Schlieren study of circular and square cylinder wakes: Effect of buoyancy and oscillation This presentation contains videos of schlieren patterns generated during flow past circular and square cylinders. The effect of heating and cylinder oscillation on the wake patterns is investigated. The experimental apparatus from which the images have been recorded is also described. The overall flow is in the vertically upward direction. Cylinder oscillations across the flow (transverse) and along (inline) are considered. 1 1

Experimental apparatus The schematic drawing of the experimental apparatus is shown here. The flow is created in a vertical test cell by using the suction side of a blower. The cylinder axis is horizontal. The cylinder is internally heated to create thermal gradients in the flow. These gradients are then imaged as schlieren patterns. The cylinder is held on electromagnetic actuators to provide the necessary oscillatory movement as a function of both frequency and amplitude. The schlieren imaging system has a laser and a camera. Optical glass windows are employed where the light beam enters the apparatus. Images are recorded in the computer in a time sequence. 2

Photographs These are photographs of the components of the experimental apparatus. The overall assembly is seen on the right. 3

Calibration of actuators Flow geometry Without Circular Square Circular Square load inline inline transverse transverse Various modes of oscillation of cylinders with square and circular cross-sections are shown. The amplitude of oscillation is determined from images of the cylinder motion under unheated conditions. Sample videos can be seen by clicking on the respective images. Oscillation geometry 4

Influence of Buoyancy 5

Suppression of vortex shedding (Circular cylinder) T∞ =21oC Tw = 40oC 60oC 75oC 77oC 79oC 80oC 82oC Schlieren patterns formed in the wake of a stationary circular cylinder are shown here for various temperature differences between the cylinder wall and the incoming fluid. Buoyancy effects become stronger at higher temperature differences, ultimately resulting in the suppression of vortex shedding. Click on each image to see the video. 40oC : Vortex shedding from opposed shear layers. 60oC and 75oC : More distinct Shedding. Fringes inside the vortices. 77oC : Detached shear layer is elongated like slenders. 79oC and 80oC : Thin plume slowly oscillates in transverse direction. 82oC : Plume becomes steady depicting suppression. Cylinder Flow Re = 110 6

Suppression of vortex shedding (Square cylinder) T∞ =23oC Tw = 40oC 45oC 55oC 58oC 60oC 63oC 70oC These are individual videos of vortex shedding from a square cylinder that is heated with respect to the incoming flow. The main flow is in the vertically upward direction. As the temperature difference between the cylinder surface and the incoming fluid increases, buoyancy effects become significant. Ultimately, vortex shedding is suppressed and a steady plume is obtained. 40oC and 45oC : Regular Vortex shedding. 55oC : Distinct vortex Shedding with more no. of fringes in the wake. 58oC : Fringes inside the vortices means temperature distribution. 60 oC : Detached shear layer is more elongated. 63oC : Mild unsteadiness of the shear layer. 70oC : Single steady plume at the centre of the cylinder. Cylinder Flow Re = 109 7

transverse oscillation Influence of buoyancy and transverse oscillation 8

Effect of excitation frequency Circular cylinder Re = 105 T∞ =24oC Square cylinder Re = 116 T∞ =25oC Tw = 37 oC 51 oC 68 oC 76 oC Tw = 35 oC 55 oC 68 oC 86 oC Stationary Cylinder (fe/fs=0) Regular alternate vortex shedding at lower Ri. With increase in Ri, length of heated zone increases with higher number of interference fringes and finally at critical Ri, the wake degenerates into a thin elongated steady plume at the centre of the cylinder depicting suppression of vortex shedding. a/d=0.08 Fundamental oscillation Vortex patterns in the wakes of circular and square cylinders are shown for mild and strong heating conditions. For a stationary cylinder, buoyancy leads to suppression of vortex shedding. The second row shows images for cylinders transversely oscillated at the vortex shedding frequency of an unheated cylinder. Here, buoyancy is not adequate to suppress vortex shedding even at the highest heating level. (fe/fs=1) One vortex is alternatively shed from each shear layer in one oscillation cycle. Inclination of the vortices with wake centreline is greater resulting in enhanced interactions compared to the stationary cylinder. At higher Ri, large size vortices are formed. At critical Ri, the vortex shedding reappears for the oscillating cylinder. 9

Effect of excitation frequency Circular cylinder Re = 105 T∞ =24oC Square cylinder Re = 116 T∞ =25oC Tw = 37 oC 51 oC 68 oC 76 oC Tw = 35 oC 55 oC 68oC 86 oC a/d=0.08 Sub-harmonic oscillation (fe/fs=0.5) Two vortices from each shear layer are shed in one oscillation cycle except at critical Ri for both the cylinders. At critical Ri, only one vortex from each side shear layer is shed in one oscillation cycle. Non-harmonic oscillation (fe/fs=1.5) These videos show vortex shedding patterns from heated cylinders – circular and square. The cylinders are transversely oscillated at 0.5 times and 1.5 times the frequency of vortex shedding from an unheated cylinder. At lowest Ri, two vortices from each shear layer are shed for every three oscillation cycles for the circular cylinder and one vortex from each shear layer is shed in one oscillation cycle for the square cylinder. With increase in Ri, vortex formation is periodic with fe. However, shed vortices initially show irregularity and loss of coherency. 10

effect of excitation frequency Circular cylinder Re = 105 T∞ =24oC Square cylinder Re = 116 T∞ =25oC Tw = 37 oC 51 oC 68 oC 76 oC Tw = 35 oC 55 oC 68 oC 86oC a/d=0.08 Super-harmonic oscillation (fe/fs = 2) At lowest Ri, one vortex from each shear layer is shed for every two oscillation cycles for the circular cylinder and one vortex from each shear layer is shed in one oscillation cycle for the square cylinder. With increase in Ri, vortex formation is periodic with fe. However, shed vortices show small intermittency which disappears at the highest Ri. Super-harmonic oscillation These videos show vortex shedding patterns from heated cylinders – circular and square. The cylinders are transversely oscillated at twice and three times the frequency of vortex shedding from an unheated cylinder. (fe/fs = 3) At lowest Ri, one vortex from each shear layer is shed for every three oscillation cycles for the circular cylinder and one vortex from each shear layer is shed in one oscillation cycle for the square cylinder. With increase in Ri, vortex formation is periodic with fe. Much difference in the shape of the vortices are seen between the two cylinders. 11

Influence of buoyancy and Inline oscillations 12

Effects of oscillation frequency Tw = 34 oC 45 oC 63 oC 77 oC Circular cylinder Tw = 34 oC 45 oC 63 oC 77 oC Re=104 a/d=0.08 Unperturbed flow fe/fs=1 Antisymmetric Symmetric Regular vortex shedding at lower Ri and at elevated temperature the wake degenerates into a steady plume. Mode switching at lower Ri (forced convection regime). Symmetric vortex shedding at higher Ri. Steady plume transformed into symmetric vortex structures at suppression. fe/fs=1.5 These are videos of wake patterns formed during flow past a heated circular cylinder with and without inline oscillations. fe/fs=2 The alternate vortex shedding is transformed into symmetric vortex shedding for all the Richardson number considered. Shedding is alternate but size, shape and period of vortex structures are different than that of a stationary cylinder. Two vortices are shed during each cycle of cylinder oscillation. 13

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