Experimental and Numerical Study of Surface Flow Pattern on Delta Wing

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Experimental and Numerical Study of Surface Flow

Pattern on Delta Wing

Sukanta Saha

, Bireswar Majumdar

1_{Research Fellow, Dept. of Power Engineering, Jadavpur University (Salt Lake Campus), India} 2_{Professor, Dept. of Power Engineering, Jadavpur University (Salt Lake Campus), India}

1_{[email protected]}

2_{[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

α angle of attack

θ leading edge bevel angle

Λ wing sweep angle

ρ density

ω specific dissipation rate

I. INTRODUCTION

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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-ω 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 0.6m×0.6m 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 Re≈106/m at 15°C. A line diagram of the wind tunnel is shown in Fig.1.

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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 2×105 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.

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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-ω 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

R

esi

d

u

a

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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 ω. 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 2×10-5. 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 2×105 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

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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 15°AoA, 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-ω 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 15°AoA

Fig.11. Secondary separation line locations at 15°AoA

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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 15°AoA.

 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-ω turbulence model based RANS CFD analysis

can predict surface flow topological structure and the vortex breakdown phenomenon over delta wing up to 15°AoA 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.

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[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 65°delta 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. 39:185–248.

[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+

v

a

lu

e

Chordwise distance

y+

v

a

lu

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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.