Numerical Study on Low Reynolds Number Flows Over an Aerofoil

This study is a numerical investigation on laminar separation bubble over a NACA2415 aerofoil at low Reynolds numbers and various angles of attack. The numerical results were compared with the experimental results of our previous study. Oil flow visualization technique, an external three-component balance system and pressure measurements were used for the experiments. In the experimental results, stall angle was 12°, 13° and 15° for Re=0.5x105, Re=1x105 and Re=3x105, respectively. The flow separation, reattachment and forming the laminar separation bubble were clearly seen by using the aforementioned experimental methods. It was indicated that the point of separation moved towards the leading edge as the angle of attack increased. Moreover, the flow visualization results showed that as the angle of attack increased further, the bubble burst and the separated flow was not able to reattach to the aerofoil surface, which indicated stall. In the numerical results, the transition models are shown to accurately predict the location of the separation bubble experimentally determined at lower angles of attack. Furthermore, the numerical prediction using the transition models are more successful than the turbulence model suitable for low Re number flows. completes since the flow is more energetic the flow reattaches the surface and in this region CP recovers to the same value of the in viscid flow as shown in Figure 2. Laminar separation bubbles are classified as short and long bubbles [4,5]. For the short bubble case, the flow may reattach to the surface of the aerofoil and long bubble occurs after bursting of short bubbles and fails to reattach and this causes early stall. In parallel with modern developments in experimental researches, in the prediction methods it has been devised to account for transition mechanisms over the aerofoils [6,7] and incorporated modern experimental and numerical means. Recently developed transport Figure 1: Section view of two dimensional short laminar separation bubble [4]. Figure 2: Pressure distribution over an aerofoil has laminar separation bubble [6]. Journal of Applied Mechanical Engineering J o u r n al o f A pp lied ical Eninee r i n g


Introduction
Low Reynolds number flow has gained popularity because of increasing numbers of applications of Unmanned Aerial Vehicles (UAV), Micro Air Vehicles (MAV) and wind turbines. At low Reynolds number flows, viscous effects are dominant and momentum of the flow is incapable to move downstream and adverse pressure gradient causes the laminar flow to separate, and separated flow reattach to the surface because of the transition (Figure 1). The region between laminar separation and turbulent reattachment is called as laminar separation bubble which has adverse effects on the aerofoil such as decreased lift coefficient, increased drag coefficient. It changes the moment coefficient, causing abrupt stall [1], decreasing control surface effectiveness [2] and vibration [3]. Because of the delicate nature of the flow regime, extended research on low Reynolds number aerodynamics should be conducted and also numerical models must be developed and present numerical models must be validated.
When laminar separation bubble occurs over an aerofoil, it causes changes on pressure distribution; in dead air region laminar separation bubble causes sudden increase in CP after the transition process completes since the flow is more energetic the flow reattaches the surface and in this region CP recovers to the same value of the in viscid flow as shown in Figure 2. Laminar separation bubbles are classified as short and long bubbles [4,5]. For the short bubble case, the flow may reattach to the surface of the aerofoil and long bubble occurs after bursting of short bubbles and fails to reattach and this causes early stall.
In parallel with modern developments in experimental researches, in the prediction methods it has been devised to account for transition mechanisms over the aerofoils [6,7] and incorporated modern experimental and numerical means. Recently developed transport equation models have helped to incorporate certain benchmark experimental data that were expressed in terms of global boundary layer parameters into current RANS based solvers. Genc et al. [8] performed experimental and numerical survey over aerofoil with leading edge slat at low Reynolds number of 2x10 5 using FLUENT RANS based solver. NACA2415 were used as aerofoil, and NACA22 was used as leading edge slat. In the numerical investigation, for the aerofoil without slat, k-ε RNG and k-ω SST turbulence models, the k-k L -ω Transition and k-ω SST Transition models; and for the slat configuration k-k L -ω Transition and SST Transition models were used. For the single element aerofoil, the turbulence models under predicted on the prediction laminar separation bubble, while the transition models gave the better results, moreover the k-k L -ω Transition model gave the best results. For the aerofoil with the leading edge slat, the effects of the slat on laminar separation bubble was investigated for α=8°, and while k-k L -ω Transition could not eliminate the bubble, SST Transition model could eliminate the bubble and showed good agreement with the surface oil visualization experiments. Genc et al. [9] also carried out an investigation flow over NACA 2415 aerofoil and effects of blowing and suction on laminar separation bubble at Re=2×10 5 . For the numerical investigation k-ε RNG, k-ω SST turbulence models and k-k L -ω Transition and SST Transition models were used, and when there was no blowing or suction none of the model was superior for prediction of all performance parameters, the most reasonable predictions were gained by k-k L -ω Transition model.
Catalona and Tognaccini [10] studied numerically the flow over a SD 7003 aerofoil by using k-ω SST-LR turbulence model and they concluded that this model provided satisfactory results for their investigation. Sanders et al. [11] conducted a numerical investigation over two different low pressure turbine blade aerofoil cascade configuration at Re ranging 1.5×10 4 to 1×10 5 . In this investigation, kε and k-ω SST turbulence models and k-k L -ω Transition model were used and k-k L -ω Transition model predicted better transition behavior at low Reynolds number than other two 2-D RANS method. Catalona and Tognaccini [12] presented a numerical survey over SD7003 aerofoil. In this survey RANS and LES methods were used and results were compared with each other. In the RANS computations S-A k-ε -MK and k-ω BSL and k-ω SST were used as turbulence models. The performance of the k-ω SST model were investigated deeply and a modification was offered by the authors and the modified version of k-ω SST model was called k-ω SST-LR model and results of this model for Re=60000 and α=4° showed very good agreement with LES results. Chitta et al. [13] performed a numerical investigation over an elliptical aerofoil. S-A, k-ω SST, curvature-sensitive SST k-ω-v 2 which was modified version of SST k-ω model turbulent models and k-k L -ω and SST Transition were used. Transition models predicted lift characteristics, separation and reattachment points more accurately than the other three fully turbulent models, furthermore except curvature-sensitive SST k-ω-v 2 model, none of these models could predict the stall angle correctly. Ibrahim et al. [14] carried out an experimental and numerical study over L1A aerofoils used for low    pressure turbine blades of gas turbine engines at different Reynolds number ranging 2.5x10 4 to 3x10 5 . In the numerical study, k-ω SST, v2-f model turbulence models and SST Transition model were used. Their results showed that at Reynolds numbers below 1.5×10 5 the separated flow could not reattach but at Reynolds number higher than 1.5×10 5 the separated flow could reattach to surface. According to numerical results, at Re=2.5×10 4 and Re=1×10 5 , SST Transition model gave best results at Re=3×10 5 all models gave similar results each other.
In this study, the evaluation of performance of k-ω SST turbulence model suitable for low Re number flows, k-k L -ω and SST Transition models were made based on prediction laminar separation bubble of NACA2415 at different angles of attack and Reynolds numbers. Experimental results for the validation of numerical results were taken from an experimental study performed by the authors of this study [15].

Numerical Study Solution Grid
Structural C type grid which has 32000 cells and 32380 nodes was constructed by the GAMBIT TM software (Figures 3 and 4). The aerofoil has 180 mm chord (c) length. The grid extends from -10 c to 10 c in the x direction and -10 c to 10 c in the y direction ( Figure 5). The mesh got finer around the aerofoil to ensure y + values below unity. Different sized grids such as 22000 (A), 26000 (B), 32000 (C), 40400 (D), 50000 (E) for Re=1×10 5 at α=8° were compared to ensure grid independence of the calculations and finally the 32000 grids was chosen since difference of the results of C L values were negligible after this grid size as shown Figure 6.

Numerical Method and Boundary Conditions
ANSYS FLUENT ™ 12.1.2 software which is based on the finite volume method was used perform numerical calculations. The domain except the aerofoil was selected as pressure far field and no slip condition was applied to the aerofoil surface. All calculations were conducted on as density based, and steady-state solution. In the calculations implicit method for formulation, and second order upwind discretization in space was used for all parameters of the models. Solutions converged when all residuals reached to 10-5. A free stream turbulence level was used as Tu = 1%. In the numerical calculations, the k-ω SST model with low Re correction as turbulence model, and Transition k-k L -ω and k-ω SST Transition models as two transition models were used. Genc et al. [8,9] was evaluated the turbulence and transition models and concluded that the k-ω SST turbulence model gave better results than the other turbulence models at low Re number flows. Therefore, the k-ω SST model k-k L -ω and k-ω SST Transition models were chosen in this study. Furthermore, Genc et al. [9] was tested the performance of these transition models on the prediction of flow over the NACA2415 aerofoil at Re number of 2x10 5 ; and showed the success of the transition models. Moreover, the performance of the low Re number turbulence model and the transition models should be investigated at lower Reynolds numbers, and the aim of this study is to indicate the prediction capability of the low Re number turbulence model and the transition models at different and lower Reynolds numbers such as 0.5x10 5 , 1x10 5 and 3x10 5 .

The Summary of Previous Experimental Studies
The experiments were carried out in a low speed wind tunnel. The free stream turbulence intensity of the wind tunnel is lower than 0.7% at lowest speed [15]. A NACA2415 aerofoil with a chord of c=180 mm and a span of b= 280 mm was used in experiments. Oil flow visualization technique was employed for the flow visualization because this technique was simple to apply and effective to see flow conditions. A pitot-static tube, a scanivalve, a pressure transducer and a NACA2415 aerofoil with 24 pressure taps on upper and lower surfaces were used for the pressure measurements. In the pressure measurement experiments a computer-controlled data acquisition system was used. The pressure was measured by using Honeywell 163PC01D75 model differential pressure transducers with a pressure range of 623 Pa. However, as this pressure range was not enough for the measurement of pressure difference over the aerofoil at Re=3x10 5 experimental pressure distributions for Re=3x10 5 could not be obtained. For measuring the lift and drag forces on the aerofoil, an external three-component loadcell system was used [15,16]. The force data was collected at a sampling frequency of 1000 Hz over 120 s. Mean forces and moment and their coefficients were calculated using Microsoft Excel Software. The detailed information can be found in the References15 and 16.

Results
In the experiments, the stall angle was 12°, 13° and 15° for Re=0.5x10 5 , Re=1x10 5 and Re=3x10 5 , respectively (Figure 7). In the numerical results, the prediction of the lift coefficient of the models gave the different results and the k-k L -ω Transition model predicted more successfully the lift and drag coefficients, however all models under predicted the coefficients at Re=0.5x10 5 .   [15][16].   For the computational investigation of pressure distribution and flow phenomena over the NACA2415 aerofoil, two angles of attack for pre-stall condition (4°, 8°) and an angle of attack near stall condition (12°) and an angle of attack for post stall condition (15°) were chosen. Figure 8 shows the experimental [15] and the numerical results of Cp distribution over the aerofoil at different angels of attack, and Figure 9 and 10 indicate experimental oil flow visualization results for the angles of attack of 4°, 8°, 12° and 15° at Re=1x10 5 and Re=3x10 5 . The results of the experiments of pressure coefficients and oil-flow visualization provide to see the formation and progress of the laminar separation bubble, transition and re-attached flow. In the oil-flow visualization experiments, the dense area of pigment points out where the flow has decelerated, which correlates with the point, at which the flow separation and turbulent reattachment occur.
In Figure 8, at Re=0.5x10 5 the turbulence and transition models predicted the pressure coefficient values lower than the experiments while at Re=1x10 5 the transition models gave the better results. At lower Re numbers, the flow includes the more viscous forces which affect adversely the flow and cause flow separation to occur, therefore the numerical simulation is too difficult at lower Re number flows. Furthermore the low Re number turbulence model and transition model are successful on laminar separation bubble prediction although the bubble length and location are not predicted correctly. Consequently, as seen in Figures 8-10, as angle of attack increases, laminar separation bubble moves towards to leading edge and length of the laminar separation bubble decreases. Table 1 shows the Separation Point (X S ), the Reattachment Point (X R ), and the Bubble Length (L b ) for numerical and experimental studies. Because of the limited numbers of pressure taps on the suction side of the aerofoil (15 taps), the some locations of the X S and X R , and L B were determined by the help of oil visualization experiments. All locations were calculated via dividing the location by the chord of the aerofoil to obtain dimensionless numbers. Both transition models showed good agreement for the X S and X R , and L b at 4°, 8°, 10° and 12° for Re=0.5x10 5 but the k-ω SST turbulence model did not predict the X R and L b . Generally, the transition models are more successful than the k-ω SST turbulence model on prediction the X S and X R , and L B . Figures 11 and 12 shows numerical stream traces and turbulent Kinetic Energy (k T ) contours over the NACA2415 aerofoil at the angle of attack of 8° at Re=1x10 5 and Re=3x10 5 . The laminar separation bubbles predicted by the turbulence and transition models can be seen clearly. In the Laminar Part k T is minimum (0), after the transition completes k T starts to increase and goes on increasing. By means of the increase in the k T after the transition point, the flow has gained the kinetic energy and overcomes the adverse pressure gradient and a subsequent turbulent reattachment happens. In this way, the bubble is trapped under the separated shear layer between the separated and reattachment points.

Conclusions
In this study, the performance of the k-ω SST Transition, the k-k L -ω Transition and the k-ω SST Transition models were investigated for predicting the laminar separation bubbles over a NACA 2415 aerofoil on various cases of angles of attack and Reynolds numbers. Lower Re numbers higher the viscous forces generated. Higher viscous forces affect the flow adversely and cause flow separation to occur, therefore the numerical simulation is relatively more difficult at lower Re number flows. Furthermore the low Re number turbulence model and transition models are both successful on prediction of laminar separation bubble, although the bubble length and location is not predicted correctly. The numerical results were showed that the flow gained kinetic energy because of the increase on the kT after the transition point and overcame the adverse pressure gradient and a subsequent turbulent reattachment occurred. Moreover, as seen in the results of numerical and experimental pressure distribution and oil-flow visualization experiment results, as angle of attack increases, laminar separation bubble moves towards to leading edge and length of the laminar separation bubble decreases. Consequently, the transition models are more successful than the k-ω SST turbulence model on prediction the laminar separation bubble and low Re number flow.