A theory is presented for predicting the production rate of turbulent spots. The theory, based on that by Mayle–Schulz for bypass transition, leads to a new correlation for the spot production rate in boundary layer flows with a zero pressure gradient. The correlation, which agrees reasonably well with data, clearly shows the effects of both free-stream turbulence level and length scale. In addition, the theory provides an estimate for the lowest level of free-stream turbulence causing bypass transition.

1.
Baines
W. D.
, and
Pederson
E. G.
,
1951
, “
An Investigation of Flow Through Screens
,”
Trans. ASME
, Vol.
73
, pp.
467
480
.
2.
Chen
K. K.
, and
Thyson
N. A.
,
1971
, “
Extension of Emmons’ Spot Theory to Flows on Blunt Bodies
,”
AIAA Journal
, Vol.
9
, pp.
821
825
.
3.
Dhawan
S.
, and
Narasimha
R.
,
1958
, “
Some Properties of Boundary Layer Flow During Transition From Laminar to Turbulent Motion
,”
J. Fluid Mech.
, Vol.
3
, pp.
418
436
.
4.
Dullenkopf
K.
, and
Mayle
R. E.
,
1995
, “
An Account of Free-Stream-Turbulence Length Scale on Laminar Heat Transfer
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
117
, pp.
401
406
.
5.
Dyban, E., and Epik, E., 1985, Thermal/Mass Transport and Hydrodynamics of Turbulent Flows, Kiev [in Russian].
6.
Emmons
H. W.
,
1951
, “
The Laminar–Turbulent Transition in a Boundary Layer—Part I
,”
J. Aero. Sci.
, Vol.
18
, pp.
490
498
.
7.
Emmons, H. W., and Bryson, A. E., 1951, “The Laminar–Turbulent Transition in a Boundary Layer—Part II,” Proc. 1st U.S. Nat. Cong. Theoretical and Appl. Mech., pp. 859–868.
8.
Gostelow
J. P.
, and
Blunden
A. R.
,
1989
, “
Investigations of Boundary Layer Transition in Adverse Pressure Gradient
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
111
, pp.
366
375
.
9.
Hinze, J. O., 1975, Turbulence, McGraw-Hill, New York.
10.
Kuan
C.
, and
Wang
T.
,
1990
, “
Some Intermittent Behavior of Transitional Boundary Layers
,”
Exp. Thermal & Fluid Sci.
, Vol.
3
, pp.
157
170
.
11.
Mayle
R. E.
,
1991
, “
The Role of Laminar–Turbulent Transition in Gas Turbine Engines
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
113
, pp.
509
537
.
12.
Mayle
R. E.
,
Dullenkopf
K.
, and
Schulz
A.
,
1998
, “
The Turbulence That Matters
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
120
, pp.
402
409
.
13.
Mayle
R. E.
, and
Schulz
A.
,
1997
, “
The Path to Predicting Bypass Transition
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
119
, pp.
405
411
.
14.
Narasimha
R.
,
1957
, “
On the Distribution of Intermittency in the Transition Region of a Boundary Layer
,”
J. Aero. Science
, Vol.
24
, pp.
711
712
.
15.
Narasimha
R.
,
1985
, “
The Laminar–Turbulent Transition Zone in the Boundary Layer
,”
Prog. Aerospace Science
, Vol.
22
, pp.
29
80
.
16.
Paxson, D. E., 1989, “An Investigation of the Steady and Unsteady Near Wake and Its Effect on a Laminar Boundary Layer,” Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.
17.
Roach
P. E.
,
1987
, “
The Generation of Nearly Isotropic Turbulence by Means of Grids
,”
Int. J. Heat & Fluid Flow
, Vol.
8
, pp.
82
92
.
18.
Rolls-Royce, 1993, Data transmitted by J. Coupland from Rolls-Royce Applied Science Laboratory.
19.
Savill, A. M., 1991, “Synthesis of T3 Test Case Computations,” Proc. 1st ERCOFTAC Workshop on Numerical Simulation of Unsteady Flows, Transition to Turbulence and Combustion, Lausanne.
20.
Schlichting, H., 1979, Boundary-Layer Theory, McGraw-Hill, New York.
21.
Schubauer, G. B., and Klebanoff, P. S., 1955, “Contribution to the Mechanism of Boundary-Layer Transition,” NACA TN 3489.
22.
Sieger, K., Schulz, A., Wittig, S., and Crawford, M. E., 1993, “An Evaluation of Low-Reynolds-Number k–ε Turbulence Models for Predicting Transition Under the Influence of Free-Stream Turbulence and Pressure Gradient,” Proc. 2nd Int. Sym. Engng. Turb. Modeling & Measurements, Florence, Italy, pp. 593–602.
23.
Steelant, J., and Dick, E., 1994, “Modelling of By-Pass Transition With Conditioned Navier–Stokes Equations and K–E Model Adapted for Intermittency,” ASME Paper No. 94-GT-12.
24.
Steelant
J.
, and
Dick
E.
,
1996
, “
Modelling of By-Pass Transition With Conditioned Navier–Stokes Equations Coupled to an Intermittency Transport Equation
,”
Intern. J. Num. Methods in Fluids
, Vol.
23
, pp.
193
220
.
25.
Walker, G. J., 1987, “Transitional Flow on Axial Turbomachine Blading,” AIAA Paper No. 87-0010.
26.
Walker
G. J.
, and
Gostelow
J. P.
,
1990
, “
Effects of Adverse Pressure Gradients on the Nature and Length of Boundary Layer Transition
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
112
, pp.
196
205
.
27.
Westin
K. J. A.
,
Boiko
A. V.
,
Klingmann
B. G. B.
,
Kozlov
V. V.
, and
Alfredsson
P. H.
,
1994
, “
Experiments in a Boundary Layer Subjected to Free Stream Turbulence. Part 1. Boundary Layer Structure and Receptivity
,”
J. Fluid Mech.
, Vol.
281
, pp.
193
218
.
28.
Zhou
D.
, and
Wang
T.
,
1995
, “
Effects of Elevated Free-Stream Turbulence on Flow and Thermal Structures in Transitional Boundary Layers
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
117
, pp.
407
417
.
This content is only available via PDF.
You do not currently have access to this content.