A boundary layer with Re = 106 is simulated numerically on a flat plate using morphing continuum theory. This theory introduces new terms related to microproperties of the fluid. These terms are added to a finite-volume fluid solver with appropriate boundary conditions. The success of capturing the initial disturbances leading to turbulence is shown to be a byproduct of the physical and mathematical rigor underlying the balance laws and constitutive relations introduced by morphing continuum theory (MCT). Dimensionless equations are introduced to produce the parameters driving the formation of disturbances leading to turbulence. Numerical results for the flat plate are compared with the experimental results determined by the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) database. Experimental data show good agreement inside the boundary layer and in the bulk flow. Success in predicting conditions necessary for turbulent and transitional (T2) flows without ad hoc closure models demonstrates the theory's inherent advantage over traditional turbulence models.

References

References
1.
Berger
,
K.
,
Rufer
,
S.
,
Kimmel
,
R.
, and
Adamczak
,
D.
,
2009
, “
Aerothermodynamic Characteristics of Boundary Layer Transition and Trip Effectiveness of the HIFiRE Flight 5 Vehicle
,”
AIAA
Paper No. 2009-4055.
2.
Reynolds
,
O.
,
1883
, “
An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
,”
Philos. Trans. R. Soc. London
,
174
(
0
), pp.
935
982
.
3.
Smith
,
A.
, and
Gamberoni
,
N.
,
1956
, “
Transition, Pressure Gradient, and Stability Theory
,” Douglas Aircraft Co., Inc., El Segundo, CA, Report No. ES 26388.
4.
Van Ingen
,
J. L.
,
1956
, “
A Suggested Semi-Empirical Method for the Calculation of the Boundary Layer Transition Region
,” Delft University of Technology, Delft, Netherlands, Technical Report No. 74.
5.
Joslin
,
R. D.
,
Streett
,
C. L.
, and
Chang
,
C.-L.
,
1993
, “
Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory
,”
Theor. Comput. Fluid Dyn.
,
4
(
6
), pp.
271
288
.
6.
Fürst
,
J.
,
Straka
,
P.
,
Příhoda
,
J.
, and
Šimurda
,
D.
,
2013
, “
Comparison of Several Models of the Laminar/Turbulent Transition
,”
EPJ Web Conf.
,
45
, p.
01032
.
7.
Chen
,
J.
,
Liang
,
C.
, and
Lee
,
J. D.
,
2012
, “
Numerical Simulation for Unsteady Compressible Micropolar Fluid Flow
,”
Comput. Fluids
,
66
, pp.
1
9
.
8.
Van Ingen
,
J.
,
2008
, “
The eN Method for Transition Prediction: Historical Review of Work at TU Delft
,”
AIAA
Paper No. 2008-3830.
9.
von Doenhoff
,
A. E.
, and
Braslow
,
A. L.
,
1961
, “
Effect of Distributed Surface Roughness on Laminar Flow
,”
Boundary Layer and Flow Control: Its Principles and Applications
, Vol.
2
,
Pergamon Press
, New York.
10.
Lucas
,
J.-M.
,
2014
, “
Étude et modélisation du phénomène de croissance transitoire et de son lien avec la transition bypass au sein des couches limites tridimensionnelles
,” Ph.D. thesis, ISAE, Toulouse, France.
11.
Aupoix
,
B.
,
Arnal
,
D.
,
Bézard
,
H.
,
Chaouat
,
B.
,
Chedevergne
,
F.
,
Deck
,
S.
,
Gleize
,
V.
,
Grenard
,
P.
, and
Laroche
,
E.
,
2011
, “
Transition and Turbulence Modeling
,”
J. AerospaceLab
,
2
, pp.
1
13
.
12.
Walters
,
D. K.
, and
Cokljat
,
D.
,
2008
, “
A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow
,”
ASME J. Fluids Eng.
,
130
(
12
), p.
121401
.
13.
Heinloo
,
J.
,
2004
, “
Formulation of Turbulence Mechanics
,”
Phys. Rev. E
,
69
(
5
), p.
056317
.
14.
Kirwan
,
A. D.
,
1986
, “
Boundary Conditions for Micropolar Fluids
,”
Int. J. Eng. Sci.
,
24
(
7
), pp.
1237
1242
.
15.
Mehrabian
,
R.
, and
Atefi
,
G.
,
2008
, “
A Cosserat Continuum Mechanical Approach to Turbulent Channel Pressure Driven Flow of Isotropic Fluid
,”
J. Dispersion Sci. Technol.
,
29
(
7
), pp.
1035
1042
.
16.
Peddieson
,
J.
,
1972
, “
An Application of the Micropolar Fluid Model to the Calculation of a Turbulent Shear Flow
,”
Int. J. Eng. Sci.
,
10
(
1
), pp.
23
32
.
17.
Eringen
,
A. C.
,
1964
, “
Simple Microfluids
,”
Int. J. Eng. Sci.
,
2
(
2
), pp.
205
217
.
18.
Kirwan
,
A. D.
, and
Newman
,
N.
,
1969
, “
Plane Flow of a Fluid Containing Rigid Structures
,”
Int. J. Eng. Sci.
,
7
(
8
), pp.
883
893
.
19.
Kawai
,
S.
, and
Larsson
,
J.
,
2012
, “
Wall-Modeling in Large Eddy Simulation: Length Scales, Grid Resolution, and Accuracy
,”
Phys. Fluids
,
24
(
1
), p.
015105
.
20.
Chen
,
J.
,
2016
, “
Advanced Kinetic Theory for Polyatomic Gases at Equilibrium
,”
AIAA
Paper No. 2016-4094.
21.
Alizadeh
,
M.
,
Silber
,
G.
, and
Nejad
,
A. G.
,
2011
, “
A Continuum Mechanical Gradient Theory With an Application to Fully Developed Turbulent Flows
,”
J. Dispersion Sci. Technol.
,
32
(
2
), pp.
185
192
.
22.
Drouot
,
R.
, and
Maugin
,
G. A.
,
1983
, “
Phenomenological Theory for Polymer Diffusion in Non-Homogeneous Velocity-Gradient Flows
,”
Rheol. Acta
,
22
(
4
), pp.
336
347
.
23.
Stokes
,
V. K.
,
2012
,
Theories of Fluids With Microstructure: An Introduction
,
Springer Science & Business Media
, New York.
24.
Mindlin
,
R. D.
,
1964
, “
Micro-Structure in Linear Elasticity
,”
Arch. Ration. Mech. Anal.
,
16
(
1
), pp.
51
78
.
25.
Ahmadi
,
G.
,
1975
, “
Turbulent Shear Flow of Micropolar Fluids
,”
Int. J. Eng. Sci.
,
13
(
11
), pp.
959
964
.
26.
Coupland
,
J.
,
1990
, “
ERCOFTAC Special Interest Group on Laminar to Turbulent Transition and Retransition: T3A and T3B Test Cases
,” Report No. A309514.
You do not currently have access to this content.