The modelling of differential diffusion with a conditional moment closure (CMC) method is considered. Direct numerical simulations for scalar fields in homogeneous isotropic decaying turbulence are used to quantify the non-unity Schmidt number effects. Unlike the equal molecular diffusion case, where terms involving deviations from the conditional average usually make a negligible contribution, these terms contribute significantly to the equations governing the evolution of the conditional average scalar in the presence of different molecular diffusion coefficients. Together with the conditional scalar dissipation they come to balance conditional scalar diffusion, the driving force of the differential diffusion effects. The shape of the conditional averages of these terms in mixture fraction space coincides with the approximate shape of the conditional average differential diffusion, Qz. Therefore, dividing by Qz they are only functions of time. Conditional moment closure leads to good predictions of Qz provided the time function is properly modelled. A model for the time scale is suggested.

1.
R. W. Bilger, “Turbulent flows with nonpremixed reactants,” Turbulent Reactive Flows, edited by F. A. Libby and F. A. Williams (Springer, New York, 1980), pp. 65–113.
2.
G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1982).
3.
M. C. Drake, M. Lapp, C. M. Penney, S. Warshaw, and B. W. Gerhold, “Measurements of temperature and concentration fluctuations in turbulent diffusion flames using pulped Raman spectroscopy,” 18th Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1521–1531.
4.
M. C. Drake, R. W. Pitz, and M. Lapp, “Laser measurements on nonpremixed H2-air flames for assessments of turbulent combustion models,” AIAA 22nd Aerospace Science Meeting, AIAA-84–0544, Reno (1984).
5.
A. R. Kerstein, R. W. Dibble, M. B. Long, B. Yip, and K. Lyons, “Measurement and computation of differential molecular diffusion in a turbulent jet,” Seventh Symposium on Turbulent Shear Flows, pp. 14.2.1–14.2.5 (1989).
6.
L. L.
Smith
,
R. W.
Dibble
,
L.
Talbot
,
R. S.
Barlow
, and
C. D.
Carter
, “
Laser Raman scattering measurements of differential molecular diffusion in nonreacting turbulent jets of H2/CO2 mixing with air
,”
Phys. Fluids
7
,
1455
(
1995
).
7.
L. L. Smith, R. W. Dibble, L. Talbot, R. S. Barlow, and C. D. Carter, “Laser Raman scattering measurements of differential diffusion in nonreacting and reacting laminar and turbulent jet flow,” 31st Aerospace Science Meeting & Exhibit, AIAA-93–0804, Reno (1993).
8.
P. K. Yeung and B. Luo, “Simulation and modelling of differential diffusion in homogeneous turbulence,” Tenth Symposium on Turbulent Shear Flow, pp. 31.7–31.12 (1995).
9.
P. K.
Yeung
and
S. B.
Pope
, “
Differential diffusion of passive scalars in isotropic turbulence
,”
Phys. Fluids A
5
,
2467
(
1993
).
10.
R. W.
Bilger
and
R. W.
Dibble
, “
Differential diffusion effects in turbulent mixing
,”
Comb. Sci. Tech.
28
,
161
(
1982
).
11.
R. W.
Bilger
, “
Molecular transport effects in turbulent diffusion flames at moderate Reynolds number
,”
AIAA J.
20
,
962
(
1982
).
12.
A. Yu.
Klimenko
, “
Multicomponent diffusion of various admixtures in turbulent flow
,”
Fluid Dyn.
25
,
327
(
1990
).
13.
R. W.
Bilger
, “
Conditional moment closure for turbulent reacting flow
,”
Phys. Fluids A
5
,
436
(
1993
).
14.
N. S. A. Smith, R. W. Bilger, and J.-Y. Chen, “Modelling of nonpremixed hydrogen jet flames using a conditional moment closure method,” Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1992), pp. 263–269.
15.
W. E.
Mell
,
V.
Nilsen
,
G.
Kosály
, and
J. J.
Riley
, “
Investigation of closure models for nonpremixed turbulent reacting flows
,”
Phys. Fluids
6
,
1331
(
1994
).
16.
W. E. Mell, “A validity investigation of the conditional moment closure model for turbulent combustion,” submitted to Phys. Fluids (1995).
17.
N.
Swaminathan
and
S.
Mahalingam
, “
Assessment of conditional moment closure for single and multistep chemistry
,”
Comb. Sci. Tech.
112
,
301
(
1996
).
18.
P.
Givi
, “
Model-free simulations of turbulent reactive flows
,”
Prog. Energy Combust. Sci.
15
,
1
(
1989
).
19.
V. Nilsen and G. Kosály, “Differentially diffusing scalars in turbulence,” submitted to Phys. Fluids (1996).
20.
S. S.
Girimaji
, “
On the modelling of scalar diffusion in isotropic turbulence
,”
Phys. Fluids A
4
,
2529
(
1992
).
21.
R. M.
Kerr
, “
Higher-order derivative correlations and alignment of smallscale structures in isotropic numerical turbulence
,”
J. Fluid Mech.
153
,
31
(
1985
).
22.
N. Swaminathan, “Structure and dynamics of turbulent and laminar reaction zones,” Ph.D. thesis, University of Colorado, 1994.
23.
W. E. Mell, “An investigation of closure models for nonpremixed turbulent reacting flow,” Ph.D. thesis, University of Washington, 1994.
24.
V. Nilsen, “Investigation of differential diffusion effects in isotropic decaying turbulence,” APS conference (1995).
25.
A. Yu. Klimenko, “Conditional moment closure and diffusion in conserved scalar phase space,” ECOLEN Report (1992).
26.
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
).
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