# Numerical Simulation of Ground Effect on Circulation Control Airfoil

Authors: Quanbing Sun; Zhiwei Shi; Weilin Zhang; Zhikun Sun; Yongliang Chen
Journal: International Journal of Aerospace Engineering
 (2022)

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## Abstract

Circulation control (CC) is used extensively to control the attitude of rudderless aircraft experiencing ground effect in take-off and landing phases. The investigation of ground effect on airfoil CC is necessary to improve flight performance and quality in proximity to the ground. The aerodynamics and flow field of a modified NACA0012 airfoil with CC in ground effect are investigated with numerical simulations. The compressible Reynolds-averaged Navier–Stokes equations with the shear-stress transportk−ω turbulence model equations are solved using the Finite Volume Method (FVM). Simulation results show that the ground effect changes the lift increment per unit jet momentum coefficient, and CC can reverse the polarity ground effect. The effective angle of attack αE and the downwash space downstream airfoil are altered by the ground effect resulting in variations of airfoil surface pressure and lift. Unlike the unbounded flow field, the jet attachment distance is not only determined by the jet momentum coefficient but it can change with the ride height, which is the distance from the ground to the center of the semicircular Coanda surface, for the same jet momentum coefficient.


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## Body

## 1. Introduction

Active flow control (AFC) has the potential to fly aircraft without control surfaces [1, 2]. Using AFC could reduce vehicle weight and the complexity of the mechanical structure while maintaining the same flight performance. The absence of the edges and gaps, resulting from movement control surfaces, reduces the signatures of military aircraft [3], enhancing their survivability in increasingly sophisticated threat environments.Circulation control (CC) is one of the most widely used AFC techniques in rudderless aircraft and is based on the Coanda effect, changing wing circulation and lift by blowing air tangentially along the rounded trailing edge. CC was first proposed by Davidson [4] in 1962, and several researchers further developed the flow mechanism. Englar [5–7] investigated high lift performance and proposed that the lift increment increased with jet moment coefficient as long as the jet remained attached to the Coanda trailing edge. It was also found that the slot height to Coanda surface radius ratio hs/r and Coanda surface radius to chord length ratio r/c impacted the maximum lift increment ∆CL,max generated by CC. Abramson and Rogers [8] found that a supersonic jet would separate from the Coanda trailing edge because of shock wave and boundary layer interaction, leading to severe lift reduction. Llopis-Pascual [9] and Forster and Steijl [10] suggested that introducing a step between the jet exit and the Coanda surface can delay the separation of the supersonic Coanda jet. Chu et al. [11] showed that the elliptical Coanda trailing edge has better control consistency at different free-stream Mach numbers and better control stability with a supersonic jet.Many applications of CC have been achieved. As early as the 1970s, circulation control technology was applied to aircraft. The US Navy used CC to enhance the lift of the A-6A in take-off and landing processes [12, 13]. In 1976, the University of Virginia used CC to improve lift and the performance improvement is equivalent to a 20% increase in chord length [12, 13]. The Tutor UAV without ailerons using CC as a rolling controller completed flight experiments in 2005 [3]. Wind tunnel experiments showed that the control moment produced by CC is sufficient to meet a rudderless fly-wing aircraft’s trim and maneuvering requirements [14]. The DEMON UAV [15–19], using CC as the rolling and pitching controller, achieved flight without control surfaces in 2008. A V-tail aircraft [20] flew with a CC rolling controller in 2014, and a rudderless canard layout UAV [21] completed flight tests in 2015.When an aircraft flies near the ground, the surrounding airflow is compelled to be parallel to the ground, and the flow field changes cause aerodynamics variations, which is ground effect. All aircraft experience and are greatly affected by ground effect during take-off and landing, and rudderless aircraft are no exception. Studying ground effect to increase the stability and safety of aircraft during take-off and landing is essential.The aerodynamics and flow physics of two-dimensional (2D) airfoils in ground effect have been broadly investigated. The exploration of the effect of camber and thickness on the aerodynamics of a 2D airfoil in ground effect was conducted by Hsiun and Chen [22] using numerical simulation. It was found that the channel between the lower airfoil surface and the ground determined the aerodynamics of the airfoil. Ahmed et al. [23] experimentally investigated ground effect on a NACA4412 airfoil, and it was indicated that the drag increased with the decrease of the ride height. However, the lift variations depended on the passage’s shape between the lower airfoil surface and the ground. Zerihan and Zhang [24] and Mahon and Zhang [25] studied ground effect on a Tyrrell-02 airfoil with numerical simulations and wind tunnel experiments, and it was found that the reduction in ride height caused an initial increase of downforce, followed by a significant decrease as the ride height decreased. Qu et al. [26] performed numerical simulations to investigate ground effect on a NACA4412 airfoil for a wide angle of attack range and showed that the flow physics changed with the angle of attack. Nirooei [27] investigated the aerodynamic and static stability characteristics of airfoils in extreme ground effect using a computational method. However, there are few studies on ground effect for airfoils with CC. It is necessary to study aerodynamics and flow physics of the ground effect on an airfoil with CC to improve the performance of rudderless aircraft.This paper investigates the aerodynamics and flow physics of a modified NACA0012 airfoil with CC in ground effect using Computational Fluid Dynamics (CFD). This paper is organized as follows. Section1 introduces the present research achievement of the circulation control and the ground effect and puts forward the study focus of this paper. Section 2 gives the computational configuration and the validation of the numerical method. Section 3 shows the numerical result and analyses the flow physics of the ground effect on CC and Section 4 is the conclusion.


## 2. Computational Configuration and Grid Resolution

### 2.1. Physical Model

The trailing edge of the baseline NACA0012 airfoil is truncated and replaced by a semicircular Coanda surface, and the chord lengthc of the modified airfoil is 0.93c0, where c0 is the chord length of the baseline airfoil. Figure 1 shows the Coanda trailing edge of the modified airfoil. The radius of the Coanda surface is 0.01c0, and the slot height to radius ratio hs/l is set to be 0.1 in this investigation. In addition, the height of the lip hl between the lower surface of the airfoil and the slot is 0.001c0.Figure 1
Coanda trailing edge of the modified airfoil.


### 2.2. Numerical Method

The flow field for the airfoil is computed using the FLUENT CFD software. The compressible Reynolds-averaged Navier–Stokes (RANS) equations are solved with the shear-stress transport (SST)k−ω turbulence model using the finite-volume spatial discretization method. A second-order upwind scheme is used for calculating the convection terms, and a central difference scheme is used for the diffusion terms. The flux is discretized using Roe’s approximate Riemann solver.The rectangular computational domain used in the investigation is shown in Figure2. The top, left, and right boundaries are located 20c0 away from the airfoil. The airfoil and jet plenum are set as no-slip static walls, and the jet source is set as the pressure inlet. The top, left, and right boundaries are set as pressure far field and the bottom boundary is a no-slip moving wall with a translational velocity equal to the free-stream velocity. The distance from the ground (the bottom boundary) to the center of the semicircular Coanda surface is defined as the ride height h, and its non-dimensional form is denoted as h/c.Figure 2
Rectangular computational domain and airfoil boundary: (a) rectangular computational domain; (b) airfoil boundary.
(a)(b)The Reynolds number based on the chord length is4.3×106 with free-stream Mach number M=0.2. The non-dimensional ride heights h/c=inf,1.0,0.8,0.6,0.4,0.2 with α=0, 4, and 8° are considered in this investigation. For the h/c=inf cases, the bottom boundary is located 20c0 away from the airfoil and is set as pressure far field.


### 2.3. Jet Momentum Coefficient

The jet momentum coefficient is an important parameter measuring the jet strength in circulation control. The 2D jet momentum coefficient is defined as:(1)Cμ=ṁUjetq∞c,where c is reference chord length. The mass flow rate ṁ and jet velocity Ujet are determined by the nozzle pressure ratio NPR, defined as the ratio of the total plenum pressure P0 to the free-stream static pressure P∞, and the total temperature T0. The total temperature is fixed at 300K, and the jet momentum coefficient changes with the preset pressure ratio in the numerical simulation.Because of the air viscosity, the jet is not isentropic, leading to non-uniform fluid density and jet velocity profiles at the nozzle outlet. Equation (1) can be rewritten in summation form to obtain a more accurate jet momentum coefficient:
(2)Cμ=∑i=1Nρivi2∆hiq∞c,where ∆hi is the spacing between neighboring grid points at the jet slot, and ρi and vi are the fluid density and jet velocity of each cell on the interface boundary, respectively.


### 2.4. Validation of Numerical Method

First, a grid refinement study is conducted using the modified NACA0012 airfoil for upper slot blowing withCμ=0.013 at α=0° and h/c=0.2 and the free-stream Mach number is 0.2. The results are listed in Table 1. The Richardson extrapolation [28] method is used to estimate the coefficients on an “infinite” grid density. The formulation is defined as:
(3)finf=f2+f2−f1r2−1,where f1 and f2 are the simulation results of two sets of grids, and r=1.2 is the grid refinement ratio of this investigation. As shown in Figure 3, CL and Cm change significantly when the cell count increases from 1.16×105 to 1.68×105. However, CL and Cm change inconspicuously when the cell count increases from 1.68×105 to 2.44×105. Richardson extrapolation results are listed in Table 1 and CL and Cm produced by the medium grid are 0.6% greater and 0.34% less than the extrapolated results, respectively. It is concluded from these results that the medium grid gives acceptably accurate results while being computationally cost-effective.Table 1
Grid refinement study results.
GridCell countCLCmCoarse1.16×1050.6304-0.1492Medium1.68×1050.5202-0.1342Fine2.44×1050.5192-0.1341ExtrapolationInfinite0.5171-0.1338Figure 3
Curves of lift coefficient and pitch moment coefficient versus cell count.Alexander et al. [29] conducted a range of experiments on a 0.75% cambered elliptical airfoil with a thickness of 6% chord to study the effects of CC. The span of the model was two chord lengths, and an end plate one chord length in diameter was installed. The aft 10% of the airfoil is truncated and installed with a 2.98 : 1 elliptical Coanda surface, and the slot height to chord ratio is 0.12%. The CC airfoil is illustrated in Figure 4.Figure 4
Elliptical airfoil with elliptical Coanda surface [29].Li and Qin [30] pointed out that the 2D airfoil case over-predicted the pressure coefficients on the surface, while the 3D model agreed well with the experimental data. Li and Qin [30] and Forster and Steijl [10] used an enlarged plate with a 1.1 chord length diameter to arrange the structured grid around the leading edge and improve the accuracy of the simulation. Thus, a 3D model with an enlarged plate is used in the simulation. The mesh domain of the model used in the investigation is shown in Figure 5 and Table 2 lists the size information of the model. The 3D mesh is generated with ICEM CFD and there are 221 cells on the main airfoil, 121 cells on the Coanda surface, 149 cells in the wall-normal direction, and 221 cells over the span of the airfoil. The distribution of grid points mentioned above is the same as that in Ref. [30] and the y+ is less than 1.Figure 5
Mesh domain of the elliptical airfoil.Table 2
3D model and mesh information.
NameSizeChord length30 inchSpan60 inchCell counts341×221×149 cellsWall distancey+≤1A numerical simulation is conducted atα=3° with free-stream Mach number M=0.3. Figure 6 compares the pressure coefficients from the numerical simulation and the experimental investigation at the model mid-span section, for upper slot blowing with jet momentum coefficient Cμ=0.054 and lower slot blowing with jet momentum coefficient Cμ=0.028. The computational pressure coefficients on the airfoil surface match the experimental data reasonably well, and the pressure distribution on the Coanda surface follows the trends of the experiment results.Figure 6
Comparison of pressure coefficient at the model mid-span section for CC validation: (a) upper slot blowing; (b) lower slot blowing.
(a)(b)There was a validation on the simulation of the ground effect of the airfoil using FLUENT [26] in the investigation of airfoil aerodynamics in ground effect for a wide angle of attack range. To further demonstrate that the aerodynamics of the airfoil with ground effect can be simulated with FLUENT, experimental data for a 2D NACA4412 airfoil with ground effect are used in the validation. As shown in Figure 7, the numerical pressure coefficient distribution agrees quite well with the experimental data from Ref. [23].Figure 7
Comparison of pressure coefficient for ground effect validation.


## 2.1. Physical Model

The trailing edge of the baseline NACA0012 airfoil is truncated and replaced by a semicircular Coanda surface, and the chord lengthc of the modified airfoil is 0.93c0, where c0 is the chord length of the baseline airfoil. Figure 1 shows the Coanda trailing edge of the modified airfoil. The radius of the Coanda surface is 0.01c0, and the slot height to radius ratio hs/l is set to be 0.1 in this investigation. In addition, the height of the lip hl between the lower surface of the airfoil and the slot is 0.001c0.Figure 1
Coanda trailing edge of the modified airfoil.


## 2.2. Numerical Method

The flow field for the airfoil is computed using the FLUENT CFD software. The compressible Reynolds-averaged Navier–Stokes (RANS) equations are solved with the shear-stress transport (SST)k−ω turbulence model using the finite-volume spatial discretization method. A second-order upwind scheme is used for calculating the convection terms, and a central difference scheme is used for the diffusion terms. The flux is discretized using Roe’s approximate Riemann solver.The rectangular computational domain used in the investigation is shown in Figure2. The top, left, and right boundaries are located 20c0 away from the airfoil. The airfoil and jet plenum are set as no-slip static walls, and the jet source is set as the pressure inlet. The top, left, and right boundaries are set as pressure far field and the bottom boundary is a no-slip moving wall with a translational velocity equal to the free-stream velocity. The distance from the ground (the bottom boundary) to the center of the semicircular Coanda surface is defined as the ride height h, and its non-dimensional form is denoted as h/c.Figure 2
Rectangular computational domain and airfoil boundary: (a) rectangular computational domain; (b) airfoil boundary.
(a)(b)The Reynolds number based on the chord length is4.3×106 with free-stream Mach number M=0.2. The non-dimensional ride heights h/c=inf,1.0,0.8,0.6,0.4,0.2 with α=0, 4, and 8° are considered in this investigation. For the h/c=inf cases, the bottom boundary is located 20c0 away from the airfoil and is set as pressure far field.


## 2.3. Jet Momentum Coefficient

The jet momentum coefficient is an important parameter measuring the jet strength in circulation control. The 2D jet momentum coefficient is defined as:(1)Cμ=ṁUjetq∞c,where c is reference chord length. The mass flow rate ṁ and jet velocity Ujet are determined by the nozzle pressure ratio NPR, defined as the ratio of the total plenum pressure P0 to the free-stream static pressure P∞, and the total temperature T0. The total temperature is fixed at 300K, and the jet momentum coefficient changes with the preset pressure ratio in the numerical simulation.Because of the air viscosity, the jet is not isentropic, leading to non-uniform fluid density and jet velocity profiles at the nozzle outlet. Equation (1) can be rewritten in summation form to obtain a more accurate jet momentum coefficient:
(2)Cμ=∑i=1Nρivi2∆hiq∞c,where ∆hi is the spacing between neighboring grid points at the jet slot, and ρi and vi are the fluid density and jet velocity of each cell on the interface boundary, respectively.


## 2.4. Validation of Numerical Method

First, a grid refinement study is conducted using the modified NACA0012 airfoil for upper slot blowing withCμ=0.013 at α=0° and h/c=0.2 and the free-stream Mach number is 0.2. The results are listed in Table 1. The Richardson extrapolation [28] method is used to estimate the coefficients on an “infinite” grid density. The formulation is defined as:
(3)finf=f2+f2−f1r2−1,where f1 and f2 are the simulation results of two sets of grids, and r=1.2 is the grid refinement ratio of this investigation. As shown in Figure 3, CL and Cm change significantly when the cell count increases from 1.16×105 to 1.68×105. However, CL and Cm change inconspicuously when the cell count increases from 1.68×105 to 2.44×105. Richardson extrapolation results are listed in Table 1 and CL and Cm produced by the medium grid are 0.6% greater and 0.34% less than the extrapolated results, respectively. It is concluded from these results that the medium grid gives acceptably accurate results while being computationally cost-effective.Table 1
Grid refinement study results.
GridCell countCLCmCoarse1.16×1050.6304-0.1492Medium1.68×1050.5202-0.1342Fine2.44×1050.5192-0.1341ExtrapolationInfinite0.5171-0.1338Figure 3
Curves of lift coefficient and pitch moment coefficient versus cell count.Alexander et al. [29] conducted a range of experiments on a 0.75% cambered elliptical airfoil with a thickness of 6% chord to study the effects of CC. The span of the model was two chord lengths, and an end plate one chord length in diameter was installed. The aft 10% of the airfoil is truncated and installed with a 2.98 : 1 elliptical Coanda surface, and the slot height to chord ratio is 0.12%. The CC airfoil is illustrated in Figure 4.Figure 4
Elliptical airfoil with elliptical Coanda surface [29].Li and Qin [30] pointed out that the 2D airfoil case over-predicted the pressure coefficients on the surface, while the 3D model agreed well with the experimental data. Li and Qin [30] and Forster and Steijl [10] used an enlarged plate with a 1.1 chord length diameter to arrange the structured grid around the leading edge and improve the accuracy of the simulation. Thus, a 3D model with an enlarged plate is used in the simulation. The mesh domain of the model used in the investigation is shown in Figure 5 and Table 2 lists the size information of the model. The 3D mesh is generated with ICEM CFD and there are 221 cells on the main airfoil, 121 cells on the Coanda surface, 149 cells in the wall-normal direction, and 221 cells over the span of the airfoil. The distribution of grid points mentioned above is the same as that in Ref. [30] and the y+ is less than 1.Figure 5
Mesh domain of the elliptical airfoil.Table 2
3D model and mesh information.
NameSizeChord length30 inchSpan60 inchCell counts341×221×149 cellsWall distancey+≤1A numerical simulation is conducted atα=3° with free-stream Mach number M=0.3. Figure 6 compares the pressure coefficients from the numerical simulation and the experimental investigation at the model mid-span section, for upper slot blowing with jet momentum coefficient Cμ=0.054 and lower slot blowing with jet momentum coefficient Cμ=0.028. The computational pressure coefficients on the airfoil surface match the experimental data reasonably well, and the pressure distribution on the Coanda surface follows the trends of the experiment results.Figure 6
Comparison of pressure coefficient at the model mid-span section for CC validation: (a) upper slot blowing; (b) lower slot blowing.
(a)(b)There was a validation on the simulation of the ground effect of the airfoil using FLUENT [26] in the investigation of airfoil aerodynamics in ground effect for a wide angle of attack range. To further demonstrate that the aerodynamics of the airfoil with ground effect can be simulated with FLUENT, experimental data for a 2D NACA4412 airfoil with ground effect are used in the validation. As shown in Figure 7, the numerical pressure coefficient distribution agrees quite well with the experimental data from Ref. [23].Figure 7
Comparison of pressure coefficient for ground effect validation.


## 3. Results and Discussion

### 3.1. Lift Characteristics

Lift coefficient curves versus jet momentum coefficient at various ride heights are shown in Figure8. A negative jet momentum coefficient indicates that the jet is ejected from the lower slot and a positive jet momentum coefficient indicates that the jet issues from the upper slot. It can be observed that the decrease of the ride height alters the slope of the lift coefficient curve, meaning that the ground effect has an impact on CC.Figure 8
Curves of lift coefficient at various ride heights: (a)α=0°; (b) α=4°; (c) α=8°.
(a)(b)(c)For the negative and a large range of the positive jet momentum coefficients, the lift decreases with reduced ride height atα=0° and decreases dramatically when the ride height h/c decreases to 0.2. For α=0°, ∆CL decreases with increasing jet momentum coefficient, where ∆CL is defined as the difference between the lift of the unbounded flow field and the lift of the ground effect flow field with the same jet momentum coefficient. As the jet momentum coefficient increases further, negative ground effect evolves into positive ground effect, and the lift increases with reduced ride height for the airfoil with upper slot blowing at Cμ=0.021.When the angle of attack increases to4°, the lift increases with reduced ride height for the case without blowing and for upper slot blowing with Cμ<0.021. With increasing lower slot blowing Cμ, positive ground effect evolves into negative ground effect for h/c=0.2 and h/c=0.4, showing that the ground effect polarity can be reversed by lower slot blowing.The lift coefficient curves are almost parallel to each other for lower slot blowing atα=8°, where ground effect has little influence on ∆CL/∆Cμ. Positive ground effect appears for h/c ranging from 0.2 to 0.6 for upper slot blowing with Cμ<0.014. For h/c=0.8~1.0, the lift changes modestly for cases without blowing and for upper slot blowing with Cμ<0.014.It can be found in Figure8 that the distribution of data points is complicated when Cμ>0.018 for α=4° and Cμ>0.014 for α=8°. The preset NPR corresponding to the rightmost points of each curve for α=4° are the same (NPR=1.25), and the preset NPR corresponding to the two rightmost points of each curve for α=8° are 1.2 and 1.25, respectively. However, the jet momentum coefficient changes significantly with changing ride height, which is different from the other cases where the jet momentum varies little with decreasing h/c for the same preset NPR and α. As shown in Figure 9, Cμ decreases with reduced ride height instead of only depending on the preset NPR in these cases, where h/c=20 represents the unbounded flow field.Figure 9
Curves of jet momentum coefficient versus ride height.


### 3.2. Results forα=0°

Figure10 shows the pressure coefficient distribution on the CC airfoil without blowing at various ride heights. The solid line represents the pressure distribution of the upper airfoil surface, and the dotted line with the same color is the pressure distribution on the lower airfoil surface for the same ride height. In the discussion to follow, Cpup and Cplow are the pressure coefficient of the main airfoil upper and lower surfaces, respectively, and CL,up and CL,low are the lift generated by the upper and lower airfoil surfaces, respectively. When the ride height is reduced, Cpup decreases, resulting in the increasing CL,up, while Cplow decreases first slowly and then quickly, resulting in the decreasing CL,low; because ∆CL,low>∆CL,up, ∆CL is less than zero and decreases with the ride height. As shown in Figure 11, the flow channel between the lower airfoil surface and the ground is a convergent-divergent nozzle, and the flow accelerates to a maximum velocity at the throat and then decelerates. This is known as the Venturi effect, which creates a suction peak at the lower airfoil surface and an attractive lift reduction at h/c.Figure 10
Pressure coefficient of the CC airfoil without blowing atα=0°.Figure 11
Mach number contours for airfoil without blowing ath/c=0.2 and α=0°.The two key streamlines are the leading and trailing edge stagnation streamlines [26] and are drawn with solid and dashed lines, respectively, in Figure 12 for cases without blowing at various ride heights. These two streamlines are nearly straight and located near y/c=0 in the unbounded flow field. Although the stagnation streamlines are almost parallel to the ground in the far field, they deflect and become oblique lines as they approach the airfoil in the ground effect flow field. The section parallel to the ground gets closer to the ground with reduced ride height, and the deflection position approaches the airfoil, increasing the slope of the oblique section. As a result, the αE close to the leading edge and the downwash space downstream of the trailing edge become larger with decreasing ride height so that the flow velocity and pressure of the upper airfoil surface increase and decrease, respectively.Figure 12
Leading and trailing edge stagnation streamlines for the no-blowing case atα=0°.In an unbounded flow field, the flows above the upper airfoil surface and below the lower airfoil surface are symmetrical about the airfoil chord. Thus, the pressure on either side of the streamline is virtually equivalent, and the stagnation streamline is level at aroundy/c=0. The defection of streamlines in the ground effect flow field can be explained by assuming that the streamlines stay at their original locations when the ground appears below the airfoil, as illustrated in Figure 13. As the flow accelerates in the narrower passage between the lower airfoil surface and the ground, there are a higher flow velocity and a lower pressure, propagating upstream and downstream. However, the original higher pressure is maintained on the upper side of the streamlines because there is no change in the upper flow field. Consequently, the two stagnation streamlines are extruded toward the passage and the ground under the action of the pressure difference. Finally, these streamlines stay in their new pressure equilibrium positions. A smaller ride height corresponds to a narrower passage formed by the lower airfoil surface and the ground. Thus, the pressure difference and offset of the streamline increase with reduced ride height.Figure 13
Principle of streamline deflection for the no-blowing case atα=0°.The cases withCμ=−0.014 are selected for investigating the pressure distribution variation on the airfoil surface with decreasing ride height at α=0°, as illustrated in Figure 14. For h/c ranging from infinity to 0.4, Cpup decreases slightly with reduced height. For h/c=0.2, Cpup on the front section of the airfoil is almost the same as that for the h/c=0.4 case, while it increases near x/c=0.85 and becomes greater than that for the h/c=inf case near x/c=0.95. Cplow decreases with decreasing ride height and shows an especially sharp reduction at h/c=0.2 resulting from the Venturi effect.Figure 14
Pressure coefficient of the CC airfoil for blowing withCμ=−0.014 at α=0°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)Forh/c ranging from infinite to 0.4, the pressure coefficient of the upper Coanda surface Cpco,up decreases slightly with reduced height. Yet for h/c=0.2, Cpco,up is first greater than that for the h/c=inf case and then decreases, forming a negative pressure zone near the trailing edge. The pressure coefficient of the lower Coanda surface Cpco,low decreases with reduced ride height, and there is a similarly sharp reduction in Cpco,low near the trailing edge for h/c=0.2. Cpup and Cpco,up change slightly with reduced ride height, resulting in little change in CL,up. Remarkable decreases in Cplow and Cpco,low lead to a large decrease in CL,low with reduced ride height, which is the main cause of the negative lift increment.The two key streamlines for the blowing case are the streamline terminating at the airfoil leading edge stagnation and the streamline beginning from the jet separation point on the Coanda surface. These streamlines are shown in Figure15 for various ride heights. The two streamlines deflect to approach and become parallel to the ground because of the pressure reduction below them with reduced ride height, similar to the no-blowing case. The deflection of the two streamlines relaxes the flow blockage up the airfoil, decreasing Cpup with reduced ride height. Weakness of the upstream downwash and downstream upwash generally leads to a decrease of flow velocity below the airfoil and increase of Cplow. However, the Venturi effect is stronger, resulting in decreasing Cplow. Compared to the no-blowing case, a higher suction peak and lower Cplow is formed on the lower airfoil surface for h/c=0.2, because of a higher flow velocity resulting from the entrainment of the jet injected from the lower slot.Figure 15
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=−0.014 at α=0°.It can be observed that there is an obvious deformation of the jet streamline near the trailing edge forh/c=0.2 in Figure 15. As shown in Figure 16, the higher pressure zone on the top right of the trailing edge narrows with the streamline deflection because of the relaxation of the local flow blockage. As the higher pressure zone continues to shrink, the jet gets closer to the upper airfoil surface when h/c=0.2. It is considered that air gathers near the trailing edge and is squeezed toward the Coanda surface owing to the downward streamline deflection, forcing the jet to attach to the Coanda surface. Therefore, a small higher pressure zone approaches the upper airfoil surface, causing Cpup to increase near x/c=0.85 and Cpco,up to become greater than that for the unbounded flow field at h/c=0.2. The jet separation point then moves to the upper Coanda surface, resulting in a negative Cpco,up near the trailing edge.Figure 16
Pressure contours forCμ=−0.014 and α=0° at various ride heights.Figure16 shows that the jet attachment distance changes with ride height for the same jet momentum coefficient. In Figure 17, the jet attachment distance is compared using separation angle, defined as the central angle between the lower slot location and the jet separation location on the Coanda surface for the case with lower slot blowing. The central angle of the whole Coanda surface is 180° for the present specific Coanda surface design.Figure 17
Definition of separation angle for the case with lower slot blowing.Curves of separation angle versus ride height for various jet momentum coefficients are shown in Figure18, with h/c=20 representing the unbounded flow field. For the same ride height, the jet attachment distance increases with the jet momentum coefficient, which is consistent with previous studies. For h/c ranging from infinite to 0.4, the separation angle changes slightly with reduced ride height for the same jet momentum coefficient. Compared to the unbounded flow field, obvious increments of the jet attachment distance can be seen at h/c=0.2 for various jet momentum coefficients.Figure 18
Curves of separation angle versus ride height for lower slot blowing withα=0°.Figure19 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=0.014 at various ride heights. The Cpup decreases with the ride height, and Cplow increases for h/c ranging from infinite to 0.8 and decreases for h/c ranging from 0.8 to 0.4. When the ride height decreases to 0.2, Cplow is greater than the other cases in proximity to the leading edge, and there is a remarkable suction peak in the Cplow curve resulting from the Venturi effect. Cpco,up and Cpco,low change slightly with the reduced ride height. As a result, there is almost no change in lift for h/c=0.4~inf, while the airfoil with an intense Venturi effect is subjected to negative ground effect at h/c=0.2.Figure 19
Pressure coefficient of the CC airfoil for blowing withCμ=0.014 at α=0°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)The two sets of key streamlines at various ride heights are shown in Figure20. The two streamlines deflect to approach and become parallel to the level line at y/c=0. In contrast to the no-blowing cases, the upstream upwash and the downstream downwash space are reduced with decreasing ride height so the flow velocity and pressure of the upper airfoil surface decrease and increase, respectively.Figure 20
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=0.014 at α=0°.The pressure on either side of the streamline is balanced for the unbounded flow field, so streamlines stay at their original locations. As shown in Figure21, the two streamlines, the lower airfoil surface, and the ground form a divergent–convergent channel when the airfoil approaches the ground. Thus, the flow decelerates and then accelerates in the channel resulting in higher pressure below the lower airfoil surface. Higher pressure propagates upstream and downstream and breaks the pressure balance, forcing the two streamlines to deflect upward. Hence, the two streamlines move to new positions forming a new pressure equilibrium.Figure 21
Principle of streamline deflection for upper slot blowing withCμ=0.014 at α=0°.


### 3.3. Results forα=4°

Figure22 shows the pressure coefficient distribution on the CC airfoil without blowing at various ride heights. Cpup increases slightly with reduced ride height and Cplow increases a little more quickly, resulting in a small positive ground effect. For h/c=0.2 and h/c=0.4, the upper airfoil surface suction peak is higher than that for the other cases. A moderate suction peak appears near x/c=0.55 on the lower airfoil surface because the throat of the convergent-divergent passage moves backward with increasing α.Figure 22
Pressure coefficient of the CC airfoil without blowing atα=4°.The two sets of key airfoil streamlines at various ride heights are shown in Figure23. The main characteristics of streamline deflection are similar to the α=0°, Cμ=0.014 cases, so the theory for the pressure coefficient variations is similar. A distinction is that the oblique section of the leading edge streamline is closer to the airfoil and the slope of the oblique section is higher for h/c=0.2 and h/c=0.4, which increases the αE and the suction peak.Figure 23
Leading and trailing edge stagnation streamlines for the no-blowing case atα=4°.Figure24 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=−0.013 at various ride heights. Cpup decreases slightly with reduced ride height and Cplow varies little except the h/c=0.2 case. Thus, the lift changes slowly for h/c=0.4~inf. For h/c=0.2, a higher pressure zone appears on the lower airfoil surface close to the leading edge, and a greater Venturi effect strengthens the lower airfoil surface suction. This enhanced Venturi effect is caused by flow acceleration due to jet entrainment, resulting in negative ground effect. There is a little difference of Cpco,up and Cpco,low between various ride heights.Figure 24
Pressure coefficient of the CC airfoil for blowing withCμ=−0.013 at α=4°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)The streamline terminating at the airfoil leading edge stagnation point and the streamline beginning from the jet separation point on the Coanda surface at various ride heights are shown in Figure25. The streamlines are drawn toward the ground and the passage between the lower airfoil surface and the ground because of the lower pressure in the passage, similar to the case without blowing at α=0°. The slope of the oblique section, namely, the αE, increases more obviously with reduced ride height, accounting for the higher suction peaks with smaller ride height.Figure 25
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=−0.013 at α=4°.Figure26 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=0.013 at various ride heights. Cpup, Cplow, and Cpco,low increase when the ride height is reduced. Cpco,up decreases with ride height for x/c ranging from about 0.998 to 0.9995 and increases for the other x/c range. The increment of Cplow is slightly greater than that of Cpup, resulting in positive ground effect. As shown in Figure 27, the deflection of the streamline is similar to the case with Cμ=0.014 at α=0°.Figure 26
Pressure coefficient of the CC airfoil for blowing withCμ=0.013 at α=4°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)Figure 27
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=0.013 at α=4°..For the case with upper slot blowing, the jet separation angle is defined as the central angle between the upper slot location and the jet separation location on the Coanda surface, as illustrated in Figure28. As shown in Figure 29, the jet attachment distance increases with the reduced ride height for Cμ ranging from 0.004 to 0.017. When the preset NPR increases to 1.25, Cμ decreases with reduced ride height as mentioned above. And as shown in Figure 30, the CC evolves into the super-CC regime [31], and the separation point no longer varies with the change of the ride height. The maximum jet separation angle can only reach around 152° because there is a step between the lower wing and the Coanda surface. The attached jet travels over almost the entire Coanda surface, which can be seen as a jet flap. The effect of the jet flap on the lift enhancement is positively correlated with the jet momentum coefficient.Figure 28
Definition of separation angle for upper slot blowing.Figure 29
Curves of separation angle versus ride height for the airfoil with upper slot blowing atα=4°.Figure 30
Pressure contours forα=4°, NPR=1.25 at various ride heights.


### 3.4. Results forα=8°

Figure31 shows the pressure coefficient distribution on the CC airfoil at various ride heights. Cplow increases with reduced ride height for the airfoil without blowing and the airfoil with blowing at Cμ=−0.013 and Cμ=0.013. There is no suction peak on the lower airfoil surface because the passage between the lower surface and the ground is only a convergent passage. Cpup increases for the airfoil without blowing and the airfoil with blowing at Cμ=0.013, and yet Cpup changes very little with changing ride height for blowing with Cμ=−0.013.Figure 31
Pressure coefficients of the main airfoil atα=8°: (a) without blowing; (b) with Cμ=−0.013; (c) with Cμ=0.013.
(a)(b)(c)As shown in Figure32, the pressure on the upper and lower Coanda surfaces changes a little at various ride heights for the airfoil with blowing at Cμ=−0.013. Cpco,up and Cpco,low increase with reduced ride height for the airfoil with blowing at Cμ=0.013.Figure 32
Pressure coefficients of the Coanda surface atα=8°: (a) with Cμ=−0.013; (b) with Cμ=0.013.
(a)(b)The main characteristics of streamline deflections shown in Figure33 are similar to the result for blowing with Cμ=0.014 at α=0°. A more obvious slope increase can be observed with reduced ride height in the oblique section of the streamline for the airfoil with blowing at Cμ=−0.013, which is responsible for the increase of the suction peak.Figure 33
Two key streamlines for various ride heights atα=8°: (a) without blowing; (b) with Cμ=−0.013; (c) with Cμ=0.013.
(a)(b)(c)As shown in Figure34, the jet attachment distance increases with reduced ride height for jet momentum coefficients ranging from 0.004 to 0.013. As mentioned above, when the preset NPR is increased to 1.2, Cμ decreases with ride height. However, as shown in Figure 35, the jet attachment distance increases when Cμ is reduced, which is different from the unbounded flow field cases in previous investigations. Air gathers near the trailing edge and is squeezed toward the Coanda surface because of the upward streamline deflection, forcing the jet to attach to the Coanda surface, as illustrated in Figure 36. A higher pressure zone grows with reduced ride height, indicating the air gathering and blocking near the trailing edge. The CC also evolves into the super-CC regime when the preset NPR increases to 1.25, so the jet separation angle remains near 152°.Figure 34
Curves of separation angle versus ride height for the airfoil with upper slot blowing andCμ=0.004~0.013 at α=8°:.Figure 35
Curves of separation angle versus ride height for the airfoil with upper slot blowing andNPR=1.2~1.25 at α=8°.Figure 36
Pressure contours forα=8°, NPR=1.2 at various ride heights.


## 3.1. Lift Characteristics

Lift coefficient curves versus jet momentum coefficient at various ride heights are shown in Figure8. A negative jet momentum coefficient indicates that the jet is ejected from the lower slot and a positive jet momentum coefficient indicates that the jet issues from the upper slot. It can be observed that the decrease of the ride height alters the slope of the lift coefficient curve, meaning that the ground effect has an impact on CC.Figure 8
Curves of lift coefficient at various ride heights: (a)α=0°; (b) α=4°; (c) α=8°.
(a)(b)(c)For the negative and a large range of the positive jet momentum coefficients, the lift decreases with reduced ride height atα=0° and decreases dramatically when the ride height h/c decreases to 0.2. For α=0°, ∆CL decreases with increasing jet momentum coefficient, where ∆CL is defined as the difference between the lift of the unbounded flow field and the lift of the ground effect flow field with the same jet momentum coefficient. As the jet momentum coefficient increases further, negative ground effect evolves into positive ground effect, and the lift increases with reduced ride height for the airfoil with upper slot blowing at Cμ=0.021.When the angle of attack increases to4°, the lift increases with reduced ride height for the case without blowing and for upper slot blowing with Cμ<0.021. With increasing lower slot blowing Cμ, positive ground effect evolves into negative ground effect for h/c=0.2 and h/c=0.4, showing that the ground effect polarity can be reversed by lower slot blowing.The lift coefficient curves are almost parallel to each other for lower slot blowing atα=8°, where ground effect has little influence on ∆CL/∆Cμ. Positive ground effect appears for h/c ranging from 0.2 to 0.6 for upper slot blowing with Cμ<0.014. For h/c=0.8~1.0, the lift changes modestly for cases without blowing and for upper slot blowing with Cμ<0.014.It can be found in Figure8 that the distribution of data points is complicated when Cμ>0.018 for α=4° and Cμ>0.014 for α=8°. The preset NPR corresponding to the rightmost points of each curve for α=4° are the same (NPR=1.25), and the preset NPR corresponding to the two rightmost points of each curve for α=8° are 1.2 and 1.25, respectively. However, the jet momentum coefficient changes significantly with changing ride height, which is different from the other cases where the jet momentum varies little with decreasing h/c for the same preset NPR and α. As shown in Figure 9, Cμ decreases with reduced ride height instead of only depending on the preset NPR in these cases, where h/c=20 represents the unbounded flow field.Figure 9
Curves of jet momentum coefficient versus ride height.


## 3.2. Results forα=0°

Figure10 shows the pressure coefficient distribution on the CC airfoil without blowing at various ride heights. The solid line represents the pressure distribution of the upper airfoil surface, and the dotted line with the same color is the pressure distribution on the lower airfoil surface for the same ride height. In the discussion to follow, Cpup and Cplow are the pressure coefficient of the main airfoil upper and lower surfaces, respectively, and CL,up and CL,low are the lift generated by the upper and lower airfoil surfaces, respectively. When the ride height is reduced, Cpup decreases, resulting in the increasing CL,up, while Cplow decreases first slowly and then quickly, resulting in the decreasing CL,low; because ∆CL,low>∆CL,up, ∆CL is less than zero and decreases with the ride height. As shown in Figure 11, the flow channel between the lower airfoil surface and the ground is a convergent-divergent nozzle, and the flow accelerates to a maximum velocity at the throat and then decelerates. This is known as the Venturi effect, which creates a suction peak at the lower airfoil surface and an attractive lift reduction at h/c.Figure 10
Pressure coefficient of the CC airfoil without blowing atα=0°.Figure 11
Mach number contours for airfoil without blowing ath/c=0.2 and α=0°.The two key streamlines are the leading and trailing edge stagnation streamlines [26] and are drawn with solid and dashed lines, respectively, in Figure 12 for cases without blowing at various ride heights. These two streamlines are nearly straight and located near y/c=0 in the unbounded flow field. Although the stagnation streamlines are almost parallel to the ground in the far field, they deflect and become oblique lines as they approach the airfoil in the ground effect flow field. The section parallel to the ground gets closer to the ground with reduced ride height, and the deflection position approaches the airfoil, increasing the slope of the oblique section. As a result, the αE close to the leading edge and the downwash space downstream of the trailing edge become larger with decreasing ride height so that the flow velocity and pressure of the upper airfoil surface increase and decrease, respectively.Figure 12
Leading and trailing edge stagnation streamlines for the no-blowing case atα=0°.In an unbounded flow field, the flows above the upper airfoil surface and below the lower airfoil surface are symmetrical about the airfoil chord. Thus, the pressure on either side of the streamline is virtually equivalent, and the stagnation streamline is level at aroundy/c=0. The defection of streamlines in the ground effect flow field can be explained by assuming that the streamlines stay at their original locations when the ground appears below the airfoil, as illustrated in Figure 13. As the flow accelerates in the narrower passage between the lower airfoil surface and the ground, there are a higher flow velocity and a lower pressure, propagating upstream and downstream. However, the original higher pressure is maintained on the upper side of the streamlines because there is no change in the upper flow field. Consequently, the two stagnation streamlines are extruded toward the passage and the ground under the action of the pressure difference. Finally, these streamlines stay in their new pressure equilibrium positions. A smaller ride height corresponds to a narrower passage formed by the lower airfoil surface and the ground. Thus, the pressure difference and offset of the streamline increase with reduced ride height.Figure 13
Principle of streamline deflection for the no-blowing case atα=0°.The cases withCμ=−0.014 are selected for investigating the pressure distribution variation on the airfoil surface with decreasing ride height at α=0°, as illustrated in Figure 14. For h/c ranging from infinity to 0.4, Cpup decreases slightly with reduced height. For h/c=0.2, Cpup on the front section of the airfoil is almost the same as that for the h/c=0.4 case, while it increases near x/c=0.85 and becomes greater than that for the h/c=inf case near x/c=0.95. Cplow decreases with decreasing ride height and shows an especially sharp reduction at h/c=0.2 resulting from the Venturi effect.Figure 14
Pressure coefficient of the CC airfoil for blowing withCμ=−0.014 at α=0°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)Forh/c ranging from infinite to 0.4, the pressure coefficient of the upper Coanda surface Cpco,up decreases slightly with reduced height. Yet for h/c=0.2, Cpco,up is first greater than that for the h/c=inf case and then decreases, forming a negative pressure zone near the trailing edge. The pressure coefficient of the lower Coanda surface Cpco,low decreases with reduced ride height, and there is a similarly sharp reduction in Cpco,low near the trailing edge for h/c=0.2. Cpup and Cpco,up change slightly with reduced ride height, resulting in little change in CL,up. Remarkable decreases in Cplow and Cpco,low lead to a large decrease in CL,low with reduced ride height, which is the main cause of the negative lift increment.The two key streamlines for the blowing case are the streamline terminating at the airfoil leading edge stagnation and the streamline beginning from the jet separation point on the Coanda surface. These streamlines are shown in Figure15 for various ride heights. The two streamlines deflect to approach and become parallel to the ground because of the pressure reduction below them with reduced ride height, similar to the no-blowing case. The deflection of the two streamlines relaxes the flow blockage up the airfoil, decreasing Cpup with reduced ride height. Weakness of the upstream downwash and downstream upwash generally leads to a decrease of flow velocity below the airfoil and increase of Cplow. However, the Venturi effect is stronger, resulting in decreasing Cplow. Compared to the no-blowing case, a higher suction peak and lower Cplow is formed on the lower airfoil surface for h/c=0.2, because of a higher flow velocity resulting from the entrainment of the jet injected from the lower slot.Figure 15
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=−0.014 at α=0°.It can be observed that there is an obvious deformation of the jet streamline near the trailing edge forh/c=0.2 in Figure 15. As shown in Figure 16, the higher pressure zone on the top right of the trailing edge narrows with the streamline deflection because of the relaxation of the local flow blockage. As the higher pressure zone continues to shrink, the jet gets closer to the upper airfoil surface when h/c=0.2. It is considered that air gathers near the trailing edge and is squeezed toward the Coanda surface owing to the downward streamline deflection, forcing the jet to attach to the Coanda surface. Therefore, a small higher pressure zone approaches the upper airfoil surface, causing Cpup to increase near x/c=0.85 and Cpco,up to become greater than that for the unbounded flow field at h/c=0.2. The jet separation point then moves to the upper Coanda surface, resulting in a negative Cpco,up near the trailing edge.Figure 16
Pressure contours forCμ=−0.014 and α=0° at various ride heights.Figure16 shows that the jet attachment distance changes with ride height for the same jet momentum coefficient. In Figure 17, the jet attachment distance is compared using separation angle, defined as the central angle between the lower slot location and the jet separation location on the Coanda surface for the case with lower slot blowing. The central angle of the whole Coanda surface is 180° for the present specific Coanda surface design.Figure 17
Definition of separation angle for the case with lower slot blowing.Curves of separation angle versus ride height for various jet momentum coefficients are shown in Figure18, with h/c=20 representing the unbounded flow field. For the same ride height, the jet attachment distance increases with the jet momentum coefficient, which is consistent with previous studies. For h/c ranging from infinite to 0.4, the separation angle changes slightly with reduced ride height for the same jet momentum coefficient. Compared to the unbounded flow field, obvious increments of the jet attachment distance can be seen at h/c=0.2 for various jet momentum coefficients.Figure 18
Curves of separation angle versus ride height for lower slot blowing withα=0°.Figure19 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=0.014 at various ride heights. The Cpup decreases with the ride height, and Cplow increases for h/c ranging from infinite to 0.8 and decreases for h/c ranging from 0.8 to 0.4. When the ride height decreases to 0.2, Cplow is greater than the other cases in proximity to the leading edge, and there is a remarkable suction peak in the Cplow curve resulting from the Venturi effect. Cpco,up and Cpco,low change slightly with the reduced ride height. As a result, there is almost no change in lift for h/c=0.4~inf, while the airfoil with an intense Venturi effect is subjected to negative ground effect at h/c=0.2.Figure 19
Pressure coefficient of the CC airfoil for blowing withCμ=0.014 at α=0°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)The two sets of key streamlines at various ride heights are shown in Figure20. The two streamlines deflect to approach and become parallel to the level line at y/c=0. In contrast to the no-blowing cases, the upstream upwash and the downstream downwash space are reduced with decreasing ride height so the flow velocity and pressure of the upper airfoil surface decrease and increase, respectively.Figure 20
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=0.014 at α=0°.The pressure on either side of the streamline is balanced for the unbounded flow field, so streamlines stay at their original locations. As shown in Figure21, the two streamlines, the lower airfoil surface, and the ground form a divergent–convergent channel when the airfoil approaches the ground. Thus, the flow decelerates and then accelerates in the channel resulting in higher pressure below the lower airfoil surface. Higher pressure propagates upstream and downstream and breaks the pressure balance, forcing the two streamlines to deflect upward. Hence, the two streamlines move to new positions forming a new pressure equilibrium.Figure 21
Principle of streamline deflection for upper slot blowing withCμ=0.014 at α=0°.


## 3.3. Results forα=4°

Figure22 shows the pressure coefficient distribution on the CC airfoil without blowing at various ride heights. Cpup increases slightly with reduced ride height and Cplow increases a little more quickly, resulting in a small positive ground effect. For h/c=0.2 and h/c=0.4, the upper airfoil surface suction peak is higher than that for the other cases. A moderate suction peak appears near x/c=0.55 on the lower airfoil surface because the throat of the convergent-divergent passage moves backward with increasing α.Figure 22
Pressure coefficient of the CC airfoil without blowing atα=4°.The two sets of key airfoil streamlines at various ride heights are shown in Figure23. The main characteristics of streamline deflection are similar to the α=0°, Cμ=0.014 cases, so the theory for the pressure coefficient variations is similar. A distinction is that the oblique section of the leading edge streamline is closer to the airfoil and the slope of the oblique section is higher for h/c=0.2 and h/c=0.4, which increases the αE and the suction peak.Figure 23
Leading and trailing edge stagnation streamlines for the no-blowing case atα=4°.Figure24 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=−0.013 at various ride heights. Cpup decreases slightly with reduced ride height and Cplow varies little except the h/c=0.2 case. Thus, the lift changes slowly for h/c=0.4~inf. For h/c=0.2, a higher pressure zone appears on the lower airfoil surface close to the leading edge, and a greater Venturi effect strengthens the lower airfoil surface suction. This enhanced Venturi effect is caused by flow acceleration due to jet entrainment, resulting in negative ground effect. There is a little difference of Cpco,up and Cpco,low between various ride heights.Figure 24
Pressure coefficient of the CC airfoil for blowing withCμ=−0.013 at α=4°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)The streamline terminating at the airfoil leading edge stagnation point and the streamline beginning from the jet separation point on the Coanda surface at various ride heights are shown in Figure25. The streamlines are drawn toward the ground and the passage between the lower airfoil surface and the ground because of the lower pressure in the passage, similar to the case without blowing at α=0°. The slope of the oblique section, namely, the αE, increases more obviously with reduced ride height, accounting for the higher suction peaks with smaller ride height.Figure 25
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=−0.013 at α=4°.Figure26 shows the pressure coefficient distribution on the CC airfoil for blowing with Cμ=0.013 at various ride heights. Cpup, Cplow, and Cpco,low increase when the ride height is reduced. Cpco,up decreases with ride height for x/c ranging from about 0.998 to 0.9995 and increases for the other x/c range. The increment of Cplow is slightly greater than that of Cpup, resulting in positive ground effect. As shown in Figure 27, the deflection of the streamline is similar to the case with Cμ=0.014 at α=0°.Figure 26
Pressure coefficient of the CC airfoil for blowing withCμ=0.013 at α=4°: (a) pressure coefficient of the main airfoil; (b) pressure coefficient of the Coanda surface.
(a)(b)Figure 27
Leading edge stagnation streamlines and the streamlines beginning from the jet separation point on the Coanda surface forCμ=0.013 at α=4°..For the case with upper slot blowing, the jet separation angle is defined as the central angle between the upper slot location and the jet separation location on the Coanda surface, as illustrated in Figure28. As shown in Figure 29, the jet attachment distance increases with the reduced ride height for Cμ ranging from 0.004 to 0.017. When the preset NPR increases to 1.25, Cμ decreases with reduced ride height as mentioned above. And as shown in Figure 30, the CC evolves into the super-CC regime [31], and the separation point no longer varies with the change of the ride height. The maximum jet separation angle can only reach around 152° because there is a step between the lower wing and the Coanda surface. The attached jet travels over almost the entire Coanda surface, which can be seen as a jet flap. The effect of the jet flap on the lift enhancement is positively correlated with the jet momentum coefficient.Figure 28
Definition of separation angle for upper slot blowing.Figure 29
Curves of separation angle versus ride height for the airfoil with upper slot blowing atα=4°.Figure 30
Pressure contours forα=4°, NPR=1.25 at various ride heights.


## 3.4. Results forα=8°

Figure31 shows the pressure coefficient distribution on the CC airfoil at various ride heights. Cplow increases with reduced ride height for the airfoil without blowing and the airfoil with blowing at Cμ=−0.013 and Cμ=0.013. There is no suction peak on the lower airfoil surface because the passage between the lower surface and the ground is only a convergent passage. Cpup increases for the airfoil without blowing and the airfoil with blowing at Cμ=0.013, and yet Cpup changes very little with changing ride height for blowing with Cμ=−0.013.Figure 31
Pressure coefficients of the main airfoil atα=8°: (a) without blowing; (b) with Cμ=−0.013; (c) with Cμ=0.013.
(a)(b)(c)As shown in Figure32, the pressure on the upper and lower Coanda surfaces changes a little at various ride heights for the airfoil with blowing at Cμ=−0.013. Cpco,up and Cpco,low increase with reduced ride height for the airfoil with blowing at Cμ=0.013.Figure 32
Pressure coefficients of the Coanda surface atα=8°: (a) with Cμ=−0.013; (b) with Cμ=0.013.
(a)(b)The main characteristics of streamline deflections shown in Figure33 are similar to the result for blowing with Cμ=0.014 at α=0°. A more obvious slope increase can be observed with reduced ride height in the oblique section of the streamline for the airfoil with blowing at Cμ=−0.013, which is responsible for the increase of the suction peak.Figure 33
Two key streamlines for various ride heights atα=8°: (a) without blowing; (b) with Cμ=−0.013; (c) with Cμ=0.013.
(a)(b)(c)As shown in Figure34, the jet attachment distance increases with reduced ride height for jet momentum coefficients ranging from 0.004 to 0.013. As mentioned above, when the preset NPR is increased to 1.2, Cμ decreases with ride height. However, as shown in Figure 35, the jet attachment distance increases when Cμ is reduced, which is different from the unbounded flow field cases in previous investigations. Air gathers near the trailing edge and is squeezed toward the Coanda surface because of the upward streamline deflection, forcing the jet to attach to the Coanda surface, as illustrated in Figure 36. A higher pressure zone grows with reduced ride height, indicating the air gathering and blocking near the trailing edge. The CC also evolves into the super-CC regime when the preset NPR increases to 1.25, so the jet separation angle remains near 152°.Figure 34
Curves of separation angle versus ride height for the airfoil with upper slot blowing andCμ=0.004~0.013 at α=8°:.Figure 35
Curves of separation angle versus ride height for the airfoil with upper slot blowing andNPR=1.2~1.25 at α=8°.Figure 36
Pressure contours forα=8°, NPR=1.2 at various ride heights.


## 4. Conclusion

The ground effect on the CC of a modified NACA0012 airfoil is investigated with numerical simulations using the FLUENT code. The variations of the lift coefficient and pressure distribution on the airfoil surface with changing ride height are illustrated and analyzed with the exhibition of the flow field. The following conclusions can be summarized from these investigations:(1)
The slope of the lift coefficient curve versus jet momentum coefficient varies with decreasing ride height, meaning that ground effect alters the lift increment per unit jet momentum coefficient. The polarity of the ground effect can be reversed by CC(2)
As the ground approaches, the original pressure balance on both sides of the stagnation streamline or the streamline beginning from the jet separation point on the Coanda surface is broken. Streamlines move under the action of pressure differences and then remain in the new pressure equilibrium position, which alters the flow field on either side of the streamlines resulting in changes of pressure distribution and lift coefficient(3)
The jet attachment distance increased with reduced ride height for the airfoil with lower slot blowing atα=0° and the airfoil with upper slot blowing at α=4° and α=8° for the same jet momentum coefficient. For α=8°, the jet momentum coefficient decreases with ride height when the preset NPR is 1.2, while the jet attachment distance increases, which is different from the cases with unbounded flow field



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*Source: 4985193-2022-08-23.xml*