This paper considers the mixture fraction which is often used to quantify the turbulent mixing efficiency in fluid engineering devices. We contrast a volume-based approach, where the mixture fraction is quantified directly using the volume bounded by the interface between mixed versus pure fluid, to a surface-based approach that requires area integrals of all mixed-fluid interfaces. Experimentally, we investigate the resolution-scale robustness of the volume-based approach compared to the small-scale sensitivity of the surface-based approach. The difference in robustness between these approaches has implications for examining, modeling, and optimizing the turbulent mixing efficiency.
Issue Section:
Technical Papers
1.
Mi
, J.
, Nathan
, G. J.
, and Nobes
, D. S.
, 2001, “Mixing Characteristics of Axisymmetric Free Jets From a Contoured Nozzle, an Orifice Plate and a Pipe
,” ASME J. Fluids Eng.
0098-2202, 123
, pp. 878
–883
.2.
deBruynKops
, S. M.
, and Riley
, J. J.
, 2001, “Mixing Models for Large-Eddy Simulation of Nonpremixed Turbulent Combustion
,” ASME J. Fluids Eng.
0098-2202, 123
, pp. 341
–346
.3.
Roshko
, A.
, 1991, “The Mixing Transition in Free Shear Flows
,” In The Global Geometry of Turbulence
, J.
Jiménez
, ed., Plenum
, New York
, pp. 3
–11
.4.
Dimotakis
, P. E.
, 1991, “Turbulent Free Shear Layer Mixing and Combustion
,” In High Speed Flight Propulsion Systems
, S.
Murthy
and E.
Curran
eds., 137
, Progress in Astronautics and Aeronautics
, AIAA
, Washington, DC
.5.
Catrakis
, H. J.
, 2004, “Turbulence and the Dynamics of Fluid Interfaces With Applications to Mixing and Aero-Optics
,” In Recent Research Developments in Fluid Dynamics
, N.
Ashgriz
and R.
Anthony
, eds., 5
. Transworld Research Network Publishers
, Kerala, India
, pp. 115
–158
.6.
Dimotakis
, P. E.
, 2005, “Turbulent Mixing
,” Annu. Rev. Fluid Mech.
0066-4189, 37
, pp. 329
–356
.7.
Broadwell
, J. E.
, and Briedenthal
, R. E.
, 1982, “A Simple Model of Mixing and Chemical Reaction in a Turbulent Shear Layer
,” J. Fluid Mech.
0022-1120, 125
, pp. 397
–410
.8.
Koochesfahani
, M. M.
, and Dimotakis
, P. E.
, 1986, “Mixing and Chemical Reactions in a Turbulent Liquid Mixing Layer
,” J. Fluid Mech.
0022-1120, 170
, pp. 83
–112
.9.
Sreenivasan
, K. R.
, Ramshankar
, R.
, and Meneveau
, C.
, 1989, “Mixing, Entrainment and Fractal Dimensions of Surfaces in Turbulent Flows
,” Proc. R. Soc. London, Ser. A
1364-5021, 421
, pp. 79
–108
.10.
Dahm
, W. J. A.
, and Dimotakis
, P. E.
, 1990, “Mixing at Large Schmidt Number in the Self-Similar Far Field of Turbulent Jets
,” J. Fluid Mech.
0022-1120, 217
, pp. 299
–330
.11.
Dowling
, D. R.
, and Dimotakis
, P. E.
, 1990, “Similarity of the Concentration Field of Gas-Phase Turbulent Jets
,” J. Fluid Mech.
0022-1120, 218
, pp. 109
–141
.12.
Broadwell
, J. E.
, and Mungal
, M. G.
, 1991, “Large-Scale Structures and Molecular Mixing
,” Phys. Fluids A
0899-8213, 3
(5
), pp. 1193
–1206
.13.
King
, G. F.
, Dutton
, J. C.
, and Lucht
, R. P.
, 1999, “Instantaneous, Quantitative Measurements of Molecular Mixing in the Axisymmetric Jet Near Field
,” Phys. Fluids
1070-6631, 11
, pp. 403
–416
.14.
Villermaux
, E.
, and Innocenti
, C.
, 1999, “On the Geometry of Turbulent Mixing
,” J. Fluid Mech.
0022-1120, 393
, pp. 123
–147
.15.
Catrakis
, H. J.
, Aguirre
, R. C.
, Ruiz-Plancarte
, J.
, Thayne
, R. D.
, McDonald
, B. A.
, and Hearn
, J. W.
, 2002, “Large-Scale Dynamics in Turbulent Mixing and the Three-Dimensional Space-Time Behaviour of Outer Fluid Interfaces
,” J. Fluid Mech.
0022-1120, 471
, pp. 381
–408
.16.
Fiedler
, H. E.
, 1998, “Control of Free Turbulent Shear Flows
,” In Flow Control: Fundamentals and Practices
, M.
Gad-el Hak
, A.
Pollard
, and J.-P.
Bonnet
, eds., Springer
, Berlin
, pp. 335
–429
.17.
Hale
, C. A.
, Plesniak
, M. W.
, and Ramadhyani
, S.
, 2000, “Film Cooling Effectiveness for Short Film Cooling Holes Fed by a Narrow Plenum
,” ASME J. Turbomach.
0889-504X, 122
, pp. 553
–557
.18.
Dimotakis
, P. E.
, Catrakis
, H. J.
, and Fourguette
, D. C. L.
, 2001, “Flow Structure and Optical Beam Propagation in High-Reynolds-Number Gas-Phase Shear Layers and Jets
,” J. Fluid Mech.
0022-1120, 433
, pp. 105
–134
.19.
Gad-el Hak
, M.
, 2000, Flow Control: Passive, Active, and Reactive Flow Management
, Cambridge University Press
, Cambridge
.20.
Jumper
, E. J.
, and Fitzgerald
, E. J.
, 2001, “Recent Advances in Aero-Optics
,” Prog. Aerosp. Sci.
0376-0421, 37
, pp. 299
–339
.21.
Catrakis
, H. J.
, and Aguirre
, R. C.
, 2004, “New Interfacial Fluid Thickness Approach in Aero-Optics With Applications to Compressible Turbulence
,” AIAA J.
0001-1452, 42
(10
), pp. 1973
–1981
.22.
Dimotakis
, P. E.
, Miake-Lye
, R. C.
, and Papantoniou
, D. A.
, 1983, “Structure and Dynamics of Round Turbulent Jets
,” Phys. Fluids
0031-9171, 26
, pp. 3185
–3192
.23.
Sreenivasan
, K. R.
, 1991, “Fractals and Multifractals in Fluid Turbulence
,” Annu. Rev. Fluid Mech.
0066-4189, 23
, pp. 539
–600
.24.
Catrakis
, H. J.
, Aguirre
, R. C.
, and Ruiz-Plancarte
, J.
, 2002, “Area-Volume Properties of Fluid Interfaces in Turbulence: Scale-Local Self-Similarity and Cumulative Scale Dependence
,” J. Fluid Mech.
0022-1120, 462
, pp. 245
–254
.25.
Dimotakis
, P. E.
, 2000, “The Mixing Transition in Turbulent Flows
,” J. Fluid Mech.
0022-1120, 409
, pp. 69
–98
.26.
Koochesfahani
, M. M.
, Dimotakis
, P. E.
, and Broadwell
, J. E.
, 1985, “A ‘Flip’ Experiment in a Chemically Reacting Turbulent Mixing Layer
,” AIAA J.
0001-1452, 23
, pp. 1191
–1194
.27.
Koochesfahani
, M. M.
, and Dimotakis
, P. E.
, 1985, “Laser-Induced Fluorescence Measurements of Mixed Fluid Concentration in a Liquid Plane Shear Layer
,” AIAA J.
0001-1452, 23
, pp. 1700
–1707
.28.
Catrakis
, H. J.
, and Aguirre
, R. C.
, 2004, “Interfacial-Fluid Dynamics and the Mixing Efficiency of Turbulent Flows
,” Phys. Fluids
1070-6631, 16
(12
), pp. 4746
–4749
.29.
Aguirre
, R. C.
, Nathman
, J. C.
, and Catrakis
, H. J.
, 2006, “Flow Geometry Effects on the Turbulent Mixing Efficiency
,” ASME J. Fluids Eng.
0098-2202, 129
, pp. 874
–879
.30.
Caulfield
, C. P.
, and Kerswell
, R. R.
, 2001, “Maximal Mixing Rate in Turbulent Stably Stratified Couette Flow
,” Phys. Fluids
1070-6631, 13
(4
), pp. 894
–900
.31.
Everson
, R.
, Manin
, D.
, Sirovich
, L.
, and Winter
, M.
, 1998, “Quantification of Mixing and Mixing Rate From Experimental Observations
,” AIAA J.
0001-1452, 36
(2
), pp. 121
–127
.32.
Geurts
, B. J.
, 2001, “Mixing Efficiency in Turbulent Shear Layers
,” J. Turbul.
1468-5248, 2
(17
), pp. 1
–23
.33.
LaRue
, J. C.
, and Libby
, P. A.
, 1975, “Temperature and Intermittency in the Turbulent Wake of a Heated Cylinder
,” Phys. Fluids
0031-9171, 17
, pp. 873
–878
.34.
Bisset
, D. K.
, Hunt
, J. C.
, and Rogers
, M. M.
, 2002, “The Turbulent/Non-Turbulent Interface Bounding a Far Wake
,” J. Fluid Mech.
0022-1120, 451
, pp. 381
–410
.35.
Joseph
, D. D.
, and Preziosi
, L.
, 1989, “Heat Waves
,” Rev. Mod. Phys.
0034-6861, 61
, pp. 41
–73
.36.
Brown
, G. L.
, and Roshko
, A.
, 1974, “On Density Effects and Large Scale Structure in Turbulent Mixing Layers
,” J. Fluid Mech.
0022-1120, 64
, pp. 775
–816
.37.
Paizis
, S. T.
, and Schwarz
, W. H.
, 1974, “An Investigation of the Topography and Motion of the Turbulent Interface
,” J. Fluid Mech.
0022-1120, 63
(2
), pp. 315
–343
.38.
Catrakis
, H. J.
, Aguirre
, R. C.
, Ruiz-Plancarte
, J.
, and Thayne
, R. D.
, 2002, “Shape Complexity of Whole-Field Three-Dimensional Space-Time Fluid Interfaces in Turbulence
,” Phys. Fluids
1070-6631, 14
, pp. 3891
–3898
.39.
Frederiksen
, R. D.
, Dahm
, W. J. A.
, and Dowling
, D. R.
, 1996, “Experimental Assessment of Fractal Scale Similarity in Turbulent Flows. Part 1: One-Dimensional Intersections
,” J. Fluid Mech.
0022-1120, 327
, pp. 35
–72
.40.
Catrakis
, H. J.
, and Dimotakis
, P. E.
, 1996, “Mixing in Turbulent Jets: Scalar Measures and Isosurface Geometry
,” J. Fluid Mech.
0022-1120, 317
, pp. 369
–406
.41.
Prasad
, R. R.
, and Sreenivasan
, K. R.
, 1989, “Scalar Interfaces in Digital Images of Turbulent Flows
,” Exp. Fluids
0723-4864, 7
, pp. 259
–264
.42.
Aguirre
, R. C.
, and Catrakis
, H. J.
, 2005, “Scalar-Threshold Dependence and Internal Dynamics in Turbulent Jets
,” Phys. Fluids
1070-6631, 17
, p. 038103
.43.
Aguirre
, R. C.
, and Catrakis
, H. J.
, 2004, “Aero-Optical Wavefronts and Scale-Local Characterization In Large-Reynolds-Number Compressible Turbulence
,” AIAA J.
0001-1452, 42
(10
), pp. 1982
–1990
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
