A Numerical Investigation of Co-ow Jet Effects on Airfoil Aerodynamic Characteristics

The present paper numerically investigates the performance of a Co-Flow Jet (CFJ) on the static and dynamic stall control of the NACA 0024 airfoil at Reynolds number 1.5 × 10 5 . The two-dimensional Reynolds-averaged Navier-Stokes equations are solved using the SST k - ω turbulence model. The results show that the lift coefficients at the low angles of attack (up to α = 1 5̊ ) are significantly increased at C μ = 0.06, however for the higher momentum coefficients, it is not seen an improvement in the aerodynamic characteristics. Also, the dynamic stall for a range of α between 0̊ and 2 0̊ at the mentioned Reynolds number and with the reduced frequency of 0.15 for two CFJ cases with C μ = 0.05 and 0.07 are investigated. For the case with C μ = 0.07, the lift coefficient curve did not present a noticeable stall feature compared to C μ = 0.05. The effect of this active flow control by increasing the Reynolds numbers from 0.5 × 10 5 to 3 × 10 5 is also investigated. At all studied Reynolds numbers, the lift coefficient enhances as the momentum coefficient increases where its best performance is obtained at the angle of attack α = 1 5̊ .


Introduction
Wind turbines are used to convert the wind's kinetic energy into electrical energy and are categorized into two main types of vertical axis and horizontal axis. Generally, although horizontal-axis wind turbines (HAWT) are popular all around the world, they cannot be used in municipal areas, damage the environment, and need a high initial cost. Wind energy is considered as one the cheapest and most available renewable energy resources. However, due to different problems of HAWTs, wind turbines are not widely employed. Thus, vertical-axis wind turbines (VAWT) take on paramount importance [1]. The most important superiority of this type of wind turbines is that they do not need to be adjusted relative to the wind direction. Regarding that the axis is vertical, gearbox and generator can be installed near the ground leading to facilitating the maintenance and repair of these pieces of equipment. Since the blade tip is closer to the rotating axis in VAWTs, in comparison to HAWTs, they make lower noise. Furthermore, due to the smaller size of them, the peripheral collisions are reduced. NACA airfoils are designed for aircraft and wind turbines. Investigating airfoil characteristics, particularly in incompressible low-Reynolds flows, and changes in aerodynamic performance of airfoils, due to the amount of the Reynolds number, is of paramount importance. Several investigations were conducted to study the performance of airfoils in low Reynolds number region [2][3][4]. Some studies indicated that for below Reynolds number of about 500,000 the flow has not a specific behavior and serious aerodynamic problems maybe occur [5][6][7]. In this range of Reynolds number, the trend of flow in suction surface of the airfoil is to be separated. On the other hands, the reverse pressure gradient that occurs in low Reynolds number airfoils causes the flow separation [8]. As the angle of attack increases, the vertical velocity and, consequently, the lift coefficient are escalated. Furthermore, since the vertical velocity depends on the air resistance, the drag coefficient is also enhanced. This trend continues up to a specific angle, called the stall angle. When stall happens, devastating effects on aerodynamic performance occur; the lift coefficient dramatically decreases while the drag coefficient continues to increase [9,10]. Thus, applying methods to control the stall phenomenon and control the separation flow is of great importance. The airfoil aerodynamic performance can be enhanced, with the adequate energy and momentum transported to the boundary layer using flow control methods, in order to reach desired aerodynamic goals including delaying the transition, delaying the separation, and improving the aerodynamic efficiency. To control the flow separation and prevent the consequences of that, many effective methods presented so far [11][12][13][14][15][16].
In aerodynamics with low Reynolds number, the change of airfoil geometry is usually used to control the separation and improve the lift coefficient. One of the active flow control techniques is Co-Flow Jet (CFJ) that developed by Zha et al. [17,18]. In this technique, there are two slots on the suction surface of the airfoil, an injection slot near the leading edge, and a suction slot near the trailing edge. The whole process does not add any mass flow to the system and hence is a zero-net mass flux flow control and the energy loss are minimized. Use of suction and injection in the airfoil surface especially at the high angles of attack, with resistance to the reverse pressure gradient makes the main flow to be attached and they both enhance the boundary-layer momentum. The suction slot helps to achieve zero net mass flow rate of the jet. Zha et al. [17] in wind tunnel investigated the effects of injection slot size on the NACA 0025 at Reynolds number Re = 3.8×10 5 .
Their result presented that to increase the stall margin and maximum lift the smaller injection slot size airfoil is more efficient whereas, to reduce drag the larger slot is more useful. Zha et al. [19] numerically investigated the effect of the suction slot on the efficiency of the CFJ. For this purpose, two airfoils with the same injection slot (0.65% c) studied that one of them with the suction slot equal to 1.96% c and the other without the suction slot. This study showed that the airfoil with the suction slot had better aerodynamic performances. For both airfoils compare the baseline airfoil, the lift coefficient increased and the angle of attack was delayed. The airfoil without a suction slot the stall occurred at 39̊ and the other until 43̊ the stall did not happen. Zha and Gao [20] experimentally performed the effects of the CFJ on the NACA 0025 at Reynolds 3.8 × 10 5 . They examined several pressure ratios, and their results showed that the lift coefficient of the CFJ compared to baseline increased by 220%. They also numerically performed their experimental results and there was a good agreement between the data for the lift coefficient. However, the angle of attack of the stall was forecasted in numerical results 3 degrees more than experiments. Wells et al. [21] experimentally investigated the size changes of the injection slot on the lift coefficient, drag coefficient, and angle of stall occurrence. Their result showed to achieve the equivalent lift coefficient, an airfoil with a smaller injection slot will consume less energy from the airfoil with a larger injection slot. Chng et al. [22] experimentally studied the performance of the CFJ concept as applied to a Clark-Y airfoil. Furthermore, they prepared a comparison between the aerodynamic performance of the CFJ, pure injection, and pure suction. Their results showed that the CFJ is more effective, compared pure injection and pure suction. Abinav et al. [23] by using ANSYS FLUENT conducted a comparison of the performance of NACA 6409 baseline airfoil and the three CFJ airfoils with varying positions of injection and suction slots. Xu et al. [24] numerically investigated the effect of CFJ on the S809 airfoil at three jet momentum coefficient levels. Their result indicated that the CFJ significantly decrease the drag coefficient and has a positive effect in increasing the lift and stall margin. Ethiraj [25] numerically investigated on effect of CFJ and his result for angle of attack of 12̊ shows 25-30 percent reduction in drag and 10-20 percent increase in lift coefficient.
Siddanathi [26] used CFJ on NACA 652-415 airfoil to investigated this active flow control on increasing the lift. Mirhosseini and Khoshnevis [27] experimentally investigated the effect of CFJ on the boundary layer and provided valuable information about the adverse pressure gradient.
Their result showed the CFJ can overcome the adverse pressure gradient at angle higher than 12.
Amzad Hossain et al. [28] experimentally studied the baseline NACA 0015 airfoil and CFJ0015-065-065 to investigate and compare the airfoil aerodynamic characteristics over a wide range of angles of attack with free stream velocity of 12 m/s , Re = 1.89 × 10 5 , and Cµ = 0.07. Their result showed the CFJ airfoil compare to the baseline airfoil CL max increased by 82.5% and the drag decreased by 16.5% at stall angle of attack. Lefebvre and Zha [29] numerically studied the effect of CFJ flow control on a pitching airfoil at the Reynolds number of 3.93×106 and reduce frequency between 0.05 and 0.2. Moreover, Xu et al. [30] simulated the dynamic stall phenomenon for a wind turbine blade using the CFJ.
In the present paper, an active flow control on the NACA 0024 airfoil defined as co-flow jet (CFJ) at the chord-based Reynolds number of 1.5×10 5 is studied. The two-dimensional incompressible unsteady Reynolds-Averaged Navier-Stokes equations with the SST k-ω turbulence model is utilized to study the effects of CFJ on the aerodynamic characteristics of the static and dynamic stall phenomena. The implementation of the CFJ is conducted with several momentum coefficients to investigate the turnover of them. Moreover, the present paper is aimed to evaluate the CFJ performance by changing the Reynolds number and jet momentum coefficient and compare all the states with the baseline airfoil which has not been investigated in the previous research studies.

Model Description
The CFJ is constructed at the suction surface of the baseline NACA 0024 airfoil to produce a jet tangential to the main-flow; the heights of an injection slot and a suction slot are considered 0.006 and 0.019 times the chord length, respectively. The injection and suction slots are located at distances of 0.07 and 0.83 times the chord length from the leading edge, respectively. Based on the considered geometry, various meshing strategies can be employed where we choose a "C" grid to solve the flow using the elliptic method. Fig. 1 shows a close-up view of this grid together with the situation of a CFJ on the airfoil. As it can be observed, the nodes possess an appropriate perpendicular to one another.

Mathematical and Numerical Formulation
The integral formulations of the Reynolds-averaged Navier-stokes equations including the continuity and momentum can be written as follows [32]: where ρ denotes the density, Ω is a volume surrounded by the control surface ∂Ω, V is the velocity perpendicular to the surface element dS, ⃗⃗⃗ denotes the conservative variables vector, and consists of the convective and diffusive fluxes which can be written as follows [7]: where μ and μt denote the laminar and turbulent viscosity, respectively. The flow equations (1) and (2) are solved by a pressure-based method proposed by Rajagopalan and Lestari [33]. The momentum equation is discretized with second-order temporal and special accuracy. Furthermore, the pressure equation is numerically solved using a Strongly Implicit procedure (SIP) developed by Stone [34]. In order to simulate the turbulent viscosity (μt), the SST k-ω turbulence model is used. The flow variables are normalized as express in [35].
By solving the above-mentioned equations numerically, the required flow parameters such as pressure and velocity components are computed, and then, the streamlines and the drag and lift coefficients can be obtained. The jet momentum coefficient Cμ is a parameter used to measure the jet intensity. It is defined as follow [16]: where ̇ is the injection mass flow, Uj the injection velocity, ρ∞ and U∞ denote the free stream density and velocity, respectively and c is the airfoil chord length. For cases with a CFJ on, the total aerodynamic force is computed according to the analysis in Ref. [19,24]. The total lift and drag coefficients can be expressed as follows: where subscripts pressure, stress and jet indicate the pressure force, frictional force and jet mass flow thrust, respectively. , + , and , + can be calculated by standard integral algorithm in the solver, while , , , are achieved using relations as follows: (9) where ( , ) is the unit vector representing the drag and lift direction and ⃗ 1 , ⃗ 2 are the jet velocity vectors at injection and suction slot, respectively.
The pitching motion of the airfoil for dynamic stall analysis is described by the following equation: where k = ωc / 2U∞ is the reduced frequency and τ = tU∞ /c denotes the non-dimensional time.
For quantifying the improvement of the results from the CFJ to enhance the lift and decrease the drag coefficients for the dynamic stall study, the differences in the area under the Cl and Cd curves between the control cases and the baseline airfoil are calculated. This is accomplished as follows (where q is either lift or drag): where φ denotes the phase angle of the pitching motion in radians.
In order to compare the results of the CFJ airfoil with the baseline airfoil, three performance parameters are used defined as follows:

Grid resolution study
In order to investigate the grid independency of the computational domain, meshes with different numbers of cells were evaluated and their results were compared with each other. As shown in

4.2.Code validation study
Before using the written code and in order to validate its accuracy, it is necessary to test the validity of the flow solver. Experimental data obtained by Zha et al. [17] used to evaluate the solver ability, for the configuration of NACA 0025 and CFJ0025-65-196 at Reynolds number of 3.8×10 5 . Fig. 4 shows the comparison of the lift to drag ratio between the present solver and experimental data.
The prognostications are in nearby conjunction with the experimental data [17].      One of the important parameters for the aerodynamic performance of aircraft is the lift to drag ratio. Fig. 9 shows the lift to drag coefficient curves with respect to angle of attack for several    Within the range of 15°< α <23° by increasing the momentum coefficient, the ratio of the lift to the drag is enhanced, and it makes an increases in the energy consumption of the CFJ. It can also be seen that the CFJ has the highest ratio of the lift to the drag at 14°. It should be noted that the required momentum coefficient at this angle compared to other angels has the smallest value. Fig.   12a and 12b show the velocity profiles for the baseline and CFJ cases with the momentum coefficients Cµ = 0.05 and 0.09 at x / c = 0.3 and 0.6, respectively. In both sections, the boundarylayer momentum of the CFJ cases is significantly increased, compared to the baseline airfoil.   Table 1 shows the comparison of the maximum lift coefficients and locations of the stall onset between the baseline and CFJ cases. The maximum lift is greatly enhanced by use of the CFJ. Another investigation in this paper is about the effect of CFJ on the dynamic stall phenomenon.
The simulation is performed at k = 0.15 for the baseline airfoil and two CFJ cases with Cμ = 0.05 and 0.07. By increasing the momentum coefficient, more energy can be transferred into the boundary layer; consequently, the lift coefficient is increased. Fig. 13 shows the lift coefficient curve for the CFJ control cases and the baseline airfoil. As can be seen, the lift coefficient curve Therefore, for the case with Cμ = 0.07 the maximum drag coefficient is decreased by 61%, furthermore, its hysteresis loop becomes smaller and smoother.   Table 2 presents the averages of the aerodynamic hysteresis loops for two cases with Cμ = 0.05 and 0.07. In order to quantify the enhancement in the lift and the reduction in the drag coefficients over a pitch cycle due to CFJ cases, the differences within the area under the Cl and Cd curves between the control and baseline cases are computed. The resulting values due to the CFJ control are summarized in Table 2. It is observed that the average lift coefficient can be significantly increased by implementing the CFJ, and the average drag coefficient also slightly be increased.
Finally, the results at cμ = 0.07 show that the relative difference of the lift and drag coefficients (∆ , ∆ ) are improved compared to the baseline airfoil.

Effects of Reynolds number
The effect of the CFJ method on the aerodynamic performance of the airfoil is studied at five Reynolds numbers from 0.5 × 10 5 to 3 × 10 5 . This evaluation is carried out for different jet momentum coefficients of 0.03, 0.06, 0.09, and 0.13 in a range of angle of attack from 0 o to 20 o .   Fig. 16 shows the performance of the drag coefficient for the CFJ at different Reynolds numbers and momentum coefficients. In most cases, by increasing the Reynolds number the value of the drag coefficient for CFJ airfoil increases more than that for the baseline airfoil. Furthermore, in most cases, the drag coefficient for the CFJ airfoil at Reynolds number of 50000 increases by a lower percentage. In addition, the performance of the lift to drag coefficient for the CFJ at different Reynolds numbers and momentum coefficients are calculate as shown in Fig. 17. The most enhancements and the best performance of the CFJ airfoil, compared to the baseline airfoil, is observed at the Reynolds number of 0.5 × 10 5 , particularly at lower angles of attack. In other cases, the optimum lift to drag ratio for the CFJ airfoil is observed at α = 15 o . At this angle of attack, although the drag coefficient of the CFJ airfoil is increased compared to the baseline airfoil, there is a more significant increase in the lift coefficient. Therefore, the lift to drag ratio is enhanced that can be attributed to the absence or delay of the stall phenomenon. By occurrence of the stall phenomenon in the baseline airfoil in the vicinity of this angle, the lift and drag coefficients are substantially reduced and increased, respectively. Applying the flow control prohibits the stall and there would be a great enhancement within the range of the stall angles and after them.

Conclusions
In this paper, a numerical study was conducted to investigate the effect of Co-Flow Jet (CFJ) on the stall and the flow separation of the NACA 0024 airfoil at different Reynolds number from 0.5 × 10 5 to 3 × 10 5 . The CFJ control, involved two slots on the suction surface of the airfoil, an injection slot near the leading edge, and a suction slot near the trailing edge. For this investigation, an in-house computer code based on the Reynolds-averaged Navier-Stokes equations, twodimensional, incompressible, and unsteady with the SST-k-ω turbulence model was prepared. The solver was validated by comparing with the previous experiment results and the comparisons showed the fairly good agreement. In the present study, the performance of the CFJ control was investigated by implementing the CFJ control at several momentum coefficients and compared the results with the baseline airfoil. Furthermore, the effects of this flow control on the dynamic stall at two momentum coefficients were studied. The conclusions for Re = 1.5 × 10 5 are as follows: (1) The CFJ airfoils compared to the baseline airfoil had a dramatic gain in the lift coefficients and caused the stall occurred at the higher angles of attack maintained with higher values of Cµ.
(2) For all the CFJ airfoils with various momentum coefficients, the stall angles and maximum lift coefficients were increased with raising the momentum coefficients.
(3) For the angles of attack lower than the stall angles, by increasing the momentum coefficient, no improvement was seen compared to the lower momentum coefficients and the trend had almost been stable.
(4) The baseline airfoil result showed the stall occurring around α = 10°, whereas the CFJ airfoils results for Cµ = 0.05 -0.07 showed the stall occurring at α = 15°. With further increase in the momentum coefficients, the stall angles were increased, and at Cµ = 0.13 the stall was not occurred until α = 30°.
(5) by increasing the momentum coefficient, the drag coefficient increased compared to the baseline airfoil, while for higher angles, increasing the momentum coefficient led to reduction in the flow separation zone and consequently, the drag coefficient decreased compared to the baseline airfoil. (9) Investigation of the Reynolds number effect indicated that by applying the CFJ, the highest enhancement in the aerodynamic coefficients was observed at the Reynolds numbers lower than 10 5 . The separated flow did not reattach to the surface at the Reynolds numbers lower than 10 5 that could be yield a great reduction in the aerodynamic performance.

Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.