Reynolds number. Phys. Fluids 26 (4), 045110.Google Scholar
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet. J. Fluid Mech. 246, 225–247.Google Scholar
Papanicolaou, P. N. & List, E. J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341–391.Google Scholar
Patrick, M. 2007 The gas content and buoyancy of strombolian ash plumes. J. Volcanol. Geotherm. Res. 166 (1), 1–6.CrossRefGoogle Scholar
Patte-Rouland, B., Lalizel, G., Moreau, J. & Rouland, E. 2001 Flow analysis of an annular jet by particle image velocimetry and proper orthogonal decomposition. Meas. Sci. Technol. 12 (9), 1404.Google Scholar
Poggi, D. & Katul, G. G. 2007 The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment. Boundary-Layer Meteor. 122 (3), 493–515.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Raffel, M., Willert, C. E. & Kompenhans, J. 2013 Particle Image Velocimetry: a Practical Guide. Springer.Google Scholar
Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363–382.Google Scholar
Recker, E., Wagemakers, R., Janssens, B. & Gilson, B.2012 PIV study of variable-density round jets. In 9th National Congress on theoretical and applied mechanics, Brussels, 9-10-11 May 2012.Google Scholar
Ricou, F. P. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11 (01), 21–32.Google Scholar
Rona, P. A., Klinkhammer, G., Nelsen, T. A., Trefry, J. H. & Elderfield, H. 1986 Black smokers, massive sulphides and vent biota at the Mid-Atlantic ridge. Nature 321 (6065), 33–37.Google Scholar
Saffaraval, F., Solovitz, S. A., Ogden, D. E. & Mastin, L. G. 2012 Impact of reduced near-field entrainment of overpressured volcanic jets on plume development. J. Geophys. Res. 117 (B05209).Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Q. Appl. Maths 45 (3), 561–571.Google Scholar
Solovitz, S. A., Mastin, L. G. & Saffaraval, F. 2011 Experimental study of near-field entrainment of moderately overpressured jets. Trans. ASME J. Fluids Engng 133 (5), 051304.CrossRefGoogle Scholar
Sorey, M. L., Kennedy, B. M., Evans, W. C., Farrar, C. D. & Suemnicht, G. A. 1993 Helium isotope and gas discharge variations associated with crustal unrest in Long Valley Caldera, California, 1989–1992. J. Geophys. Res. 98 (B9), 15871–15889.Google Scholar
Sparks, R. S. J. 1986 The dimensions and dynamics of volcanic eruption columns. Bull. Volcanol. 48 (1), 3–15.Google Scholar
Sparks, R. S. J., Bursik, M. I., Carey, S. N., Gilbert, J. S., Glaze, L. S., Sigurdsson, H. & Woods, A. W. 1997 Volcanic Plumes. Wiley.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1978 Joint probability densities and quadrant contributions in a heated turbulent round jet. AIAA J. 16, 867–868.Google Scholar
Stevenson, D. S. 1993 Physical models of fumarolic flow. J. Volcanol. Geotherm. Res. 57 (3–4), 139–156.CrossRefGoogle Scholar
Suresh, P. R., Srinivasan, K., Sundararajan, T. & Das, S. K. 2008 Reynolds number dependence of plane jet development in the transitional regime. Phys. Fluids 20 (4), 044105.Google Scholar
Suzuki, Y. J., Costa, A., Cerminara, M., Ongaro, T. E., Herzog, M., Van Eaton, A. R. & Denby, L. C. 2016 Inter-comparison of three-dimensional models of volcanic plumes. J. Volcanol. Geotherm. Res. 326, 26–42.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Thring, M. W. & Newby, M. P. 1953 Combustion length of enclosed turbulent jet flames. In Symposium (International) on Combustion, vol. 4, pp. 789–796. Elsevier.Google Scholar
Tinney, C. E., Glauser, M. N. & Ukeiley, L. S. 2008 Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition. J. Fluid Mech. 612, 107–141.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.CrossRefGoogle Scholar
Wallace, J. M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.Google Scholar
Wang, H. & Law, A. W.-K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397–428.Google Scholar
Wang, P., Fröhlich, J., Michelassi, V. & Rodi, W. 2008 Large-eddy simulation of variable-density turbulent axisymmetric jets. Intl J. Heat Fluid Flow 29 (3), 654–664.Google Scholar
White, F. M. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.Google Scholar
Woods, A. W. 1993 Moist convection and the injection of volcanic ash into the atmosphere. J. Geophys. Res. 98 (B10), 17627–17636.Google Scholar
Yoon, J.-H. & Lee, S.-J. 2003 Investigation of the near-field structure of an elliptic jet using stereoscopic particle image velocimetry. Meas. Sci. Technol. 14 (12), 2034.Google Scholar