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Normal- and Shear-Stress over a Flat-Surface Established an Inclined Cylinder on

Takaaki SHIZAWA1 , Masashi HIGASHIURA2 Tokyo University of Science Suwa, Chino, Nagano, 391-0292, Japan

Tsukasa SAITOU3 Recruit R&D Staffing, Yokkaichi, Mie, 510-0074, Japan

Kouji SAKAI4 ANA Aircraft Maintenance Co. Ltd, Toyonaka, Osaka, 560-8548, Japan

Teppei KANEKO5 Nideco Copal Co., Shiojiri, Nagano, 399-0731, Japan

and

Kazuki MIYAJIMA6 ART Metal MFG Co. Ltd , Ueda, Nagano, 386-1211, Japan

The structure of a wake downstream of a bluff body is one of the important problems in practical application, and the cylinder is commonly used as the base case. There is little information about the structure of the wake of an inclined cylinder interacting with the turbulent boundary layer. In this case, Karman vortex, horseshoe vortex and wake can be interacted. This paper is an experimental study focused on the complex three-dimensional structure in turbulent boundary layer interacting with the inclined cylinder. Correlation between time averaged normal-stress and shear-stress over the flat surface established an inclined cylinder is discussed. The static pressure is measured for the time averaged normal-stress and oil film flow visualization is conducted to investigate the direction of shear-stress. Inclined streamwise and spanwise cylinders at several inclined angles are installed on the flat surface where 2-D turbulent boundary layer is developed. Weak correlation between normal-stress and shear-stress is observed at upstream of the inclined cylinder. On the other hand, strong correlation is reported at downstream of the cylinder.

Nomenclature Cpw = wall static pressure coefficient normalized by the dynamic pressure D = diameter of cylinder (D = 30 mm) ReD = Reynolds number Ur = reference velocity (Ur = 13.0 m/s, ±1.0 %) X, Y, Z = Cartesian coordinate system = pitch angle of inclined spanwise cylinder 1 = angle between bisector of the tunnel and separation point

1 Professor, Mechanical Systems Engineering, 5000-1 Toyohira, Chino, Nagano, AIAA Senior Member 2 Assistant, Mechanical Systems Engineering, 5000-1 Toyohira, Chino, Nagano, AIAA Member 3 Engineer, Recruit R&D Staffing. 1-3-20 Unomori, Yokkaichi, Mie, Non AIAA Member 4 Engineer, ANA Aircraft Maintenance co. Ltd., 3-8-1 Minowa, Toyonaka, Osaka, Non AIAA Member 5 Engineer, Nideco Copal Co., 6-3-48 DAimnn, Shiojiri,Non AIAA Member 6 Engineer, ART Metal MFG Co. Ltd, 2-2-43 Tokiwajo, Ueda, Nagano, Non AIAA Member

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-1441

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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2 = angle between bisector of the tunnel and boundary of the wake line at inclined-side x, z = streamwise shear stress and spanwise shear stress = yaw angle of inclined streamwise cylinder + = inclined downstream cylinder (IDC) = inclined upstream cylinder (IUC)

I. Introduction number of investigators have been concerned with the problems of formation and development of three-dimensional structure in turbulent shear flow. One of the research works about complex turbulent shear flow is

the flow around a bluff body, and a circular cylinder is commonly tested as a base case. The wake of a cylinder is oscillated even at low Reynolds number by Karman type of vortex. The non-dimensional shedding frequency of the oscillation in a wake is basically constant at wide range of Reynolds number. On the other hand, the vortex structure and shedding frequency are affected by the inclined direction and the inclined angle of the cylinder. Furthermore, the effects of horseshoe vortex must take into account when the cylinder is established on the flat-surface. The interaction between Karman vortex, horseshoe vortex and wake is the primary interest for the investigator. The circular cylinder established on a flat-surface includes several complex problems in the structure of the flow field. First problem is the interaction between boundary layer and the flow around the cylinder. This results in the interaction between horseshoe vortex and Karman vortex. Second problem is the inclined angle and the inclined direction of the cylinder. The inclined angle, even it is small, also affects on the three-dimensionality of the wake structure. Third problem is the end effects of the cylinder. Close to the surface, basically, a horseshoe vortex affects on the near surface structure, and an arch vortex also affects on the wake of the cylinder when another end of the cylinder is not fixed to the surface. Many are the cases that the wake of cylinder interacts with the boundary layer when the cylinder is established on the surface. Then, the near surface structure of the wake is changed and the shedding frequency of the wake becomes oblique. Last problem is the turbulence of the approaching free-stream. Gerrard (1966) reported the formation region of a Karman vortex in the wake. Humphreys (1960) presented the spanwize change of flow field close to the cylinder. The characteristics of Karman vortex based on the Strouhal number at very low Reynold number were reported by Williamson (1989), the transition region were reported by Humphreys (1960) and the critical Reynolds number region were presented by Bearman (1969). The structure of the wake far downstream of the cylinder was reported by Cimbala et al. (1988). The effects of inclined angle on the Strouhal number of circular cylinder were reported by Hanson (1966), Van Atta, (1968), Smith et al. (1972) and Mangalam et al (1994). Shizawa et al. (1998) reported that the twin type of vortex was observed in the wake, in case of inclined backward cylinder. Eckerle and Langston (1987) presented a new aspect of the formation of horseshoe vortex around the circular cylinder. Eckerle and Awad (1991) shown that the types of vortex formation were classified into two and proposed the flow parameter following the classification of the flow field. Gerich and Eckelmann (1982), Eibeck (1990) and Stansby (1974) reported the end effects of cylinder on the shedding frequency and the wake structure. Ramberg (1983) concluded that the end condition affects very sensitive to the formation of the vortex shedding. There is only a little information about wake downstream of an inclined cylinder interacting with the boundary layer. This paper reports an experimental study focuses on the complex three-dimensional structure in turbulent boundary layer as a base case of the influence of the inclined cylinder, with particular emphasis on the wall region. There are expected that the complex interaction between horseshoe vortex, Karman vortex and wake. Time averaged distribution of normal-stress and shear–stress over the flat-surfaces established on an inclined cylinder are presented experimentally. The time averaged normal-stress over the surface is to investigate the static pressure. The direction of shear stress is examined by oil film flow visualization. These results of the paper are the useful information to understand the structure of the wake under the influence of inclined streamwise (X-direction) cylinder and inclined spanwise (Z-direction) cylinder at several inclined angles interacting with the boundary layer.

II. Experimental Setup and Techniques

A. Experimental Setup An inclined cylinder is established on the bisector of the wind tunnel where two-dimensional turbulent boundary layer is developed, as shown in Figure 1. The test tunnel has 700 mm x 230 mm cross section and 3,040

A

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mm in length. A tripping wire of 1.2 mm in diameter is installed at the outlet straight part of two-dimensional contraction nozzle. The cylinder is installed carefully into the wind tunnel with zero-yaw angle to the approaching free-stream in case of inclined streamwise cylinder as shown in Figure 1 (1). Also, the cylinder is set with zero-pitch angle in case of inclined spanwise cylinder as shown in Figure 1 (2). The root of the cylinder is carefully attached and shielded to the surface to avoid the leakage from the point of contact. The blockage factor of the cylinder diameter to the width of wind tunnel is 4.3 %. Then, the effects of side walls on the structure of the cylinder wake are negligible. The favorable streamwise pressure gradient is obtained because the wind tunnel has constant cross section. The boundary layer parameters at the origin of the coordinate system are shown in Table 1.

The circular cylinder has D = 30 mm in diameter and covers the whole height of the wind tunnel as shown in Figure 2. The surface roughness of each cylinder is less than 2 m to minimize the effects of roughness on the separation over the cylinder surface. The aspect ratio of the tunnel height to the cylinder diameter is 7.7. Nine cases of streamwise inclined angle of = ±30°, ±20°, ±15°, ±10° and 0° to the free stream are investigated. On the other hand, four cases of spanwise incline angle of = 30°, 20°, 15° and 10° to the free stream are also investigated. The cylinder is established on lower surface of the wind tunnel where two-dimensional turbulent boundary layer is developed. The boundary layer thickness is about the same order as the cylinder diameter. All the measurements are conducted over the lower surface. Then, the cylinder is merged in the same turbulent boundary layer thickness. The negative angle corresponds to an inclined forward cylinder (IFC), and the positive angle corresponds to an inclined backward cylinder (IBC) in case of inclined streamwise cylinder, respectively. On the other hand, the positive angles are selected in case of inclined spanwise cylinder (ISC). The coordinate system employed is also shown in Figure 1. The origin of streamwise X-direction is set at the center of the cylinder, Y-direction is the normal distance from the surface and Z-direction is the spanwise direction. The reference velocity at the reference location of X = 2,260 mm is Ur = 13.0 m/s (±1.0 %) and the turbulence intensity is 0.2 %.

B. Experimental Technique An oil film flow visualization technique is used to measure the direction of wall shear-stress. A black thin PV sheet with 0.8 mm thick painted frosting black paint is carefully installed to the lower surface of the wind tunnel. Firstly, the 'Base Oil', ingredients with (1) Liquid Paraffin: 25 cc, (2) Oleic Acid: 3 cc, (3) Linseed Oil: 1 cc and (4) Titanium Dioxide: 5 g with 0.01 to 0.03 m in diameter of particle is carefully mixed to minimize and equalize the particle size of Titanium Dioxide. The Base Oil is left more than a whole day and night to chemical attraction between Liquid Paraffin and Titanium Dioxide. Before the run, mix again the Base Oil and add Liquid Paraffin to control the viscosity depended on the flow speed and the flow pattern. Followings are the procedure of oil film flow visualization used. (1) Clean up the sheet by Oleic Acid and wipe up perfectly to familiar with Basic Oil, and (2) Spread the small oil spot uniformly by a squirt. Small amount of oil with large number of spots is the better. (3) Beat rhythmically the oil spots on the sheet by the use of moderately larger size of sponge with thin fine texture. Weaker beat is the best. If one beat hardly, oil will form small bubbles. (4) Run the tunnel. (5) Make up the flow pattern roughly on the sheet and stop the tunnel. (6) Spread again the small oil spot with different viscosity depended on the flow pattern. The boundary of each pattern is obtained by the run (5). (7) Run the tunnel again and wipe up the piled oil carefully or locally light up the sheet to dry out the oil. (8) Stop the tunnel after making up the clear flow pattern and the careful treatment of the piled oil. The period of the run of wind tunnel is depends on the oil streak. (9) Take photo of the resultant pattern of oil film. (10) During the run, monitoring the oil flow by video camera is one of the useful information while recognizing and quantitatively analyzing the flow pattern. Wall static pressure is measured by a displacement micro manometer with an accuracy of 0.01 Pa to presents the wall normal-stress qualitatively, because the recognition of correlation between normal stress pattern and shear stress pattern are the most priority subjects of this work. The static pressure tap drilled to the lower surface of the wind tunnel has 0.5 mm in diameter and 2 mm in height. The number of static pressure taps on the surface is 462 as shown in Figure 2. The spacing of each tap is 3 mm is the minimum case. The region of pressure measurement is from -210 mm (X/D = -7) to 300 mm (X/D = 10) in streamwise X-direction and ±180 mm (Z/D = ±6) in spanwise Z-direction. The half domain of pressure taps to bisector of wind tunnel plus several lines of pressure taps at spanwise -direction, opposite side to the bisector of wind tunnel, are also measured to check the symmetric pattern of pressure distribution. On the other hand, all 462 taps are used to measure the static pressure in case of inclined spanwise cylinder because the flow pattern would present an asymmetric profile to the bisector.

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Uncertainties in measurements, calculated using the method of Kline and Mclintock (1953) are ±3 % for static pressure to the dynamic pressure at the reference point of X = -150 mm. The result is a ±0.3 mm uncertainty for the oil width by the oil film flow visualization.

III. Results and Discussions

A. Inclined Streanwise Cylinder The upper half of each Figure 3 shows the results of oil film flow visualization and the lower half presents the contours plot of wall static pressure coefficient in case of inclined streamwise cylinder. Figure 3 (1) presents the case of inclined streamwise angle of 15° and Figure 3 (2) corresponds inclined angle of 20°. Figure 3 (a) shows the flow pattern of IFC and Figure 3 (b) is the case of IBC, respectively. In case of inclined streamwise cylinder, the results both are expected symmetric to the bisector of the wind tunnel. Then, it is enough to present a half of each Figure. The flow is left to right and the distances are normalized by the diameter of the cylinder of D = 30 mm. The positive pressure is presented in warm colors and negative pressure is shown in cool colors in the wall static pressure distributions. As shown in upper Figures of oil film flow visualization, the separation point is observed at the upstream of the cylinder. The separation point is located much longer way off from leading edge of the cylinder in case of IFC compared with the case of IBC. The separation point and following separation line, and low mean shear stress line are the footprint of the presence of horseshoe vortex. Then, the limited stream-lines wrapped around the cylinder and converged to downstream in case of IFC. The limited stream-line at the wake of cylinder shows recirculation and the region of recirculation is expanded both in streamwise and spanwise direction as the inclined angle is increased from -15º to -20º. On the other hand, the limited stream-lines of the wake are diverged in case of IBC and the effects of inclined angle on the limited stream-lines are apparently small. The upstream extent of horseshoe vortex is larger in case of IFC compared with IBC. Footprint of horseshoe vortex is converged in case IFC and diverged in case of IBC at downstream of the cylinder. The effect of inclined angle of the cylinder is large in case of IFC and the extent of horseshoe vortex is expanded both streamwise and spanwise direction. In case of upstream contours plots of static pressure coefficient on the flat surface as shown in lower Figures, the high pressure contours are increased going toward leading edge of the cylinder and the contours are enveloped in an isosceles triangle, the summit of it is to the stagnation point of the cylinder (X/D = -0.5 and Z/D = 0.0). The vertical angle of the isosceles triangle is smaller in case of IFC compare with IBC. Larger extent of high pressure region is observed in case of IFC. On the other hand, the change of vertical angle is small in case of IBC and the reduction of pressure coefficient is large as the change of inclined 15º cylinder to the 20º one. The effects of inclined angle on the upstream surface static pressure of the inclined cylinder are much larger in case of IBC. In case of downstream profile of the static pressure coefficient, the remarkable differences between IFC and IBC are observed. In case of IFC, the pressure recovers from X/D = 0.5 to X/D = 3.0 and the profile presents as a series of circles that touch each other tangentially at the stagnation point of trailing edge of the cylinder. On the other hand, in case of IBC, the pressure recovers faster from X/D = 0.5 to X/D = 1.0. The minimum pressure is shown at symmetric locations to the bisector of the wind tunnel (Z/D = 0.0) and is about 65 % lower in case of IBC. The pressure recovery processes at downstream of the cylinder have larger differences between IFC and IBC. The pressure recovers as the series of circles that touch each other tangentially at the stagnation point in case of IFC. On the other hand, the pressure recovers along diagonal line in case of IBC. The faster recover of pressure is observed in case IBC. Figure 4 presents the spanwise distribution of wall static pressure coefficient. The maximum values of wall static pressure at X/D = 4.0 where is the most downstream location in Figure 3 are shown at Z/D = 1.0 and Z/D = 1.5 at inclined angle of -15º and -20º cylinder in case of IFC (open symbol), respectively. Then the higher pressure region is shifted to spanwise direction as the increase of inclined angle. The results make clear that the recirculation region is developed as the increase of inclined angle in case of IFC. The spanwise location of minimum pressure and the minimum value show little differences between = -15º and = -20º and is almost the same from X/D = 0.5 to X/D = 1.5 in case of IFC. In case of IBC (solid symbol) of X/D = 0.5, this station is the tangent line of trailing edge of inclined cylinder on the surface, the spanwise location of the minimum peak in static pressure is observed about Z/D = 0.2 in spite of the inclined angle. The value of minimum peak is increased as the increase of streamwise distance. Also the spanwise location of the peaks of X/D = 1.1 and X/D =1.5 are shifted spanwaise direction as the increase of

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streamwise distance. The minimum peak is large in case of inclined angle of 20º compared with inclined angle of 15º. Then, the weak normal stress is reported as the increase of inclined angle. The station X/D =1.5 is close to the location of formation region of Karman vortex at normal cylinder.

B. Correlation between stresses in case of inclined streamwise cylinder The correlation between direction of shear stress evaluated by the oil film flow visualization and normal stress evaluated by the contours plots of wall static pressure are the followings. Upstream of the cylinder, the shear stress is distributed like the circle bounded by the separation line and line of low mean shear stress line. The center of each bounded line is roughly the center of the cylinder tested. On the other hand, the normal stress contours are distributed like enveloped in an isosceles triangle and the summit is the stagnation point on the cylinder. The profile both are the results of horseshoe vortex and the weak correlations are observed at the upstream profile of the cylinder. Downstream of the IFC, the region of recirculation of oil film and negative static pressure are almost the same. Also, the spanwise extent of negative pressure and separation line in oil film flow visualization is approximately the same in case of IFC. On the other hand, the region of negative static pressure is different between IFC and IBC. In case of IFC, the area is approximately the same as the horseshoe vortex and the streamwise extent of the area is also roughly the same as the recirculation region. On the other hand, the minimum static pressure downstream of the IBC is shifted spanwaise direction and is away from the bisector of the wind tunnel. The spanwise extent of negative pressure is not corresponded to the region of horseshoe vortex downstream of the cylinder. The weak negative pressure is observed at the wake region. In case of IFC, the strong correlation is observed between normal stress and direction of shear stress, and weak correlation is shown in case of IBC. C. Inclined Spanwise Cylinder Results of oil film flow visualization show the direction of wall shear stress. The quantitative evaluation of wall shear-stress is not presented in this paper. The limited streamline by oil film flow visualization parallel to streamwise X-direction can be possible to figure out the primary shear stress τX and the line parallel to spanwise Z -direction can be represented the secondary shear stress τZ.. The slanted profile of the limited stream line corresponds to the ratio of shear stress between τX and τZ. Figure 5 presents the photo of oil film flow visualization in case of ISC. Flow is left to right and the cylinder is inclined positive Z-direction. Then, the axis of ordinate is positive at lower part and negative at upper part in the Figure following Cartesian coordinate. The limited stream-line should basically symmetric to bisector of the wind tunnel in case of normal cylinder and inclined streamwise cylinder. The effects of ISC are clearly observed even at small inclined angle of 10º. Upstream of the cylinder, the stream-line shows that the stagnation point is shifted to positive Z-direction. Also, the separation line and low mean shear stress line are asymmetric to the bisector of the wind tunnel and also shifted toward positive Z-direction. At the side of the cylinder (Z/D = 0), the distances from the surface of cylinder to separation line are long at positive Z-direction. The remarkable effects of ISC are also observed at downstream of the cylinder. The wake is shifted to positive Z-direction and the boundary of wake is shifted largely at positive Z-direction compare with the negative one. The structure of wake at inclined angle of 30º, the separation line at the side of the cylinder located closer to the cylinder and the positive side of separation line is further away from the cylinder. The upper boundary of wake line is disappeared and the only positive side of the wake line is observed. It might be the results of the deformed horseshoe vortex wrapped around the cylinder. In case of negative side of the cylinder, the high momentum fluid penetrates to the surface. On the other hand, in case of positive side of the cylinder, low momentum fluid is suppressed to the surface. Therefore, the characteristic points and the angles tested in Figure 5 are presented in Figure 6. Followings are the explanation of the characteristic points. Labeled 1 is the separation point at upstream of the cylinder. Label 2: the location of low mean shear stress point at bisector of the wind tunnel, Label 3: the location of separation line, Label 4: separation point on the cylinder, Label 5: node point, Label 6: saddle point, Label 7: location of the edge of the wake line and Label 8: inflection point of the outer edge of the wake. The approaching angle of stagnation point from the origin of the coordinate is defined as 1 in case of upstream. 2 is defined as the angle between bisector of wind tunnel and boundary of the wake located positive-side and the angle is corresponds to the width of wake. Figure 7 presents the characteristic points mentioned above in case of upstream of the ISC. The location of separation point and low mean shear stress point are shifted toward positive Z-direction linearly as the increase of the inclined angle. The low mean shear stress point is located inside of the separation point. Again, the positive Z-direction is the same direction as the inclined direction of the cylinder. The distances between center of the cylinder to the edge of separation line at both sides of the cylinder show Z/D = ±1, in case of

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normal cylinder. Then, the distances are linearly decreased as the increase of the inclined angle. The separation line at negative side of the cylinder shifts toward positive Z-direction. It means that the separation line approaches to the cylinder. On the other hand, the separation line leaves away from the cylinder in case of positive side of the cylinder. These results show that all characteristic points upstream of the inclined spanwise cylinder shift to positive Z-direction as the same as inclined-direction of the cylinder. All the characteristic point is observed linearly shifted within this small spanwise inclined angle. Figure 8 presents the characteristic points in case of downstream of the ISC. As shown in Figure 8 (1), the node point and the saddle point both shift toward positive Z-direction as the increase of the inclined angle. Saddle points both sides of the cylinder shift positive Z-direction as the same slope as the separation and low mean shear stress points upstream of the cylinder as shown in Figure 7. Especially the saddle point located at negative Z-direction in case of normal cylinder shifts across the bisector of the wind tunnel and toward positive Z-location. Furthermore, the saddle point labeled (L) shifts toward positive Z-direction and passes away the node point after inclined angle of 15°. Figure 8 (2) presents the location of the edge of wake and inflection point formed limited stream lines of the wake. The location of the edge of wake and limited streak line of the wake is shifted to positive Z-direction. The location of the wake labeled 7 at negative position changes remarkable. The edge both are shifted to positive Z-direction and the streak lines are coincides each other. The deformation of horseshoe vortex is supposed following to the inclined spanwise angle. D. Correlation between stresses in case of inclined spanwise cylinder Figure 9 presents the same pattern as Figure 3 but these Figures show ISC case. The upper photo presents the results of oil film flow visualization and the lower Figure shows the contours plot of coefficient of wall static pressure. The Figure coded (1) to (4) corresponds to the inclined angle of 10° to 30°, respectively. The Figure coded (a) presents the result of minus side of the test surface in spanwise-direction and the Figure coded (b) presents the plus side of the test surface. Again, plus side of the test surface corresponds to the inclination direction of the cylinder. As shown in Figure 9 (1-a) and Figure 9 (1-b), the contours of static pressure at upstream of ISC, the contour is enveloped in an isosceles triangle and the summit is the stagnation point as shown at Figure 9 (1-b) of positive side of the Figure. The pressure is increased toward the stagnation point at the leading edge of the cylinder. Upstream of the cylinder, the stagnation point is not defined from the oil film flow visualization. Then the stagnation point is defined by the mid location of high static pressure region on the cylinder colored red. Then, the stagnation point is shifted positive Z-direction. The separation point over the root of cylinder is the firstly detached point by oil film flow visualization as shown in upper Figure. On the other hand, the separation point over the root of cylinder is closely the same as the location where the pressure coefficient is zero. The point is colored yellow in Figure 9 and the points both at negative and positive side of the cylinder are almost coincide with the location observed at the results of flow visualization. The separation point is clearly different from negative side of the inclined cylinder and positive side, as shown in Figure 9 (1-a) and Figure 9 (1-b). The separation point is located upstream in case of negative side of the cylinder compared with the location at positive side. It means that the separation point is located larger angle in case of positive side of the cylinder. On the other hand, region of horseshoe vortex, the separation region, over the surface observed at flow visualization is corresponds to the negative region in static pressure distribution as shown in cool color. The spanwise extent of separation region and negative static pressure region is almost the same as shown in Figure 9 (1-a) and Figure 9 (1-b). The separation region is clearly large in case of positive side compare with the negative side. Downstream of the cylinder, the negative pressure region is closed at the same position of saddle point defined from the photo of flow visualization. Further downstream, the wake region observed at flow visualization there is no footprint of wake started from trailing edge of the inclined cylinder and Karman vortex. Finally, low pressure region is observed at trailing edge of the cylinder. The low pressure region is closely coincided with the location of node point and the point is shifted to positive Z-direction as same as inclination direction of spanwise inclined cylinder. Figure 9 (2), Figure 9 (3) and Figure 9 (4) present the ISC and the inclined angle of = 15°, 20°, and 30° respectively. In case of inclined angle of = 15°, as shown in Figure 9 (2), the differences between the profiles of inclined angle of = 10° and = 15° are apparently small. The detailed observation makes clear the effects of inclined angle on the structure of the flow around the root of the cylinder. First, the stagnation

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point at the reading edge of the cylinder shifts to positive Z-direction as shown in Figure 9 (2-b) both at flow visualization and pressure distribution. The asymmetry of horseshoe vortex to the bisector of the cylinder is remarkable as the increase of the inclined angle of the cylinder. The area of horseshoe vortex at negative side is decreased and the positive side is increased. Second, the separation points at the root of the cylinder are also shifted. In case of negative side of the cylinder, the separation point shifted upstream. On the other hand, in case of positive side of inclined cylinder, the separation point shifts downstream. Third, the shape of horseshoe vortex downstream of the cylinder makes smaller, in case of negative side, and the region makes larger in case of positive side as the increase of inclined angle. The spanwise extent of separation region is smaller in case of negative side and is larger in case of positive side. Fourth, the saddle points at the downstream of the cylinder are also changed as the increase of the inclined angle. The saddle point at negative side of the cylinder shifts downstream in case of inclined angle of = 15° observed both at oil film flow visualization and static pressure. The saddle point located almost on the bisector of the cylinder, as shown in Figure 9 (2-a). The saddle point at positive side shifts upstream. Then, the difference between locations of saddle points at negative and positive side of the cylinder becomes remarkable as the results of increase of inclined angle. Also, the saddle point shifts to streamwise direction as the increase of inclined angle. The saddle point, in case of negative side, shift to downstream as the increase of inclined angle. But, the saddle point at positive side shifts to upstream. These phenomena both are observed in oil film flow visualization and static pressure measurements. Fifth, the node point also shifts to positive Z-direction. The area of negative pressure which corresponds to node pint is increased as the increase of inclined angle of the cylinder. Finally, the footprint of wake observed in the photo of flow visualization is not observed in contours plot of surface static pressure as shown in Figure 9 (2) same as the case of inclined angle of 10° as shown in Figure 9 (1). As shown in Figure 9 (3) and Figure 9 (4), in case of inclined angle of = 20° and 30°, all the effects, as shown above, on the inclined angle are all followed even at this larger inclined angle. The stagnation point at upstream of the cylinder is completely shifted to positive Z-direction and only small region is observed at negative side. The difference of horseshoe vortex is remarkably changed and the spanwise distance is almost equal to the circumference of the cylinder in case of inclined angle is = 30° as shown in Figure 9 (4-a). The saddle point at the downstream of the cylinder, streamwise distance goes larger and larger in case of negative side as the increase as the inclined angle, and is shorter and shorter in case of positive side. The node point close to the downstream stagnation point is completely shifted to positive side of the cylinder. The effects of spanwise inclined angle on the distribution of normal stress and wall shear stress are discussed. The criterion of normal stress is used wall static pressure and wall shear stress is used oil film flow visualization. Upstream of the cylinder, normal stress is increased to the stagnation point at the leading edge of the cylinder. On the other hand, wall shear stress is affected largely by the horseshoe vortex. Therefore, the weak correlation between these stresses is observed at upstream of the cylinder. Also, the structure of horseshoe vortex at the upstream of the cylinder is little correlation between these two stresses until the separation point at the root of cylinder. Downstream of the separation point at the root of cylinder, the separation region owing to the horseshoe vortex with low shear stress region and negative static pressure region are strongly correlated. The highly correlated regions are maintained to the saddle point at the downstream of the cylinder. The separated region in photo of oil film flow visualization has strong correlation between low static pressure regions. The node point obtained from flow visualization and the low pressure region are strongly related. On the other hand, the wake started from node point at the downstream of the inclined cylinder, there has no footprint of the wake in static pressure distribution.

IV. Conclusions 1. The high pressure contours observed at upstream of the cylinder are increased going toward leading edge of the cylinder. The contours are enveloped in an isosceles triangle and the summit is at the stagnation point on the cylinder. 2. The static pressure recovers as the series of circles that touch each other tangentially at the stagnation point in case of inclined forward cylinder. On the other hand, the pressure recovers as the series of circles that touch each other tangentially along diagonal line in case of inclined backward cylinder. The faster recover of static pressure is observed in case inclined backward cylinder. 3. Downstream of inclined forward cylinder, the region of recirculation and negative static pressure are almost the same. Also, the spanwise extent of negative pressure and separation line is approximately the same. In case of

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inclined forward cylinder, the strong correlation is observed between normal stress and direction of shear stress, and weak correlation is shown in case of IBC. 4. All the characteristic points upstream of the inclined spanwise cylinder shift to the same inclined-direction of the cylinder. The separation line and low mean shear stress line are asymmetric to the bisector of the wind tunnel and also shifted toward inclined-direction. At the side of the cylinder (Z/D = 0), the distances from the surface of cylinder to separation line are wider at inclined-side. The saddle point shifts toward inclined-direction and passes away the node point after inclined angle of 15°. 5. The separation point over the root of the cylinder is closely the same as the location where the pressure coefficient is zero. The separation point is located larger angle in case of inclined-side of the cylinder. The spanwise extent of separation region and negative static pressure region is almost the same. 6. The structure of horseshoe vortex at the upstream of the cylinder is little correlation between these two stresses until the separation point at the root of cylinder. Downstream of the separation point, the separation region with low shear stress and negative static pressure region has strong correlation. The highly correlated regions are maintained to the saddle point at the downstream of the cylinder.

Acknowledgments The authors greatly appreciate the collaborative efforts of entire this work to Mr. Tatsuya TAKEMATSU and Mr.

Ryo MIYASHITA who are the under-graduate students in Tokyo University of Science Suwa.

References 1Azuma, A., “The Biokinetics of Flying and Swimming”, Second Edition, AIAA Education Series, 2006. 2Tucker, V, A. “Drag reducatction by Wing Tip Slots in a Gliding Harris’Hawk, Parabuteo Unicinctus”, The Jounal of Experimental Biology, 198, 1995, pp. 775－781. 3Drovetski, S, V. “Influence of the Trailing-Edge Notch on Flight Performance of Galliforms”, The Auk, Vol. 113,No. 4, 1996, pp. 802－810. 4Roche, U, La., and Roche, H , L, La., “Induced Drag Reduction using Multiple Winglet, looking beyond the Prandtl-Munk Linear Model(rev.05)”, AIAA Paper 2004-2120, 2004. 5Lazos, S, B., and Visser , K, D., “Aerodynamic Comparison of Hyper-Elliptic Cambered Span(HECS) Wings with Conventional Configurations”, AIAA Paper 2006-3469, 2006. 6Smith, M, J., Komerath, N., Ames, R., Wong, O., and Person, J., “Performance Analysis of a Wing with Multiple Winglet”, AIAA Paper 2001-2407, 2001.

7Isogai, K., Shinmoto, Y., and Watanabe, Y., “Effects of Dynamic Stall on Propulsive Efficiency and Thrust of Flapping Airfoil”, AIAA Journal, Vol. 37, No. 10, 1999, pp. 1145 – 1151.

8Sunada, S., Kawachi, K., Matsumoto, A., and Sakaguchi, A., “Unsteady Forces on a Two-Dimensional Wing in Plunging and Pitching Motion”, AIAA Journal, Vol. 39. No. 7, 2001, pp. 1230 – 1239.

9Parker, K., Soria, J., and von Ellenrieder, K. D., Thrust Measurements from a Finite-Span Flapping Wing, AIAA Journal, Vol. 45, No. 1, 2007, pp. 58 – 70.

10Isaac, K. M., Rolwes, J., and Colozza, A., 2008, Aerodynamics of a Flapping and Pitching Wing Using Simulation and Experiments, AIAA Journal, Vol. 46, No. 6, 2008, pp. 1505 – 1515. 11Spedding, G, R., Hedenstorm, A. and Rosen, M., “Quantitative Studies of the wakes of Freely Flying Birds in a Low-Turbulence Wind Tunnel”, Experimental in Fluid, 34, 2003, pp. 291-303. 12Albertani, R., “Wind-Tnnnel Study of Gurney Flaps Applied to Micro Aerial Vehicle Wing”, AIAA Journal, Vol. 46, No. 6, 2008, pp. 1560 – 1562.

13Jones, A. R., and Babinsky, H., “Leading EdgeFlaps at Low Reynolds Numbers”, AIAA Paper 2008-424.2008. 14Berger, A. J., Bird Study, Dover, 1961.

Table 1 Boundary layer parameters

mm

mm

ReD Re2

Boundary layer 32.3 3.47 2.6 x 103 3,500

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(1) Streamwise (X-direction) inclined cylinder (2) Spanwize (Z-direction) inclined cylinder

Fig. 1 Experimental setup (Dimensions in mm)

Fig. 2 Surface static pressure taps drilled around streamwise inclined cylinder

(1-a) Inclined forward -15° cylinder (1-b) Inclined backward +15° cylinder

(2-a) Inclined forward -20° cylinder (2-b) Inclined backward +20° cylinder

Fig. 3 Oil film flow visualization and contours of surface static pressure (upper: oil film, lower: static pressure)

FlowFlow

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(1) Cpw at ± 15˚ (2) Cpw at ± 20˚

Fig. 4 Spanwise distribution of surface static pressure in case of streamwise inclined cylinder

(1) ISC+10° (2) ISC+15°

(3) ISC+20° (4) ISC+30°

Fig. 5 Photo of oil film flow visualization in case of spanwise inclined cylinder (ISC)

(1) Upstream (2) Downstream

Fig. 6 Characteristic points and definition of angle 1 and 2

0 1 2 3–1.2

–0.8

–0.4

0

0.4

Z/D

Cp

w

②

1.5

①+15° = –15°

4.0

X/D0.5

1.1

θ

0 1 2 3–1.2

–0.8

–0.4

0

0.4

Z/D

Cp

w

+20° = –20°①

②

1.54.0

X/D0.51.1

θ

0˚-β˚

β20°

β˚

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Fig 7 Characteristic points at upstream

(1) Location of node and saddle point (2) Location of edge of limited stream line

Fig. 8 Characteristic points on downstream

0 10 20 302

1

0

-1

-2

Z/D

① Saparation② Low mean shear stress③ Separation line (L)③ Separation line (R)④ Separation on cylinder (L)

θ

0 10 20 301

0.5

0

-0.5

⑤ Node⑥ Saddle (L)⑥ Saddle (R)

θ

Z/D

0 10 20 301

0.5

0

-0.5

θ

Z/D ⑦Wake (L)

⑦Wake (R) ⑨Inflection point

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(1-a) Inclined spanwise +10° cylinder (minus side) (1-b) Inclined spanwise +10° cylinder (plus side)

(2-a) Inclined spanwise +15° cylinder (minus side) (2-b) Inclined spanwise +15° cylinder (plus side) (3-a) Inclined spanwise +20° cylinder (minus side) (3-b) Inclined spanwise +20° cylinder (plus side)

(4-a) Inclined spanwise +20° cylinder (minus side) (4-b) Inclined spanwise 20° cylinder (plus side)

Fig 9 Oil film flow visualization and contours of wall static pressure (upper: oil film, lower: static pressure)