The relation between the velocity and the enthalpy in steady shear flow is expressed by the Crocco–Busemann relation, which states that for adiabatic conditions the total enthalpy remains constant throughout the shear layer when the Prandtl number is one. The subject of the present Technical Brief is the rational extension of this concept in case the Prandtl number differs from one. The comparison between wall-bounded and free shear flows is studied in particular, as well as the possible application of the concept in turbulent shear flow.

1.
Schlichting
,
H.
, 1979,
Boundary-Layer Theory
,
7th ed.
McGraw-Hill
, NY.
2.
White
,
F. M.
, 1991,
Viscous Fluid Flow
,
2nd ed.
McGraw-Hill
, New York.
3.
Schetz
,
J. A.
, 1993,
Boundary Layer Analysis
,
Prentice–Hall
, Englewood Cliffs, NJ.
4.
Eckert
,
E. R. G.
, 1986, “
Energy Separation in Fluid Flows
,”
Int. Commun. Heat Mass Transfer
0735-1933,
13
, pp.
127
143
.
5.
Smits
,
A. J.
, and
Dussauge
,
J. P.
, 1996,
Turbulent Shear Layers in Compressible Flow
,
American Institute of Physics
, Woodbury, NY.
6.
Van Oudheusden
,
B. W.
, 1997, “
A Complete Crocco Integral for Two-Dimensional Laminar Boundary Layer Flow Over an Adiabatic Wall for Prandtl Numbers Near Unity
,”
J. Fluid Mech.
0022-1120,
353
, pp.
313
330
.
7.
Van Oudheusden
,
B. W.
, 2005, “
Energy Separation in Steady Separated Wake Flow
,”
J. Fluids Eng.
0098-2202,
127
, pp.
611
614
.
8.
Anderson
,
J. D.
, 1989,
Hypersonic and High Temperature Gas Dynamics
,
McGraw-Hill
, New York.
9.
Van Oudheusden
,
B. W.
, 2004, “
Compressibility Effects on the Extended Crocco Relation and the Thermal Recovery Factor in Laminar Boundary Layer Flow
,”
J. Fluids Eng.
0098-2202,
126
, pp.
32
41
.
10.
Dorrance
,
W. H.
, 1962,
Viscous Hypersonic Flow
,
McGraw-Hill
, New York.
11.
Tennekes
,
H.
, and
Lumley
,
J. L.
, 1972,
A First Course in Turbulence
,
MIT Press
, Cambridge, MA.
12.
Rubesin
,
M. W.
, 1953, “
A Modified Reynolds Analogy for the Compressible Turbulent Boundary Layer on a Flat Plate
,” NACA Technical Note 2917.
13.
Guarini
,
S. E.
,
Moser
,
R. D.
,
Shariff
,
K.
, and
Wray
,
A.
, 2000, “
Direct Numerical Simulation of a Supersonic Turbulent Boundary Layer at Mach 2.5
,”
J. Fluid Mech.
0022-1120,
414
, pp.
1
33
.
14.
Van Oudheusden
,
B. W.
, 2004, “
The Reference Temperature Method Reconsidered and its Relation to Compressible Couette Flow
,”
IUTAM Symposium on One Hundred Years of Boundary Layer Research
, Göttingen, Germany, August 2004.
15.
Whitfield
,
D. L.
, and
High
,
M. D.
, 1977, “
Velocity–Temperature Relations in Turbulent Boundary Layers with Nonunity Prandtl Numbers
,”
AIAA J.
0001-1452,
15
, pp.
431
434
.
You do not currently have access to this content.