Effects of coarse riblets on air f low structures over a slender delta wing using particle image velocimetry

Mhdi NILI-AHMADABADI, Omid NEMATOLLAHI, Kyung Chun KIM ,*

a Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

b School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea

KEYWORDS Aerodynamic performance;Coarse riblet;Delta wing;Flow structures;Particle image velocimetry;Vortex

Abstract This research investigates the aerodynamic performance and f low characteristics of a delta wing with 65° sweep angle and with coarse axial riblets, and then compares with that of a smooth-surface delta wing.Particle Image Velocimetry(PIV)were utilized to visualize the f low over the wing at 6 cross-sections upright to the wing surface and parallel to the wing span, as well as 3 longitudinal sections on the leading edge, symmetry plane, and a plane between them at Angles of Attack (AOA)=20° and 30° and Re=1.2×105,2.4×105, and 3.6×105. The effects of the riblets were studied on the vortices diameter, vortex breakdown location, vortices distance from the wing surface, f low lines pattern nearby the wing, circulation distribution, and separation. The results show that the textured model has a positive effect on some of the parameters related to drag reduction and lift increase. The riblets increase the f low momentum near the wing's upper surface except near the apex. They also increase the f low momentum behind the wing.

1. Introduction

There has been an overwhelming weight of obsession on aerodynamic scientists mind regarding maneuverability of wings in high angles of attack.Unique geometric conf iguration of delta wings entails to spiral vortex production as shown in the Fig. 11. These vortices increase the axial and circumferential velocities between twice and three times of the free stream velocities.2The diameter of these vortices can be around 30% of local span.3The low pressure regions created by these vortices increase the lift force which is called vortex lift.4

Therefore, higher lift force in comparison with typical wings with the same conditions improve the maneuverability in higher AOA that reported by some authors.5,6Consequently, this type of wing is highly recommended for highmaneuverability airplanes.

The vortex dynamics of a delta wing is related to the AOA,leading edge geometry,wing thickness,free stream conditions,and Reynolds number (Re).7However, at high AOA, primary vortices are the most dominant characteristics in delta wing and, they are Reynolds independent while secondary vortices are signif icantly Reynolds dependent.2Polhamus8calculated this lift increase using a theoretical method for the f irst time.Comparisons showed that the vortex lift is independent of

Nomenclature

A area of vortices region

AOA angle of attack

c wing chord

dcdistance of vortex center to the wing surface

dvdiameter of vortex

h height

l length of delta wing leading edge

Q criterion of vortex region

S strain rate

s wing span

t time

U velocity

x distance from apex

y height from delta wing trailing edge

Γ circulation

Ω vorticity

α angle of attack

Subscripts

Fig. 1 Leading Edge vortices and shear layer.1

∞ free stream the wing aspect ratio in the typical range of use. At higher AOA,vortex breakdown occurs.The features of vortex breakdown are:

· Fast deceleration of the vortex core in the f low axis direction

· Fast increases in vortices diameter

· Reverse f low region

· Vortex degradation to a f low similar turbulent wake2

The breakdown leads to instabilities downstream and buffets the trail.9Furthermore,breakdown stops the suction pressure decrease downstream of the breakdown place and thus,decreases the lift. Therefore, postponing this breakdown will prevent the lift reduction. There are a large number of studies which investigated the f low around delta wings and methods concerning drag reduction and breakdown postponing. For example, Lu and Zhu10studied different conf iguration of vortex breakdown around a delta wing. They found three other forms in addition of spiral and bubble which previously wellknown. These new forms named: double spiral, f iliform spiral and frog-jump conf iguration. Ol and Gharib11presented the velocity distribution near the trailing edge using the Particle Image Velocimetry (PIV) method. They concluded that the secondary vortices are weak at low Reynolds numbers.Taylor and Gursul12investigated unstable vortical f lows and showed that at low Reynolds number, the vortex breakdown is significantly delayed.Also,a recently study have been done to study the effect of pusher propeller on delta wing. The results showed that using propeller creates large moment excursions.13Also, Qin et al.14numerically studied the dynamic ground effects around a delta wing at AOA=23°. They showed that at static ground effect stagnate the f low below the wind. Furthermore, Hadidoolabi and Ansarian15investigated the f low structure over a pitching delta wing using pressure measurements and numerical study. They studied the Mach number effects and AOA on pressure distribution.They concluded that increasing AOA makes stronger vortices.

Many studies have investigated the methods for drag reduction on airplanes.The methods include using f laps,16changing sweep angle,17creating a round edge,18vortex generators,19f lexible wings,20and riblets.21Skin friction drag reduction techniques include postponing the change in transition f low regime and structure variation of the turbulent boundary layer f low.

Riblets are ribbed conf iguration which arranged streamwise for reduction of turbulent skin drag on airfoils.A number of studies reported turbulent skin drag reduction.22-26When there are riblets on an aerodynamic body,regarding riblets size and shape they decrease the skin friction drag. The idea of using riblets comes from shark skin. Walsh27used riblets for the f irst time. They used U- and V-shaped riblets on a f lat plane with different sizes using a direct drag equilibrium to reduce measurement cost. A symmetrical V-shaped conf iguration was observed as an optimum design. A couple of streamwise and counter rotating vortices (Fig. 2) were reported that interact with cross f low secondary vortex.28The main vortices(stream-wise one) are weekend by the secondary cross-wise vortices in a low speed f low which results the reduction of friction drag and consequently the total drag force.29

The riblets effects on a number of commercial airplane have been studied in a few researches.25,30,31Furthermore, the effects of riblets were investigated on different airfoils with different geometries in different conditions by other researchers.32-37Sareen investigated the effects of riblets with jagged prof ile on a Du 96-w-180 airfoil in wind turbine application38Sidhu evaluated the performance of riblets using a NACA0012 airfoil.39Recently,Hasegawa studied a micro-f iber coating riblets on a NACA0012 airfoil.40The results showed more than 50% drag reduction.

Fig. 2 Interaction of main vortices and riblets.28

Lee and Jang21investigated the effect of riblets on 40°delta wing at Re=2.5×105(based on chord length of 75 mm).Their results showed that a V-shaped riblet with a size of h=s=0.2 mm(height to chord ratio of 0.0027)has the highest effect. A 40% of drag reduction at AOA=6° was observed.From the literature review,it is found that all riblets are used for skin drag reduction in boundary layer. However there is no studies about the hybrid effects of coarse riblet and vortex generating mechanisms.

Thereafter, saeedi et al.41made Flow visualizations and force measurements on a smooth-surface as well as the other two riblet-surface models with height-to-chord ratios of 0.006 and 0.013, height-to-distance ratio of 1, sweep angle of 63.5°, and at Reynolds number of 2×105and 0 to 35° angles of attack. The results showed that the textured surface with height-to-chord ratio of 0.013 increases the lift-to-drag ratio at the whole range of angles of attack from 0 to 35°.

Regarding the previous study made by Saeedi et al.41the current study experimentally investigates the f low characteristics and effects of coarse riblets on a textured delta wing with height-to-chord ratio of 0.013. To visualize the f low f ield, the PIV method was utilized to measure the f low velocity f ield over the wing surface with and without riblets.

2. Experimental setup

All Experiments were done in a horizontal wind tunnel with a 30 cm×30 cm rectangular test section which has air speed of 30 m/s in maximum produced by a centrifugal blower. The wind tunnel consists of an air blower, a motor, an inverter to change the f low velocity, an air inlet duct, a three-mesh screen, and a honeycomb mesh to create a uniform air f low.The inverter changes the f low free stream velocity of the wind tunnel from the maximum velocity.The f low tests were carried out on both normal (without riblet) and textured models of a delta wing.The delta wings have a same chord length of 15 cm and sweep angle of 65°,as shown in Fig.3.The height to chord ratio of 0.013 and a height to distance of 1 for riblet have selected regarding to Ref. 41. Furthermore, a sharp chamfer with angle of 45°is applied on the leading edges of the models.

A two-component PIV system was applied to the setup to observe the f low. The f low was visualized on 6 cross-section planes upright to the wing suction surface and parallel to the wing span, as well as 3 longitudinal-section planes vertical to the wing suction surface, as shown in the Fig. 2. The conf iguration of laser and camera are shown in the Fig. 3. The PIV parameters during the experiments were preserved constant.

The PIV system includes a PIVCAM 10-15 CCD camera,a double pulsed Nd-Yag laser with maximum power of 200 mJ/pulse,a TSI 610032 synchronizer,and a PC.The image resolution is 1280 by 1024 pixel.Olive oil droplets are used as tracer particles. Olive oil satisf ies the general requirements for PIV seeding particles of being non-corrosive,non-toxic,chemically non-volatile,and non-abrasive.Furthermore,droplets of olive oil which have a diameters nearly 1-2 μm give an acceptable aerodynamic reaction to velocity f ield in the f low.Two Laskin nozzle chambers with six nozzles are used to generate particles.Also,a high-pressure air supplier is used at the chamber inlet to generate an even spreading of compressed air to each nozzles.

Fig. 3 PIV setup and model conf iguration.

The time difference between two images for recording suitable image f low nearby the model can be changed from 10 to 100 μs. An 80 to 200 mm Nikon lens is utilized to have a f ield of view (FOV) 110 mm by 110 mm. The size of the interrogation window for the velocity calculation is 32×32 pixels, and 50% overlap is allowed. PIVLab software is utilized to make PIV processing including false vectors removing, ensemble averaging and additional statistical calculations.42

3. Results and discussion

Considering that the f low f ield over a delta wing is completely transient, in this research, the mean f low f ield is obtained by averaging 50 instantaneous velocity contours from 50 PIV images.These 50 images are enough to reach an independency in mean velocity contours.To prove the independency of mean velocity contours from the numbers of averaged instantaneous images, on a cross-section, two mean velocity contours are computed by averaging 50 and 100 instantaneous velocity contours and then compared together in Fig. 4. To make a more detailed comparison,the mean span-wise velocity distributions over the wing (by averaging 5 and 100 instantaneous images)are plotted and compared in Fig. 5. As seen, there is no much difference between the two contours or distributions.

Figs. 6 and 7 shows the mean projected velocity contours and vorticity on the cross-sections 6 to 2 for the smooth and textured surfaces at Re=2.4×105and AOA=30°.By averaging 50 instantaneous velocity contours, two nearly symmetrical vortices with approximately the same vorticity are created on the wing. The maximum projected velocity and vorticity occurs at the f irst cross-section,and then they decreases further away from the apex. The diameter of the vortices, their distance from the wing surface, and the distance of the two symmetrical vortices from each other increase along the chord line.

At the leading edge of a delta wing, two primary vortices are produced and move over the wing. Away from the apex along the chord line,the primary vortices intensify due to feeding from the produced vorticity along the leading edge. They then dissipate due to the f luid viscosity,the secondary vortices,and vortex breakdown. At each cross-section in Fig. 7, there are two large blue- and red-colored regions indicating two nearly symmetrical vortices as the primary vortices with opposite direction.Moreover,the small green-colored regions under the primary vortices(close to corner of wing cross-section)are the secondary vortices having opposite vorticity direction relative to the corresponding primary vortex.The primary vortices are independent of the Reynolds number while the secondary ones are not. Comparison of the vorticity contours for the two wings in Fig. 7 shows that the primary vortex on the smooth wing is larger than that on the textured wing. On the other hand, the secondary vortex on the textured wing becomes larger relative to that on the smooth wing. At each cross-section, the secondary vortex produces an opposite span-wise velocity so that it decreases the mean span-wise velocity from the chord line to the leading edge. Due to this secondary vortex effect, the span-wise velocity near the wall of each cross-section for the textured wing is less that for the smooth wing.

Fig. 5 Mean velocity distribution on wing by averaging over 50 and 100 instantaneous PIV images.

Fig. 8 shows the span-wise velocity distribution along the half of the wing span (from the wing center line to the leading edge) at each 6 cross-sections. It indicates that the span-wise velocity near the wall decreases near the leading edge. As explained above, the f irst reason of this phenomena is related to the reinforcement of secondary vortex by the textured wing.The second reason is the exchange of f low momentum on the suction surface from span-wise to chord-wise direction. Afterwards,it will be shown that the riblets increase the chord-wise component of f low momentum.

To measure the vortex diameter quantitatively, it is necessary to def ine a criteria to specify the boundary of the vortices.Hunt et al.43def ines the Q-criterion for a vortex as a connected region with a positive Q according to the following equation:

where Ω and S are vorticity and strain rate, respectively. This criteria applies another constraint on the pressure,making it to be less than inf inity pressure inside the vortex.In other words,Q causes a local balance between shear strain rate and vorticity magnitude so that it def ines vortices as areas in which the vorticity magnitude is greater than the magnitude of the rate-of-strain.43,44Fig. 9 shows the contour of Q (for 4 cross-sections of the two wings) in which the colored-regions are as the representatives of vortices. By separating the bluecolored region, the area inside the vortices can be computed numerically.Then,the diameter is obtained from the following equation:

Fig. 4 Mean velocity contours by averaging over 50 and 100 instantaneous PIV images.

Fig. 6 Mean velocity contours at cross-sections 6 to 2.

Fig. 7 Contour of averaged vorticity on 6th, 5th and 4th and 3rd cross-sections.

where A is the total area of Q ＞0 including the two vortices at each cross-section.

After measuring the vortex diameters in all cross-sections for the three Reynolds numbers, it was concluded that the measured diameters are independent of the Reynolds number.Fig. 10 shows a plot of the vortex diameters averaged for the three Reynolds numbers at each cross-section for the smooth and textured surfaces. Overall, the diameters of the vortices on the textured wing are less than those on the smooth wing.

Fig 8 Span-wise veocity distribution on the wall at half of the span of all cross-sections.

Fig. 11 shows a plot of the distance of the vortex center from the wing surface versus the chord-wise length for both the smooth and textured wings at Re=2.4×105and AOA=20° and 30°. The riblets on the delta wing decrease the distance of the vortex center from the wing's upper surface.This is due to the riblets sucking the boundary layer inwards.In addition, increasing the AOA increases the distance of vortex centers from the wing surface.

Unsteady vortex breakdown phenomenon is leaded by increasing AOA in the delta wings. This breakdown is characterized by completely destruction of steady leading edge vortices. The stability, maneuverability and aerodynamic features of aircrafts are meaningfully affected by this unsteady phenomenon.24Vortex conf iguration, breakdown and their stability in the delta wings are effected using Riblets.Recognizing the vortex breakdown section on a delta wing is very complicated because the vortex breakdown phenomenon oscillates within a distinct region on the wing,which is about 10%of the chord length.

Fig. 12 show instantaneous vortex structures for the smooth and textured wings at AOA=30° at Cross-section 3,in which vortex breakdown is starting.The qualitative criterion for vortex breakdown in this f igure is that each vortex core divides into two or more vortices with opposite directions such that they neutralize each other.The vortex streamlines at 9 sequential time steps were compared for the smooth and textured surfaces. The vortices over the textured model are more stable. This indicates that the riblets can slightly postpone the vortex breakdown.

Fig. 13 compares the instantaneous vortex streamlines for the two models at AOA=20° on the sixth cross-section.The sixth cross-section at AOA=20° similar to the third one at AOA=30°, which is where the start of vortex breakdown occurs. In some time steps, the core vortex has broken down. Although, the riblets do not make a big change to the cross-section of the vortex breakdown, the vortex structures for the textured wing is a little more stable in Fig. 13.

We need a quantitative criterion to specify the exact section of vortex breakdown. Fig. 12 showed that when a vortex breaks down, the vortex core divides into two or more vortex cores with opposite directions, which are surrounded by a larger vortex. This phenomenon can cause the integral of vorticity through the area of the divided vortex cores to decrease.Thus, circulation (the integral of vorticity on an area) can be introduced as a quantitative criterion for vortex breakdown.To measure the circulation, it is necessary to specify the area on which we want to compute the integral of vorticity.

Fig. 9 Q-criterion at cross-sections of models.

Fig. 10 Distribution of vortex diameter at AOA=30°.

Fig. 14 shows the contour of the mean vorticity at half of the sixth section of the textured wing at AOA=20°.The positive and negative vorticity region is related to the primary and secondary vortex, respectively. By separating the region of positive vorticity as shown in Fig.14,the projected circulation of the primary vortex at each cross-section can be computed from the following equation.

where Γ is projected circulation,Ω is vorticity and S is the area of the positive vorticity region. It is worth noting that the two symmetric vortices produced at each cross-section neutralize each other so that the circulation on the whole domain of each cross-section will be almost zero.

Fig. 11 Distribution of vortex distances from wing surface at AOA=30° and 20°.

Fig. 12 Instantaneous vortex structures for two wing at AOA=30° at cross-section 3.

Fig. 13 Instantaneous vortex structures for the two models at AOA=20° at cross-section 6.

Fig. 14 Contour of mean vorticity at the sixth section of textured wing at AOA=20°.

Fig. 15 Distribution of vortex circulation versus chord-wise length.

Fig. 15(a) shows a plot of the projected circulation of the primary vortex at all cross-sections for the two models at AOA=20°. As mentioned before, at AOA=20°, the breakdown starting occurs at the 6th cross-section for both the models. Therefore, as expected, the circulation increases almost linearly from the f irst to the 5th cross-sections. Comparison between the circulations of the two models shows that the riblets decrease the projected circulation at all cross-sections.As mentioned before,the riblets exchange the span-wise velocity on the delta wing to the chord-wise velocity and it causes this projected circulation to decrease. In other words, considering that the streamlines of the two leading edge primary vortices on a delta wing move along a helix, the riblets actually increase the helix pitch causing the projected circulation to decrease. Increasing the pitch of the spiral streamlines can increase the leading edge vortex lift. As a matter of fact, the total lift includes vortex lift and potential f low lift which is closely related to the near surface f low (including main primary and secondary vortices) around the wing and related pressure distribution. As noted before, the riblets decrease the spanwise velocity and increase the chord-wise velocity. Therefore,it cannot be judged about the lift from these PIV results and it needs force measurement.

Fig. 15(b) shows a plot of the non-dimensional circulation of primary vortex at all cross-sections at AOA=30° for the two models and three Reynolds numbers. By def ining this dimensionless parameter (Γ/U∞Sinα·s), the diagrams related to the different Reynolds numbers matched well with each other. This proves the independency of the primary vortex from the Reynolds number. Here, a sudden decrease in the rate of circulation increase along the chord line is considered as the breakdown criterion. According to Fig. 12, we can say the vortex breakdown has occurred at the 3rd cross-section that is conf irmed by the results of Fig. 12. However, due to 1 cm distance between each two consecutive cross-sections,the accuracy of the vortex breakdown location is about 1 cm. Indeed, to increase the accuracy of the breakdown location, it is necessary to increase the numbers of cross-sections or PIV planes.

In Fig.16,the mean projected velocity and its u-component at section A (near the leading edge) is compared for the two models. Although decreasing the mean velocity near the leading edge, the riblets increase the u-component that proves the decrease of the v-component. In other words, the riblets produce a resistance for the f low passing over the leading edge from the pressure surface to the suction surface. It increases the pressure near the leading edge on the pressure surface of the textured wing. The riblets increase the f low momentum through the chord-wise direction,which reduces the wake area and drag force. However, increasing the chord-wise velocity along the leading edge means that the vortex streamlines tend to follow the chord-wise f low direction.This increases the pitch of spiral streamlines through the leading edge vortices leading to increases the lift force.In other words,adding the riblets to the delta wing causes the vortex plane to tilt, and its angle becomes closer to the chord direction.

Fig. 17(a) shows that the riblets increase the u-component of the mean projected velocity of section A along the leading edge. Fig. 17(b) plots the u-component along the back side of the section A, which indicates that the momentum parallel to the chord direction increases for the textured model. This proves that the drag is reduced through the lateral side of the textured delta wing.

In Fig.18,the mean velocity and its u-component at section C(symmetric plane)is compared for the two models.Although the f low momentum near the wing apex decreases, the riblets increase the momentum along the chord line when x/c ＞0.3.Thus,to increase the aerodynamic performance of the textured delta wing, removing the riblets near the apex is a good idea for future works.The riblets also increase the f low momentum behind the wing that reduce the wake area and drag force.

Fig. 16 Mean velocity and its u-component contours at section A at AOA=30°.

Fig. 17 Distribution of u-velocity at section A for AOA=30°.

Fig. 18 Mean velocity and its u-component contours at symmetric plane at AOA=30°.

Figs.19(a) and (b) plot the mean velocity distributions along the chord line and the back side of the section B,respectively. It shows the chord-wise momentum increases over the chord line except near the apex. Also, the wake region behind the textured wing is signif icantly less than that behind the smooth wing.

Fig. 20 compares the mean projected velocity and its ucomponent at section B for the smooth and textured models.A low momentum region is produced, which almost shows a region of vortex breakdown. Although the maximum velocity over the textured model is lower than that over the smooth model, the riblets slightly postpone the vortex breakdown.This postponement is lower than the distance between two consecutive cross-sections. The negative u-component velocity inside the low momentum region is less for the textured model that conf irms the vortex breakdown postponement. The wake regions behind the wing for the textured models are less than that for the smooth model.

Fig. 19 Distribution of mean velocity at symmetric section (section B) for AOA=30° .

Fig. 20 Mean velocity and its u-component contours at section B at AOA=30°.

Fig. 21 u-velocity distribution at section B for AOA=30°.

Fig. 21(a) shows that the riblets increase the u-component of mean projected velocity of section B near the wall. Figs. 17(a), 19(a) and 21(a) indicate that the chord-wise velocity increase by using riblets. However, it was before mentioned that the span-wise velocity decreases by using riblets. Thus,the lift increment cannot be proved by these PIV results and needs force measurement tests. Fig. 21(b) shows the ucomponent of the mean projected velocity along the back side of section B, which indicates that the momentum parallel to the riblet direction increases for the textured model. Indeed,this proves the drag reduction of the textured wing.

4. Conclusions

The riblets effects on the aerodynamic characteristics of delta wings were studied in a horizontal wind tunnel. To f ind the reason for the positive effects of the riblets and to compare the f low structures of the models, 2D PIV measurements were performed at different cross-sections for different AOA and Reynolds numbers. Due to the unsteady f low f ield over the wing, the mean velocity contour was considered as a criterion for comparison by averaging 50 instantaneous velocity contours on each section. The results showed that the riblets decrease the vortex diameters and decrease the distance of the vortex center to the wing surface.

The PIV observations proved that when the vortices on the delta wing break down,the vortex core divides into more vortices with opposite directions, and the rate of increase of the circulation along the f low direction suddenly decreases after the vortex breakdown section.Although the riblets make a little postponement in the vortex breakdown,they decreased the circulation at all 6 cross-sections. The riblets also increase the chord-wise momentum near the wing upper surface except near the apex. Moreover, they increase the f low momentum behind the wing.

Acknowledgments

This work was supported by the Brain Pool Program through the Korean Federation of Science and Technology Societies (KOFST), which is funded by the Ministry of Science, ICT and Future Planning. Support was also provided by the National Research Foundation of Korea(NRF) grant, which is funded by the Korean government(MSIT) (Nos. 2011-0030013, 2018R1A2B2007117 and NRF-2017K 1A3A1A30084513).