Computational Modelling of Steady and Unsteady Low Speed Wing in Ground Effect Aerodynamics

American Institute of Aeronautics and Astronautics

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COMPUTATIONAL MODELING OF STEADY AND UNSTEADY

LOW SPEED WING IN GROUND EFFECT AERODYNAMICS

R. Prasad

* and M. Damodaran

†

Mechanical Engineering Discipline,

Indian Institute of Technology Gandhinagar,

VGEC Complex, Visat-Gandhinagar Highway,

Chandkheda, Ahmedabad 382424, GJ, INDIA

Steady and unsteady low speed Wing in Ground (WIG) Effect Aerodynamics as a result if its

close proximity to the ground is studied in detail computationally by solving the unsteady

incompressible Navier-Stokes equations. WIG effects for both an airfoil and a finite span

wing have been carried out and have been validated with experimental data. Behavior of the

computed flow patterns and aerodynamic force and moment coefficients has been studied

for varying proximity from the ground and compared with published experimental data to

assess the quality and reliability of the numerical predictions. A comparative study has also

been done to better comprehend and assess the results obtained by using different boundary

conditions used to simulate the ground, in order to establish which condition is apt in

approximating the boundary layer at the ground during real flight. It is also observed that

the trailing vortex system of the wing has a stronger interaction with the ground in the case

of a fixed ground. The nature of the interaction of vortex shed from the wing with the

ground boundary layer has also been studied for natural vortex shedding at low Reynolds

number laminar flow. Formation of a vortex street is observed in the wake region which

comprises of alternatively shed vortices of opposite vorticity. The ground effect in the case of

a wing attached with high lift devices has also been studied. The case has been calibrated by

comparing with experimental data provided by NASA. The ground effect has a significant

impact on the flow pattern around the multi element wing, radically effect the pressure

distribution profile over the wing.

Nomenclature

Density of air

P Static Pressure

Free stream pressure

Free stream velocity

c

h

Chord length of airfoil or mean aerodynamic chord length of wing

Height of aerodynamic centre above the ground plane

Coefficient of pressure

Drag Coefficient

Lift Coefficient

Skin friction Coefficient

Cm Pitching Moment Coefficient

Angle of attack

I. Introduction

This study is primarily motivated by the desire to understand the aerodynamics of airfoil/wing in close proximity

with a rigid boundary such as a ground or an air-sea interface with the ultimate goal of developing and using the

computational flow model for aiding the computational design of ground-effect vehicles which is the next step

planned by the authors. In this work, after reviewing the state of the current research activities in Wing-In-Ground

* Graduate Student, E-mail: [email protected] † Professor, Associate Fellow AIAA, E-mail: [email protected]


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(WIG) effect aerodynamics, the authors computed steady and unsteady WIG effects to establish reliable high fidelity

Eulerian based computational flow model for use in computational design optimization of WIG vehicles.

The application of WIG effect can be seen in the design of sea planes, F1 race cars, ground effect light rail

transport systems for metros and micro aerial vehicles designed specifically to fly near the ground. The effect of

ground on the wing aerodynamics has been known for quite some time and the first study done to analyze this

problem was carried out by Weiselsburger1 who did a theoretical investigation on determining the landing and take-

off conditions using Prandtl’s Lifting Theory which is based on a potential flow model. In practical applications, this

effect has been successfully used to design sea planes and race cars since the 70s and 80s. Numerous notable and

recent works have focused on the Wing-In-Ground (WIG) aerodynamics. Most of these experiments and numerical

computational studies have been carried out for steady flow over a finite or infinite wing. In most of these studies,

WIG aerodynamic characteristics of airfoils/wings have been analyzed and measured for different angles of attack

and at different proximities (heights of the aerodynamic centers) from the ground. In the case of experimental

studies carried out by Moore et al.2 for finite wings observes an increase in lift and a decrease in induced drag due to

a decrease in downwash because of its close proximity to the ground. As observed by Ahmed and Sharma3, an

increase in lift is also observed for the case of an airfoil. The effect of wing tip devices and dihedral angle on finite

wings in the presence of the ground has been studied by Lee etal.4 A computational study on the performance of lift

enhancing devices in WIG effect has been carried out by Lin et al.5

Filippone and Selig6 have computationally

studied the WIG effect for low aspect ratio wings. Henry and Walker7have studied the effect of using wing tip

devices in a high aspect ratio Cataraman vehicle. Genua8 has discussed the use of the correct turbulence model and

the corresponding mesh in a computational analysis that should be used to obtain results more accurate with the

experimental values. Much work has also been done from the perspective of race car aerodynamics, where the

objective of the study is to produce downward force to keep the wheels in contact with the ground and hence these

studies are carried out for inverted wings which are commonly found in race cars. Zhang and Zerihan9,10

give some

insightful results for inverted airfoils in WIG effect for a single element as well as double element wing. Also, while

carrying out a computational study for the WIG effect, different boundary conditions are used to simulate the

boundary layer flow near the ground. However, little thought has been put into inspecting which method is best

suited to simulate real time physics of the WIG effect. Firooz and Gadami11

and Chengjionget al12

have compared

results from using a moving ground and a fixed ground.

II. Computational Modeling of Wing-In-Ground Effect Aerodynamics

1. Governing Equations

In this section, the governing equations and entire numerical procedure of solving has been discussed. The

governing equations which describes the air flow around the wing are the unsteady Navier-Stokes equations given

by

. . . .c visw dV F dS F dS B dVt

(1)

where w is a vector of flow variables, and

are the convective and viscous fluxes which are functions of

pressure and the flow variables respectively, B is the body force per unit mass acting on the body. Equation (1)is

first discretized using the Finite Volume Method on a variety of unstructured meshes as shown in Figure 1. The

convective flux in the momentum equation is discretized using a second order upwind scheme with flow variables

being advanced in time using an implicit time stepping scheme for steady flow computations and explicit time

stepping schemes for unsteady flow computations. The mesh created has been refined at the leading and the trailing

edge as flow around this region is complex and requires higher resolution mesh. The computational mesh has also

been refined in the wake region to effectively capture the trailing vortex system of the finite wing. Since the focus is

on low speed aerodynamic flows, the uncoupled continuity and momentum equations are solved by the Semi-

Implicit Pressure Linked (SIMPLE) algorithm within the framework of CD-Adapco’sStar-CCM+13

flow modeling

software.


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(a) Mesh (view zoomed around airfoil) used for

studying laminar flows over an airfoil.

(b) Mesh (view zoomed around airfoil) used

for studying turbulent flow over an airfoil.

A structured mesh is used around the

airfoil and ground to effectively capture

the turbulent boundary layer.

(c) Three dimensional polyhedral mesh used for an analysis of the WIG effect

(d) Mesh generated for the NASA High Lift trapezoidal wing configuration

Figure 1: An overview of the various computational meshes used in the present study

2. Turbulence Modeling for High Reynolds Number Flows

For the case of flows for which the Reynolds number is above critical value, the Spalart-Allmaras14

turbulence

model which solves a transport equation to determine the turbulence kinematic viscosity T to account for

turbulence in the flow has been used. In order to resolve the boundary layer on the ground and wing surface, a thin,


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conformal, structured mesh is created along the ground and wing surface. In this study, 10 layers of structured cells

have been created over the wall surface in order to obtain a y+ value of 40. This y

+ value is further used in the wall

functions to approximate the velocity at the first grid point off the surface of the wall.

3. Boundary Conditions

Figure 2(a) and (b) show the computational domains used for the computational study of WIG effects pertaining

to the airfoil and the wing in ground effect. For the case of flow past an airfoil, uniform free stream velocity is

specified at the upstream boundary and a pressure outlet boundary where the pressure is set as the atmospheric

pressure at far-field boundaries and at downstream boundary. The airfoil surface and the ground are modeled as a

wall with no slip boundary condition imposed on it. However, two different assumptions have also been considered

and compared for the ground wall boundary condition. In one case the ground is assumed to be fixed with respect to

the reference frame and in the other case the ground is assumed to be moving and a velocity same as free stream

velocity is also given to the nodal points along the ground. A comparison of using a moving or a fixed ground has

been considered in detail in the results section of this paper. The additional difference in the case of a three

dimensional wing would be the addition of two boundary surfaces in the wing span direction. One surface will be

given the pressure outlet boundary condition. Since only half of the wing is being simulated, symmetry boundary

conditions are imposed at the boundary surface at y/c = 0.

(a) Flow past airfoil

(b) Flow past wing

Figure 2: Computational domain along with boundary regions for different cases in this study

III. Results and Discussions

A. Laminar Flow Past Airfoils in Ground Effect

Considering the flow speeds and chord lengths in real flows, complete laminar flow is seldom observed for the

case flow over aircraft and race car wings. The flow is mostly turbulent for these cases as the Reynolds number is

high and above the critical value. However, this may not be the case for Micro Aerial Vehicles (MAVs) where the

chord length is sufficiently small so that the Reynolds number is low enough to have complete laminar flow over the

wing. Hence, a laminar study over an airfoil is first conducted to get a handle on several numerical issues affecting

accuracy of prediction. The flow past a NACA 0012 airfoil section at two angles of attacks of 8 and 12 degrees

placed at various heights from the ground varying from 0.2c to 1.0c was first computed. The freestream velocity of

the flow is 0.225 m/s. The Reynolds number of the flow is 15000, which is well within the laminar range.

Figure 3 shows the computed vorticity contour plots are various instants of time for a fixed height above the

ground. Figure 4 (a)-(c) shows the time variation of the computed lift, drag and pitching moment coefficient about

the aerodynamic center from the start of the computation till the attainment of periodic flows for the given flow

configuration. A characteristic phenomenon seen in the case of laminar flows is in the case of vortex shedding from

airfoils leading to the formation of a vortex street. The vortex street is formed only when the angle of attack of the

wing is high.

While natural vortex shedding like the Karman vortex street is typically observed from flow past bluff bodies,

airfoils with sharp trailing edges can also create such vortex shedding patterns as a result of flow separation

upstream of the trailing edge leading to the creation of a blunt trailing edge which in turn leads to the airfoil having a

natural frequency associated with natural vortex shedding which causes the variation of the aerodynamic force and

moment coefficients


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(a) Time = 10 seconds

(b) Time = 20 seconds

(c) Time = 30 seconds

(d) Time = 40 seconds

Figure 3: Contours of Vorticity magnitude plotted at various time intervals

(a) (b)

(c)

Figure 4: Time variation of (a) Lift, (b) Drag and (c) Pitching Moment coefficient about the quarter chord point with

respect to time for NACA 0012 airfoil at an angle of attack of 12 degrees and ground height of 0.2c.

It is observed from Fig. 3 and 4, that once the transient stage of the flow is over, vortices of equal and opposite

magnitude are shed from the airfoil at periodic intervals in a steady manner and a periodic flow is reached after this

regular pattern of vortex shedding is attained. The vortex shedding causes an oscillating pattern in the time variation

of the aerodynamic force and moment coefficients. Since the flow is oscillating in nature, a Strouhal number can be

defined as fc

StU

where f is the frequency of the vortex shedding, c is the chord length of the airfoil or the mean

aerodynamic chord length of the wing and V is the free stream velocity. It is observed that, on varying the ground

height, the Strouhal number decreases as shown in fig. 5(a) implying that the frequency of the vortex shedding gets


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reduced. This indicates that interference due to the proximity to the ground slows down the formation of vortices

from the trailing edge. Figure 5(b) shows the variation of the amplitude of the lift coefficient, defined as

,max ,min

2

L LC Cwhere

,maxLC and ,minLC are the maximum and minimum lift coefficient in a periodic cycle shown in

Fig. 4(a) with ground proximity indicating that the amplitude increases when the airfoil is brought closer to the

ground.

Figure 5: Variation of the (a) Strouhal number and (b) and Lift coefficient amplitude

as a function of varying ground height.

Figure 6(a) shows an instantaneous snapshot of computed vorticity shedding pattern for the airfoil located at

h/c=1.0 above the ground. Figure 6(b) which shows a similar plot for the same case based on a stream function-

vorticity approach conducted by Johri and Sengupta15

on a structured mesh. For the computation shown in Fig. 6(a)

a moving ground boundary condition was used while that shown in Figure 6(b) used a fixed ground boundary

condition which explains the different structure of the boundary layer on the ground. Figure 6(c) shows the

computed vorticity shedding pattern for the case h/c=0.1. From this plot, it can be seen that the presence of a ground

in close proximity of the airfoil distorts the formation length of the shed vortices .

(a) h/c=1.0

(b) h/c=1.0

(c) h/c = 0.1

Figure 6: Vorticity contours around the airfoil at different ground heights

It can be seen that the vortex shed from the pressure side gets distorted and slowed down due to interaction with the

vorticity present in the ground boundary layer. The vortices shed from the suction side gets pulled towards the

slowed down, pressure side vortices. This leads to uneven spacing in the evolving vortex street. The slowing down

of the vortices can also explain the decrease in the frequency of vortex shed and hence decrease in Strouhal’s

number as the ground height is decreased as shown in Fig. 5(a). Vortex induced instability on the ground boundary

layer is also observed along the ground which is caused due to vortices shed from the airfoil.


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B. Turbulent Flow past an Airfoil in Ground Effect

The WIG effect has also been studied from the point of view of race car aerodynamics for which the flow can

become turbulent. For race cars, the primary objectives of aerodynamics is to produce the required downforce,

which helps in maintaining ground contact of the tires and helps in taking turns without reducing the speed. This

study has been carried out for the Tyrell 026 airfoil at an angle of attack of 3.6 degrees. The computational mesh

used for this study is shown in Fig. 1(b). In order to study the ride height sensitivity, the ground height has been

varied and the corresponding downward force computed and the computed results are compared with the

experimental measurements obtained by Zhang and Zerihan9 for the same case. The results from the present study

and experimental data agree well as can be seen from the discussions which follow.

1. Model Validation and Mesh Dependency Study

In order to ascertain that the problem has been modeled correctly and is simulating the correct physics, it is first

ensured that the solution is converging as the mesh is refined. In the mesh dependency study, the number of mesh

elements is repeatedly increased by a factor of two till there is little difference in the computed force and moment

coefficients. The mesh size, at which there is little difference in force coefficients, is then used for other cases as

well. For this study, four meshes consisting of 10K, 20K, 40K and 80K cells respectively have been considered.

Figure 7(a) shows the variation of the force and moment coefficient vs. the number of elements (N) for the case

corresponding to h/c=0.09c.

(a) Convergence plot for lift coefficient

(b) Convergence plot for drag coefficient

Figure 7: Mesh Dependence Study for a case with angle of attack = 3.6 degrees; ground height = 0.09c

2. Comparison with Experimental Results

In the experimental study of the Wing in Ground Effect by Zhang and Zerihan9, wind tunnel tests had been

carried out for a rectangular wing. The wing is placed between the walls of the tunnel from end to end, hence

cancelling out the end effects, effectively making the flow two dimensional. The Reynold’s number of the flow

corresponding to the experiment is 500,000. The computations have been done for different ground height and angle

of attack. Numerical study was performed for the same cases which were showcased in the experimental study.

Figure 8(a) compares the variation of the lift coefficient (in this case the downward force coefficient) with different

values of h/c. The trend of the computed results seems to show agreement to a fair extent with slight differences

between the computed results and experimental study showing up as the proximity to the ground increases. Figures

8(b) and (c) show the variation of computed results of drag coefficient and pitching moment coefficient with

different values of h/c for which there are no experimental data.


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(a) (b)

(c)

Figure 8: (a)Lift (b)drag and (c)pitching moment coefficient (about quarter chord point)

as a function of ground height

From Fig. 8, it can be seen that both downward force coefficient and drag coefficient are seen to increase with

decreasing ground height. The substantial increase in downward force on decreasing the ground height is due to

what is known as the venturi effect which can be seen in Fig. 9 which shows the computed pressure contours and

streamlines in the vicinity of the airfoil in proximity to the ground for various values of h/c. In the venturi effect, the

gap between the pressure side of the airfoil and ground acts as a constriction. Here the velocity of the air

substantially increases and this further leads to reduction of pressure which leads to an increase in the downward

force. As the ground height is increased, the gap between the pressure side and ground increases and there is little

acceleration of velocity in that region and hence there is lesser pressure drop. Hence as the ground height is

increased there is a drop in the downward force. However, when the airfoil is very close to the ground, the

downward force is seen to decrease slightly. An increase in drag is also observed when the ground height is

decreased. This increase is due to increase in pressure drag. It can be seen in Fig 9(a), that as the airfoil gets closer to

the ground, flow separation occurs away from the trailing edge and this accounts for a higher pressure drag. Figure

10 shows the computed airfoil surface pressure distribution corresponding to the different values of h/c.

(a) h/c=0.09

(b) h/c=0.179

(c) h/c=0.313

Figure 9: Ambient pressure coefficient contours and streamline patterns for various ground heights.


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Figure 10: Pressure distribution over the airfoil for different ground heights

C. Computation of Turbulent Three-Dimensional Wing-in-Ground Effects

1. Model Validation and Mesh Dependency Study

As discussed earlier, a mesh dependency study needs to be done to ascertain whether the study is consistent or

not. For this study, four meshes were taken with mesh elements of the order ~150,000; 300,000; 600,000 and

1,200,000 respectively. Figure 14 shows that a fairly good convergence can be attained with 1.2 million cells.

Further parametric study has been carried out


(b) Convergence plot for lift coefficient

Figure 14: Mesh Dependence Study for a case with angle of attack = 2 degrees; ground height = 0.3c

2. Comparison with Experimental Results

Once the appropriate grid size was evaluated using the mesh dependence study and it was verified that the solution

converged in successive refining of the mesh, the model further validated by emulating and comparing with

experimental data. The experimental data used here was obtained from wind tunnel experiments done to study the

Wing in Ground Effect by Moore, et al2. In the experimental study, wind tunnel tests have been carried out for a

rectangular wing of aspect ratio 4.0 having a NACA 0012 airfoil. The Reynolds number is 800,000. Computation of

steady WIG effects past this wing have been considered for different values of ground height and angle of attack for

the same cases as that were done in the experimental study. Computed variation of the aerodynamic force and

moment coefficients for selected fixed angle of attack and different values of h/c are compared with experimental

studies in Fig. 15 and the trends of the variation appear to agree to a good extent.


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(a) (b)

(c)

Figure 15: (a) Lift coefficient (b) Drag Coefficient (c) Moment Coefficient of the wing as a function of ground

height for various angles of attack. Here the numerical results are compared with experimental result from the works

of Moore et al.2

3. Assessment of Fixed and Moving Ground Boundary Conditions for WIG Aerodynamics

In a number of numerical studies that have been carried out for ground effect, some have modeled the ground as

a fixed ground by applying a boundary condition of no slip velocity the wall surface. However, in some of the

studies the ground has been modeled as a moving wall. A moving wall boundary is modeled by applying a condition

of no-normal flow and giving a velocity to the fluid at the wall surface equal to the free stream velocity. Another

method that has been used by researchers to study the wing in ground effect is the mirror image method termed as

symmetry boundary condition, in which an inverted airfoil is placed at double the distance of the ground from the

position of the airfoil above the ground to ensure zero normal flux at the wall and a slip velocity on the ground. In

this section, the issue of the choice of these different boundary conditions and how these choices affect the

computed results and which boundary condition better represents real time flight condition is addressed

computationally for the same wing considered in Section C1.

Figure 16(a)-(b) shows the computed variation of the lift and drag coefficients with h/c corresponding to the

application of the three different wall boundary conditions imposed on the ground. It can be seen that the wall

boundary conditions produce a difference in results only when the wing is close to the ground. From Figure 16(a) it

can be observed that, when there is a variation in values of force coefficients up to a height of 0.3c and below the

case based on the moving ground boundary condition produces results which are closer to the experimental values.

At very small ground heights, it can be seen that there is a large deviation of the lift coefficient for the case based on

the fixed ground boundary condition. The lift coefficient of the wing is observed to be higher for the case based on

the fixed ground boundary condition and almost negligible suction effect is observed (as in the case of moving

ground and experimental results).


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(a)

(b)

Figure 16: (a) Lift and (b) Drag coefficient versus ground height for different boundary conditions

This is can be explained as follows. For the case based on a fixed ground boundary condition the velocity along

the ground will be zero and there will be a boundary layer as shown in fig. 17(a) which is a plot of the variation of

the horizontal velocity component parallel to the ground with respect to the distance from the ground, because of

which less air will flow between the pressure side and ground and more of it will get diverted to the suction side.

This will increase pressure on the pressure side and decrease pressure on the suction side. Figure 17(b) shows the

boundary layer velocity profiles for the case based on the moving ground boundary condition.

(a) Fixed ground

(b) Moving ground

Figure 17: Boundary Layer profiles along the ground for different boundary conditions used.

As more air flows over the suction side in the case of fixed ground, flow over the suction side is further

energized and separation near the trailing edge gets delayed. Figure 18(a)-(b) shows the variation of the computed

wing lift and drag coefficient with angle of attack respectively.

(a)

(b)

Figure 18: (a) Lift and (b) Drag coefficient versus angle of attack for fixed and moving ground


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Figure 19 and 20 shows the computed surface pressure coefficient contours and skin friction lines on the wing

surface, the symmetry plane and the ground plane. It can be seen that for the case using a fixed ground boundary

condition, more of the air flows around the wing, instead of flowing below the wing. An increased flow along the

span gives rise to reduced pressure increase on the pressure side, as observed in Fig. 21 and also in Fig. 19(b) and

20(b).

(a)

(b)

Figure 19: Surface Pressure Coefficient Contours and Skin friction lines on the wing, ground and symmetry

plane surfaces for the case of fixed ground boundary condition

(a)

(b)

Figure 20: Surface Pressure Coefficient Contours Skin friction lines plotted along the wing, ground and

symmetry plane surfaces for the case of moving ground boundary condition.

Figure 21: Comparison of pressure distribution over the wing at the mid span in different cases of fixed and

moving ground boundary condition

Figures 22 and 23 show the plots of the contours of the computed pressure coefficient and skin friction lines at

various stations along the span placed at the wing root, mid span and wing tip, for the cases corresponding to the use

of moving ground and fixed ground boundary conditions. By comparing the computed flow patterns at the different

stations along the span of the wing, it can be seen that the flow separates from the leading edge itself without

reattaching to the wing surface for the cased based on the moving ground boundary condition. This leads to low


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pressure on the suction side of the wing which gives rise to higher lift and drag. An earlier leading edge separation

occurs because of the weaker air flow over the suction side as more air flows from the pressure side due to the

moving ground boundary condition.

Moving Ground Fixed Ground

(a) Wing root

(a) Wing root

(b) 50% span

(b) 50% span

(c) Wing tip

(c) Wing tip

Figure 22: Streamlines plotted over pressure coefficient

contours at stations along the span for moving ground

boundary condition. The ground height of the wing is 0.05c

and the angle of attack is 10 degrees.

Figure 23: Streamlines plotted over pressure contours at spanwise

stations for fixed ground boundary condition. The ground height

of the wing is 0.05c and the angle of attack is 10 degrees.

Figures 24 and 25 show the plots of the contours of the computed pressure coefficient and isocontours of vorticity

on various Trefftz planes located at the wing trailing edge and aft of the wing trailing edges for the case

corresponding to the use of moving ground and fixed ground boundary conditions. These plots show how the wake

and ground boundary layer interact for both moving ground and fixed ground boundary condition. On planes

downstream, it can be observed that vortex weakens from interaction of the boundary layer on the ground computed

with a fixed ground boundary condition as against interaction of the boundary layer with moving ground boundary

condition. This is due to the interaction of the trailing vortex with vorticity present in the ground boundary layer.

From Fig. 17 which shows the boundary layer velocity profiles it can be seen that for the boundary layer present in

the case of fixed ground boundary condition, there will be higher vorticity in the fixed ground boundary layer as

compared to that from the moving ground boundary condition and hence there will be greater dissipation of wing tip

vortices due to interaction with the ground for the case of fixed ground boundary condition.


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Figure 24: Trailing vortex interacting with the ground boundary layer in the case of moving ground. The contours

have been plotted on Trefftz planes

Figure 25: Trailing vortex interacting with the ground boundary layer in the case of fixed ground. The contours have

been plotted on Trefftz planes

Figure 26 shows the computed pressure coefficient distribution and skin friction lines on the ground plane, for the

case corresponding to the use of moving ground and fixed ground boundary conditions. Dissipation of the trailing

vortex system due to interaction with ground boundary layer can also been seen in these figures by looking at the

contours of the pressure coefficient distribution along the ground The red patch represents the high pressure zone in

front of the leading edge of the wing. The blue streak of low pressure zone with skin friction lines twisting around it,

which extends downstream, is the low pressure zone of the trailing vortex core. It can be seen for the case based on

the fixed ground, the low pressure zone dies out quickly moving further downstream as compared to the case based

on moving ground boundary condition. It is also observed that for the case based on fixed ground boundary

condition, the streamlines twist greatly but doesn’t flow below the pressure side but travels along the span and to

further strengthen the trailing vortex system.


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(a) Moving ground

(b) Fixed Ground

Figure 26: Skin friction lines along the ground

D. Flow past NASA High Lift Trap Wing Configuration in Ground Effect

In this section, the study of flow past wing in ground effect has been extended to a trap wing configuration. The

study has been carried out to study the effect of increased camber due to high lift devices on a wing. The trap wing

profile is one that was used in NASA’s 1st High Lift Prediction Workshop (Fig. 27). The mesh created for the study

has first been validated for a free flow case and compared with the experimental data provided in the workshop.

Following the mesh dependence study, parametric study has been carried out for varying ground height, angle of

attack and flap angle.

Figure 27: Geometry of the NASA High Lift Wing Configuration with Slats and Flaps

1. Mesh Dependency Study and Validation with experimental data

The NASA high lift wing of aspect ratio 4.561 has a flap angle set at 25 degrees and the slat angle set at 30

deg (Figure 27). In case of ground effect analysis, the body in the geometry has been removed so that the wing

can be brought within close proximity of the ground. Other geometric parameters of the wing can be found at the

website of the workshop16

.

In order to check whether the mesh generated is consistent, a mesh dependency study has been carried out.

Different meshes with different element sizes has been used in order to check on sensitivity of force coefficients

with changing elements sizes, from coarse to fine. The variation in force coefficients with changing mesh sizes

can be seen in Fig. 28. Also, in order to establish and validate the parameter settings for the CFD simulation, first

a couple of test cases were varied and compared to the experimental data that was provided by NASA for the 1st

High Lift Prediction workshop17

. Free flow test cases for angle of attack of 5 and 13 degrees were carried out.

The mach number of the flow is 0.2 corresponding to a Reynolds number at 550,000. Computed contours of


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pressure coefficient and streamlines are shown in Fig. 29 and the computed lift and drag coefficients match to a

good extent with the experimental data as shown in Fig 30.


(b) Convergence plot for drag coefficient

Figure28: Mesh dependence study for the trapezoidal wing test case.

(a)

(b)

Figure 29: Computed surface pressure distribution and skin friction lines for flow past the NASA High Lift

Wing-Body configuration for an angle of attack of 13 degrees

(a) Lift coefficient

(b) Drag coefficient

Figure 30: Comparison of Computed force coefficients with the experimental data for the

NASA High Lift Wing-Body configuration

2. WIG Aerodynamics of the NASA High Lift Wing

Flow over the default configuration available from NASA was carried out for different ground heights. From

Fig. 31 it can be seen that the presence of ground restricts the flow leaving from the trailing edge of the flap.

This leads to forced separation of flow on the suction side of the flap, in the case of ground effect (fig. 32).


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(a) Free flow

(b) Ground height = 0.2c

Figure 31: Streamlines emanating from the surface of the wing

(a) Free flow

(b) Ground height = 0.2c

Figure 32: Computed skin friction lines on the symmetry plane, wing surface and ground

(in the case of ground effect)

(a)

(b)

Figure 33: Force Coefficients with varying ground height

Comparing the pressure distribution over the flap and main wing (fig. 34 and 35), it can be observed that as one

moves from the wing root to the wing tip, the pressure difference between the pressure and suction side decreases.

As the pressure difference on the bottom and top surface decreases, so does the resultant force on the wing and flap.

Hence, from these plots, the reduction of lift and drag is justified.


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(a) wing root

(b) mid span

(c) Wing tip

Figure 34: Surface Pressure Coefficient Distribution over wing at different sections along the span

(a) Wing root

(b) Mid span

(c) Wing tip

Figure 35: Comparison between surface pressure distribution over flap at different span stations for ground

effect and free flow cases

Also, comparing skin friction lines plotted on sections along the span (in fig. 37 and 38), it can be observed

that the constriction between the slat and the ground deters air flow between the pressure side and the

ground. Hence there is lesser increase in pressure on the pressure side which is one of the factors

responsible for lesser resultant force. It has also been observed that there is reduced drop in pressure on the

suction side of the wing and flap. The reason for this can also be observed in the comparison made in Fig.

37 and 38. It can be observed that in the ground effect case, the weakening boundary layer along the

suction side is not adequately reinforced by flow from the slots, as the flow from the pressure side is not

strong enough to reinforce it to extent that is done in the case of free flow.


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(a) Wing root

(b) Mid span

(c) Wing tip

Figure 36: Comparison between pressure distribution over flap at different span stations for ground effect

and free flow cases

Free flow Ground height = 0.2c

(a) Wing root

(a) Wing root

(b) Mid span

(b) Mid span

(c) Wing tip

(c) Wing tip

Figure 37: Pressure coefficient contours and

streamlines at stations along the span for the free flow

case.

Figure 38: Pressure coefficient contours and streamlines at

stations along the span for the ground effect case.


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E. Inverted wing in ground effect

To assess the potential for using the NASA High Lift Trap Wing section for race car applications a computation is

carried out by inverting a rectangular wing and flap profile and using it to model an inverted wing. The wing

modeled from the profile had an aspect ratio of 1.7. The purpose of this test case was to demonstrate the inverted

wing’s utility in race car aerodynamics. An inverted wing is used as a front/back wing in a race car, with the goal of

producing increased down force, as discussed earlier in the two dimensional case. An inverted wing is seen to

produce a down force coefficient of 0.514 in free flow. As the inverted wing is brought closer to the ground at

h/c=0.13 the down force coefficient increases to 0.925. The corresponding drag coefficient increases from 0.093 to

0.170 when the wing is brought closer to the ground. This is again due to the Venturi effect described earlier.

(a) Pressure side

(b) Suction side

Figure 39: Surface Pressure Contours and Skin Friction lines on the inverted wing surfaces, ground and

symmetry plane corresponding to WIG case.

(a) Pressure side

(b) Suction side

Figure 40: Surface Pressure Contours and Skin Friction lines on the inverted wing surfaces and symmetry plane

corresponding to free flow

Contrary to the flow pattern in the case of a normal wing, it is observed that the wing tip vortex shed from the tip

moves towards the inside converging with the vortex from the other wing tip, creating a complex wake pattern(fig

41). The venturi effect has also been highlighted when comparing the pressure distribution (fig. 42 and 43) for the

two cases at different span section of the wing. It can be observed that venture effect leads to decreased pressure on

the suction side of the wing, leading to increased down force. The authors plan to carry out further work on different

configurations of the inverted wing to get a better assessment of the role of inverted wings in race car aerodynamics.


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Figure 41: Trailing vortex interacting with the ground boundary layer. The contours have been plotted on Trefftz

planes

(a) Wing root

(b) Mid span

(c) Wing Tip

Figure 42: Comparison of pressure distribution over the wing at various sections along the span

(a) Wing root

(b) Mid span


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(c) Wing tip

Figure 43: Comparison of pressure distribution over the flap at various sections along the span

F. Conclusion and Future Work

So far the computational study addressed a number of different cases to study different phenomena related to the

wing in ground effect problem which has seen an active interest from many researchers for applications in race car

and WIG vehicles. The phenomenon of vortices alternatively being shed from the leading edge and trailing edge

respectively leading to vortex street formation was studied. For naturally shed vortices in the case of laminar flows

that the lower the ground height the greater is the variation in lift coefficient. It was also observed for lower ground

heights there was a reduction in the frequency of the vortex shedding. The reduction in the frequency observed is

due to slowing down of the whole shedding process due to interaction with the ground vorticity.

For steady flow past an airfoil, it was observed that there was an increase in lift and drag due to ground effect. Due

to the presence of ground, the air tends to stagnate between the pressure side and ground. This leads to higher

pressure on the pressure side and hence higher lift. Since the air slows down on the pressure side, more of it gets

diverged to the suction side leading to early separation and hence higher drag.

A study comparing results obtained from different boundary conditions for the ground was addressed. It was

observed that reasonable deviation in results occurred only for ground height less than 0.3c. In the case of fixed

ground, there is lesser flow between ground and airfoil and more air gets diverted to the suction side. Because of this

there is little or no venture effect in the case of fixed ground. However, the venture effect is witnessed in the case of

moving ground and this difference leads to difference in value of force coefficients at low ride heights and low angle

of attack. At higher angle of attack it was observed that the wing, in the case of moving ground, encountered earlier

separation and hence earlier stall as compared to the wing in the case of fixed ground. The early separation was

encountered in the case of moving ground because of weak flow over the suction side as more air flowed from the

pressure side, unlike the fixed ground case.

The ground effect was also studied for a NASA High Lift trapezoidal (Trap) wing attached with high lift devices. It

was found that increased camber (due to the presence of slat) showed decrease in both lift and drag on the wing

when within close proximity to the ground. This is contrary to the situation which is generally observed in the case

of a simple wing (without any high lift devices). The reduction in resultant force acting on a wing is due to the fact

that there is reduced air flow along the pressure side due to constriction between slat and the ground and hence there

is not only reduced increase in pressure on the pressure side but also reduced decrease in pressure on the suction

side.

An analogy can be drawn here between the fixed ground case, when compared with the moving ground case, and the

ground effect case of the multi element wing when compared to the free flow case. In both cases, a similar kind of

air flow pattern saw the reduction of lift and drag on the wing. From these two cases, it can be concluded that,

decreasing the distance between the ground and the wing will cause increase in lift, however, the configuration of

the wing shouldn’t avoid air flow between the ground and wing.

The authors plan to expand on the base that has been established here by further carrying out a study of the stability

and control of the wing. It is also planned to replace the rigid ground surface with a water surface using multiphase

modeling to study the effect of the wake patterns on the fluid water surface. The authors also plan to further carry

out an extensive analysis of the role of ground effect in race car aerodynamics.


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17

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Computational Modelling of Steady and Unsteady Low Speed Wing in Ground Effect Aerodynamics

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