Steady state, twodimensional computational investigations performed on NACA 0012 airfoil to analyze the effect of variation in Reynolds number on the aerodynamics of the airfoil without and with a Gurney flap of height of 3% chord are presented in this paper. RANS based oneequation SpalartAllmaras model is used for the computations. Both lift and drag coefficients increase with Gurney flap compared to those without Gurney flap at all Reynolds numbers at all angles of attack. The zero lift angle of attack seems to become more negative as Reynolds number increases due to effective increase of the airfoil camber. However the stall angle of attack decreased by 2° for the airfoil with Gurney flap. Lift coefficient decreases rapidly and drag coefficient increases rapidly when Reynolds number is decreased below critical range. This occurs due to change in flow pattern near Gurney flap at low Reynolds numbers.
A Gurney flap (GF) is a microtab fitted perpendicular to the airfoil near the trailing edge on its pressure surface which increases the lift by altering the Kutta condition and increasing effective camber. They are extensively used on helicopter stabilizers [
A semiempirical formula linking flap height to free stream velocity and the airfoil chord is proposed by Brown and Filippone [
Keeping this in mind, computations on the effect of six Reynolds numbers from high Reynolds number to low Reynolds number well below the critical range are carried out to analyze the performance of the airfoil.
The airfoil considered in this study is NACA 0012 airfoil with chord length of 5 cm. Ctype domain and grid are created in ICEMCFD with farfield boundaries 12.5 chords away from trailing edge in all directions (Figure
(a) Entire domain of the grid used. (b) Near surface grid and blocking near the airfoil surfaces. (c) Boundary layer elements near the leading and trailing edges of the airfoil.
Previous studies show that out of two equation RANS based models of FLUENT,
The airfoil boundary is assigned as solidwall with noslip condition while inlet is assigned as velocity inlet and outlet is assigned as pressureoutlet conditions. Density based implicit solving scheme is used with the flow medium being air and Mach number less than 0.3. Hence the fluid is assumed to be incompressible with constant density of 1.225 kg/m^{3} and dynamic viscosity of 1.7894 × 10^{−5 }kg/ms. Under relaxation factors for all the transport variables are set to 0.8. Solution initialization is computed from velocity inlet followed by FMG initialization with solution steering. Equations are solved until a convergence criterion of 10^{−5} for all the residuals is satisfied.
Lift and drag coefficients,
Variation of
For high Reynolds number,
Comparison of

RNG  SA  Expt.  % difference between  

RNG and Expt.  SA and Expt.  RNG and SA  
0°  0.542  0.538  0.406  25.1  24.5  0.7 
4°  0.990  0.997  0.868  12.3  12.9  −0.7 
8°  1.405  1.435  1.285  8.5  10.5  −2.1 
12°  1.756  1.827  1.646  6.3  9.9  −4.0 
Comparison of

RNG  SA  Expt.  % difference between  

RNG and Expt.  SA and Expt.  RNG and SA  
0°  0.0250  0.0212  0.0233  6.8  −9.9  15.2 
4°  0.0347  0.0264  0.0199  42.7  24.6  23.9 
8°  0.0510  0.0348  0.0245  52.0  29.6  31.8 
12°  0.0766  0.0496  0.0331  56.8  33.3  35.2 
Computations are carried out for the airfoil without and with a GF of height of 3% chord at six different Reynolds numbers (Re = 3.0 × 10^{5}, 1.5 × 10^{5}, 1.0 × 10^{5}, 8 × 10^{4}, 5 × 10^{4} and 3 × 10^{4}). Based on the equation for optimum GF given by Traub and Agarwal [
The lift coefficient
Percentage Decrement in
Reynolds number range  

AoA, 





4°  
Without GF  0.12  0.25  0.37  0.57  1.12 
With GF  0.18  0.49  0.86  1.57  3.41 
8°  
Without GF  0.15  0.31  0.45  0.72  1.30 
With GF  0.20  0.50  0.82  1.40  2.74 
12°  
Without GF  0.25  0.50  0.66  0.98  1.62 
With GF  0.42  0.85  1.17  1.65  2.51 
Variation of
For the airfoil without GF, variation in
Table
The variation of the lift coefficient,
Variation of
Apart from decreasing
Variation of
Variation of
The percentage increment in
Percentage Increment in
Reynolds number range  

AoA, 





4°  
Without GF  1.27  2.52  3.59  5.71  10.30 
With GF  0.73  1.51  2.18  3.45  6.40 
8°  
Without GF  1.30  2.58  3.66  5.78  10.26 
With GF  0.83  1.62  2.31  3.56  6.25 
12°  
Without GF  1.39  2.65  3.69  5.81  10.07 
With GF  1.03  1.91  2.62  3.94  6.60 
The lifttodrag ratio is presented as
Variation of lifttodrag ratio with Reynolds number for the airfoil without and with GF.
The decrease in
Decrement in lifttodrag ratio per every 10,000 decrease in Reynolds number for different ranges of Reynolds number.
Reynolds number range  

AoA, 





4°  
Without GF  0.262  0.454  0.595  0.793  1.161 
With GF  0.255  0.483  0.663  0.990  1.551 
8°  
Without GF  0.386  0.641  0.824  1.095  1.552 
With GF  0.317  0.551  0.734  0.987  1.465 
12°  
Without GF  0.375  0.572  0.698  0.910  1.256 
With GF  0.363  0.512  0.593  0.710  0.910 
The lifttodrag ratio as a function of lift coefficient for the airfoil without and with GF is presented in Figure
Variation of lifttodrag ratio with lift coefficient at different Reynolds numbers for the airfoil without and with GF.
Static pressure distribution in terms of nondimensional coefficient
Static pressure distributions for different Reynolds numbers at AoA = 12° for the airfoil without and with GF.
Maximum pressure buildup is almost the same for the airfoils with and without GF. Value of maximum
Pathlines are highly affected by the variation in the Reynolds number and the formation of vortices experience drastic change. Pathlines superimposed with the contours of turbulent viscosity at AoA = 12° for the airfoil without and with GF at four different Reynolds numbers presented in Figure
Pathlines and turbulent viscosity for different Reynolds numbers at AoA = 12° of the airfoil with and without Gurney flap.
A laminar separation bubble starts its formation. As the Reynolds number is decreased, the flow loses its ability to make transition into turbulent flow in the attached boundary layer, hence forming a laminar separation bubble. Below Re = 1.0 × 10^{5}, no vortex is present behind the Gurney flap. The increased pressure on pressure surface is only due to vortex ahead of the Gurney flap which might explain absence of sudden pressure increase near the Gurney flap as shown in static pressure distribution. This laminar separation bubble increases the effective thickness of the airfoil, thereby increasing the pressure drag over the region, which explains the increase in drag at low Reynolds number and degraded performance of the airfoil at low Reynolds numbers. For each Reynolds number, flow is turned towards the Gurney flap whereas, due to absence of any suction, the flow leaves at the airfoil at higher angle without Gurney flap. However the turning of flow towards GF is reduced at lower Reynolds numbers.
A computational investigation on the effects of Reynolds number on the aerodynamics of NACA0012 airfoil without and with Gurney flap of height of 3% airfoil chord has been carried out. ANSYS FLUENT commercial CFD code with oneequation SpalartAllmaras turbulence model is used for the six Reynolds numbers varying from 3.0 × 10^{5} to 3.0 × 10^{4}. From this investigation, the following major conclusions are drawn.
Reynolds number plays a very major role in the airfoil aerodynamics for the NACA0012 airfoil without and with Gurney flap. Lift decreases and drag increases when Reynolds number is decreased.
For the airfoil with GF, Reynolds number has adverse effects on lift coefficient, while drag coefficient of the airfoil with GF has some beneficial effects compared to the airfoil without GF.
For high Reynolds number above critical range, decrease in
As the Reynolds number is decreased below the critical Reynolds number range,
For lower Reynolds numbers, the two vortices behind the Gurney flap vanish. The Gurney flap seems to increase the effective camber of the airfoil, causing negative zero lift angle and reduced stall angle.
Angle of attack (deg.)
Drag coefficient =
Airfoil chord (m)
Lift coefficient =
Static pressure coefficient = 2(
Drag force (N)
Optimum Gurney flap (m)
Gurney flap height as percentage of chord
Lift force (N)
Static pressure (Pa)
Reynolds number =
Freestream velocity (m/s)
Rate of dissipation of turbulent kinetic energy (m^{2}/s^{3})
Turbulent kinetic energy (m^{2}/s^{2})
Air density (kgm/m^{3})
Kinematic viscosity (m^{2}/s).
Exit.
Computational fluid dynamics
Gurney flap
Reynolds averaged Navier Stokes equations
SpalartAllmaras turbulence model.
The authors declare that there is no conflict of interests regarding the publication of this paper.