Effects of CoFlow-Jet Active Flow Control on Airfoil Stall

Purpose – Active flow control on the NACA 0024 airfoil defined as suction-injection jet at the chord-based Reynolds number of 1.5×10 5 is studied. Design/methodology/approach – The three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes equations with the SST k-ω turbulence model are utilized to study the effects of CoFlow-Jet on the dynamic and static stall phenomena. CoFlow-Jet implementation is conducted with several momentum coefficients to investigate their turnover. Furthermore, the current work intends to analyze the CoFlow-Jet performance by varying the Reynolds number and jet momentum coefficient and comparing all states to the baseline airfoil, which has not been studied in prior research investigations. Findings – It is observed that at the momentum coefficient ( C μ ) of 0.06, the lift coefficients at low attack angles (up to α = 15 ° ) dramatically increase. Furthermore, the dynamic stall at the given Reynolds number and with the lowered frequency of 0.15 is explored. In the instance of C μ = 0.07, the lift coefficient curve does not show a noticeable stall feature compared to C μ = 0.05, suggesting that a more powerful stronger jet can entirely control the dynamic stall. Originality/value – Furthermore, the current work intends to analyze the CoFlow-Jet performance by varying the jet momentum coefficient and comparing


Introduction
Wind turbines convert the kinetic energy of the wind into electrical energy and are categorized into two types: 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 (M.S. Hameed and S.K. Afaq, 2013).The most important superiority of this type of wind turbine is that they do not need to be adjusted relative to the wind direction.Regarding that the axis is vertical, the gearbox and generator can be installed near the ground, leading to 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 their smaller size, 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 the 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 the low Reynolds number region (Yarusevych et al., 2006b, Lissaman, 1983, Mueller and DeLaurier, 2003).Some studies indicated that serious aerodynamic problems might occur for below Reynolds number of about 500,000 (Yarusevych et al., 2006a, Srinath and Mittal, 2009, Salimipour, 2019a).The flow tendency through the airfoil's suction surface is to be separated in this Reynolds number range.On the other hand, the reverse pressure gradient that occurs in low Reynolds number airfoils causes the flow separation (Gim and Lee, 2013).
As the angle of attack increases, the vertical velocity and, consequently, the lift coefficient are escalated.Furthermore, the drag coefficient is also enhanced since the vertical velocity depends on the air resistance.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 increases (Salimipour andYazdani, 2020, Abbasi andYazdani, 2019).In other words, stall angle is a point beyond which the lift-to-drag ratio starts declining with angle of attack.Thus, applying methods to control the stall phenomenon and the separation flow are important.
The airfoil aerodynamic performance can be enhanced with the adequate energy and momentum transported to the boundary layer using flow control methods to reach desired aerodynamic goals, including delaying the transition, delaying the separation, and improving the aerodynamic efficiency.Many successful strategies have been developed (Velasco et al., 2017, Salimipour and Salimipour, 2019, Salimipour et al., 2021) to regulate flow separation and avoid the stall effects.In low Reynolds number aerodynamics, changing the shape of the airfoil is often employed to regulate separation and enhance the lift coefficient.Coflow-Jet (CFJ) is one of the active flow control approaches.The airfoil's suction surface features two slots in this technique: an injection slot near the leading edge and a suction slot near the trailing edge.In this flow control no mass adds to the system.Suction and injection in the airfoil surface, especially at high angles of attack, along with resistance to the reverse pressure gradient, connects the main flow and boosts boundary-layer velocity.Zha et al. (2006) in wind tunnel investigated the effects of injection slot size on the NACA 0025 at Reynolds number Re = 3.8×10 5 .Their research revealed that although a smaller injection slot size airfoil is better for boosting lift, a wider slot minimizes drag.Zha et al. (2007) studied the influence of the suction slot on efficiency numerically.For this purpose, two airfoils with the same injection slot (0.65% c) were studied with the suction slot equaled 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 compared to the baseline airfoil, the lift coefficient was increased, and the angle of attack was delayed.
The airfoil without a suction slot, the stall occurred at 39°, and the other until 43° the stall did not happen.Zha and Gao (2006) experimentally performed the effects of the CFJ on the NACA 0025 at Re = 3.8 × 10 5 .They looked at various pressure ratios and found that the lift coefficient rose by 220% compared to the baseline in the jet case.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 three degrees more than experiments.The effects of adjusting the injection slot size on the lift coefficient, stall angle, and drag coefficient were explored experimentally by Wells et al. (2006).Their findings revealed that an airfoil with a smaller injection slot would need less energy to attain the same lift coefficient as one with a bigger injection slot.Chng et al. (2009) experimentally investigated the jet concept's performance on a Clark-Y airfoil.Furthermore, they compared the aerodynamic performance of the synchronous suction and injection, pure injection, and pure suction.Their findings demonstrated that the simultaneous suction and injection mechanism is more effective than pure injection and pure suction.Abinav et al. (2016), using Ansys Fluent software, compared the performance of the NACA 6409 baseline airfoil and three jet airfoils with different injection and suction slot locations.The influence of jet on the S809 airfoil was numerically examined by Xu et al. (2015) at three jet momentum coefficient values.According to their findings, the jet greatly reduces the drag coefficient and positively influences lift and stall margin.Ethiraj (2017) examined the impact of jet mathematically, and obtained results for a 12° angle of the attack suggest a 25-30% decrease in drag and a 10-20% increase in lift coefficient.Siddanathi (2016) used a jet on NACA 652-415 airfoil to investigate this active flow control on increasing the lift.Lefebvre and Zha (2013) numerically studied the effect of jet flow control on a pitching airfoil at the Reynolds number of 3.93×10 6 and reduced frequency between 0.05 and 0.2.Moreover, Xu et al. (2016) simulated the dynamic stall phenomenon for a wind turbine blade using the jet.Khoshnevis et al. (2020) examined the effects of jets on symmetric NACA airfoils in transitional flow, considering thickness variation.In another investigation, they analyzed the influence of this flow control on NACA 0025 at different Reynolds numbers (Khoshnevis et al., 2020).Some interesting results on this topic can be found in (Gleize et al., 2022, Nived et al., 2022).
In the present paper, active flow control on the NACA 0024 airfoil defined as suction-injection jet at the chord-based Reynolds number of 1.5×10 5 is studied.The three-dimensional incompressible unsteady Reynolds-Averaged Navier-Stokes equations with the SST k-ω turbulence model are utilized to study the effects of CFJ on the dynamic and static stall phenomena.CFJ implementation is conducted with several momentum coefficients to investigate their turnover.Furthermore, the current work intends to analyze the CFJ performance by varying the jet momentum coefficient and comparing all states to the baseline airfoil, which has not been studied in prior research investigations.

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 suction and injection slots are located at distances of 0.83 and 0.07 times the chord length from the leading edge.Based on the considered geometry, various meshing strategies can be employed where a "C" grid is chosen to solve the flow field.Figure 1 shows a close-up view of this grid together with the situation of the CFJ on the airfoil.The nodes have an adequate perpendicular to one another, as can be shown.A width equal to the chord length is considered in the z direction, as shown in Figure 1.
Figure 2 shows the solution domain and boundary conditions.The velocity inlet boundary includes a constant value of U ∞ for the horizontal velocity component, zero for the vertical velocity component, and a zero normal gradient for the pressure (Ghalambaz et al., 2020).On the pressure outlet boundary, a fixed value of p ∞ is applied for the pressure, and the normal gradient of the velocities is assigned to zero.On the solid wall, a no-slip boundary condition is considered.The periodic boundary condition is used for the lateral boundaries.

Mathematical and Numerical Formulation
The integral formulations of the Reynolds-averaged Navier-Stokes equations, which include continuity and momentum, are as follows (Salimipour, 2019b): 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,  ̄ represents the conservative variables vector, and  ̄ consists of the convective and diffusive fluxes which can be written as follows (Salimipour, 2019a, Kalkote et al., 2020): 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 (2016).The momentum equation is discretized with the second-order precision in time and space (Stone, 1968).
To simulate the turbulent viscosity (µt), the SST k-ω turbulence model is used.The flow variables are normalized as expressed in (Hashem Zadeh et al., 2020).The flow parameters required, such as velocity and pressure components, streamlines, and drag and lift coefficients, could be obtained by numerically solving the previously given equations.The jet momentum coefficient Cμ is a parameter that is used to determine the strength of the jet.It is as follows (Bak Khoshnevis et al., 2020): (5) where Uj and ̇ denote the velocity and mass flow of injection; U∞ and ρ∞ are the free stream velocity and density; and c is the airfoil chord length.For cases with a CFJ on, the overall aerodynamic force is estimated according to the analysis in (Zha et al., 2007, Xu et al., 2015).The following is an expression for the overall lift and drag coefficients: where subscripts pressure, stress and jet indicate the pressure force, frictional force and jet mass flow thrust, respectively.  =  ,+ and   =  ,+ be computed using the solver's standard integral approach, while  , and  , are achieved using relations as follows: where (, ) is the unit vector indicating the lift and drag direction and  ̄1 ,  ̄2 are velocity vectors of the jet at injection and suction slots, respectively.
The pitching motion of the airfoil for dynamic stall analysis is described by the following equation: where is the reduced frequency and  =  ∞  denotes the non-dimensional time.For quantifying the improvement of results from CFJ to enhance lift and decrease drag coefficients for the dynamic stall study, the differences in the area under Cl and Cd curves between 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.

Results and Discussion
The Grid Convergence Index (GCI) is applied to evaluate the uncertainty caused by the grid spacing.For three mesh resolutions of 1: coarse, 2: medium, and 3: fine, the GCI formulation based on the Richardson's extrapolation theory can be written as follows (Lee et al., 2020): where FS, ε, r, p, and f are the safety factor, relative error, ratio of grid refinement, accuracy order, and solution value, respectively.For three meshes, FS = 1.25 (Lee et al., 2020).The lower value of the GCI is the lower the grid sensitivity.
In the present study, three meshes with 1: 640000, 2: 900000, and 3: 1260000 points on three directions with a constant r = 1.4 are generated and 30 points are considered at z direction to capture the three-dimensional effects.Two solution values of Cl and Cd are examined for the GCI study at α = 15 o , Re = 1.5 × 10 5 , and Cμ = 0.13.Table 1 presents the GCI calculations for the above-mentioned meshes.Due to the low percentage of the GCI23, the medium mesh is used for the computations.The y + dimensionless parameter is an important parameter for determining the grid quality used to solve turbulent flow problems.Figure 3 depicts the wall y + distribution of the CFJ airfoil at Cμ = 0.07 and α = 15 o .As can be seen, the maximum value of y + reaches about 1.5.In this study, several momentum coefficients (Cμ) for the angles of attack in the range of 0-30 degrees at Re = 1.5×10 5 on the NACA 0024 airfoil are investigated to understand which momentum coefficient has an agreeable act at each attack angle.Figure 7 shows the pressure coefficients streamtraces and contours for the baseline geometry at the angles of attack α = 5°, 10°, and 15°.The growth of the vortices can be seen for α ≥ 5°.The entanglement of the streamtraces in    It can be seen that all the curves finally become unchanged over time, and thus, the flow at this angle of attack has been steady.Furthermore, the baseline airfoil curve trend indicates that the stall occurs at this angle of attack, unlike the other curves.The lift to drag ratio is an essential statistic for aircraft aerodynamic performance.Figure 11 depicts the lift to drag coefficient curves for various momentum coefficients with respect to the angle of attack.The CFJ airfoils, compared to the baseline airfoil, have a dramatic gain in the lift to drag coefficients and cause the stall to occur at the higher angles of attack maintained with higher values of Cµ.As observed, increasing the momentum coefficient increases the stall angles and maximum lift to drag coefficients for all CFJ airfoils.The lift to drag coefficient diagram shows that for the CFJ airfoil with Cµ = 0.05, there is a significant increase for the Cl / Cd, and the stall angle is delayed compared to the baseline airfoil.At Cµ = 0.06 and α ≤ 15°, the highest Cl / Cd is observed.As the angle of attack increases from α = 20° to 30°, the Cl / Cd decreases.At Cµ = 0.13 and α ≤ 10°, the use of CFJ is not optimum because of the drag increment, while for α ≥ 15°, a significant Cl / Cd is obtained because of the significant lift generation.For the other angles, the maximum Cl / Cd is distinct at each angle of attack.The baseline airfoil result shows the stall occurrence around α = 10°, whereas for the CFJ airfoils results with Cµ = 0.05-0.07, the stall occurs at α = 15°.With further increase in the momentum coefficients, the stall angles increase, and at Cµ = 0.13, the stall does not occur up to α = 30°.Figure 12 shows the stall angles versus the different momentum coefficients.As the momentum coefficient increases, the stall angle increases.Figure 13 shows the optimum Cμ corresponding to (Cl / Cd) max for different angles of attack.In other words, each Cμ that leads to maximizing the lift-to-drag ratio is defined as optimum.Within the range of 15°< α < 23°, by increasing the momentum coefficient, the lift to the drag ratio is enhanced, increasing the energy consumption of the CFJ.It can also be seen that the CFJ has the highest lift ratio 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.Table 2 shows the comparison of the maximum lift coefficients and locations of the stall onset between the baseline and CFJ cases.The CFJ significantly increases the maximum lift.Another investigation in this paper is about the influence of CFJ on the dynamic stall phenomena.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.Figure 15 shows the lift coefficient curve for the CFJ control cases and the baseline airfoil.As can be seen, the lift coefficient curve for the CFJ case with Cμ = 0.05 shifts up and is increased, compared to the baseline airfoil; however, the stall still occurs and this behavior is almost similar to the baseline airfoil.As expected, raising the momentum coefficient from 0.05 to 0.07 reduces the lift coefficient hysteresis loop.Furthermore, in the case of Cμ = 0.07, the lift coefficient curve lacks the stall feature, indicating that a more powerful jet may fully control the dynamic stall.The maximum lift coefficient for the baseline airfoil is equal to 1.15 and for the CFJ cases for Cμ = 0.05 and 0.07 is equivalent to 2.06 and 2.16, respectively.Regarding the drag curves, Figure 16 shows the CFJ control cases with Cμ = 0.05 and 0.07 and the baseline airfoil.The maximum drag coefficient for the baseline airfoil and two CFJ cases is 0.54, 0.32, and 0.21.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 3 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 3.It is discovered that by adopting the CFJ, the average lift coefficient can be greatly raised, and the average drag coefficient can also be somewhat raised.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.

Conclusions
The goal of this study is to use numerical analysis to assess the effect of CoFlow-Jet on the stall and flow separation of the NACA 0024 airfoil at the Reynolds number of 1.5 × 10 5 .The CFJ control used two slots on the airfoil suction surface, one for injection and one for suction.An in-house computer code based on the Reynolds-averaged Navier-Stokes equations, three-dimensional, incompressible, and unsteady with the SST k-ω turbulence model, was prepared for this investigation.
The solver was verified by comparing it to experimental data, which revealed a reasonably good agreement.In the present study, the performance of CFJ control was evaluated by executing CFJ control at various momentum coefficients and comparing the results to 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: − The CFJ airfoils compared to the baseline airfoil had a dramatic gain in the lift coefficients and caused the stall to occur at the higher angles of attack maintained with higher values of Cµ.
− Increased momentum coefficients improved the stall angles and maximum lift coefficients of all CFJ airfoils.
− For the angles of attack lower than the stall angles, no improvement was seen by increasing the momentum coefficient compared to the lower momentum coefficients.The trend had almost been stable.
− The baseline airfoil result showed the stall occurring around α = 10°, whereas the CFJ airfoil results at Cµ = 0.05 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 did not happen until α = 30°.
− By increasing the momentum coefficient, the drag coefficient increased compared to the baseline airfoil, while for higher angles, increasing the momentum coefficient led to a reduction in the flow separation zone, and consequently, the drag coefficient decreased compared to the baseline airfoil.
− The CFJ had the highest ratio of the lift to the drag at α = 14° and Cµ = 0.06.− In the dynamic stall situation, raising the momentum coefficient from 0.05 to 0.07 resulted in a reduced lift coefficient hysteresis loop.Additionally, with Cµ = 0.07, the lift coefficient curve lacked the stall feature, indicating that a stronger jet could completely manage the dynamic stall.

Figure 1 .
Figure 1.The grid used in flow computations and situation of the CFJ on the airfoil.

Figure 4 .
Figure 4. Comparison of pressure coefficient distribution of NACA 0025 airfoil between present result and experimental data (Ziadé et al., 2018) at Re = 10 5 and α = 12 o

Fig. 7
Fig. 7(c) indicates the presence of three-dimensional effects that arise from the third dimension (zdirection) disturbances.

Figure 9 .
Figure 9.Comparison of the pressure coefficient distributions at α = 15° for various Cμ levels.

Figure 11 .
Figure 11.Comparison of lift to drag coefficients for different Cμ levels.

Figure 12 .
Figure 12.Variation of stall angles for different Cμ levels.

Figures
Figures 14(a) and 14(b) show the tangential velocity (Vt) 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 boundary-layer momentum of the CFJ cases is significantly increased compared to the baseline airfoil.

Figure 13 .
Figure 13.Optimum Cμ and maximum Cl/Cd for different angles of attack.

Figure 15 .
Figure 15.Lift coefficient comparison between the CFJ and baseline airfoils.

Figure 16 .
Figure 16.Drag coefficient comparison between the CFJ and baseline airfoils.

Table 2 .
Comparison of maximum lift coefficients and locations of stall onset.

Table 3 .
Effects of CFJ control compared to the baseline (k = 0.15).