Abstract

This report presents an investigation of the characteristics for transitional natural-convection flow in an open-ended inclined channel heated from below in the air under uniform heat flux intensity and non-Boussinesq condition. The investigated range of modified Rayleigh number and inclination is from 5.93×106 to 1.45×109 and 3090deg to the horizontal, respectively. Fine-resolution implicit large Eddy simulation is performed to solve the compressible governing equations using the modified preconditioned all-speed Roe scheme, hybrid boundary condition, and dual-time-stepping technique. The Nusselt number based on the maximum wall-temperature differs significantly while based on averaged wall-temperature is closer to the previously proposed laminar correlations. Transition is found to be pronounced at a lower angle of inclination (30deg) for the considered heat flux intensity. The absolute magnitude of the critical length for the start and end of the transition when converted to nondimensional parameters is found to be higher compared to similar data for natural convection flow over a flat plate in water but the ratio of the end to start of the transition is found to be comparable. Single-roll longitudinal vortices periodically placed in spanwise direction exists in the transition region whose wavelength is found to be higher than those reported for channel flow under the isothermal condition and flow over a flat plate in water. Correlations for Nusselt number, critical aspect ratio, and vortex wavelength to the modified Rayleigh number are presented.

References

References
1.
Azevedo
,
L. F. A.
, and
Sparrow
,
E. M.
,
1985
, “
Natural Convection in Open-Ended Inclined Channel
,”
ASME J. Heat Transfer
,
107
(
4
), pp.
893
901
.10.1115/1.3247518
2.
Onur
,
N.
,
Sivrioğlu
,
M.
, and
Aktaş
,
M. K.
,
1997
, “
An Experimental Study on the Natural Convection Heat Transfer Between Inclined Plates (Lower Plate Isothermally Heated and the Upper Plate Thermally Insulated as Well as Unheated)
,”
Heat Mass Transfer
,
32
(
6
), pp.
471
476
.10.1007/s002310050147
3.
Manca
,
O.
, and
Nardini
,
S.
,
2001
, “
Thermal Design of Uniformly Heated Inclined Channels in Natural Convection With and Without Radiative Effects
,”
Heat Transfer Eng.
,
22
(
2
), pp.
13
28
.10.1080/014576301462227
4.
Chen
,
Z. D.
,
Bandopadhayay
,
P.
,
Halldorsson
,
J.
,
Byrjalsen
,
C.
,
Heiselberg
,
P.
, and
Li
,
Y.
,
2003
, “
An Experimental Investigation of a Solar Chimney
,”
Building Environ.
,
38
(
7
), pp.
893
906
.10.1016/S0360-1323(03)00057-X
5.
Zuercher
,
E. J.
,
Jacobs
,
J. W.
, and
Chen
,
C. F.
,
1998
, “
Experimental Study of the Stability of Boundary-Layer Flow Along a Heated Inclined Plate
,”
J. Fluid Mech.
,
367
, pp.
1
25
.10.1017/S0022112098001347
6.
Jeschke
,
P.
, and
Beer
,
H.
,
2001
, “
Longitudinal Vortices in a Laminar Natural Convection Boundary Layer Flow on an Inclined Flat Plate and Their Influence on Heat Transfer
,”
J. Fluid Mech.
,
432
, pp.
313
339
.10.1017/S0022112000003190
7.
Biertumpfel
,
R.
, and
Beer
,
H.
,
2003
, “
Natural Convection Heat Transfer Increase at the Laminar-Turbulent Transition in the Presence of Instationary Longitudinal Vortices
,”
Int. J. Heat Mass Transfer
,
46
(
16
), pp.
3109
3117
.10.1016/S0017-9310(03)00079-6
8.
Alzwayi
,
A. S.
,
Paul
,
M. C.
, and
Navarro-Martinez
,
S.
,
2014
, “
Large Eddy Simulation of Transition of Free Convection Flow Over an Inclined Upward Facing Heated Plate
,”
Int. Comm. Heat Mass Transfer
,
57
, pp.
330
340
.10.1016/j.icheatmasstransfer.2014.08.009
9.
Kaiser
,
A. S.
,
Zamora
,
B.
, and
Viedma
,
A.
,
2009
, “
Numerical Correlation for Natural Convective Flows in Isothermal Heated, Inclined and Convergent Channels for High Rayleigh Numbers
,”
Comput. Fluids
,
38
(
1
), pp.
1
15
.10.1016/j.compfluid.2007.07.024
10.
Tsuji
,
T.
,
Nagano
,
Y.
, and
Tagawa
,
M.
,
1991
, “
Themally Driven Turbulent Boundary Layer
,”
Proceedings of the 8th Symposium on Turbulent Shear Flows
, Vol.
1
,
Munich, Germany
, Sept. 9–11, pp.
24.3.1
24.3.6
11.
Abedin
,
M. Z.
,
Tsuji
,
T.
, and
Hattori
,
Y.
,
2009
, “
Direct Numerical Simulation for a Time-Developing Natural-Convection Boundary Layer Along a Vertical Flat Plate
,”
Int. J. Heat Mass Transfer
,
52
(
19–20
), pp.
4525
4534
.10.1016/j.ijheatmasstransfer.2009.03.061
12.
Fusegi
,
T.
, and
Hyun
,
J. M.
,
1994
, “
Laminar and Transitional Natural Convection in an Enclosure With Complex and Realistic Conditions
,”
Int. J. Heat Fluid Flow
,
15
(
4
), pp.
258
268
.10.1016/0142-727X(94)90011-6
13.
Quere
,
P. L.
,
Weisman
,
C.
,
Paillere
,
H.
,
Vierendeels
,
J.
,
Dick
,
E.
,
Becker
,
R.
,
Braack
,
M.
, and
Locke
,
J.
,
2005
, “
Modelling of Natural Convection Flows With Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers—Part 1: Reference Solutions
,”
ESAIM: Math. Modell. Numer. Anal.
,
39
(
3
), pp.
609
616
.10.1051/m2an:2005027
14.
Gray
,
D. D.
, and
Giorgini
,
A.
,
1976
, “
The Validity of the Boussinesq Approximation for Liquids and Gases
,”
Int. J. Heat Mass Transfer
,
19
(
5
), pp.
545
551
.10.1016/0017-9310(76)90168-X
15.
Fu
,
W.-S.
,
Li
,
C.-G.
,
Huang
,
C.-P.
, and
Huang
,
J.-C.
,
2009
, “
An Investigation of a High Temperature Difference Natural Convection in a Finite Length Channel Without Bossinesq Assumption
,”
Int. J. Heat Mass Transfer
,
52
(
11–12
), pp.
2571
2580
.10.1016/j.ijheatmasstransfer.2009.01.012
16.
Li
,
C. G.
,
Tsubokura
,
M.
,
Fu
,
W. S.
,
Jansson
,
N.
, and
Wang
,
W. H.
,
2015
, “
Compressible Direct Numerical Simulation With a Hybrid Boundary Condition of Transitional Phenomena in Natural Convection
,”
Int. J. Heat Mass Transfer
,
90
, pp.
654
664
.10.1016/j.ijheatmasstransfer.2015.06.058
17.
Fu
,
W.-S.
,
Wang
,
W.-H.
, and
Li
,
C.-G.
,
2014
, “
An Investigation of Natural Convection in Parallel Plates With a Heated Top Surface by a Hybrid Boundary Condition
,”
Int. J. Therm. Sci.
,
84
, pp.
48
61
.10.1016/j.ijthermalsci.2014.04.009
18.
Hoffmann
,
K. A.
, and
Chiang
,
S. T.
,
1993
,
Computational Fluid Dynamics for Engineers
, Vol.
I
,
Engineering Education System
.
19.
Hoffmann
,
K. A.
, and
Chiang
,
S. T.
,
1993
,
Computational Fluid Dynamics for Engineers
, Vol.
II
,
Engineering Education System
.
20.
Li
,
Z.
,
Zhang
,
Y.
, and
Chen
,
H.
,
2015
, “
A Low Dissipation Numerical Scheme for Implicit Large Eddy Simulation
,”
Comput. Fluids
,
117
, pp.
233
246
.10.1016/j.compfluid.2015.05.016
21.
Li
,
X. S.
, and
Gu
,
C. W.
,
2013
, “
Mechanism of Roe-Type Schemes for All-Speed Flows and Its Application
,”
Comput. Fluids
,
86
, pp.
56
70
.10.1016/j.compfluid.2013.07.004
22.
Weiss
,
J. M.
, and
Smith
,
W. A.
,
1995
, “
Preconditioning Applied to Variable and Constant Density Flows
,”
AIAA J.
,
33
(
11
), pp.
2050
2056
.10.2514/3.12946
23.
Shen
,
Y.
, and
Zha
,
G.
, “
Simulation of Flows at All Speeds With Implicit High-Order WENO Schemes
,”
AIAA Paper No. 1312
24.
Talukdar
,
D.
,
Li
,
C. G.
, and
Tsubokura
,
M.
,
2018
, “
Numerical Investigation of Buoyancy-Driven Compressible Laminar Flow Using New Method Preconditioned All-Speed Roe Scheme
,”
Int. Commun. Heat Mass Transfer
,
98
, pp.
74
84
.10.1016/j.icheatmasstransfer.2018.08.007
25.
Kim
,
K. H.
, and
Kim
,
C.
,
2005
, “
Accurate, Efficient and Monotonic Numerical Methods for Multi-Dimensional Compressible Flows—Part-II: Multi-Dimensional Limiting Process
,”
J. Comput. Phys.
,
208
(
2
), pp.
570
615
.10.1016/j.jcp.2005.02.022
26.
Xu
,
X. F.
,
Lee
,
J. S.
, and
Pletcher
,
R. H.
,
2005
, “
A Compressible Finite Volume Formulation for Large-Eddy Simulation of Turbulent Pipe Flows at Low Mach Number in Cartesian Coordinates
,”
J. Comput. Phys.
,
203
(
1
), pp.
22
48
.10.1016/j.jcp.2004.08.005
27.
Chen
,
T. S.
,
Tien
,
H. C.
, and
Armaly
,
B. F.
,
1986
, “
Natural Convection on Horizontal, Inclined and Vertical Plates With Variable Surface Temperature or Heat Flux
,”
Int. J. Heat Mass Transfer
,
29
(
10
), pp.
1465
1478
.10.1016/0017-9310(86)90061-X
28.
Vliet
,
G. C.
,
1969
, “
Natural Convection Local Heat Transfer on Constant Heat Flux Inclined Surfaces
,”
Trans. ASME: J. Heat Transfer
,
91
(
4
), pp.
511
517
.10.1115/1.3580235
29.
Sakonidou
,
E. P.
,
Karapantsios
,
T. D.
,
Balouktsis
,
A. I.
, and
Chassapis
,
D.
,
2008
, “
Modelling of the Optimum Tilt of a Solar Chimney for Maximum Air Flow
,”
Sol. Energy
,
82
(
1
), pp.
80
94
.10.1016/j.solener.2007.03.001
30.
Khanal
,
R.
, and
Lei
,
C.
,
2011
, “
Solar Chimney—A Passive Strategy for Natural Ventilation
,”
Energy Build.
,
43
(
8
), pp.
1811
1819
.10.1016/j.enbuild.2011.03.035
31.
Mahajan
,
R. L.
, and
Gebhart
,
B.
,
1979
, “
An Experimental Determination of Transition Limits in a Vertical Natural Convection Flow Adjacent to a Surface
,”
J. Fluid Mech.
,
91
(
01
), pp.
131
154
.10.1017/S0022112079000070
32.
Chen
,
C. C.
,
Labhabi
,
A.
,
Chang
,
H.-C.
, and
Kelly
,
R. E.
,
1991
, “
Spanwise Pairing of finite-Amplitude Longitudinal Vortex Rolls in Inclined Free-Convection Boundary Layers
,”
J. Fluid Mech.
,
231
, pp.
73
111
.10.1017/S0022112091003324
33.
Clifford
,
P. B.
,
1974
, “
The Thermal Structure of Free Convection Turbulence From an Inclined Isothermal Flat Plate and Its Influence on Heat Transfer
,” Master's thesis,
Georgia Institute of Technology
, Atlanta, GA. 
34.
Shaukatullah
,
H.
, and
Gebhart
,
B.
,
1978
, “
An Experimental Investigation of Natural Convection Flow Over an Inclined Surface
,”
Int. J. Heat Mass Transfer
,
21
(
12
), pp.
1481
1490
.10.1016/0017-9310(78)90004-2
35.
Jaluria
,
Y.
, and
Gebhart
,
B.
,
1973
, “
An Experimental Study of Nonlinear Disturbance Behavior in Natural Convection
,”
J. Fluid Mech.
,
61
(
2
), pp.
337
365
.10.1017/S0022112073000753
36.
Wu
,
X.
, and
Moin
,
P.
,
2009
, “
Direct Numerical Simulation of Turbulence in a Nominally Zero-Pressure-Gradient Flat-Plate Boundary Layer
,”
J. Fluid Mech.
,
630
, pp.
5
41
.10.1017/S0022112009006624
You do not currently have access to this content.