This article was downloaded by: [106.219.50.223]On: 23 February 2015, At: 10:41Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Engineering Applications of Computational FluidMechanicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tcfm20

Ground Viscous Effect on 2d Flow of Wing in GroundProximityZhi-Gang Yanga, Wei Yanga & Qing Jiaa

a Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, P. R.ChinaPublished online: 19 Nov 2014.

To cite this article: Zhi-Gang Yang, Wei Yang & Qing Jia (2010) Ground Viscous Effect on 2d Flow of Wingin Ground Proximity, Engineering Applications of Computational Fluid Mechanics, 4:4, 521-531, DOI:10.1080/19942060.2010.11015338

To link to this article: http://dx.doi.org/10.1080/19942060.2010.11015338

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose ofthe Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be reliedupon and should be independently verified with primary sources of information. Taylor and Francis shallnot be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and otherliabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4, pp. 521–531 (2010)

Received: 7 Apr. 2010; Revised: 7 Jun. 2010; Accepted: 10 Jun. 2010

521

GROUND VISCOUS EFFECT ON 2D FLOW OF WING IN GROUND PROXIMITY

Zhi-Gang Yang, Wei Yang* and Qing Jia

Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, P. R. China * E-Mail: david_yangwei@yahoo.cn (Corresponding Author)

ABSTRACT: Viscous effect of wing in ground effect in wind tunnel test was investigated numerically. Ground settings in wind tunnel test were simulated by specifying different ground boundary conditions in CFD. It was revealed for fixed-ground based wind tunnel test that: boundary layer developed from the ground deforms effective ground surface and introduces a decreased effective ground clearance; a sharp increase in boundary layer thickness and adverse pressure gradient are captured, which is attributed to deceleration of flow under the leading edge; a separation bubble on ground forms in very small ground clearance and large angle of attack, which helps air flow around the leading edge and delays the stall; measured aerodynamics in fixed-ground based wind tunnel test are not accurate due to ground viscous boundary layer flow; ground viscous flow simulation is of great importance in in-depth studies on ground effect. The results obtained will be useful in developing and evaluating wind tunnel tests and studies for wing in ground effect craft.

Keywords: wing in ground effect, aerodynamics, viscous effect, boundary layer separation, numerical method

1. INTRODUCTION

Favorable aerodynamic performance is obtained when a wing is in close proximity to the ground. Many works have been carried out on development of Wing-in-ground effect (WIG) craft to fully utilize the advantages of ground effect (Rozhdestvensky, 2006). The benefits of ground effect are also mentioned in the context of race cars (Zerihan and Zhang, 2000; Mahon and Zhang, 2005 and 2006; Ahmed et al., 2007). Both potential effect and viscous effect play a role in ground effect. When air flows through the narrow region between the wing and the ground, an air cushion with high pressure is created. A substantial increase in lift can be captured as the wing is approaching the ground. On the other hand, air flow is viscous, and near wall viscous flow for both wing and ground may affect the flow pattern. Study of these two kinds of effect helps to fully understand the mechanism of ground effect. Various studies have been undertaken to examine and to explain the effect of ground on wings, through analytical, numerical and experimental methods (Firooz and Gadami, 2006; Zhang and Zerihan, 2003; Kang and Zhao, 2007; Ahmed and Sharma, 2005; Yang and Yang, 2008a, 2008b and 2009; Yang et al., 2009). Aerodynamic characteristics such as lift, drag, and pressure were focused on in these studies; chord dominated and span dominated ground effect were investigated respectively; efficiency

of endplate in holding high pressure under wing was verified; some experiments predicted adverse pressure gradient over the upper surface and a boundary layer separation near the trailing edge. In these studies, the potential effect and viscous effect were combined and roughly estimated. Furthermore, experiments were mainly done in wind tunnels with fixed ground, only few tests were conducted with a moving road. In regions very close to ground proximity, viscous effect could become dominant and the accurate simulation of the viscous effect would improve the accuracy of prediction for ground effect. For wind tunnel test, moving belt is an effective facility for studying viscous effect of ground effect. But not all of the wind tunnels have moving belt systems. From this point of view, the current work numerically investigates wing in ground effect in wind tunnel test with and without moving belt in 2D and attempts to find a correction method. Also, in order to capture the near wall flow features, such as transition, a computational method is established and validated. Then, based on numerical simulation, the present work focuses on revealing the viscous effect of ground effect flow and the flow pattern under fixed-ground based wind tunnel test. Both effects of inlet boundary turbulence level and viscous near ground flow are taken into consideration. The work will hopefully achieve a better understanding of the mechanism of ground effect.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

522

2. DESCRIPTION OF COMPUTATIONS

2.1 Governing equations

The computation simulates the NACA0012 airfoil in ground effect. We aim to study the viscous effect of ground in modeling ground effect. Further details of wing in ground effect can be referred to Yang and Yang (2009). The flow velocity is set at 60m/s. The Reynolds number is 4×106 based on the chord length c. The flow was modeled as incompressible because of the low Mach number. The governing equations are the incompressible RANS equations for continuity and momentum (Fluent 6.2 User's Guide, 2005):

0

i

i

x

U (1)

21i j ' 'i ii j

j i j j j

(U U )U UP( u u )

t x x x x x

(2)

where ''jiuu is the Reynolds stress term, which

must be determined with a statistical turbulence model. The incompressible RANS equations are solved using an implicit, segregated, two-dimensional finite volume method. A second-order accurate scheme is used for the convective and viscous terms of the RANS equations. Pressure-velocity coupling is implemented with the SIMPLE algorithm.

2.2 Turbulence modeling

Before numerically investigating the viscous flow, four turbulence models were evaluated by comparing the calculation of the turbulent stresses for flat plate and airfoil in freestream, they are one-equation Spalart-Allmaras (S-A) model (Spalart and Allmaras, 1992), the two-equation Standard k (SKE) model (Launder and Spalding, 1972), the Realizable k (RKE) model (Shih et al., 1995) and the Menter’s

sstk / (shear stress transport) turbulence model (Menter, 1994). The Spalart-Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. The standard k model is based on model transport equations for the turbulence kinetic energy ( k ) and its dissipation rate ( ). Accuracy for a wide range of turbulent flows explains its popularity in industrial flow. The Realizable k model represents a more advanced version of two-equation turbulence model. It has been

shown by its authors to perform well for flows involving rotating and large-scale separation. The SST model is a zonal two-equation turbulence model that is k near the wall and transitions to k model away from the wall. It employs blending functions to take advantage of the superior performance of the k-ω model in the near wall regions and the freestream independence of the k model in the farfield. One of the above turbulence models will be applied to study viscous flow in ground effect based on performance in resolution of boundary layer flow.

2.3 Computational domain and boundary conditions

The computational domain is shown in Fig. 1. The airfoil has a chord length, c, of 1m. The inflow boundary was placed a distance x1/c=6 upstream of the trailing edge of airfoil and the outflow boundary a distance x2/c=10 downstream of the trailing edge of airfoil. The height of domain was y/c=6. The domain was thought by the authors to be large enough to minimize the influence of the boundaries on the final solution and small enough to minimize the number of grid cells. C-H type grids were adopted. For the resolution of turbulent boundary layer profiles, a minimum normal spacing of 1×10-5

c is selected and the near wall grid consists of approximately

50 prism layers, so that the y at the cells next to the wall are around 1 along the airfoil surface and ground. The grid between airfoil and ground contains 120 layers at h/c=0.05 to 200 layers at h/c=0.3. Ground clearance, or flight height, h is defined by distance from the ground to the trailing edge of airfoil. A velocity inlet boundary condition is specified with a uniform profile at 60m/s. Inlet turbulence level (Tu) is set at 0.2% for study of near ground viscous effect and 0.2%, 0.5%, 1% for study of inlet boundary turbulence level effect at certain ground clearance and angles of attack. At the outflow boundary, a pressure outlet boundary condition is prescribed with a gauge pressure of zero. A slip boundary condition (symmetry) was specified on the top boundary. The effect of boundary layer on wind tunnel test was simulated

u

x1

x2x3

Ground

Pressure

Symmetry

Fig. 1 Placement of the airfoil and computational

domain.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

523

1.5 2 2.5 3 3.5 4

x 105

10-3

10-2

Rx

Cf

12,000 Cells60,000 Cells120,000 Cells

Fig. 2 Skin friction for different mesh densities.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

x 105

10-3

10-2

Rx

Cf

S-AS-KER-KEKW-SSTH. Lee, 2000

Cf=0.664/R

x0.5

Cf=0.0592/R

x0.2

Fig. 3 Skin friction for lower surface of NACA0012.

by specifying slip boundary condition on the ground from the inlet boundary to a position x3/c=2 upstream of the trailing edge of airfoil (Mcmanus and Zhang, 2006). Non-slip boundary condition was specified on airfoil and ground. Three experimental cases were considered, a fixed-ground based wind tunnel test with velocity of the ground set to zero, a mirror-image method based wind tunnel test with a symmetry “ground” and a moving-belt based wind tunnel test with velocity of the ground set to the freestream velocity of 60m/s.

3. COMPUTATIONAL RESULTS AND DISCUSSION

Flow of wing in ground effect is complex. To simulate this complex flow, turbulence models were firstly evaluated for turbulent boundary layer flows, and a turbulence model was chosen based on the performance for these flows. Then, viscous effect of wing in ground effect flow was numerically studied. Finally, the results for different kinds of ground boundary conditions

were compared to clarify the viscous effect and to emphasize the importance of viscous ground simulation in wind tunnel test.

3.1 Evaluation of turbulence models

Different turbulence models were evaluated based on their capability to capture characteristics of near wall viscous flow, such as boundary layer transition. For wing in ground effect, both viscous flows near the wing and ground are important. Therefore, the turbulence model evaluation was conducted for two cases, an airfoil in freestream and a flat plate with uniform velocity. For airfoil in freestream, the computation simulates the experiment carried out by Lee and Kang (2000). The computational domain for evaluation has the same size as the test section in experiment, 300mm(H)×2000mm(L). The airfoil was mounted at the center of the domain. The Reynolds Number is 6×105 based on a chord of 0.3m and a flow velocity of 30m/s. The background turbulence level is 0.3 percent, which is the same as in the experiment. As shown in Fig. 2, mesh independence was determined with a mesh of 60,000 cells. The turbulence model used in mesh independence study is sstk / model. All computations presented later in the present study are implemented with mesh densities similar or greater to that of the mesh-independent case. Variations of skin friction coefficient on the lower surface of NACA0012 airfoil with different turbulence models are shown in Fig. 3. Transition is assumed to start and end at the locations of local minimum and maximum values of skin friction, respectively. The experiment reported that the transition starts at x/c=0.617 (x=185mm) and ends at x/c=0.783 (x=235mm). The S-A model, SKE model and RKE model failed to capture the transition of the boundary layer. The

sstk / model gives a better description about transition characteristics over the airfoil surface. However, more viscous effect is introduced and the transition takes place earlier than that of experiment as shown in Fig. 3. For evaluation of the flat plate flow, the computation was conducted based on the same setting and domain as described in section 2.3. The ground part served as the flat plate. Computation based on sstk / model predicts the skin friction acceptably (Fig. 4). The airfoil in the following computations will be placed in the region between x=1m and x=2m. It is thought by authors that the sstk / model is a reasonable choice for our computations.

Lee H, 2000

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

524

0 0.5 1 1.5 2 2.51.5

2

2.5

3

3.5

4

4.5

5x 10

-3

x (m)

Cf

Cf=0.0592/R

x0.2

Computation

Fig. 4 Skin friction for flat plate.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-3

x/c

* /m

stationarysymmetrymoving wall

(a) Displacement thickness.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

x/c

/m

stationarysymmetrymoving wall

(b) Boundary layer thickness.

Fig. 5 Displacement thickness and boundary layer thickness of airfoil, h/c=0.1.

3.2 Viscous effect of ground boundary layer

In the numerical simulation of the airfoil, the angle of attack was set at 6 degrees. Two main parameters were used in the present work to characterize the size and shape of a boundary layer, the boundary layer thickness and the

displacement thickness. Because the main effect of viscosity is to slow down the fluid near a wall, so the edge of the boundary layer is defined to be the point at which the fluid velocity equals 99% of the local free-stream velocity. The boundary layer thickness, denoted by , is simply the thickness of the viscous boundary layer region.

The displacement thickness, denoted by * , is the distance a streamline just outside the boundary layer is displaced away from the wall compared to the inviscid solution. Fig. 5 shows the displacement thickness and boundary layer thickness of wing with different ground boundary conditions. They are very small compared to flight height, and ground setting in numerical simulation has no effect on development of boundary layer along the airfoil. Nevertheless, the boundary layer development on stationary ground can be affected by the ramming effect under airfoil (Fig. 6). The displacement thickness and boundary layer thickness for h/c=0.1 are smaller than those for h/c=0.3. It is

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 12

2.5

3

3.5

4

4.5

5

5.5

6x 10

-3

x/c

* /m

h/c=0.1h/c=0.3

(a) Displacement thickness.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

0.016

x/c

/m

h/c=0.1h/c=0.3

(b) Boundary layer thickness.

Fig. 6 Displacement thickness and boundary layer thickness of airfoil with stationary ground.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

525

indicated that the high static pressure which distributed between airfoil and ground compressed the boundary layer. The smaller the ground clearance is, the more the boundary layer is compressed. The development of boundary layer from the ground is sketched in Fig. 7. u is the velocity at

the edge of boundary layer. Due to ramming action, the velocity is low under the airfoil near the leading edge, and then the flow accelerates along the lower surface. Accordingly, the velocity at edge of boundary layer experiences a process of increase after decrease. Decrease of velocity leads to an increase of pressure, and fluid transforms part of its kinetic energy into potential energy. In other words, local adverse pressure gradient is highly increased, which results in a significant growth in boundary layer. The development of boundary layer restores to original state with the acceleration of flow. The effect of viscous boundary layer flow on study of wing in ground effect is illustrated in Fig. 8. It is clear that viscous effect of fixed ground causes an effective deforming of the ground surface. The ground is raised by displacement

thickness, which leads to a change in effective flight height and an over-estimation of the ground effect. For example, the effective relative flight height is he/c=0.076 for h/c=0.1 and he/c=0.2878 for h/c=0.3, when the ground is considered to be stationary. The viscous boundary layer effect is of increasing importance as the ground clearance is reduced or the angle of attack is increased.

3.3 Separation bubble on ground

The adverse pressure gradient along the ground is increased near the leading edge with airfoil approaching to ground (Fig. 9). At certain flight height the boundary layer, after losing a part of its energy due to friction, no longer has sufficient amount of energy to overcome the adverse pressure gradient, and boundary layer separation occurs (Fig. 10). The momentum transfer due to turbulent mixing eventually eliminates the reverse flow near the wall and the flow reattaches downstream. Breakdown of boundary layer flow is recovered by reattachment. The separation-reattachment region is featured with “dead air zone”, which could modify the effective shape of

-0.4 -0.2 0 0.2 0.4 0.6 0.8 130

40

50

60u

/m s

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.01

0.02

0.03

0.04

x/c

/m

u h/c=0.1

u h/c=0.3

no wingh/c=0.3 h/c=0.1

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

-0.1

-0.05

0

0.05

0.1

x/c

y/m

Actual ground surface

Effective ground surface

Effective airfoil surface

Actual airfoil surface

he h

*

Fig. 7 Near wall flow with stationary ground. Fig. 8 Changes of effective shape of the body with stationary ground, h/c=0.1.

0.6

0.637

0.4

0.2

0

-0.2

-0.4

-0.6-0.8

0.40.6

0.8

(a) h/c=0.1

-0.2

-0.4

-0.6

-0.1

0

0.2

0.4

0.6

0.8

0.6

-0.8

0.4

0.637 0.637

(b) h/c=0.05

Fig. 9 Static pressure coefficient distribution with stationary ground.

-0.4

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

526

ground. Fig. 10 describes the fact that a large angle of attack can lead to boundary layer separation on ground and the separation region is growing with angle of attack, which is attributed to the strengthened air cushion under airfoil. The viscous boundary layer flow near ground is sensitive to flight height and angle of attack, so is the prediction accuracy of flow for fixed ground based CFD and wind tunnel test. A separation bubble can be captured near ground when the ground was set to be stationary in Fig. 11. Flows for the other two ground boundary conditions are similar without separation. The separation bubble grows with increase of the angle of attack. It continues growing until the airfoil stalls (Fig. 12). The oncoming viscous flow near ground is pushed upwards away from ground by the separation bubble towards the airfoil,

tending to flow around the leading edge. Thus, the stagnation point on airfoil moves forwards when being compared with that of moving wall ground boundary condition. It can also be noticed in Fig. 13 that the ramming effect under airfoil in ground effect with small ground clearance stagnates the flow at a further distance away from the leading edge of airfoil for cases of moving wall; while the separation bubble effect at small ground clearance shifts the stagnation point towards leading edge more than that in larger ground clearance. High static pressure stored near the trailing edge of airfoil is released when airfoil stalls at big angle of attack. High favorable pressure gradient is present behind the separation bubble. The separation bubble shrinks to some extent accordingly (Fig. 14).

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

x 10-3

x/c

Cf

Without airfoilh/c=0.05h/c=0.1h/c=0.3

(a) 6

-0.5 0 0.5 10

0.5

1

1.5

2

2.5

3x 10

-3

x/c

Cf

=6

=8

=10

=12

(b) h/c=0.1

Fig. 10 Skin friction of the stationary ground.

(a) Stationary (b) Symmetry (c) Moving wall

Fig. 11 Streamlines in flow with different ground settings, h/c=0.05, 6 .

(a) 8 (b) 12 (c) 16

Fig. 12 Streamlines in flow with stationary ground, h/c=0.05.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

527

Fixed-ground based wind tunnel test reduces flow that is fundamentally different from the actual flow in extreme ground effect. The viscous effect of the near ground flow plays a decisive role in the study of wing in ground effect, which is characterized by complex flow between wing and ground surface (or water surface). Viscous effect in fixed-ground based wind tunnel test imposes

limitations of height and angle of attack on insight into ground effect.

3.4 Ground viscous effect on aerodynamics

Aerodynamics of 2D wing in extreme ground effect with different ground boundary conditions is presented in Fig. 15. It is generally agreed that

8 9 10 11 12 13 140.02

0.03

0.04

0.05

0.06

0.07

0.08

x/c

h/c=0.05 stationaryh/c=0.05 moving wallh/c=0.1 stationaryh/c=0.1 moving wall

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-1500

-1000

-500

0

500

1000

1500

2000

2500

x/c

Pa

=6

=12

=16

Separation region

Fig. 13 Stagnation point. Fig. 14 Static pressure distribution near ground.

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

CD

CL stationary

symmetrymoving wall

6 7 8 9 10 11 12 13 14 15 16

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

CL

stationarysymmetrymoving wall

(a) h/c=0.05

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

CD

CL stationary

symmetrymoving wall

6 7 8 9 10 11 12 13 14 15 16

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

CL

stationarysymmetrymoving wall

(b) h/c=0.1

Fig. 15 Lift and drag coefficient.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

528

fixed ground in wind tunnel test slows down the flow under wing or vehicle, static pressure increases due to decrease of dynamic pressure and pressure effect under lower surface of airfoil is strengthened. Furthermore, effective flight height is reduced by displacement thickness due to viscous boundary layer flow, and ground effect is over-estimated. Accordingly, higher lift is expected. However this is not true when the separation bubble appears on the ground in very small ground clearance or at large angle of attack for airfoil in ground effect, in which case lift is underestimated and stall can be delayed under strong separation bubble effect. As mentioned in previous sections that the separation bubble can grow with decrease of flight height and increase of angle of attack. Under these situations, air flow upstream is blocked and deflected by the separation bubble. Less air flows through the narrow space between airfoil and ground. Ramming effect under airfoil is weakened. Synchronously, stagnation point moves upstream. The separation bubble also helps the air flow around the leading edge with less energy consumption. This change represents decrease of suction over airfoil. It is obvious that adverse pressure gradient decreases and stall is delayed. Growth of the separation bubble means more pressure effect leaks out, resulting indistinct difference from reality or reductions of the other two cases. Aerodynamics and pressure distribution based on ground boundary conditions of symmetry and moving wall are well matched. Shear flow near moving ground leads to a high pressure near the trailing edge, which contributes to separating the flow over airfoil. So, airfoil under moving ground boundary condition stalls slightly earlier at flight height of h/c=0.05.

As one can expect, air flow will speed up firstly and then slow down along the airfoil surface when air flows over an airfoil. The minimum static pressure is achieved where the flow velocity reaches the maximum. As shown in Fig. 16, less suction effect is realized with induced flow over airfoil due to the separation bubble on ground. Loss of pressure effect under lower surface spreads from leading edge to trailing edge with airfoil pitching up. Reduction of suction effect and loss of pressure effect result in poor performance in aerodynamics for wing in ground effect based on stationary ground boundary condition. Near the trailing edge, flow over airfoil is uninfluenced by ground boundary conditions at small angle of attack, while it is affected at large angle of attack. Curves for ground boundary conditions of symmetry and moving wall coincide. Prediction of aerodynamics for wing in ground effect is essentially determined by reasonable simulation of ground effect. Fixed-ground based wind tunnel test or CFD study introduces complex viscous ground boundary layer flow which deforms the effective ground shape and leads to unrealistic results, while wind tunnel test and CFD study based on “mirror method” or especially facilities such as boundary layer suction and moving belt can simulate more realistically the ground effect phenomenon.

3.5 Effect of background turbulence level

All kinds of viscous flow are complex and sensitive to Reynolds number and background turbulence level. Generally, an increasing inlet turbulence level could result in forward motion of transition point and change of boundary layer separation. Effect of background turbulence level on ground boundary layer separation occurrence

(a) 6

(b) 12

Fig. 16 Pressure coefficient, h/c=0.05.

C

2

1

x/c 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

p

stationarysymmetrymoving wall

-7.5

-7

-6.5

-6

0.85 0.9 0.95 10

0.1

0.2

0.3

0.4

0.5

1

1.5

x/c

C

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

p

stationarysymmetrymoving wall

0.7 0.75 0.8 0.85 0.9 0.95 1

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

-3

-2.5

-2

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

529

was studied by changing the turbulence level at inlet boundary from 0.2% to 1%. The angle of attack is 6 degrees. As analyzed previously, boundary layer under wing in extreme ground effect encounters high adverse pressure gradient and grows significantly. Higher adverse pressure gradient would trigger the separation of boundary layer. Fig. 17 presents the boundary layer developments under wing in ground effect along stationary ground with different background turbulence levels at h/c=0.1. Change of background turbulence level does not bring significant variation in boundary layer development under wing in ground effect. Fig. 18 shows the skin friction under wing for stationary ground at h/c=0.05. Fig. 19 shows the streamlines at h/c=0.05. Boundary layer separation occurs. Curves of skin friction for different inlet turbulence level coincide. Skin friction was less affected by changes of inlet boundary turbulence level. The separation bubble is also insensitive to the background turbulence level. It is clear that viscous flow under wing in extreme ground effect is more affected by ground simulation than by inlet boundary turbulence level.

4. CONCLUSIONS

The present work is driven by the need to reveal mechanism of ground effect. A variety of investigations on wing in ground effect is in progress based on wind tunnel tests. In order to evaluate the viscous effect in ground effect, especially for fixed-ground based wind tunnel test, detailed numerical investigations that simulated wind tunnel test on wing in ground effect with different ground boundary conditions were carried out. The conclusions of the present study are as follows:

Viscous ground boundary layer flow for fixed ground based wind tunnel test raises the floor because of the displacement thickness. It is thought that ground effect is over predicted due to viscous effect, which causes decrease of effective ground clearance.

A separation bubble is created on the ground under the leading edge due to high adverse pressure gradient in very small ground clearance and at large angle of attack for fixed ground. It is affected by background turbulence level. The resulting flow not deviates from actual ground effect flow for craft or race cars.

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10.01

0.015

0.02

0.025

0.03

0.035

0.04

x/c

/m

Tu = 0.2%

Tu = 1%

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

0.5

1

1.5

2

2.5

3x 10

-3

x/c

Cf

Tu = 0.2%Tu = 0.5%Tu = 1%

Fig. 17 Boundary layer thickness near stationary

ground, h/c=0.1 and 6 . Fig. 18 Skin friction for stationary ground with

different inlet turbulence level, h/c=0.05 and 6 .

(a) Tu=0.2% (b) Tu=0.5% (c) Tu=1%

Fig. 19 Streamlines with different background turbulence levels, h/c=0.05 and 6 .

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

530

The ground separation bubble grows with decrease of flight height and increase of angle of attack. It deflects the oncoming flow and makes more air flow over the upper surface. The formation of a boundary layer separation bubble results in delaying stall for small ground clearance.

It is precisely because of viscous effect that wind tunnel test based on fixed ground falls into difficulty in accurately predicting aerodynamics and ground effect. Aerodynamics is overestimated before separation bubble occurs and is underestimated after.

ACKNOWLEDGEMENT

The authors would like to recognize the support of Shanghai Automotive Wind Tunnel Center. This work was supported by Program for Changjiang Scholars and Innovative Research Team in University.

NOMENCLATURE

c mean chord length (m) CD drag coefficient CL lift coefficient Cp pressure coefficient h flight height (or ground clearance)(m) p pressure (Pa) Re Reynolds number

u velocity in freestream (m/s)

u boundary layer edge velocity (m/s)

y+ non-dimensional wall distance

Greek symbols angle of attack (deg) density (kg/m3) kinematic viscosity (m2/s)

Subscripts i, j coordinate index

REFERENCES

1. Ahmed MR, Sharma SD (2005). An investigation on the aerodynamics of a symmetrical airfoil in ground effect. Experimental Thermal and Fluid Science 29(6):633–647.

2. Ahmed MR, Takasaki T, Kohama Y (2007). Aerodynamics of a NACA4412 airfoil in ground effect. AIAA Journal 45(1):37–47.

3. Firooz A, Gadami M (2006). Turbulence flow for NACA 4412 in unbounded flow and ground effect with different turbulence models and two ground conditions: Fixed and moving ground conditions. Proceedings of the International Conference on Boundary and Interior Layers (BAIL 2006), July 24th–28th, 2006, Göttingen.

4. Fluent 6.2 User's Guide, Fluent Inc., Lebanon, NH, 2005.

5. Kang DW, Zhao LL (2007). PIV measurements of the near-wake flow of an airfoil above a free surface. Journal of Hydrodynamics, Ser. B 19(4):482–487.

6. Launder BE, Spalding DB (1972). Lectures in Mathematical Models of Turbulence. Academic Press, London, England.

7. Lee H, Kang SH (2000). Flow characteristics of transitional boundary layers on an airfoil in wakes. Journal of Fluids Engineering 122(3):522–532.

8. Mahon S, Zhang X (2005). Computational analysis of pressure and wake characteristics of an aerofoil in ground effect. Journal of Fluids Engineering 127(2):290–298.

9. Mahon S, Zhang X (2006). Computational analysis of a inverted double element airfoil in ground effect. ASME Journal of Fluids Engineering 128(6):1172–1180.

10. Mcmanus J, Zhang X (2006). A computational study of the flow around an isolated wheel in contact with the ground. Journal of Fluids Engineering-Transactions of the ASME 128(3):520–530.

11. Menter FR (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8):1598–1605.

12. Rozhdestvensky KV (2006). Wing-in-ground effect vehicles. Progress in Aerospace Science 42(3):211–283.

13. Shih TH, Liou WW, Shabbir A, Yang Z, Zhu J (1995). A new k eddy viscosity model for high Reynolds number turbulent flows. Computers & Fluids 24(3):227–238.

14. Spalart PR, Allmaras SR (1992). A one-equation turbulence model for aerodynamic flows. 30th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, 6–9 January, AIAA paper 92-0439.

15. Yang W, Yang Z (2008a). A study on longitudinal stability and configuration of wing-in-ground effect based on CFD. NASPC/TUWMAE2008, Beijing, China:

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 4 (2010)

531

Tsinghua University; 30th Oct.–2nd Nov. 2008.

16. Yang W, Yang Z (2008b). Numerical simulation on span-dominated ground effect of 3D wing in ground effect. Computer Aided Engineering 17(3):13–17. (in Chinese)

17. Yang W, Yang Z (2009). Aerodynamic investigation of a 2D wing and flows in ground effect. Chinese Journal of Computational Physics 26(2):231–240.

18. Yang Z, Yang W, Li YL (2009). Analysis of two configurations for a commercial WIG craft based on CFD. 27th AIAA Applied Aerodynamics Conference, AIAA-2009-4112, 22–25 June 2009, San Antonio, Texas.

19. Zerihan J, Zhang X (2000). Aerodynamics of a single element wing in ground effect. Journal of Aircraft 37(6):1058–1064.

20. Zhang X, Zerihan J (2003). Off-surface aerodynamic measurements of a wing in ground effect. Journal of Aircraft 40(4):716–725.

Dow

nloa

ded

by [

106.

219.

50.2

23]

at 1

0:41

23

Febr

uary

201

5