IJETAE_0312_34

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

215

Experimental and Numerical Study of Surface Flow

Pattern on Delta Wing Sukanta Saha

1, Bireswar Majumdar

2*

1Research Fellow, Dept. of Power Engineering, Jadavpur University (Salt Lake Campus), India

2Professor, Dept. of Power Engineering, Jadavpur University (Salt Lake Campus), India

[email protected] [email protected]

Abstract Vortical flow structure over sharp edged delta wings are very complex in nature. The flow field above the

upper wing surface is dominated by leading edge vortices.

These vortices create suction effect in the vicinity of leading

edge inboard which in turn enhances the lift force for higher

values of angle of attack (AoA). The aerodynamic

characteristics of delta wing aircrafts solely depend on the

structure of primary and secondary vortices over the wing. In

this study, surface flow visualization techniques are employed

to reveal the topological surface flow structure on a sharp

edged 65 delta wing model at subsonic condition. The present

study also examines the capability of steady state CFD

(computational fluid dynamics) analysis to simulate the

vortical flow field over sharp edged delta wing. Structured

grid structures are generated within the computational

domain and Reynolds Averaged Navier Stokes (RANS) based

steady state CFD simulations are performed. The

experimental and computational results are compared in

terms of surface flow pattern and vortex interaction locations

for different AoA.

Keywords Delta wing, Flow visualization, Primary and secondary vortex, Vortex breakdown, CFD.

NOMENCLATURE

b wing span

cr wing root chord

ct wing tip chord

k turbulent kinetic energy

Re Reynolds number

U0 free stream velocity

x chord wise coordinate

y span wise coordinate

y+ characteristic wall coordinate

angle of attack

leading edge bevel angle

wing sweep angle

density

specific dissipation rate

I. INTRODUCTION

The typical airfoil based aircraft wing design

methodology is based on the selection or modification of

airfoil sections for high lift to drag ratio and aerodynamic

stability [1]. However the advancement in the field of

control makes it possible to design aircrafts which are

highly unstable. The need of highly maneuverable aircrafts

has always been felt in relation to the short take off and

landing performances, combat, pre and post stall operation

etc. with superior aerodynamic characteristics. The

progress in the field of high speed aerodynamics brings the

new concept of high speed aircraft wings to break the

sound barrier. These wings are known as delta and different

configurations have been evolved to meet the superior

performances at high cruising speed. The lift generation

mechanism of delta wing is completely different from

conventional airfoil wings. The stall characteristics are also

enhanced from 18-20 AoA for typical subsonic aircraft

wings [1] to an order of 30-35 AoA for supersonic delta

wings [2]. Highly swept sharp leading edged delta wings

are appropriate for supersonic flights due to its low

supersonic wave drag [3].A delta wing aircraft is expected

to be operated at different AoA and sideslips, with the

formation of stable lift generating leading edge primary

separation vortices, secondary vortices and vortex

breakdown over the wing planform. The lift force

generated by such aircraft depends on the potential lift and

leading edge vortices induced lift [4].



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These vortices create strong suction effect near the

leading edge inboard and the static pressure drops

significantly within this zone, which in turn increases the

lift [4]. Extensive theoretical, experimental and numerical

studies have been conducted by Chu and Luckring [4],

Gurusul [5], Huang and Verhaagen [6], Nelson and

Pelletier [7], Guglieri and Quagliotti [8], to reveal the

underlying mechanism of such separated vortical flow.

These lift enhancing vortices are stable up to moderate

AoA and burst along the leeward direction at higher AoA

due to large positive pressure gradient along the vortex axis

[7],[9].

Vortex breakdown over delta wing is highly unsteady

event and produces abrupt changes on the flow variables

causing severe structural aero elastic vibrations. The

breakdown process is followed by a sudden deceleration of

fluid elements along the vortex axis and radially outward

expansion in the cross flow plane [9]. High AoA

maneuvering and associated vortex breakdown process

might cause an undesirable phenomenon known as

buffeting, due to the interaction of the vertical fins and the

unsteady wake. Moreover the asymmetry of vortex bursting

for higher AoA triggers instabilities about roll axis

[10],[11]. The interaction of post breakdown vortices with

the aircraft body can cause other instabilities and less

effective control. High speed delta aircrafts fly at low

subsonic speed during landing, takeoff, maneuvering to

avoid interception and a major part of reconnaissance

mission etc. Higher AoA is essential to generate the

required lift at low speed range. The subsonic aerodynamic

characteristics of sharp edged delta wing differ

significantly from its supersonic behavior. Study of

supersonic delta wings at subsonic condition has often been

a precursor to design breakthroughs [12],[13]. Several

experimental techniques are available, essentially non

intrusive in nature, to reveal the vortical flow structure over

delta wings such as PIV ( Particle image velocimetry),

LDV (Laser Doppler velocimetry) and surface flow

visualization. Here surface flow visualization method is

considered due to its simplicity and capability to capture

vital informations in the form of skin friction lines.

Woodiga and Liu [14] measured the skin friction field

on 65 delta wing using global oil film skin friction meter.

Surface flow topology and vortex behaviors on 65 delta

wing has been rigorously studied by Huang [15] at different

AoA. Jobe [16] investigated the vortex breakdown location

over 65 delta wing and compared with empirical methods.

CFD analysis on different sweepback delta wings have

been carried out by Le Roy and Rodriguez [17],

Benmeddour et al. [18], Kumar [19], to explain vortical

flow characteristics and vortex breakdown phenomena. The

present study is focused on identification of different zones,

lines and their extent on the upper surface of a slender

sharp edge 65 delta wing from the flow visualization

study. On the other hand CFD tools play an important role

to understand and analyze complex flow patterns. CFD

analysis of 3D vortical flow over sharp edged delta wing is

quite challenging due to the intricate geometry, sharp

corners and associated complex flow pattern with

separation. Different simulation strategies have been

evolved in accordance to the requirement to capture the real

flow structure with different degree of accuracy and cost

[20]. The present CFD study is based on steady RANS

equations. SST k- turbulence model based second order accurate discretization schemes are adopted with

appropriate boundary conditions. The present study

investigates the capacity of steady state RANS based CFD

technique to simulate vortical flow over 65 delta wing for

subsonic low (main flow) Reynolds number flow.

Qualitative and quantitative comparisons are made on the

basis of experimental results. The experimental and

numerical setup with detailed solution methodologies are

discussed in the following sections.

II. EXPERIMENTAL SETUP AND TECHNIQUE

The tests were conducted in a low turbulence subsonic

wind tunnel available in the Fluid Mechanics and M/c

Laboratory, Jadavpur University. This is a suction type

open circuit wind tunnel with a square test section of

0.6m0.6m and 1.2m in length. The wind tunnel is

equipped with two counter rotating axial flow fans

connected in series to reduce the swirling component of

velocity within the test section. The maximum free stream

velocity obtained is 15m/s corresponds to a Reynolds

number Re106/m at 15C. A line diagram of the wind tunnel is shown in Fig.1.

Fig.1. Schematic sketch of the Wind Tunnel



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The incoming airflow is guided through a closely packed

honeycomb section located upstream to the settling

chamber. A number of fine mesh size screens are placed

downstream to the honeycomb section to break the larger

eddies and to reduce the turbulence level further

downstream. Nevertheless the flow is turbulent (low

intensity) in nature throughout the test section. Therefore

the experimental and numerical analysis of transition from

laminar to turbulent flow structure over delta wing model is

not proposed for the present case. A contraction cone of

area ratio 9:1 is positioned downstream to the settling

chamber and meets the test section tangentially.

Transparent plexiglass windows are fitted on the top and

side walls of the test section for flow visualization study.

The free stream velocity at the inlet of the test section is

measured using a calibrated digital vane anemometer with

an accuracy of 0.75% of the measured value. Pressure

drop across the contraction cone is monitored throughout

the experiment to ensure same flow condition within the

test section.

The traversing arrangement for setting up different AoA,

sideslip and roll configurations on the delta wing model is

shown in Fig.2. The sliders holding the sting can rotate

with relative to each other. The central slider is guided

through a vertical tube for elevation change. The linear and

angular position accuracy for the traversing system lies

within 0.5mm and 0.5 respectively.

The solid area blockage ratio is defined as the ratio

between the projected area of the model assembly along the

axis of the tunnel and the test section area. Area blockage

ratio is an important factor and should be kept below 6% in

order to ensure the same free stream condition in presence

of the model and traversing structure [21]. Here the area

blockage ratio is less than 2.5% for the maximum AoA

configuration.

A slender 65 swept delta wing model has been

fabricated for the oil flow visualization study. The leading

edges are single beveled and sharp in shape. The root chord

diameter and thickness of the wing are 191mm and 6.5mm

respectively. A line sketch of the model is shown in Fig.3.

Aluminum and acrylic sheets are glued together to form a

composite flat plate. The wing model was fabricated from

the composite flat plate using surface grinders.

The wing model is rigidly fitted with the flat end of a

sting using slotted CSK screws. The model and sting

assembly is mounted on the traversing block to keep it

positioned at different maneuvering configurations, see

Fig.2. Furthermore some bracing wires are tied up with the

sting to reduce vibration level of the model during the

experiment.

Surface flow visualization studies are performed for 10

and 15 AoA with 0 sideslip. The onset of the vortex

breakdown process takes place at the trailing edge for 15

AoA and moves further upstream for higher AoA [8]. For

this reason these particular AoA settings are considered

here. The entire set of experiment is carried out at a free

stream velocity of 15m/s at Reynolds number of 2105

based on the root chord length. A mixture of lubricating oil,

titanium dioxide and French chalk powder is painted

uniformly as a thin layer on the upper surface of the model.

Careful attention is given to avoid the brush stroke

impressions left over the painted surface. During the run,

the oil mixture is supposed to be aligned locally to the skin

friction lines over the surface. The run is continued till the

pattern stabilizes and afterwards snapshots are taken using

a high definition digital camera. All captured images are

filtered for better visibility. A comprehensive analysis of

the experimental result is presented in the results and

discussion section.

Fig.2. Delta wing traversing arrangement.

Fig.3. Delta wing geometry and dimensions.



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III. COMPUTATIONAL TECHNIQUE

Grid generation is the most critical part of the CFD

modeling process and a major part of the computational

effort is involved to satisfy certain conditions for valuable

CFD results. Good mesh quality, grid alignment to the flow

path, proper grid resolution near the boundary zones, etc.

are the prerequisites for successful CFD simulation. The

choice of finer grid resolution on a certain zone depends on

characteristics like the non uniformity in the flow structure,

presence of distinct motion type within a flow domain,

steep gradient of the flow variables and fluid properties

close to the zone, extent of the detail feature required etc.

However excessive fine mesh structure (relative to the

major dimensions of the problem) might cause divergence

in the solution process. The steady state CFD solution of a

symmetric problem is essentially symmetric in all aspect.

Therefore the half span of the flow domain is modeled with

symmetry condition imposed on the central boundary. The

entire computational domain is divided into multiple fluid

zones to generate structured grids. Tetrahedral grid

structure was discarded due to the poor cell alignment to

the flow field and associated higher numerical false

diffusion. Structured grids can be transformed into mapped

Cartesian grids such that a particular node is indexed

uniquely. As a result its neighbors are accessed efficiently

which in turn accelerate the solution process. In the present

study multi block structured hexahedral cells are generated

except the triangular tip region with non conformal

interfaces at the zone boundaries using a preprocessor and

shown in Fig.4.

The grid structure forms an H-H type topology around

the wing model. The whole volume mesh contains

1,578,832 cells with 72 and 40 cells along the axial and

lateral direction respectively on the wing top surface. Cell

stretching ratio along the direction normal to the wall is

kept within the limit of 1.12. The individual fluid zones are

called on sequentially and appended in the analysis session.

The interface connectivity is applied between the interfaces

and coupled as pairs in accordance to the geometry.

Turbulent flow is characterized by irregular fluctuations

of flow variables and fluid properties along all possible

spatial directions within the flow field. The modified

Navier-Stokes equations, known as RANS equations

decompose an instantaneous variable/property into a mean

and a fluctuating component for turbulent flow. Then the

fluctuations are interpreted as the time averaged statistical

quantities. Therefore all scales of temporal turbulent

fluctuations are incorporated as mathematically modeled

time averaged quantities in RANS. Large Eddy Simulation

(LES) resolves larger eddies resulting more accurate

prediction in expense of much higher computational power

than RANS based models. RANS based steady state

solution is considered here within the flow domain over a

65 sharp edged delta wing using Ansys Fluent code. SST

k- turbulence model can predict the flow separation process with higher accuracy and hence preferred for the

present case of study. Near wall mesh sizes are arranged

appropriately to resolve the boundary layer velocity profile

within the viscous sub layer. Low Reynolds number flow

within the viscous sub layer always exists even for high

Reynolds number main flow. As the near wall grid

structures are prepared with intentions to capture the

viscous sub layer velocity profile, a low (near wall cell)

Reynolds number solution method is selected accordingly.

Near wall characteristic coordinate y+ is a very important

parameter to resolve the feature of the boundary layer and

found to be restricted within a maximum value of 2.5.

Fig.4. Meshing around 65 Delta wing.

Fig.5. Residual history

Iteration

Resi

du

al



219

Constant fluid properties (density and molecular

viscosity) are assumed for the prevailing incompressible

flow without any significant change in temperature. Second

order upwind discretization scheme is applied for

momentum, k and . A convergence criteria of 10-5 is set for the residuals, see Fig.5. Lift and drag convergence

histories are monitored to ensure an unchanging value

obtained during the last part of the solution process and the

iterations are stopped.

A symmetry boundary condition is applied to the central

vertical symmetry plane. The boundaries surrounding the

model surfaces (except symmetry plane) are specified as

far field with a free stream velocity magnitude of 15m/s.

The Reynolds number based on the model root chord is

equal to 210-5

. No slip wall conditions are applied to the

model surfaces without any wall roughness. Free stream

velocity directions are changed in accordance to the

imposed AoA for different simulation run. The solution is

initialized uniformly with the free stream condition

throughout the entire domain.

IV. RESULTS AND DISCUSSION

Subsonic surface flow visualization over a 65 delta

wing has been investigated using oil-powder mixture and

compared with the CFD results. The comparison is made

both qualitative and quantitatively. Surface flow

topological images were captured for 10 and 15 AoA.

The experiments are performed at a free stream velocity of

15m/s and Reynolds number of 2105 based on the root

chord length.

The main flow separates from the leading edge due to its

sharpness [12],[22]. For this reason primary separation line

is not found distinctly. The primary vortex then comes into

contact with the wing surface along the primary attachment

line [9],[22]. This primary attachment line is found on the

wing surface inboard as illustrated in Fig.6. and Fig.7.

Fig.8. Surface flow pattern at 10 AoA (CFD)

Fig.7. Surface flow pattern at 15 AoA (Experiment)

Fig.6. Surface flow pattern at 10 AoA (Experiment)

Primary attachment

Secondary

attachment

Secondary

separation



220

Secondary separation vortices are formed beneath the

primary vortex. Secondary separation and attachment lines

are appeared on the wing surface. The central zone is

unaffected from the surrounding vortices. The chord wise

and span wise locations of these lines are measured and

expressed in terms of ratios with respect to the wing root

chord length. The primary attachment line is shifted

inboard as the AoA is increased. The radial expansion rate

of the primary vortex along the downstream direction is

supposed to be increased for higher AoA, resulting larger

primary vortex cores. The vortex breakdown phenomenon

is not observed over the wing for 15AoA, however the

inception is appeared at the trailing edge.

RANS based steady state CFD analysis has been

considered for the same boundary conditions as of the

experiment.

SST k- turbulence model based low (near wall cell) Reynolds number solution is found to be the best choice for

accuracy within the limit of computational time and

resources. Surface skin friction lines predicted from the

CFD analysis are shown in Fig.8. and Fig.9. The CFD

outcomes show distinct surface flow topological zones as

observed in the experiment. It shows good agreement in

qualitative and quantitative form with the experimental

result in terms of surface flow pattern and vortex

interaction zone boundaries. The comparisons are made on

zone boundary locations and shown in Fig.10-12.

Fig.9. Surface flow pattern at 15 AoA (CFD)

Fig.10. Secondary attachment line locations at 15AoA

Fig.11. Secondary separation line locations at 15AoA

Fig.12. primary attachment line locations at 15AoA



221

The chord wise and span wise zone boundary locations

are expressed as non dimensional quantities with respect to

the wing root chord.

Near wall mesh structure is an important factor for

simulation of turbulent flow as the flow is much affected

by the presence of walls due to shear layers with a large

mean rate of strain. Therefore, to predict the flow in the

near wall region with sufficient accuracy, it is required to

resolve this region with sufficiently fine meshes. Near wall

characteristic coordinate y+ is a very important parameter

to resolve the feature of the boundary layer. The y+ value is

solution dependent and related to the wall shear stress. The

y+ distribution over the upper surface of the delta wing is

shown in Fig.13. The y+ variation is found to be restricted

within a maximum value of 2.5 whereas the average value

lies close to 1 which is the preferred criteria.

V. CONCLUSION

The following conclusions have been made based on the

present study.

Surface flow topology shows distinct features like primary attachment, secondary attachment and separation

lines.

Surface flow visualization study shows the onset of vortex breakdown at the trailing edge for 15AoA.

Experimental results are comparable with the validated published data.

CFD result shows good agreement with the experiment in terms of surface flow pattern and different zone

boundaries.

SST k- turbulence model based RANS CFD analysis can predict surface flow topological structure and the

vortex breakdown phenomenon over delta wing up to

15AoA with considerable accuracy.

References

[1] Abbott I H, Von Doenhoff A E. Theory of wing sections, including a

summary of airfoil data.1st ed. New York: Dover Publications; 1959.

[2] Wentz W H Jr, Kohlman D L. Wind tunnel investigation of vortex breakdown on slender sharp edged wings. NASA Research Grant NGR-17-002-043, 1968.

[3] Polhamus E C. A concept of the vortex lift of sharp edged delta wings based on a leading edge suction analogy. NASA TN D-3767, 1966.

[4] Chu, J. and Luckring, J. M. 1996. Experimental surface pressure data obtained on 65delta wing across Reynolds number and Mach number ranges. NASATM-4645,

[5] Gursul, I. and Yang, H. 1995. Vortex breakdown over a pitching delta wing. J Fluids Struct. 9:571-583.

[6] Huang, X. Z. and Verhaagen, N. G. 2008. Vortex flow behavior over slender delta wing configurations:experimental studies

numerical and analytical solutions. Springer.

[7] Robert, C. Nelson. and Alain, Pelletier. 2003. The unsteady aerodynamics of slender wings and aircraft undergoing large

amplitude maneuvers. Progress in Aerospace Sciences. 39:185248.

[8] Guglieri, G. and Quagliotti, F. B. Experimental investigation of vortex dynamics on a 65 delta wing. Agard report RTO-TR-AVT-

080, Chapter 10.

[9] Lambourne, N. C. and Bryer, D. W. 1962. The bursting of leading edge vortices-some observations and discussion of the phenomenon, Aeronautical Research Council. R and M No. 3282.

[10] Hummel, D. and Estorf, M. Unsymmetric vortex breakdown for symmetric free stream conditions. RTO-TR-AVT-080, Chapter 19.

[11] Gurusul, I. and Yang, H. 1995. Vortex breakdown over a pitching delta wing. Journal of fluid and structures. 9:571-583.

[12] Earnshaw, P. B. and Lawford, J. A. 1964. Low speed wind tunnel experiments on series of sharp-edged delta wings. Aeronautical

Research Council. R & M No. 3424.

[13] Verhaagen, N. G. 1999. Effect of sideslip on the flow over a 65 deg delta wing, EOARD SPC 97-4067.

[14] Woodiga, S. A. and Liu, Tianshu. 2009. Skin friction fields on delta wings. Exp fluids. 47:897-911.

[15] Huang, Xing. Comprehensive experimental studies on vortex dynamics over military wing configurations in IAR. AGARD

Report. RTO-TR-AVT-080, Chapter-5.

Fig.13. Upper surface y+ distribution at 15 AoA (CFD)

Chordwise distance

y+

valu

e

Chordwise distance

y+

valu

e



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[16] Jobe, C. E. 1998. Vortex breakdown location over 65 delta wings- empiricism and experiment. AIAA Paper 98-2526.

[17] Roy, J. F. Le. and Rodriguez, O. RANS solutions of 70 delta wing in steady flow. AGARD Report. RTO-TR-AVT-080, Chapter-16.

[18] Benmeddour, A. Mebarki,Y. and Huang, X. Z. Computational investigation of the centerbody effects on the delta wings. AGARD

Report. RTO-TR-AVT-080, Chapter-20.

[19] Kumar, Anand. 1998. On the structure of vortex breakdown on a delta wing. Proc. Royal Society London. 454: 89-110.

[20] Versteeg, H. K. and Malalasekera. 1995. An introduction to computational fluid dynamics: The finite volume method. Longman

Scientific & Technical.

[21] West, G. S. and Apelt, C. J. 1982. The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with

Reynolds numbers between 104 and 105. Journal of Fluid Mechanics 1982, 114.

[22] Wentz, W. H. and Kohlman, D. L. 1971. Vortex breakdown on slender sharp edged delta wings. J. Aircraft Vol. 8, No.3.

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