Mean pressure gradient affects the turbulence mainly through the modulation of the mean rate of strain. Modification of the turbulence structure feeds, in turn, back into the mean flow. Particularly affected is the near wall region (including the viscous sublayer) where the pressure gradient invalidates the conventional boundary-layer “equilibrium” assumptions and inner-wall scaling. Accurate predictions of such flows require application of advanced turbulence closures, preferably at the differential second-moment level with integration up to the wall. This paper aims at demonstrating the potential usefulness of such a model to engineers by revisiting some of the recent experimental and DNS results and by presenting a series of computations relevant to low-speed external aerodynamics. Several attached and separated flows, subjected to strong adverse and favorable pressure gradient, as well as to periodic alternation of the pressure gradient sign, all computed with a low-Re-number second-moment closure, display good agreement with experimental and DNS data. It is argued that models of this kind (in full or a truncated form) may serve both for steady or transient Reynolds-Averaged Navier-Stokes (RANS, TRANS) computations of a variety of industrial and aeronautical flows, particularly if transition phenomena, wall friction, and heat transfer are in focus.

1.
Akhavan
R.
,
Kamm
R. D.
, and
Shapiro
A. H.
,
1991
, “
An Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows. Part 1. Experiments
,”
Journal of Fluid Mechanics
, Vol.
225
, pp.
395
422
.
2.
Coles
D.
, and
Wadcock
A. J.
,
1979
, “
Flying-Hot-Wire Study of Flow Past a NACA 4412 Airfoil at Maximum Lift
,”
AIAA Journal
, Vol.
17
, pp.
321
329
.
3.
Guilmineau
E.
,
Piquet
J.
, and
Queutey
P.
,
1997
, “
Two-Dimensional Turbulent Viscous Flow Simulation Past Airfoils at Fixed Incidence
,”
Computers and Fluids
, Vol.
26
, pp.
135
162
.
4.
Hanjalic´, K., and Hadzˇic´, I., 1995, “Modelling the Transition Phenomena with Statistical Turbulence Closure Models,” R. A. W. M. Henkes and J. L. van Ingen, eds., Transitional Boundary Layers in Aeronautics, pp. 283–294. North-Holland Amsterdam.
5.
Hanjalic´, K., and Jakirlic´, S., 1993, “A Model of Stress Dissipation in Second-Moment Closures,” F. T. M. Nieuwstadt, ed., Advances in Turbulence IV, Applied Scientific Research 51, pp. 513–518. Kluwer Academic Publishers.
6.
Hanjalic´
K.
, and
Jakirlic´
S.
,
1998
, “
Contribution Towards the Second-Moment Closure Modelling of Separating Turbulent Flows
,”
Computers and Fluids
, Vol.
27
, No.
2
, pp.
437
456
.
7.
Hanjalic´, K., Jakirlic´, S., and Hadzˇic´, I., 1995, “Computation of Oscillating Turbulent Flows at Transitional Re-Numbers,” F. Durst et al., ed., Turbulent Shear Flows, Vol. 9, pp. 323–342, Springer Berlin.
8.
Hanjalic´
K.
,
Jakirlic´
S.
, and
Hadzˇic´
I.
,
1997
, “
Expanding the Limits of ‘Equilibrium’ Second-Moment Turbulence Closures
,”
Fluid Dynamics Research
, Vol.
20
, pp.
25
41
.
9.
Hanjalic´
K.
, and
Launder
B. E.
,
1980
, “
Sensitizing the Dissipation Equation to Irrotational Strains
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
102
, pp.
34
40
.
10.
Jakirlic´, S., 1997, “Reynolds-Spannungs-Modellierung Komplexer Turbulenter Stro¨mungen,” Ph.D. thesis, University of Erlangen-Nu¨rnberg.
11.
Jovic´
S.
, and
Driver
D.
,
1995
, “
Reynolds Number Effect on the Skin Friction in Separated Flows Behind a Backward-Facing Step
,”
Experiments in Fluids
, Vol.
18
(
6
), pp.
464
467
.
12.
Justesen
P.
, and
Spalart
P. R.
,
1990
, “
Two-Equation Turbulence Modeling of Oscillatory Boundary Layers
,”
AIAA Paper
Vol.
41
,
90
0496
.
13.
Le
H.
,
Moin
P.
, and
Kim
J.
,
1997
, “
Direct Numerical Simulation of Turbulent Flow Over a Backward-Facing Step
,”
Journal of Fluid Mechanics
, Vol.
330
, pp.
349
374
.
14.
Nagano, Y., Tagawa, M., and Tsuji, T., 1993, “Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer,” F. Durst et al., ed., Turbulent Shear Flows, Vol. 8, pp. 7–21, Springer, Berlin.
15.
Samuel
A. E.
, and
Joubert
P. N.
,
1974
, “
A Boundary Layer Developing in an Increasingly Adverse Pressure Gradient
,”
Journal of Fluid Mechanics
, Vol.
66
, pp.
481
505
.
16.
Savill, A. M., 1996, “Transition Predictions with Turbulence Models,” R. A. W. M. Henkes and J. L. van Ingen, eds., Transitional Boundary Layers in Aeronautics, pp. 311–319. North-Holland Amsterdam.
17.
Simpson
R. L.
,
Chew
Y,-T.
, and
Shivaprasad
B. G.
,
1981
, “
The Structure of a Separating Turbulent Boundary Layer. Part 1. Mean Flow and Reynolds Stresses
,”
Journal of Fluid Mechanics
, Vol.
113
, pp.
23
51
.
18.
Spalart
P. R.
, and
Coleman
G. N.
,
1997
, “
Numerical Study of a Separation Bubble with Heat Transfer
,”
European Journal of Mechanics
, Vol.
16
, pp.
169
189
.
19.
Spalart, P. R., Jou, W.-H., Strelets, M., and Allmaras, S. R., 1997, “Comments on the Feasibility of LES for Wings, and on Hybrid RANS/LES Approach,” First AFOSR Int. Conf. on Direct Numerical Simulation and Large Eddy Simulation.
20.
Spalart
P. R.
, and
Watmuff
J. H.
,
1993
, “
Experimental and Numerical Study of a Turbulent Boundary Layer with Pressure Gradient
,”
Journal of Fluid Mechanics
, Vol.
249
, pp.
337
371
.
21.
Speziale
C. G.
, and
Gatski
S. S. T. B.
,
1991
, “
Modeling the Pressure-Strain Correlation of Turbulence: an Invariant Dynamical Systems Approach
,”
Journal of Fluid Mechanics
, Vol.
227
, pp.
245
272
.
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