The effect of the uniform fluid properties approximation (Oberbeck-Boussinesq (OB)) in turbulent mixed convection is investigated via direct numerical simulation (DNS) of water flows with viscosity (μ) and thermal expansion coefficient (β) both independently and simultaneously varying with temperature (non-Oberbeck-Boussinesq conditions (NOB)). Mixed convection is analyzed for the prototypical case of Poiseuille-Rayleigh-Bénard (PRB) turbulent channel flow. In PRB flows, the combination of buoyancy driven (Rayleigh-Bénard) with pressure driven (Poiseuille) effects produce a complex flow structure, which depends on the relative intensity of the flow parameters (i.e., the Grashof number, Gr, and the shear Reynolds number, Reτ). In liquids, however, temperature variations induce local changes of fluid properties which influence the macroscopic flow field. We present results for different absolute values of the shear Richardson numbers (Riτ=|Gr/Reτ2|) under constant temperature boundary conditions. As Riτ is increased buoyant thermal plumes are generated, which induce large scale thermal convection that increases momentum and heat transport efficiency. Analysis of friction factor (Cf) and Nusselt number (Nu) for NOB conditions shows that the effect of viscosity is negligible, whereas the effect of thermal expansion coefficient is significant. Statistics of mixing show that (i) mixing increases for increasing Riτ (and decreases for increasing Reτ) and (ii) the effect of thermal expansion coefficient on mixing increases for increasing Riτ (and decreases for increasing Reτ). A simplified phenomenological model to predict heat transfer rates in PRB flows has also been developed.

References

References
1.
Wang
,
M.
,
Fu
,
S.
, and
Zhang
,
G.
,
2002
, “
Large-Scale Spiral Structures in Turbulent Thermal Convection Between Two Vertical Plates
,”
Phys. Rev. E
,
66
, p.
066306
.10.1103/PhysRevE.66.066306
2.
Hartmann
,
D. L.
,
Moy
,
L. A.
, and
Fu
,
Q.
,
2001
, “
Tropical Convection and the Energy Balance at the Top of the Atmosphere
,”
J. Climate
,
14
, pp.
4495
–4511.10.1175/1520-0442(2001)014<4495:TCATEB>2.0.CO;2
3.
Lumley
,
J. L.
,
Zeman
,
O.
, and
Siess
,
J.
,
2009
, “
The Influence of Buoyancy on Turbulent Transport
,”
J. Fluid Mech.
,
84
, pp. 581–597.10.1017/S0022112078000348
4.
Incropera
,
F. P.
, and
Dewitt
,
D. P.
,
1985
,
Fundamentals of Heat and Mass Transfer
,
John Wiley and Sons Inc.
,
New York
.
5.
Sugiyama
,
K.
,
Calzavarini
,
E.
,
Grossmann
,
S.
, and
Lohse
,
D.
,
2009
, “
Flow Organization in Two-Dimensional Non-Oberbeck-Boussinesq Rayleigh-Benard Convection in Water
,”
J. Fluid Mech.
,
637
, pp.
105
–135.10.1017/S0022112009008027
6.
Timchenko
,
V.
,
2012
, “
Eddie Leonardi Memorial Lecture: Natural Convection From Earth to Space
,”
ASME J. Heat Transfer
,
134
, p.
031014
.10.1115/1.4005149
7.
Zonta
,
F.
,
Marchioli
,
C.
, and
Soldati
,
A.
,
2011
, “
Time Behavior of Heat Fluxes in Thermally Coupled Turbulent Dispersed Particle Flows
,”
Acta Mech.
,
218
, pp. 367–373.10.1007/s00707-010-0420-8
8.
Lee
,
J.
,
Gharagozloo
,
P. E.
,
Kolade
,
B.
,
Eaton
,
J. K.
, and
Goodson
,
K. E.
,
2010
, “
Nanofluid Convection in Microtubes
,”
ASME J. Heat Transfer
,
132
, p.
092401
.10.1115/1.4001637
9.
Arcen
,
B.
,
Taniere
,
A.
, and
Khalij
,
M.
,
2012
, “
Heat Transfer in a Turbulent Particle-Laden Channel Flow
,”
Int. J. Heat Mass Transfer
,
55
, pp.
6519
–6529.10.1016/j.ijheatmasstransfer.2012.06.058
10.
Ahlers
,
G.
,
Grossmann
,
S.
, and
Lohse
,
D.
,
2009
, “
Heat Transfer and Large Scale Dynamics in Turbulent Rayleigh-Benard Convection
,”
Rev. Mod. Phys.
,
81
, pp.
503
–537.10.1103/RevModPhys.81.503
11.
Verzicco
,
R.
, and
Camussi
,
R.
,
2003
, “
Numerical Experiments on Strongly Turbulent Thermal Convection in a Slender Cylindrical Cell
,”
J. Fluid Mech.
,
477
, pp.
19
–49.10.1017/S0022112002003063
12.
Xia
,
C.
, and
Murthy
,
J. Y.
,
2002
, “
Buoyancy Driven Flow Transitions in Deep Cavities Heated From Below
,”
ASME J. Heat Transfer
,
124
, pp.
650
–659.10.1115/1.1481356
13.
Komori
,
S.
,
Ueda
,
H.
,
Ogino
,
F.
, and
Mizushina
,
T.
,
1982
, “
Turbulence Structures in Unstably-Stratified Open-Channel Flow
,”
Phys. Fluids
,
25
, pp.
1539
–1546.10.1063/1.863941
14.
Fukui
,
K.
, and
Nakajima
,
M.
,
1985
, “
Unstable Stratification Effects on Turbulent Shear Flow in the Wall Region
,”
Int. J. Heat Mass Transfer
,
28
, pp.
2343
–2352.10.1016/0017-9310(85)90053-5
15.
Fukui
,
K.
,
Nakajima
,
M.
, and
Ueda
,
H.
,
1991
, “
Coherent Structure of Turbulent Longitudinal Vortices in Unstably-Stratified Turbulent Flow
,”
Int. J. Heat Mass Transfer
,
34
, pp.
2373
–2385.10.1016/0017-9310(91)90062-J
16.
Domaradzki
,
J. A.
, and
Metcalfe
,
P. W.
,
1988
, “
Direct Numerical Simulations of the Effects of Shear on Turbulent Rayleigh-Benard Convection
,”
J. Fluid Mech.
,
193
, pp.
499
–531.10.1017/S002211208800223X
17.
Iida
,
O.
, and
Kasagi
,
N.
,
1997
, “
Direct Numerical Simulation of Unstably Stratified Turbulent Channel Flow
,”
ASME J. Heat Transfer
,
119
, pp.
53
–67.10.1115/1.2824100
18.
Zainali
,
A.
, and
Lessani
,
B.
,
2010
, “
Large-Eddy Simulation of Unstably Stratified Turbulent Channel Flow With High Temperature Differences
,”
Int. J. Heat Mass Transfer
,
53
, pp.
4865
–4875.10.1016/j.ijheatmasstransfer.2010.06.006
19.
Zonta
,
F.
,
Marchioli
,
C.
, and
Soldati
,
A.
,
2012
, “
Modulation of Turbulence in Forced Convection by Temperature-Dependent Viscosity
,”
J. Fluid Mech.
,
697
, pp.
150
–174.10.1017/jfm.2012.67
20.
Zonta
,
F.
,
Onorato
,
M.
, and
Soldati
,
A.
,
2012
, “
Turbulence and Internal Waves in Stably-Stratified Channel Flow With Temperature-Dependent Fluid Properties
,”
J. Fluid Mech.
,
697
, pp.
175
–203.10.1017/jfm.2012.51
21.
Kerr
,
R.
, and
Herring
,
J. R.
,
2000
, “
Prandtl Number Dependence of Nusselt Number in Direct Numerical Simulations
,”
J. Fluid Mech.
,
419
, pp.
325
–344.10.1017/S0022112000001464
22.
Parodi
,
A.
,
von Hardenberg
,
J.
,
Passoni
,
G.
,
Provenzale
,
A.
, and
Spiegel
,
E. A.
,
2004
, “
Clustering of Plumes in Turbulent Convection
,”
Phys. Rev. Lett.
,
92
, p.
194503
.10.1103/PhysRevLett.92.194503
23.
Dean
,
R. B.
,
1978
, “
Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow
,”
ASME J. Fluid Eng.
,
100
, pp.
215
–223.10.1115/1.3448633
24.
Sieder
,
E. N.
, and
Tate
,
G. E.
,
1936
, “
Heat Transfer and Pressure Drop of Liquids in Tubes
,”
Ind. Eng. Chem.
,
28
, pp.
1429
–1435.10.1021/ie50324a027
25.
Perry
,
A.
, and
Chong
,
M. S.
,
1987
, “
A Description of Eddying Motions and Flow Patterns Using Critical Point Concepts
,”
Annu. Rev. Fluid Mech.
,
9
, pp.
125
–155.10.1146/annurev.fl.19.010187.001013
26.
Schoppa
,
W.
, and
Hussain
,
F.
,
2002
, “
Coherent Structure Generation in Near-Wall Turbulence
,”
J. Fluid Mech.
,
453
, pp.
57
–108.10.1017/S002211200100667X
27.
Xi
,
H.
,
Lam
,
S.
, and
Xia
,
K.
,
2004
, “
From Laminar Plumes to Organized Flows: The Onset of Large Scale Circulation in Turbulent Thermal Convection
,”
J. Fluid Mech.
,
503
, pp.
47
–56.10.1017/S0022112004008079
28.
Hetsroni
,
G.
,
Yarin
,
L. P.
, and
Kaftori
,
D.
,
1996
, “
A Mechanistic Model for Heat Transfer From a Wall to a Fluid
,”
Int. J. Heat Mass Transfer
,
39
, pp.
1475
–1478.10.1016/0017-9310(95)00221-9
29.
Schlichting
,
H.
,
1979
,
Boundary Layer Theory
,
McGraw-Hill
,
New York
.
30.
Peltier
,
W. R.
, and
Caulfield
,
C. P.
,
2003
, “
Mixing Efficiency in Stratified Shear Flows
,”
Annu. Rev. Fluid Mech.
,
35
, pp.
135
–167.10.1146/annurev.fluid.35.101101.161144
31.
Fernando
,
H. J. S.
,
1991
, “
Turbulent Mixing in Stratified Fluids
,”
Annu. Rev. Fluid Mech.
,
23
, pp.
455
–493.10.1146/annurev.fl.23.010191.002323
32.
Lawrie
,
A. G. W.
, and
Dalziel
,
S. B.
,
2011
, “
Rayleigh-Taylor Mixing in an Otherwise Stable Stratification
,”
J. Fluid Mech.
,
688
, pp.
507
–527.10.1017/jfm.2011.398
33.
Sameen
,
A.
,
Verzicco
,
R.
, and
Sreenivasan
,
K. R.
,
2009
, “
Specific Role of Fluid Properties in Non-Boussinesq Thermal Convection at the Rayleigh Number of 2 × 108
,”
Europhys. Lett.
,
86
, p.
14006
.10.1209/0295-5075/86/14006
You do not currently have access to this content.