Investigation of Wings in Ground Effect using Computational Fluid Dynamics

TABLE OF CONTENTS

1 Introduction
1.1 Background
1.2 Literature Review
1.2.1 History
1.2.2 Present Research and Development
1.3 Objectives
1.4 Research Methodology

2 Mesh Generation in GAMBIT
2.1 Mesh Design - 2D
2.1.1 Known Parameters
2.1.2 Inlet Velocity Calculation
2.1.3 Boundary Layer Calculation
2.1.4 Mesh Design I
2.1.5 Mesh Design II
2.1.6 Mesh Design III (Final)
2.2 Mesh Design - 3D
2.2.1 Mesh Design I
2.2.2 Mesh Design II
2.2.3 Mesh Design III
2.2.4 Final Mesh Design

3 Fluent
3.1 Turbulence Models
3.2 Solver Settings
3.3 Boundary Conditions - 2D
3.4 Boundary Conditions - 3D
3.5 Convergence Criteria
3.6 Mesh Adaption

4 Results and Discussion - 2D Case
4.1 Mesh Sensitivity - 2D
4.1.1 NACA Airfoil Case
4.1.2 DHMTU Airfoil Case
4.2 Aerodynamics Performance at different h/c and AoA
4.3 NACA
4.3.1 Lift
4.3.2 Drag
4.3.3 Aerodynamic Efficiency
4.4 DHMTU
4.4.1 Lift
4.4.2 Drag
4.4.3 Aerodynamic Efficiency
4.5 Comparison
4.5.1 Lift
4.5.2 Drag
4.5.3 Aerodynamic Efficiency
4.6 Conclusions

5 Results and Discussions - 3D Case
5.1 Mesh Sensitivity - 3D
5.2 Conclusions

6 Further Work

7 References

Appendix A - Airfoil Nomenclature
- NACA 0012
- DHMTU 12-35.3-10.2-80.12.2

Appendix B - Airfoil Coordinates Generation
- NACA 0012[9]
- MATLAB Code for NACA Airfoil
- DHMTU 12-35.3-10.2-80.12.2
- MATLAB Code for DHMTU Airfoil

Appendix C - Final Mesh Approach - 2D (Contd.)

Appendix D - Results - 2D (Contd.)

Appendix E - CFD Results - DHMTU 2D

Appendix F - CFD Results - NACA 2D

TABLE OF FIGURES

Figure 1.1: Effect of Ground on Vortices[1]

Figure 1.2: Lun Ekranoplan[4]

Figure 1.3: KM Ekranoplan[5]

Figure 1.4: Sea Eagle[3]

Figure 2.1: Mesh Design I

Figure 2.2: Problem with Mesh Design I

Figure 2.3: Mesh Design II

Figure 2.4: Dimensions of the Final Meshing Approach for h/c = 0.3

Figure 2.5: Mesh Design I showing dimensions added in paint

Figure 2.6 Mesh Design II

Figure 2.7: Mesh Design III

Figure 2.8: Final Mesh Design

Figure 3.1: 2D Boundaries

Figure 4.1: NACA Lift Coefficient Mesh Sensitivity Study

Figure 4.2:NACA Drag Coefficient Mesh Sensitivity Study

Figure 4.3: DHMTU Lift Coefficient Mesh Sensitivity Study

Figure 4.4: DHMTU Drag Coefficient Mesh Sensitivity Study

Figure 4.5: NACA Cl vs Alpha KER

Figure 4.6: NACA Cd vs Alpha KER

Figure 4.7: NACA L/D vs Alpha KER

Figure 4.8: DHMTU Cl vs Alpha KER

Figure 4.9: DHMTU Cd vs Alpha KER

Figure 4.10: DHMTU L/D vs Alpha KER

Figure 4.11: Comparison of Cl vs Alpha KER

Figure 4.12: Comparison of Cd vs Alpha KER

Figure 4.13: Comparison of L/D vs Alpha KER

Figure 5.1: Path lines Colored by Velocity Magnitude

Figure 5.2: Close-up view of figure 5.1

Figure 5.3: Close-up view of path lines colored by Pressure Coefficient .

LIST OF TABLES

Table 4.1: Moore's Results (NACA for h/c=0.3 and AoA=5[0] )

Table 4.2: Final Mesh 2D Mesh Dependency (NACA for h/c=0.3 and AoA=5[0] ) ...

Table 4.3: Moore's Results (DHMTU for h/c=0.3 and AoA=5o)

Table 4.4: Final Mesh 2D Mesh Dependency (DHMTU for h/c=0.3 and AoA=5o)

Table 5.1: 3D Modeling SA Results

Table 5.2: 3D Modelling KER Results

Table 5.3: 3D Modelling KWSST Results

Table 5.4: 3D Modeling RSM Results

Notations

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1 Introduction

1.1 Background

In order to understand ground effect first we need to understand the creation of lift. Wing generates lift due to the pressure difference between the upper and lower surface. High pressure flow beneath the wing tries to flow around the wing tip to low pressure flow above the wing. This motion is known as wing tip vortex. The wing tip vortices generated induces downwash, which in turn reduces the amount of lift produced by the wing. When the aircraft is flying close to the ground the wing tip vortices are only partially developed which means that the strength of the downwash created while operating close to the ground is less than the one created in freestream. So the lift produced by the wing is not affected on a greater extent and we say it increases near the ground.

Wing in Ground Effect (WIGE) vehicles are ones that fly in close proximity to the ground, usually at altitudes that are a fraction of their wing span. This effect causes an increase in overall lift and a decrease in overall drag experienced by the aircraft. Ground Effect is a combination of two different phenomena, chord dominated ground effect and span dominated ground effect. Chord dominated ground effect is associated with increase in lift and span dominated ground effect is associated with decrease in drag.

Chord dominated ground effect occurs when an aircraft is flying at height to chord ratio (h/c) of one or less (h/c 1). At these altitudes the pressure beneath the wing is more than the pressure beneath the wing when operating in freestream, thus increasing the pressure difference between the upper and lower surface of the wing, which in turn affects the lift generated.

Span dominated ground effect occurs when an aircraft is flying at height to span ratio (h/b) of one or less (h/b 1). This phenomenon decreases the induced drag, because the vortices do not have enough room to fully form due to close proximity of the ground. This literally means that the ground forces the vortices away from the wing tips, which causes an effectively higher aspect ratio to the wing, thus reducing drag.

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Figure 1.1: Effect of Ground on Vortices[1]

Ground effect does not always increase lift; it depends on the shape of the airfoil. Convex bottom surface airfoil section can create a venturi flow below the wing if it is operating close to the ground, which results in reduction of pressure under the wing giving rise to a suction effect. This method is used to create down force in race cars specifically formula one.

The increase in lift and decrease in drag combined together causes the overall aerodynamic efficiency, also known as lift to drag ratio (L/D), to increase. The higher the L/D ratio, more efficient is the aircraft and lower is its fuel consumption. Higher L/D ratio also increases the overall range of the aircraft. This is illustrated by the Breguet Range equation shown below,

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Equation 1.1: Breguet Range Equation for Aircraft[2]

where SFC is the specific fuel consumption and W stands for weight.

1.2 Literature Review

The research conducted on ground effect is more experimental and there are very few airfoils developed specifically for use on aircrafts in ground effect. Research has been carried out all over the world in order to manufacture an aircraft that flies near the ground, because it is fuel efficient and able to carry more weight as compared to the conventional aircrafts due to increased lift near the ground. Most successful research in this field was by Russia during the cold war.

1.2.1 History

Small numbers of experimental vehicles were built in America before World War II, but Russia was the only nation to build WIGE vehicles on a larger extent. They started building large WIGE for military purposes when the world was trying to make small WIGE vehicles. This aircraft was called Ekranoplan, which was followed by its improved derivatives. These initial aircrafts include the Orlyonok troop assault/transport craft (140 tonnes) and the LUN anti-ship missile craft (400 tonnes).

The largest WIGE vehicle ever built was the KM Ekranoplan; it had a take-off weight of 540 tonnes and travelled at speeds over 500 km/h. During its life it was modified many times, which led to the most successful Ekranoplan so far, the 125 ton A-90 Orlyonok[3]. This improved the Russian understanding of WIGE craft until it crashed on take-off in 1980, only one was ever built. When the Soviet Union collapsed funding shortages meant that the WIGE projects ceased, and since then no large WIGE craft have been built.

WIG craft developed since the 1980s have been primarily smaller craft designed for the recreational and civilian ferry markets. Germany, Russia and the US have provided most of the momentum with some development in Australia, China, Japan and Taiwan. In these countries small crafts of up to 10 seats have been designed and built. Other larger designs as ferries and heavy transports have been proposed, though none have gone on to further development. After the collapse of the Soviet Union, smaller ekranoplans for non-military use have been under development[3].

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Figure 1.2: Lun Ekranoplan[4]

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Figure 1.3: KM Ekranoplan[5]

1.2.2 Present Research and Development

After the fall of Soviet Union, Russia has reduced its defense budget so the WIG manufacturers are focusing on the civil market. China on the other hand is making progress in this field and is trying to manufacture a larger 50 seat aircraft, called Tianxiang-5, which can be used for both military and civilian purpose. In the USA, WIG is not able to attract funding. Australia has a number of prominent enterprises, like Rada and Seawing, which made small recreational WIGs, are not currently functioning. Sea Eagle an Australian company in collaboration with China was able to manufacture civilian range aircraft in 2004.

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Figure 1.4: Sea Eagle[3]

The WIGE industry appears to have been held back by two factors, firstly poor longitudinal stability and sensitivity to wave height and wind speed[6]. The second factor is available funding, in order for a WIGE craft to fulfill efficiency expectations it will have to be very large, which increases its cost of manufacture as well as its weight[7]. Another problem occurs when the aircraft tries to make a small radius turn and banks on one side flying too close to the ground and ground on the other hand is not flat i.e. sea surface, which makes the aircraft difficult to control even by computers.

These aircrafts present designers with challenges e.g. advanced control system, corrosion, and compatible engines. Advanced controls system is required to overcome the problem related to continuously changing terrain during flight. Advanced materials are required for operation in the severe marine environment. Advanced engines are required for efficient operation in high density air at sea level and not affected by the corrosive marine environment.

If these challenges are met with financial assistance from prominent aircraft manufacturing companies this can lead to development of WIG industry, which can then takeover the slow ship industry.

1.3 Objectives

The objective of this project is to investigate the ground effect using Computational Fluid Dynamics (CFD). This report focuses on the effect of changing height, and angle of attack, on lift and drag coefficients of an airfoil section for two dimensions and a wing section for three dimensions. In this report a comparison of the results from two different airfoil sections, one of which is NACA and the other is DHMTU, especially made for wings in ground effect. Two dimensional airfoil section then extruded to the three dimensional wing section. In three dimensional study, the main focus is on the DHMTU wing section.

The CFD results produced are compared with the experimental results that are available from the PhD thesis[8] conducted using rolling wind tunnel at University of Southampton in 2004.

1.4 Research Methodology

This project focuses on both components of ground effect, chord dominated and span dominated, using computational fluid dynamics. The chord dominated ground effect is captured by analyzing the 2D airfoil sections and the span dominated ground effect is analyzed by using a 3D wing section.

The airfoil sections chosen for the 2D analysis are NACA 0012 and DHMTU 12-35.3- 10.2-80.12.2. These particular types of airfoil were chosen in order to have comparison with the experimental results available from the PhD thesis[8] and CFD results available from MSc Thesis[10],[12] and[13].

As the Russians have produced extensive research into all aspects of WIG design, especially in designing dedicated ground effect airfoils, they relied heavily on experimental methods to investigate the aerodynamics of ground effect. The University of St Petersburg has developed a series of dedicated airfoil sections known as the DHMTU (Department of Hydromechanics of the Marine Technical University) family. This airfoil is characterized by a flat lower surface and S-shaped mean line. A DHMTU airfoil section is described by 8 numbers detail is given in Appendix A. DHMTU airfoil is made of 5 curves. The 8 digits mentioned were plugged into equations that were translated from Russian by Chun Ho-Hwan and Chang Chong- Hee. Maher[11] was the first one to recognize that there were some errors with the translation. The equations listed by Maher[11] and Nuti[10] do not give the correct geometry, whereas Waterman [12] translated the equations correctly, but had a typing error in one part of the equation which is mentioned in Appendix B DHMTU Section.

NACA (National Advisory Committee for Aeronautics) 0012 is a symmetric airfoil with a maximum thickness of 0.12c, where c is the chord. This was chosen, because there are experimental results available from Moore[8].

This project is continuation of the work done by Nuti [10], Waterman [12] and Weeks [13]. All of them modeled the problem to investigate the effects of G.E. on lift, drag and pitching moments of NACA and DHMTU airfoils in two dimensions and modeled only NACA extruded wing for three dimensions. The chord dominated G.E. was measured by modeling two dimensional airfoil section and the span dominated G.E. was measured by modeling three dimensional wing. The 2D modeling gave reasonable results for lift, but the drag was overestimated, when compared with experimental data from Moore [8], who obtained data for the two types of wing in the rolling road wind tunnel at the University of Southampton.

These past projects were not able to get reasonable values for the drag coefficient in the two dimensional case and secondly the three dimensional modeling was not extensive in case of Waterman [12] and Nuti [10]. Weeks [13] does produce some reasonable CFD results for Cl i.e. he had a minimum error in Cl of 6% and a minimum error in Cd of 120% which is quiet high and unrealistic. He did not justify the three dimensional mesh dependency of the results. Waterman was not able to produce results for the three dimensional studies due to shortage of time. Nuti on the other produced results that were no way near to experimental data available. These authors only generated the 3D wing for the NACA 0012 and never investigated the wing generated from DHMTU airfoil section.

Keeping the above in mind, the first part of the investigation involves the 2D modeling of two airfoil sections to investigate the chord dominated G.E. In this study the angle of attack ( ) will be increased from 0 to +10 degrees (0, 3, 5, 7 and 10) and the height to chord ratio (h/c) was varied from 0.1 to 1.0 with increments of 0.2. The second part of the project is to investigate 3D behavior of the wing taking into account the spanwise effect of G.E. The 3D investigation will be based on investigation of DHMTU wing in G.E. Meshing is done in GAMBIT and Fluent is used as a CFD solver.

2 Mesh Generation in GAMBIT

GAMBIT is Fluent’s geometry and mesh generation software. GAMBIT is single interface for geometry creation and meshing[14]. The version used for this project was GAMBIT 2.2.30. GAMBIT was used to make geometry around the airfoil and to produce a mesh of the computational space in consideration. The steps involved in generating a mesh,

- Generate the geometry of the problem using vertices, edges and faces for 2D. For 3D problem volume needs to be defined.
- Mesh created on faces when considering 2D, while for 3D mesh creation volumes are required.
- Mesh refinement
- Specify Boundary conditions on the edges for 2D and on faces for 3D.
- Mesh exported to CFD solver (Fluent in this case).
- Refining the mesh again after running in Fluent to get good results.

2.1 Mesh Design - 2D

The mesh that was initially made was a bit different from the one that was used in the whole study. The Fluent Tutorial[15] suggested a semi-circular face around the airfoil. This is a good method to create structured mesh, but when the airfoil is in close proximity to the ground this approach cannot be used. Instead of making a semi-circular face, a rectangular face was to be used around the airfoil. It was tried to make a structured mesh around the airfoil, but the structured (rectangular) mesh had highly skewed elements near the leading and trailing edge. So it was decided that to use unstructured (triangular) mesh around the airfoil region. Different meshes were constructed and tested with fluent. The mesh that gave the best results was chosen.

2.1.1 Known Parameters

The experimental Reynolds Number [8] was 8.3 x 10⁵. Dynamic viscosity is 1.7894 x 10^-5 kg m^-1 s^-1. Density at sea level is 1.225 kg m^-3. Chord Length of the airfoil section is taken to be 1m. Span of the wing for 3D study was taken to be 1m.

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Equation 2.1: Input Parameters

2.1.2 Inlet Velocity Calculation

As Reynolds number is,

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Equation 2.2: Reynolds Number

So,

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2.1.3 Boundary Layer Calculation

The airfoil’s surface is considered to be a smooth flat plate. The boundary layer is chosen to be turbulent. Boundary layer thickness was calculated as follows,

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Equation 2.3: Boundary Layer Thickness Equation[16]

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Shear or friction velocity was calculated considering the airfoil a smooth flat plate

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Equation 2.4: Shear Velocity Calculation Equation [16]

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y+ is the normalized wall normal distance, used in defining the law of the wall also known as log law. It has been known from the turbulence studies in the masters program and [23] that it is difficult to model the viscous sublayer, which occurs between 0<y+<5. For this reason, the y1 value chosen was quiet low so that the y+ is close to 1. This value is suitable for turbulence models, discussed later, to accurately model viscous sub layer. More details in reference[23].

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Equation 2.5: y+ Calculation Equation[16]

Let,

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Then,

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2.1.4 Mesh Design I

The first approach was to make a mesh in which it was intended to have maximum structured mesh. The initial approach consisted of 10 faces. Nine of the ten faces had the structured mesh with only one having unstructured mesh (Triangular). This face is the one that is around the airfoil. Zone 1, 2, 3 and 4 are created so that the boundary layer around the airfoil is continued downstream in order to capture the effects on the trailing edge more efficiently. This mesh can only be used with the airfoil fixed at an AoA (Angle of Attack) of 0 degrees. For AoA study, instead of rotating the airfoil about the trailing edge, the inlet velocity was entered in components (x and y components). This approach gave good result for 0 degree AoA, but as the AoA was increased the results were not good.

The problem was that the inlet was quiet far from the airfoil and the ground was assumed to be a wall that is moving. This presented the problem as the angle of attack was increased, the velocity encountered by the airfoil was not equal to the inlet velocity, but was a bit lower than the inlet velocity. This was happening, because the ground was acting as a wall i.e. creating a vague, which caused the velocity to be lowered when it approached the airfoil. The dimensions of faces of the first approach are shown in the figure below.

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Figure 2.1: Mesh Design I

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Figure 2.2: Problem with Mesh Design I

2.1.5 Mesh Design II

In the second meshing approach, the computational space was divided into six faces. The airfoil in this approach was immersed in unstructured (triangular) mesh, unlike the first approach in which the face just behind the trailing edge consisted of structured (rectangular) mesh and the AoA was not fixed and was varied.

This approach was abandoned, because it had very small area around the airfoil, which had high density meshing.

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Figure 2.3: Mesh Design II

2.1.6 Mesh Design III (Final)

This final approach was a continuation of the second approach. In this approach, the computational space was increased both on the upstream and downstream side. The concerned area around the airfoil was also enlarged to have a fine and dense mesh to capture the flow properties around the airfoil accurately. This approach was used in all the meshing done in this project. More figures of the final mesh design are given in the Appendix C.

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Figure 2.4: Dimensions of the Final Meshing Approach for h/c = 0.3

2.2 Mesh Design - 3D

For the 3D mesh design, the mesh for the 2D was the starting point, but many changes were made to it. Firstly the computational space for 2D was quiet large. If a 3D mesh was made out of it, it will have more than 3 million cells. The computers used in the study can handle up to 3 million cells. Therefore it was decided to eliminate 5 of the 6 rectangular faces that made up the original 2D mesh, leaving just the face containing the airfoil. The remaining 2D model was extruded out using the method described in Fluent Tutorial[17].

As the 3D modeling and solving takes much more time than the 2D problem, at this stage instead of conducting the full 3D problem investigation, it was decided to take one part and investigate the results produced from it using different types of 3D meshes using different computational volumes. The need for different computational volumes was to incorporate that the vortex was completely generated and was not affected by the nearness any face surrounding it. The problem which was chosen had h/c (height to chord ratio) of 0.3 and the AoA of 5 degrees.

2.2.1 Mesh Design I

The basic meshing dimensions for the computational space were the same as the ones used by Weeks [13]. The computational space box used was 1.5m in z- direction, 5m in the x-direction and 2.3m in the y-direction. The wing dimensions used in the whole 3D investigation was fixed at 1m of chord length and 1m of span. The figure below shows the basic mesh design and the place from where the 3D analysis for the DHMTU airfoil was started.

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Figure 2.5: Mesh Design I showing dimensions added in paint

2.2.2 Mesh Design II

As it is noticed the change that was made in this design was to increase the z- direction by 0.5m and extend the x-direction by 1m after the trailing edge. This was done in order to see the effect of changing the computational space dimensions on the lift coefficient and drag coefficient.

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Figure 2.6 Mesh Design II

2.2.3 Mesh Design III

In this approach, the x-dimension was changed back to 5m, but the z-dimension remained 2m. The effect of these changes will be discussed later in the results section.

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Figure 2.7: Mesh Design III

2.2.4 Final Mesh Design

This design is similar to mesh design I, but having more cells.

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Figure 2.8: Final Mesh Design

3 Fluent

Fluent is a commercial CFD code that solves flow problems using a computational approach by estimating the numerical solution of the fundamental conservation equations for fluids. These equations are,

Mass Conservation

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Equation 3.1: Mass Conservation - Continuity Equation

Momentum Conservation

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Equation 3.2: Momentum Conservation - Navier-Stokes equations

Energy Conservation

This equation comes into play when the flow under consideration is compressible. Compressibility effects occur when the freestream Mach number is greater than 0.3. In this project the Mach number is below 0.3. So in this case the compressibility effects are negligible i.e. flow is incompressible.

The version of Fluent used in this project is 6.2.16. To setup a problem in Fluent, one must follow the following steps.

- Read the mesh file created by GAMBIT in Fluent
- Define the Turbulence Model
- Set up the Boundary Conditions
- Define the Solver Settings
- Iterate until the Solution converges
- Use of Adaptive functions to improve the model.

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