Conserved scalar (temperature) filtered density function (FDF) is studied experimentally in the fully developed region of a turbulent jet with Taylor-microscale Reynolds numbers of 293 and 190. We obtain the FDFs using one-dimensional box filters of widths Δ ranging from 30 to 248 scalar dissipation scales φ) as well as a two-dimensional box filter (Δ/ηφ=90) which consists of three discrete sensors. Taylor’s hypothesis is used to perform streamwise filtering operations. The mean conserved scalar FDF conditioned on the resolvable-scale scalar fluctuations 〈φ〉L and the subgrid scale (SGS) variance 〈φ″2L (log-normally distributed) is found to be bimodal when 〈φ″2L/〈φ″2 is large, indicating that the conditional SGS mixing is nearly binary. For small 〈φ″2L/〈φ″2 (<1) the conditional FDF is approximately Gaussian. The kurtosis of the conditional FDF decreases with increasing SGS variance and is independent of the filter widths for large SGS variance. The bimodal distribution can be symmetric or asymmetric depending on the curvature of the resolvable-scale scalar. As the SGS variance increases, the conditional scalar differences for separations comparable to the filter widths also change from Gaussian to bimodal distributions. At the same time the conditional SGS scalar changes from approximately isotropic to strongly anisotropic. The results show that the contributions to the bimodal distributions come primarily from the SGS scales comparable to the filter width. It is remarkable that similarities exist between the bimodal conditional FDFs obtained here in a fully developed jet and bimodal probability density functions observed in the early stages of binary scalar mixing. The present study provides a physical basis for the assumed FDF method for conserved scalars used in large-eddy simulation of turbulent combustion.

1.
P.
Givi
, “
Model free simulations of turbulent reacting flows
,”
Prog. Energy Combust. Sci.
15
,
1
(
1989
).
2.
S. B. Pope, “Computations of turbulent combustion: Progress and challenges,” in Proceedings of the 23rd International Symposium on Combustion, 1990, pp. 591–612.
3.
F.
Gao
and
E. E.
O’Brien
, “
A large-eddy simulation scheme for turbulent reacting flows
,”
Phys. Fluids A
5
,
1282
(
1993
).
4.
C. Madnia and P. Givi, “Direct numerical simulation and large eddy simulation of reacting homogeneous turbulence,” in Large Eddy Simulation of Complex Engineering and Geophysical Flows, edited by B. Galperin and S. Orszag (Cambridge University Press, Cambridge, 1993), pp. 315–346.
5.
S. Menon, P. A. McMurtry, and A. K. Kerstein, “A liner eddy subgrid model of turbulent combustion,” in Ref. 4, pp. 287–314.
6.
A. W.
Cook
and
J. J.
Riley
, “
A subgrid model for equilibrium chemistry in turbulent flows
,”
Phys. Fluids
6
,
2868
(
1994
).
7.
S. I. Moller, E. Lundgren, and C. Fureby, “Large eddy simulation of unsteady combustion,” in Proceedings of the 26th International Symposium on Combustion, 1993, pp. 241–248.
8.
J.
Jiménez
,
A.
Linan
,
M. M.
Rogers
, and
F. J.
Higuera
, “
A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows
,”
J. Fluid Mech.
349
,
149
(
1997
).
9.
A. W.
Cook
and
J. J.
Riley
, “
Subgrid-scale modeling for turbulent reacting flows
,”
Combust. Flame
112
,
593
(
1998
).
10.
P. J.
Colucci
,
F. A.
Jaberi
,
P.
Givi
, and
S. B.
Pope
, “
Filtered density function for large eddy simulation of turbulent reacting flows
,”
Phys. Fluids
10
,
499
(
1998
).
11.
P. E.
DesJardin
and
S. H.
Frankel
, “
Large eddy simulation of a nonpremixed reacting jet: Application and assessment of subgrid-scale combustion models
,”
Phys. Fluids
10
,
2298
(
1998
).
12.
W. K.
Bushe
and
H.
Steiner
, “
Conditional moment closure for large eddy simulation of nonpremixed turbulent reacting flows
,”
Phys. Fluids
11
,
1896
(
1999
).
13.
A. W.
Cook
,
J. J.
Riley
, and
G.
Kosály
, “
A laminar flamelet approach to subgrid-scale chemistry in turbulent flows
,”
Combust. Flame
109
,
332
(
1997
).
14.
F. C.
Lockwood
and
A. S.
Naguib
, “
The prediction of the fluctuations in the properties of free, round-jet, turbulent, diffusion flames
,”
Combust. Flame
24
,
109
(
1975
).
15.
J. Janicka and W. Kollmann, “A two-variables formalism for the treatment of chemical reaction in turbulent H2-air diffusion flames,” in Proceedings of the Seventh International Symposium on Combustion, 1979, pp. 421–430.
16.
S. B. Pope, “Probability distributions of scalars in turbulent shear flows,” in Turbulent Shear Flows 2, edited by L. Bradbury and F. Durst (Springer, New York, 1979), pp. 7–16.
17.
E.
Effelsberg
and
N.
Peters
, “
A composite model for the conserved scalar PDF
,”
Combust. Flame
50
,
351
(
1983
).
18.
S. B.
Pope
, “
PDF methods for turbulent reacting flows
,”
Prog. Energy Combust. Sci.
11
,
119
(
1985
).
19.
C.
Wall
,
B. J.
Boersma
, and
P.
Moin
, “
An evaluation of the assumed beta probability density function subgrid-scale model for large eddy simulation of nonpremixed, turbulent combustion with heat release
,”
Phys. Fluids
12
,
2522
(
2000
).
20.
F. A.
Jaberi
,
P. J.
Colucci
,
S.
James
,
P.
Givi
, and
S. B.
Pope
, “
Filtered mass density function for large eddy simulation of turbulent reacting flows
,”
J. Fluid Mech.
401
,
85
(
1999
).
21.
S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
22.
J. A.
Langford
and
R. D.
Moser
, “
Optimal LES formulations for isotropic turbulence
,”
J. Fluid Mech.
398
,
321
(
1999
).
23.
R. W. Bilger, “Turbulent flows with nonpremixed reactants,” in Turbulent Reacting Flows, edited by P. Libby and F. Williams (Springer, New York, 1980), pp. 65–113.
24.
N.
Peters
, “
Laminar diffusion flamelet models in non-premixed turbulent combustion
,”
Prog. Energy Combust. Sci.
10
,
319
(
1984
).
25.
R.
Bilger
, “
Conditional moment closure for turbulent reacting flow
,”
Phys. Fluids A
5
,
436
(
1993
).
26.
A. Y.
Klimenko
, “
Multicomponent diffusion of various admixtures in turbulent flow
,”
Fluid Dyn.
25
,
327
(
1990
).
27.
C. J. Chen and W. Rodi, Vertical Turbulent Buoyant Jets (Pergamon, New York, 1980).
28.
C.
Tong
,
J. C.
Wyngaard
,
S.
Khanna
, and
J. G.
Brasseur
, “
Resolvable- and subgrid-scale measurement in the atmospheric surface layer: Technique and issues
,”
J. Atmos. Sci.
55
,
3135
(
1998
).
29.
C.
Tong
,
J. C.
Wyngaard
, and
J. G.
Brasseur
, “
Experimental study of subgrid-scale stress in the atmospheric surface layer
,”
J. Atmos. Sci.
56
,
2277
(
1999
).
30.
F.
Porté-Agel
,
M. B.
Parlange
,
C.
Meneveau
,
W. E.
Eichinger
, and
M.
Pahlow
, “
Subgrid-scale dissipation in the atmospheric surface layer: Effects of stability and filter dimension
,”
J. Atmos. Sci.
57
,
75
(
2000
).
31.
S.
Cerutti
and
C.
Meneveau
, “
Statistics of filtered velocity in grid and wake turbulence
,”
Phys. Fluids
12
,
1143
(
2000
).
32.
S.
Cerutti
,
C.
Meneveau
, and
O. M.
Kino
, “
Spectral and hyper eddy viscosity in high-Reynolds-number turbulence
,”
J. Fluid Mech.
421
,
307
(
2000
).
33.
F. C.
Lockwood
and
H. A.
Moneib
, “
Fluctuating temperature measurements in a heated round free jet
,”
Combust. Flame
22
,
209
(
1980
).
34.
M. C.
Drake
,
R. W.
Pitz
, and
W.
Shyy
, “
Conserved scalar probability functions on a turbulent jet flame
,”
J. Fluid Mech.
171
,
27
(
1986
).
35.
C.
Tong
and
Z.
Warhaft
, “
Scalar dispersion and mixing in a jet
,”
J. Fluid Mech.
292
,
1
(
1995
).
36.
A. N.
Kolmogorov
, “
A refinement of previous hypothesis concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
,”
J. Fluid Mech.
13
,
82
(
1962
).
37.
K. A.
Buch
and
W. J. A.
Dahm
, “
Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. 1. Sc≫1
,”
J. Fluid Mech.
317
,
21
(
1996
).
38.
K. A.
Buch
and
W. J. A.
Dahm
, “
Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. 2. Sc≈1
,”
J. Fluid Mech.
364
,
1
(
1998
).
39.
R. A.
Antonia
and
C. W.
Van Atta
, “
Structure functions of temperature fluctuations in turbulent shear flows
,”
J. Fluid Mech.
84
,
561
(
1978
).
40.
V.
Eswaran
and
S. B.
Pope
, “
Direct numerical simulations of the turbulent mixing of a passive scalar
,”
Phys. Fluids
31
,
506
(
1988
).
41.
E. E.
O’Brien
and
T. L.
Jiang
, “
The conditional dissipation rate of an initially binary scalar in homogeneous turbulence
,”
Phys. Fluids A
3
,
3121
(
1991
).
42.
R. S.
Miller
,
S. H.
Frankel
,
C. K.
Madnia
, and
P.
Givi
, “
Johnson-Edgeworth translation for probability modeling of binary mixing in turbulent flows
,”
Combust. Sci. Technol.
91
,
21
(
1993
).
43.
M. S.
Uberoi
and
P. I.
Singh
, “
Turbulent mixing in a two-dimensional jet
,”
Phys. Fluids
18
,
764
(
1975
).
44.
W. J. A.
Dahm
and
P. E.
Dimotakis
, “
Mixing at large Schmidt number in the self-similar far field of turbulent jets
,”
J. Fluid Mech.
217
,
299
(
1987
).
45.
A. R.
Kerstein
and
R. W.
Schefer
, “
A conditional similarity concept for turbulent shear flow, with application to mixing in a round jet
,”
Phys. Fluids
6
,
642
(
1994
).
46.
C.
Tong
and
Z.
Warhaft
, “
On passive scalar derivative statistics in grid turbulence
,”
Phys. Fluids
6
,
2165
(
1994
).
47.
G. R.
Reutsch
and
M. R.
Maxey
, “
The evolution of small-scale structures in homogeneous isotropic turbulence
,”
Phys. Fluids A
4
,
2747
(
1992
).
48.
A. R.
Masri
,
R. W.
Dibble
, and
R. S.
Barlow
, “
The structure of turbulent nonpremixed flames revealed by Raman-Rayleigh-LIF measurements
,”
Prog. Energy Combust. Sci.
22
,
307
(
1996
).
49.
A. D.
Leonard
and
J. C.
Hill
, “
Scalar dissipation and mixing in turbulent reacting flows
,”
Phys. Fluids A
3
,
1286
(
1991
).
50.
M. R.
Overholt
and
S. B.
Pope
, “
Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence
,”
Phys. Fluids
8
,
3128
(
1996
).
51.
P. K.
Yeung
, “
Correlations and conditional statistics in differential diffusion: Scalars with uniform mean gradients
,”
Phys. Fluids
10
,
2621
(
1998
).
52.
C.
Gibson
,
C.
Friehe
, and
S. O.
McConnell
, “
Structure of skewed turbulent fields
,”
Phys. Fluids
20
,
S156
(
1977
).
53.
K. R.
Sreenivasan
,
R. A.
Antonia
, and
D.
Britz
, “
Local isotropy and large scale structure in a heated jet
,”
J. Fluid Mech.
94
,
745
(
1979
).
54.
S.
Tavoularis
and
S.
Corrsin
, “
Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. 2. The fine structure
,”
J. Fluid Mech.
104
,
349
(
1981
).
55.
K. R.
Sreenivasan
, “
On local isotropy of passive scalars in turbulent shear flows
,”
Proc. R. Soc. London, Ser. A
434
,
165
(
1991
).
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