VOL. 12, NO. 10, MAY 2017 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
© 2006-2017 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
3112
CFD ANALYSIS OF SD 7003 AIRFOIL AT LOW REYNOLDS NUMBER
WITH A LAIMINAR KINETIC ENERGY BASED TRANSITION MODEL
Mazharul Islam
1
, Jiří Fürst
2
and David Wood
3
1
Department of Mechanical Engineering, Kulliyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, Malaysia
2
Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovonam
Praha, Czech Republic
3
Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Canada
E-Mail: mazharul@iium.edu.my
ABSTRACT
The characteristics of laminar separation bubbles (LSBs) on the SD 7003 airfoil have been extensively studied in
the past at low Reynolds numbers. It has been found that the LSB is extensive, especially at airfoil at angle of attack (α) of
4º. To analyze separation, transition and reattachment of flow around SD 7003 airfoil effectively, Computational Fluid
Dynamics (CFD) analysis can be performed with suitable transition models. In this article, a modified version of k-kL-ω
transition model, originally proposed by Walter and Cokljat [1], has been used with open source CFD tool OpenFOAM for
analyzing SD 7003 at Reynolds number (Re) of 60,000. The article investigated k-kL-ω transition model with two recently
developed variants for analyzing SD7003 airfoil. These two variants are based on Pohlhausen and Falkner-Skan profiles to
consider effect of pressure-gradient for natural transition. It has been found that both the variants under-predicted the lift
coefficients and slightly over-predicted the drag coefficients. Both of the pressure-gradient sensitive variants gave better
prediction of separation of the laminar BL. However, the reattachment locations were delayed significantly. Among the
two variants, the Falkner-Skan based variant predicted the reattachment location slightly earlier than the Pohlhausen based
variant and thus conforming better with different experimental and computational results.
Keywords: SD7003, airfoil, LSB, transition modeling, CFD, k-kL-ω, OpenFOAM, pohlhausen, falkner-skan.
ACRONYMS AND ABBREVIATIONS
APG adverse pressure gradient
BL boundary layer
Cd drag coefficient
CFD Computational Fluid Dynamics
Cf skin friction coefficient
Cl lift coefficient
Cm moment coefficient
Cp pressure coefficient
DGM Discontinuous Galarkin Method
DNS Direct Numerical Simulation
ILES Implicit Large Eddy Simulation
LES Large Eddy Simulation
LSB Laminar Separation Bubble
PIV Particle Image Velocimetry
RANS Reynolds-average Navier-Stokes
Equation
Re Reynolds number
Tu Turbulence intensities
INTRODUCTION
At low Re, flow over airfoils can exhibit LSBs
which results from separation of the laminar boundary
layer (BL) and subsequently reattachment as turbulent BL.
The characteristic of LSB of the SD 7003 airfoil has been
extensively studied in the past at low Reynolds numbers.
Apart from different experimental methods [2], the SD
7003 has been investigated through diversified
computational techniques [3]-[8] involving Direct
Numerical Simulation (DNS), Large Eddy Simulation
(LES), Reynolds-average Navier-Stokes Equation
(RANS). Based on these previous research activities,
transition points are approximately in the range of 40 to
60%. This fact necessitates that CFD analysis of SB 7003
should properly model or simulate the separation of the
laminar BL and the subsequent development of the LSB
for acceptable results.
Though transition phenomena of airfoils can be
fairly accurately simulated with DNS and wall-resolved
LES techniques, however, the number of cells and
computational time required for these techniques are often
prohibitive (Choi & Moin 2011) [9]. Because of this
reason DNS and LES techniques are usually applied for
selected specials cases at low Re which can be used for
validation of RANS based results. CFD analysis with
RANS models requires substantially fewer cells and
computational time.
Over the year, diversified RANS-based models
have been proposed by researchers to mimic
characteristics of flows when they undergo through
transition from laminar to turbulent. The main three
classes of the transition models are: (i) linear stability
theory based e
N
models [10]-[14], (ii) local correlation
based transition models [15], [16], and (iii) laminar kinetic
energy based transition models [1], [17]. Each class of
model has its strengths and weaknesses. However, for
CFD analysis, the first class of models (i.e. e
N
models) are
considered impractical due to its need for non-local
parameters. It should be noted that modern CFD codes are
now-a-days used for unstructured grid through massively
parallel operations in High Performance Computing
(HPC) clusters. Due to this fact, now-a-days the local
correlation based γ-Reθt [18] or laminar kinetic energy
based k-kL-ω [1] models are usually used for modeling
transition and turbulence in CFD analysis. To strengthen
the modeling capacity of k-kL-ω model in flows with