A numerical method is developed with the capability to predict transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature was numerically studied on a two-dimensional semi-infinite flat plate. The compressible Reynolds-averaged boundary layer equations are transformed into incompressible form through the Dorodnitsyn–Howarth transformation and then solved with similarity transformations. Turbulence is modeled using a two-layer eddy viscosity model developed by Cebeci and Smith, and the turbulent Prandtl number formulation originally developed by Kays and Crawford. The governing differential equations are discretized with the Keller-box method. The numerical accuracy is validated through grid-independence studies and comparison with the steady state solution. In turbulent flow as in laminar, the transient heat transfer rates are very different from that obtained from quasi-steady analysis. It is found that the time scale for response of the turbulent boundary layer to far-field temperature changes is 40% less than for laminar flow, and the turbulent local Nusselt number is approximately 4 times that of laminar flow at the final steady state.

1.
Zeng
,
P.
, 2004, “
Unsteady Convective Heat Transfer Modeling and Application to Internal Combustion Engines
,” Ph.D. thesis, University of Michigan.
2.
Loubar
,
K.
,
Bellettre
,
J.
, and
Tazerout
,
M.
, 2005, “
Unsteady Heat Transfer Enhancement Around an Engine Cylinder in Order to Detect Knock
,”
ASME J. Heat Transfer
0022-1481,
127
(
3
), pp.
278
286
.
3.
Wang
,
X.
, and
Zhang
,
N.
, 2005, “
Numerical Analysis of Heat Transfer in Pulsating Turbulent Flow in a Pipe
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
3957
3970
.
4.
Zohir
,
A. E.
,
Habib
,
M. A.
,
Attya
,
A. M.
, and
Eid
,
A. I.
, 2006, “
An Experimental Investigation of Heat Transfer to Pulsating Pipe Air Flow With Different Amplitudes
,”
Heat Mass Transfer
0947-7411,
42
, pp.
625
635
.
5.
Atthey
,
D. R.
, 1988, “
An Approximate Thermal Analysis for a Regenerative Heat Exchanger
,”
Int. J. Heat Mass Transfer
0017-9310,
31
, pp.
1431
1441
.
6.
Fujii
,
N.
,
Koshi
,
M.
,
Ando
,
H.
, and
Asaba
,
T.
, 1979, “
Evaluation of Boundary-Layer Effects in Shock-Tube Studies of Chemical Kinetics
,”
Int. J. Chem. Kinet.
0538-8066,
11
, pp.
285
304
.
7.
Nalim
,
M. R.
, 2000, “
Longitudinally Stratified Combustion in Wave Rotors
,”
J. Propul. Power
0748-4658,
16
, pp.
1060
1068
.
8.
Nalim
,
M. R.
,
Li
,
H.
, and
Akbari
,
P.
, 2009, “
Air-Standard Aero-Thermodynamic Analysis of Gas Turbine Engines With Wave Rotor Combustion
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
131
, p.
054506
.
9.
Welch
,
G. E.
, 1996, “
Macroscopic Balance Model for Wave Rotors
,”
AIAA 34th Aerospace Science Meeting and Exhibit
, Reno, NV.
10.
Nalim
,
M. R.
, 1999, “
Assessment of Combustion Modes for Internal Combustion Wave Rotors
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
121
, pp.
265
271
;
(also Report No. NASA TM 107000, Paper No. AIAA-95-2801, 1995).
11.
Li
,
H.
, and
Nalim
,
M. R.
, 2008, “
Thermal Boundary Layer Response to Convected Far-Field Fluid Temperature Changes
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
101001
;
(also
ASME
Paper No. IMECE2007-42188, Seattle, 2007).
12.
Cebeci
,
T.
, and
Smith
,
A. M. O.
, 1974,
Analysis of Turbulent Boundary Layers
,
Academic
,
New York
.
13.
Kays
,
W. M.
, and
Crawford
,
M. E.
, 1993,
Convective Heat and Mass Transfer
,
3rd ed.
,
McGraw-Hill
,
New York
.
14.
Stewartson
,
K.
, 1963,
The Theory of Laminar Boundary Layers in Compressible Fluids
,
Oxford University Press
,
Oxford
.
15.
He
,
J.
,
Kazakia
,
J. Y.
, and
Walker
,
J. D. A.
, 1990, Embedded Function Methods for Supersonic Turbulent Boundary Layers, Paper No. AIAA-90-0306.
16.
Wilcox
,
D. C.
, 2006,
Turbulence Modeling for CFD
,
3rd ed.
,
DCW Industries
,
California
.
17.
Cebeci
,
T.
, and
Bradshaw
,
P.
, 1988,
Physical and Computational Aspects of Convective Heat Transfer
,
Springer-Verlag
,
New York
.
18.
Cebeci
,
T.
, 1977, “
Calculation of Unsteady Two-Dimensional Laminar and Turbulent Boundary Layers With Fluctuations in External Velocity
,”
Proc. R. Soc. London, Ser. A
0950-1207,
355
, pp.
225
238
.
19.
Kafoussias
,
N. G.
, and
Xenos
,
M. A.
, 2000, “
Numerical Investigation of Two-Dimensional Turbulent Boundary-Layer Compressible Flow With Adverse Pressure Gradient and Heat and Mass Transfer
,”
Acta Mech.
0001-5970,
141
, pp.
201
223
.
20.
Weigand
,
B.
,
Ferguson
,
J. R.
, and
Crawford
,
M. E.
, 1997, “
An Extended Kays and Crawford Turbulent Prandtl Number Model
,”
Int. J. Heat Mass Transfer
0017-9310,
40
, pp.
4191
4196
.
21.
Schlichting
,
H.
, and
Gersten
,
K.
, 2001,
Boundary Layer Theory
,
8th ed.
,
Springer-Verlag
,
Berlin
.
22.
Keller
,
H. B.
, 1978, “
Numerical Methods in Boundary-Layer Theory
,”
Annu. Rev. Fluid Mech.
0066-4189,
10
, pp.
417
433
.
23.
Cebeci
,
T.
, and
Jean
,
C.
, 2005,
Modeling and Computation of Boundary Layer Flows
,
2nd ed.
,
Springer
,
New York
.
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