Mechanisms behind the pressure distribution and skin friction within a laminar separation bubble (LSB) are investigated by large-eddy simulations around a 5% thickness blunt flat plate at the chord length based Reynolds number 5.0 × 103, 6.1 × 103, 1.1 × 104, and 2.0 × 104. The characteristics inside the LSB change with the Reynolds number; a steady laminar separation bubble (LSB_S) at the Reynolds number 5.0 × 103 and 6.1 × 103, and a steady-fluctuating laminar separation bubble (LSB_SF) at the Reynolds number 1.1 × 104, and 2.0 × 104. Different characteristics of pressure and skin friction distributions are observed by increasing the Reynolds number, such that a gradual monotonous pressure recovery in the LSB_S and a plateau pressure distribution followed by a rapid pressure recovery region in the LSB_SF. The reasons behind the different characteristics of pressure distributions at different Reynolds numbers are discussed by deriving the Reynolds averaged pressure gradient equation. It is confirmed that the viscous stress distributions near the surface play an important role in determining the formation of different pressure distributions. Depending on the Reynolds numbers, the viscous stress distributions near the surface are affected by the development of a separated laminar shear layer or the Reynolds shear stress. In addition, we show that the same analyses can be applied to the flows around a NACA0012 airfoil.
REFERENCES
1.
B.
Carmichael
, “Low Reynolds number airfoil survey,” Report No. NASA-CR-165803, NASA, 1982.2.
I.
Tani
, “Low speed flows involving bubble separations
,” Prog. Aerosp. Sci.
5
, 70
–103
(1964
).3.
M.
Gaster
, “The structure and behaviour of laminar separation bubbles
,” AGARD CP-4,
813
–854
(1966
).4.
H. P.
Horton
, “Laminar separation bubbles in two- and three-dimensional incompressible flow
,” Ph.D. dissertation (University of London
, 1968
).5.
P. B. S.
Lissaman
, “Low-Reynolds-number airfoils
,” Annu. Rev. Fluid Mech.
15
, 223
–240
(1983
).6.
T. J.
Mueller
and S. M.
Batillt
, “Experimental studies of separation on a two-dimensional airfoil at low Reynolds numbers
,” AIAA J.
20
, 457
–463
(1982
).7.
H.
Shan
, L.
Jiang
, and C.
Liu
, “Direct numerical simulation of flow separation around a NACA0012 airfoil
,” Comput. Fluids
34
, 1096
–1114
(2005
).8.
R.
Kojima
, T.
Nonomura
, A.
Oyama
, and K.
Fujii
, “Large-eddy simulation of low-Reynolds-number flow over thick and thin NACA airfoils
,” J. Aircraft
50
, 187
–196
(2013
).9.
K.
Sasaki
and M.
Kiya
, “Three-dimensional vortex structure in a leading-edge separation bubble at moderate Reynolds numbers
,” J. Fluids Eng.
113
, 405
–410
(1991
).10.
R.
Hain
, C. J.
Kähler
, and R.
Radespiel
, “Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils
,” J. Fluid Mech.
630
, 129
(2009
).11.
L. L.
Pauley
, P.
Moin
, and W. C.
Reynolds
, “The structure of two-dimensional separation
,” J. Fluid Mech.
220
, 397
–411
(1990
).12.
M.
Alam
and N.
Sandham
, “Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment
,” J. Fluid Mech.
403
, 223
–250
(2000
).13.
P. R.
Spalart
and M. K.
Strelets
, “Mechanisms of transition and heat transfer in a separation bubble
,” J. Fluid Mech.
403
, 329
–349
(2000
).14.
M. M.
O’Meara
and T. J.
Mueller
, “Laminar separation bubble characteristics on an airfoil at low Reynolds numbers
,” AIAA J.
25
, 1033
–1041
(1987
).15.
S. S.
Diwan
and O. N.
Ramesh
, “Laminar separation bubbles: Dynamics and control
,” Sadhana
32
, 103
–109
(2007
).16.
W.
Shyy
, Y.
Lian
, J.
Tang
, D.
Viieru
, and H.
Liu
, Aerodynamics of Low Reynolds Number Flyers
(Cambride University Press
, New York
, 2008
).17.
Y.
Zhou
and Z. J.
Wang
, “Effects of surface roughness on laminar separation bubble over a wing at a low-Reynolds number,” AIAA Paper No. 2011-0736, 2011.18.
A. V.
Arena
and T. J.
Mueller
, “Laminar separation, transition, and turbulent rettachment near the leading edge of airfoils
,” AIAA J.
18
, 747
–753
(1980
).19.
W. B.
Roberts
, “Calculation of laminar separation bubbles and their effect on airfoil performance
,” AIAA J.
18
, 25
–31
(1980
).20.
J. H.
Watmuff
, “Evolution of a wave packet into vortex loops in a laminar separation bubble
,” J. Fluid Mech.
397
, 119
–169
(1999
).21.
L. E.
Jones
, R. D.
Sandberg
, and N. D.
Sandham
, “Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence
,” J. Fluid Mech.
602
, 175
–207
(2008
).22.
M. D.
Ripley
and L. L.
Pauley
, “The unsteady structure of twodimensional steady Laminar separation
,” Phys. Fluids
5
, 3099
–3106
(1993
).23.
J. C.
Muti Lin
and L. L.
Pauley
, “Low-Reyonlds-number separation on an airfoil
,” AIAA J.
34
, 1570
–1577
(1996
).24.
S.
Yarusevych
, P. E.
Sullivan
, and J. G.
Kawall
, “Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers
,” Phys. Fluid
18
, 044101
(2006
).25.
H.
Hu
and Z.
Yang
, “An experimental study of the laminar flow separation on a low Reynolds-number airfoil
,” J. Fluid Eng.
130
, 051101
(2008
).26.
O.
Marxen
and D. S.
Henningson
, “The effect of small-amplitude convective distrubances on the size and bursting of a laminar separation bubble
,” J. Fluid Mech.
671
, 1
–33
(2011
).27.
J. N. N.
Counsil
and K. G.
Boulama
, “Low-Reynolds-number aerodynamic performances of the NACA0012 and Selig-Donovan 7003 airfoils
,” J. Aircraft
50
, 204
–216
(2013
).28.
I.
Karasu
, M. S.
Genç
, and H. H.
Açikel
, “Numerical study on low Reynolds number flows over an Aerofoil
,” J. Appl. Mech. Eng.
2
, 131
(2013
).29.
M.
Anyoji
, T.
Nonomura
, H.
Aono
, A.
Oyama
, K.
Fujii
, H.
Nagai
, and K.
Asai
, “Computational and experimental analysis of a high-performance airfoil under low-Reynolds-number flow condition
,” J. Aircraft
51
, 1864
–1872
(2014
).30.
M.
Anyoji
, K.
Nose
, S.
Ida
, D.
Numata
, H.
Nagai
, and K.
Asai
, “Aerodynamic measurements in the Mars wind tunnel at Tohoku university,” AIAA Paper No. 2011-0852, 2011.31.
I.
Tani
, M.
Iuchi
, and H.
Komoda
, “Experimental investigation of flow separation associated with a step or a groove,” Report No. 361, Aeronautical Research Institute, 1961.32.
AIAA Standard, “Assessment of experimental uncertainty with application to wind tunnel testing,” AIAA Paper No. S-017A-1999, 1999.
33.
S. K.
Lele
, “Compact finite difference schemes with spectral-like resolution
,” J. Comput. Phys.
103
, 16
–42
(1992
).34.
D. V.
Gaitonde
and M. R.
Visbal
, “Pade-type higher-order boundary filters for the Navier–Stokes equations
,” AIAA J.
38
, 2103
–2112
(2000
).35.
Y.
Abe
, N.
Iizuka
, T.
Nonomura
, and K.
Fujii
, “Geometric interpretations and spatial symmetry property of metrics in the conservative form for high-order finite-difference schemes on moving and deforming grids
,” J. Comput. Phys.
260
, 163
–203
(2013
).36.
S.
Obayashi
, K.
Fujii
, and S.
Gavali
, “Navier-Stokes simulation of wind-tunnel flow using LU-ADI factorization algorithm,” Report No. NASA TM-100042, NASA, 1988.37.
N.
Iizuka
, “Study of Mach number effect on the dynamic stability of a blunt re-entry capsule
,” Ph.D. dissertation (University of Tokyo
, 2006
).38.
H.
Nishida
and T.
Nonomura
, “ADI-SGS scheme on ideal magnetohydrodynamics
,” J. Comput. Phys.
228
, 3182
–3188
(2009
).39.
S. R.
Chakravarthy
, “Relaxation methods for unfactored implicit upwind schemes,” AIAA Paper No. 1984-0165, 1984.40.
S.
Kawai
, S. K.
Shankar
, and S. K.
Lele
, “Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows
,” J. Comput. Phys.
229
, 1739
–1762
(2010
).41.
S.
Kawai
and K.
Fujii
, “Compact scheme with filtering for large-eddy simulation of transitional boundary layer
,” AIAA J.
46
, 690
–700
(2008
).42.
H.
Choi
and P.
Moin
, “Effects of the computational time step on numerical solutions of turbulent flow
,” J. Comput. Phys.
113
, 1
–4
(1994
).43.
P.
Dengel
and H. H.
Fernholz
, “An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation
,” J. Fluid Mech.
212
, 615
–636
(1990
).44.
A. E.
Alving
and H. H.
Fernholz
, “Meanvelocity sacling in and around a mild, turbulent separation bubble
,” Phys. Fluids
7
, 1956
–1969
(1995
).45.
K.
Suluksan
and E.
Juntasaro
, “Assessment of intermittency transport equations for modeling transition in boundary layers subjected to freestream turbulence
,” Int. J. Heat Fluid Fl.
29
, 48
–61
(2008
).46.
D.
Lee
, T.
Nonomura
, A.
Oyama
, and K.
Fujii
, “Comparison of numerical methods evaluating airfoil aerodynamic characteristics at low Reynolds number
,” J. Aircraft
52
, 296
–306
(2015
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.
