Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T03:34:19.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Joint probabilities and mixing of isolated scalars emitted from parallel jets

Published online by Cambridge University Press:  16 March 2015

M. A. Soltys  and
J. P. Crimaldi
M. A. Soltys
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, USA
J. P. Crimaldi*
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Mixing and reaction between two scalars initially separated by scalar-free ambient fluid is important in problems ranging from ecology to engineering. Using a two-channel planar laser-induced fluorescence (PLIF) system the instantaneous spatial structure of two independent scalars emitted from parallel jets into a slow coflow is quantified. Of particular interest is the scalar covariance used to define the correlation coefficient. Joint probability distribution functions (JPDFs) and instantaneous images of the scalar fields demonstrate that initially the flow mainly consists of incursions of fluid from one jet into the other, and vice versa, before scalars have time to assemble in attracting regions of the flow and coalesce due to diffusive flux. Decomposing the joint probability distribution exhibits the effect these events have on scaler overlap and scalar covariance. Along the centreline near where the mean profiles of the jets meet, the scalar covariance is negative; however, the covariance becomes positive as the scalars converge in shared structure and diffusive flux bridges a reduced barrier of ambient fluid. The mixing path between scalar filaments can be probabilistically observed through the conditional diffusion of the two scalars at various points in the flow.

JFM classification

Wakes/Jets: Jets Reacting Flows: Reacting Flows Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 130 - 153
Check for updates
Copyright
© 2015 Cambridge University Press 

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

Anderson, E. A. & Spall, R. E. 2001 Experimental and numerical investigation of two-dimensional parallel jets. Trans. ASME J. Fluids Engng 123 (2), 401–406.CrossRefGoogle Scholar
Ball, C. G., Fellouah, H. & Pollard, A. 2012 The flow field in turbulent round free jets. Prog. Aerosp. Sci. 50, 1–26.CrossRefGoogle Scholar
Becker, H. A. & Booth, B. D. 1975 Mixing in the interaction zone of two free jets. Am. Inst. Chem. Engrs J. 21 (5), 949–958.Google Scholar
Beta, C., Schneider, K., Farge, M. & Bockhorn, H. 2003 Numerical study of mixing of passive and reactive scalars in two-dimensional turbulent flows using orthogonal wavelet filtering. Chem. Engng Sci. 58, 1463–1477.Google Scholar
Bilger, R. W., Saetran, L. R. & Krishnamoorthy, L. V. 1991 Reaction in a scalar mixing layer. J. Fluid Mech. 233, 211–242.Google Scholar
Brown, L. G. 1992 A survey of image registration techniques. ACM Comput. Surv. 24 (4), 325–376.CrossRefGoogle Scholar
Brownell, C. J. & Su, L. K. 2008 Planar laser imaging of differential molecular diffusion in gas-phase turbulent jets. Phys. Fluids 20 (3), 035109.Google Scholar
Bunderson, N. E. & Smith, B. L. 2005 Passive mixing control of plane parallel jets. Exp. Fluids 39 (1), 66–74.Google Scholar
Cai, J., Dinger, M. J., Li, W., Carter, C. D., Ryan, M. D. & Tong, C. 2011 Experimental study of three-scalar mixing in a turbulent coaxial jet. J. Fluid Mech. 685, 495–531.Google Scholar
Catrakis, H. J. & Dimotakis, P. E. 1996 Mixing in turbulent jets: scalar measures and isosurface geometry. J. Fluid Mech. 317, 369–406.Google Scholar
Cetegen, B. M. & Sirignano, W. A. 1990 Study of mixing and reaction in the field of a vortex. Combust. Sci. Technol. 72 (4), 157–181.Google Scholar
Champagne, F. H. & Wygnanski, I. J. 1971 An experimental investigation of coaxial turbulent jets. Intl J. Heat Mass Transfer 14 (9), 1445–1464.CrossRefGoogle Scholar
Costa-Patry, E. & Mydlarski, L. 2008 Mixing of two thermal fields emitted from line sources in turbulent channel flow. J. Fluid Mech. 609, 349–375.Google Scholar
Crimaldi, J. P. 2008 Planar laser induced fluorescence in aqueous flows. Exp. Fluids 44 (6), 851–863.Google Scholar
Crimaldi, J. P. 2012 The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning. J. Expl Biol. 215, 1031–1039.Google Scholar
Crimaldi, J. P. & Browning, H. S. 2004 A proposed mechanism for turbulent enhancement of broadcast spawning efficiency. J. Mar. Syst. 49, 3–18.Google Scholar
Crimaldi, J. P., Cadwell, J. R. & Weiss, J. B. 2008 Reaction enhancement of isolated scalars by vortex stirring. Phys. Fluids 20 (7), 073605.CrossRefGoogle Scholar
Crimaldi, J., Hartford, J. & Weiss, J. 2006 Reaction enhancement of point sources due to vortex stirring. Phys. Rev. E 74, 1–4.Google Scholar
Crimaldi, J. P. & Kawakami, T. R. 2013 Reaction of initially distant scalars in a cylinder wake. Phys. Fluids 25, 053604.Google Scholar
Crimaldi, J. P. & Koseff, J. R. 2001 High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume. Exp. Fluids 31 (1), 90–102.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (03), 547–591.Google Scholar
Dahm, W. J. A. & Dimotakis, P. E. 1990 Mixing at large Schmidt number in the self-similar far field of turbulent jets. J. Fluid Mech. 217, 299–330.Google Scholar
Davies, B. M. & Jones, C. D. 2000 Some field experiments on the interaction of plumes from two sources. Q. J. R. Meteorol. Soc. 126, 1343–1366.CrossRefGoogle Scholar
Duplat, J. & Villermaux, E. 2008 Mixing by random stirring in confined mixtures. J. Fluid Mech. 617, 51–86.Google Scholar
Durst, F., Ray, S., Ünsal, B. & Bayoumi, O. A. 2005 The development lengths of laminar pipe and channel flows. Trans. ASME J. Fluids Engng 127 (6), 1154–1160.Google Scholar
Erdem, G. & Ath, V.2002 Interaction of two parallel rectangular jets. In Proceedings from the 23rd Congress of International Council of the Aeronautical Sciences, 8–13 September, 2002, Toronto, Canada. Paper ICAS 2002-R15.Google Scholar
Eswaran, V. & Pope, S. B. 1988 Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids 31 (3), 506–520.Google Scholar
Fujisawa, N., Nakamura, K. & Srinivas, K. 2004 Interaction of two parallel plane jets of different velocities. J. Vis. 7 (2), 135–142.Google Scholar
Girimaji, S. S. 1991 Assumed ${\it\beta}$ -PDF model for turbulent mixing: validation and extension to multiple scalar mixing. Combust. Sci. Technol. 78, 177–196.Google Scholar
Grandmaison, E. W. & Zettler, N. L. 1989 Turbulent mixing in coflowing plane jets. Can. J. Chem. Engng 67 (6), 889–897.Google Scholar
Heikkila, J. & Silvén, O. 1997 A four-step camera calibration procedure with implicit image correction. In Proceedings of the 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1106–1112. IEEE.Google Scholar
Hodgson, J. E., Moawad, A. K. & Rajaratnam, N. 1999 Concentration field of multiple circular turbulent jets. J. Hydraul. Engng ASCE 37 (2), 249–256.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
Jayesh & Warhaft, Z. 1991 Probability distribution of a passive scalar in grid-generated turbulence. Phys. Rev. Lett. 67 (25), 3503–3506.Google Scholar
Juneja, A. & Pope, S. B. 1996 A DNS study of turbulent mixing of two passive scalars. Phys. Fluids 8 (8), 2161–2184.CrossRefGoogle Scholar
Komori, S., Hunt, J. C. R., Kanzaki, T. & Murakami, Y. 1991 The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows. J. Fluid Mech. 228, 629–659.Google Scholar
Larsen, L. G. & Crimaldi, J. P. 2006 The effect of photobleaching on PLIF. Exp. Fluids 41 (5), 803–812.Google Scholar
Lavertu, T. M., Mydlarski, L. & Gaskin, S. J. 2008 Differential diffusion of high-Schmidt-number passive scalars in a turbulent jet. J. Fluid Mech. 612, 439–475.Google Scholar
Lin, Y. F. & Sheu, M. J. 1990 Investigation of two plane parallel unventilated jets. Exp. Fluids 10, 17–22.CrossRefGoogle Scholar
Mao, K. W. & Toor, H. L. 1971 Second-order chemical reactions with turbulent mixing. Ind. Engng Chem. Fundam. 10 (2), 192–197.Google Scholar
Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J. & Swinney, H. 2007 Uncovering the Lagrangian skeleton of turbulence. Phys. Rev. Lett. 98 (14), 144502.Google Scholar
Melton, L. A. & Lipp, C. W. 2003 Criteria for quantitative (PLIF) experiments using high-power lasers. Exp. Fluids 35 (4), 310–316.Google Scholar
Mitarai, S., Riley, J. J. & Kosály, G. 2005 Testing of mixing models for Monte Carlo probability density function simulations. Phys. Fluids 17, 047101.Google Scholar
Nickels, T. B. & Perry, A. E. 1996 An experimental and theoretical study of the turbulent coflowing jet. J. Fluid Mech. 309, 157–182.CrossRefGoogle Scholar
Pani, B. & Dash, R. 1983 Three-dimensional single and multiple free jets. J. Hydraul. Engng ASCE 109 (2), 254–269.Google Scholar
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.Google Scholar
Rowinski, D. H. & Pope, S. B. 2013 An investigation of mixing in a three-stream turbulent jet. Phys. Fluids 25 (10), 105105.Google Scholar
Sawford, B. L. & de Bruyn Kops, S. M. 2008 Direct numerical simulation and Lagrangian modeling of joint scalar statistics in ternary mixing. Phys. Fluids 20 (9), 095106.Google Scholar
Sawford, B. L., Frost, C. C. & Allan, T. C. 1985 Atmospheric boundary-layer measurements of concentration statistics from isolated and multiple sources. Boundary-Layer Meteorol. 31, 249–268.Google Scholar
Saylor, J. R. & Sreenivasan, K. R. 1998 Differential diffusion in low Reynolds number water jets. Phys. Fluids 10 (5), 1135–1146.Google Scholar
Sirivat, A. & Warhaft, Z. 1981 The mixing of passive helium and temperature fluctuations in grid turbulence. J. Fluid Mech. 120, 475–504.Google Scholar
Smart, P. .L. & Laidlaw, I. M. S. 1977 An evaluation of some fluorescent dyes for water tracing. Water Resour. Res. 13 (1), 15–33.Google Scholar
Soltys, M. A. & Crimaldi, J. P. 2011 Scalar interactions between parallel jets measured using a two-channel PLIF technique. Exp. Fluids 50, 1625–1632.Google Scholar
Song, L., Van Gijlswijk, R. P. M., Young, I. T. & Tanke, H. J. 1997 Influence of fluorochrome labeling density on the photobleaching kinetics of fluorescein in microscopy. Cytometry 27, 213–223.Google Scholar
Spall, R. E., Anderson, E. A. & Allen, J. 2004 Momentum flux in plane, parallel jets. Trans. ASME J. Fluids Engng 126 (4), 665–670.Google Scholar
Stapountzis, H. 1988 Covariance and mixing of temperature fluctuations from line sources in grid turbulence. In 2nd International Symposium Transport Phenomena, Tokyo (ed. Hirata, M. & Kasagi, N.), Hemisphere.Google Scholar
Stapountzis, H., Westerweel, J., Bessem, J. M., Westendorp, A. & Nieuwstadt, F. T. M. 1992 Measurement of product concentration of two parallel reactive jets using digital image processing. Appl. Sci. Res. 49 (3), 245–259.Google Scholar
Tong, C. & Warhaft, Z. 1995 Passive scalar dispersion and mixing in a turbulent jet. J. Fluid Mech. 292, 1–38.Google Scholar
Venkataramani, K. S., Tutu, N. K. & Chevray, R. 1975 Probability distributions in a round heated jet. Phys. Fluids 18 (11), 1413–1420.Google Scholar
Villafruela, J. M., Castro, F. & Parra, M. T. 2008 Experimental study of parallel and inclined turbulent wall jets. Exp. Therm. Fluid Sci. 33 (1), 132–139.Google Scholar
Villermaux, E. 2004 Simple ideas on mixing and fragmentation. Chaos 14 (3), 924–932.Google Scholar
Villermaux, E. & Duplat, J. 2003 Mixing as an aggregation process. Phys. Rev. Lett. 91 (18), 184501.Google Scholar
Viswanathan, S. & Pope, S. B. 2008 Turbulent dispersion from line sources in grid turbulence. Phys. Fluids 20, 101514.Google Scholar
Wang, H. J. & Davidson, M. J. 2003 Jet interaction in a still ambient fluid. J. Hydraul. Engng. 129 (5), 349–357.Google Scholar
Wang, C. S., Lin, Y. F. & Sheu, M. J. 1993 Measurements of turbulent inclined plane dual jets. Exp. Fluids 16 (1), 27–35.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32 (1), 203–240.Google Scholar
Yuu, S., Shimoda, F. & Jotaki, T. 1979 Hot wire measurement in the interacting two-plane parallel jets. Am. Inst. Chem. Engrs J. 25 (4), 676–685.Google Scholar
Zarruk, G. A. & Cowen, E. A. 2008 Simultaneous velocity and passive scalar concentration measurements in low Reynolds number neutrally buoyant turbulent round jets. Exp. Fluids 44 (6), 865–872.Google Scholar
Zhang, Z.1999 Flexible camera calibration by viewing a plane from unknown orientations. In Int. Conf. Comput. Vis., Corfu, Greece, pp. 666–673.Google Scholar