Effects of separation distance on the vortical behaviour of jetimpingement

Effects of separation distance on the vortical behaviour of jetimpingement upon convex cylinders Long Jiao 1,* and New Tze How 1 1: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore * Correspondent author: long0032@e.ntu.edu.sg Abstract An experimental investigation based on laser-induced fluorescence (LIF) and digital particle image velocimetry (PIV) was conducted to provide a detailed understanding of Re=2000 circular jet impingements upon convex cylinders around their convex surfaces and along their straight edges. Detailed flow visualization analysis of the jet impinging behaviour clarifies the formation and growth of primary vortices, secondary vortices, as well as separation and breakup of the vortex-pairs, when the jet-cylinder separation distance was varied. Results show that, as the separation distance decreases, the vortex formation, separation and breakup locations will be delayed further along the convex surface. Additionally, whether jet shear layer vortices are formed before the jet impinges upon the cylindrical surface strongly influences subsequent vortex structure formation and developments. Furthermore, flow recirculation regions are observed to form at the cylinder lee-sides, which increases in physical size when the separation distance increases. These flow changes as the separation distance varies imply significant changes to jet-impingement based convective heating/cooling applications. Lastly, the effects of separation distance on the mean velocity and vorticity distributions are presented and show good agreements with the flow visualization results. 1. Introduction It is well-known that significant convective heat transfer can result from jet impingements upon solid boundaries and jet-impingement based cooling/heating has seen applications in areas such as cooling of electronic components and turbine blades. Research has shown that the cooling/heating efficacy is not simply a straight-forward function of the jet bulk velocities and temperature difference between the jets and the solid boundaries, but also dependent upon other factors such as the jet-to-surface separation distance and the surface geometry (Zuckerman and Linor, 2006). Most studies conducted so far focused either upon the flow dynamics or heat transfer behaviour of jet-impingements upon flat surfaces, such as Popiel and Trass (1991), Hammad and Milanovic (2011) and Hassan et al (2012), among many others. On the other hand, jetimpingements upon other surface geometries, such as circular cylinders that possess convex surfaces, are comparatively less well-understood, especially in terms of their resultant vortex structures and dynamic flow behaviour. While Cornaro, Fleischer and Goldstein (1999), Fleischer, Kramer and Goldstein (2001), Gilard and Brizzi (2005) and Sharif and Mothe (2010) had conducted related studies in the past, the present study seeks to shed more light through even more detailed flow visualizations and measurements, so as to seek more understanding into the flow dynamics. Hence, an experimental study was undertaken to investigate the effects of separation distance on jet-cylinder impingement behaviour 2. Experimental setup The study was performed in a recirculating water jet facility shown in Fig. 1. Water was channelled from a small reservoir into the jet apparatus by a centrifugal pump, before exhausting from a circular nozzle into the water tank. Before entering the jet apparatus, the water flow rate was controlled by a needle valve and monitored by an electromagnetic flow meter. The jet apparatus consisted of a diffuser, honeycomb flow straighteners, three layers of fine screens and a 25:1 ratio contraction chamber to straighten the flow and reduce the initial jet turbulence level. The water height in the tank was also maintained constant throughout the entire study by diverting excess water back into the small reservoir via two PVC pipes attached at the end wall of the water tank. For the experiments, a d=20mm diameter circular jet exhausting at a Reynolds number of Re=Ud/ν=2000 was used to impinge upon a D=40mm diameter round cylinder. The relative surface curvature was D/d=2. Three different jet-cylinder separation distances of H/d=1, 2 and 4 were investigated, where the separation distance was defined as the distances between the jet exit and cylindrical surface. - 1 -

Fig. 1 Schematics of the recirculating water-tank and associated experimental setup Laser-induced fluorescence (LIF) technique was used to visualize the vortex structures and it was realized by premixing the jet fluid with fluorescein disodium salt uniformly and illuminating it with an appropriatelylocated thin laser sheet produced by a 1W, 532nm wavelength, LaVision continuous-wave diode-pumped solid state (DPSS) laser with sheet-forming optics. Top-view and side-view (relative to the cylinder) LIF visualizations were performed and recorded by a digital single-lens-reflex (DSLR) camera with a f/1.4, 50mm lens. Still flow images were then extracted from the digital videos on a workstation for subsequent analysis. A Dantec Dynamics 2D particle-image velocimetry (PIV) system comprising of an Evergreen double-pulsed Nd:YAG laser, four-megapixel FlowSense CCD camera, synchronization and frame-grabber cards was used to conduct the DPIV experiments. In order to track the dynamics of the jet-impingement behaviour well, the CCD camera was subjecting to 2 1 CCD binning, which allowed capturing of particle-pairs at 2048px 1024px resolution at 14Hz. Measurements were conducted for half of the symmetric flow fields to show the intricate developments during the flow life-cycle. This was possible as the visualized flow fields demonstrated highly symmetrical flow behaviour about the flow symmetry plane. 20µm sized, 1.03g/cm 3 polyamide seeding particles were dispersed in both the jet fluid and water in the tank prior to the PIV experiments. Control of the DPIV experiments, transfer and post-processing of the particle images were performed using Dantec DynamicStudio TM software. A two-step multi-grid cross-correlation scheme with initial and final interrogation window sizes of 128px 128px and 32px 32px respectively were used to determine the raw velocity vectors. These vectors were subsequently subjected to peak, range and movingaverage validations to remove any spurious vectors, before their substitute vectors were calculated from a 3- point by 3-point neighbourhood scheme to obtain the final velocity vector maps that were used to derive other flow quantities. 3. Results and Discussions 3.1 Flow visualization results Before presenting the results, it should be noted that several jet impingement flow characteristics will be discussed here, including the primary vortex initiation location (X p ), vortex separation location (X s ) and vortex breakup location (X b ). Note that X p is where an instability wave first occurs in the free jet-shearing layer, while X s is where the fluid flow separates from the convex surface. On the other hand, X b denotes where the flow transits to a more turbulent one. These characteristics were quantified either along the convex surface or side surface of the cylinder from the top-view and side-view visualizations respectively. Note that these locations were discerned from instantaneous flow sequences over a few flow cycles, some - 2 -

Fig. 2 Time-sequenced top-view LIF images of the Re=2000 jet impinging on a D/d=2 cylinder at a separation distance of H/d=1. Flow images were captured from the top-view and jet flow is from the left towards the right. inherent uncertainties exist and the characteristic locations will hence be presented in value ranges. However, as will be seen later, these ranges are sufficiently apart such that distinct flow trends can nonetheless be discerned. (a) Top-view of jet-impingement behaviour Time-sequenced images for the circular jet impingement upon the D/d=2 cylinder at a separation distance of H/d=1 are presented in Fig. 2. As the cylinder was blocking the camera view during the experiments, the camera had to be positioned slightly sideways to capture the full flow sequence after the jet impinged upon the cylindrical surface. The figures show that after the jet impinges upon the cylindrical surface, primary vortices will be formed along the jet shear layer at close to the maximum cylindrical blockage location. Note that no primary vortices are formed before prior to jet impingement. Thereafter, they grow in size as they convect along and separate from the convex surface. Further along the cylindrical surface, secondary vortices will form as a result of local wall boundary layer separations and flow reversals. Subsequently, adjacent primary and secondary vortices will pair up together to produce highly regular mushroom-shaped vortexpairs that separate from the cylindrical surface. Occasionally, vortex-merging occurs whereby a downstream vortex-pair is caught up by and merged with an upstream vortex-pair. As a result of the merging process, the flow field will transit into a significantly more turbulent state further downstream. Interestingly, instead of separating and moving away from the cylindrical surface at this point, the vortex-pairs will continue to more or less follow the cylindrical surface contour and convect towards the cylinder lee-side to form a relatively narrow wake region as shown in Fig. 2(f). When the separation distance is increased to H/d=2, the flow is largely similar to that of the H/d=1 case (and hence their results are not included here), except that the previously mentioned vortex locations will typically occur closer to the impingement point. Note however that the vortex-merging process is less likely to manifest here as the distances between two consecutive vortex-pairs are typically larger than those observed for H/d=1 separation distance. Lastly, a wake region is also observed at the cylinder lee-side, despite a doubling of the separation distance from H/D=1 to 2. Lastly, at a relatively large separation distance of H/d =4 as shown in Fig. 3, well-formed primary vortices are formed prior to the jet impingement upon the cylindrical surface. Note that this separation distance is close to the jet potential core length. In this case, the primary vortices start to form along the jet shear layer at approximately two to three jet diameters away from the jet exit and represents the most significant difference between H/d=1 and 2 test cases. Thereafter, they grow in size as the jet flow convects towards the cylindrical surface, before finally impinging it as seen in Figs. 3(a) to 3(c). The impinged primary vortices - 3 -

Fig. 3 Time-sequenced top-view LIF images of the Re=2000 jet impinging on a D/d=2 cylinder at a separation distance of H/d=4. Flow images were captured from the top-view and jet flow is from the left towards the right. Separation distance Primary vortex initiation location (X p ) Vortex separation location (X s ) Vortex breakup location (X b ) H/d=1 73-77 109-153 142-156 H/d=2 45-66 81-129 117-144 H/d=4 2d-2.1d 72-98 89-116 Table 1 Summary of X p, X s and X b for jet impingement upon the cylinder convex surface due to variations in the separation distance appear to undergo stretching along the cylindrical surface until vortex separation occurs at about the maximum cylindrical blockage location. Secondary vortices are subsequently produced via similar flow mechanisms as before, though it should be noted that the resulting vortex-pairs are physically larger than those observed for the H/d=1 and 2 test cases. Thereafter, merging of adjacent vortex-pairs proceeds in similar fashion as observed in earlier test cases. Furthermore, it is interesting to note that the wake region is also significantly wider than the earlier test cases when the separation distances are smaller. This indicates that the vortex structures and behaviour are sensitive towards the initial jet flow conditions just prior towards the jet impingement, particularly whether primary vortices are formed before the impingement point. Table 1 summarizes and compares the differences in the primary vortex initiation, vortex separation and vortex-breakdown locations. Increasing the separation distance has strong effects on all the three jet impingement characteristics. In particular, with a larger separation distance, primary vortices appear earlier and the vortex-pairs separate and break up sooner. This signifies that the jet flow tends to detach away from the cylindrical surface earlier, which would unlikely to be favourable if a more uniform heat transfer distribution is desired in actual applications. - 4 -

Fig. 4 Time-sequenced side-view LIF images of the Re=2000 jet impinging on a D/d=2 cylinder at a separation distance of H/d=1. Flow images were captured from the side-view but the jet flow is depicted from the top towards the bottom. Fig. 5 Time-sequenced side-view LIF images of the Re=2000 jet impinging on a D/d=2 cylinder at a separation distance of H/d=4. Flow images were captured from the side-view but the jet flow is depicted from the top towards the bottom. (b) Side-view of jet-impingement behaviour Figure 4 shows the flow visualizations captured along the side-views of the cylinder for H/d=1 separation distance. For such a small separation distance, shear layer wave instabilities only start to form along the cylindrical surface at a distance of approximately one to two jet diameters away from the impingement point. Note that, unlike their counterparts observed from the top-view, these vortices are not as intense and only form sporadically. This is likely due to the significantly more intense vortex-stretching phenomenon and jet flow separations around the convex portion of the cylindrical surface seen earlier, which the flat cylinder surface here cannot reproduce well. Comparing with the earlier top-view results, it is evident that jet-cylinder impingements lead to non-uniform vortex-stretching and vorticity distribution. Flow separations are much milder here and the resulting smaller-scale vortex-pairs convect along the cylinder surface until they separate and break up. Vortex-merging occasionally occurs and it is worthwhile to mention that the merging process typically involves the amalgamation of several vortex-pairs before the entire merged vortex breaks down into incoherence. Similar to the situation observed along the top-view, the flow behaviour is typically the same even when the separation distance is increased to H/d=2. In this case however, most of the primary vortices - 5 -

Separation distance Primary vortex initiation location (X p ) Vortex separation location (X s ) Vortex breakup location (X b ) H/d=1 1.51d-1.67d 2.16d-2.78d 2.82d-3.18d H/d=2 1.13d-1.29d 1.67d-2.08d 2.29d-2.54d H/d=4 2.0d-2.1d 1.38d-1.71d 1.83d-2.21d Table 2 Summary of X p, X s and X b for jet impingement upon the cylinder flat surface due to variations in the separation distance form more coherently after impinging upon the surface. Secondary vortices also form more regularly with the resulting vortex-pairs merged into a single vortex entity. Interestingly, it appears that the number of vortex-pair merging before the single merged vortex breaks down is discernibly lower for this separation distance. When the separation distance is increased further to H/d=4 as shown in Fig. 5, the shear layer wave instabilities, which initiate at a distance of approximately two jet diameters away from the jet exit, roll up into large-scale ring-vortices and grow in size until they impinge upon the flat portion of the cylindrical surface. Thereafter, they deform and convect along the impingement surface before being rapidly stretched radially outwards. Secondary vortices are formed but subsequently entrained by the primary vortices shortly, leading to relatively small-scale vortex-pairs. Subsequent flow behaviour remains more or less the same as before with the most significant differences arising from the vortex separation and break-up locations. Intriguingly, no significant vortex-merging can be observed here and if there are any, the merged vortices are not that apparent due to the merging of only about three to four vortex-pairs. This is a clear departure from the behaviour observed for the smaller separation distance configurations earlier. Table 2 summarizes the key vortex locations associated with the jet impingement behaviour observed along the cylinder flat surface and it can be discerned that their trends are quite similar to those observed for the jet impingement behaviour along the top-view as the separation distance decreases, they occur closer to the impingement point. 3.2 PIV results (a) Top-view of jet-impingement behaviour Figure 6 shows the time-averaged flow streamlines with separation distances from H/d=1 to 4. The mean flow follows more or less the cylindrical surface contour after the jet impinges upon the cylinders. Having said that, minor recirculation regions are found at the cylinder lee-sides in all test cases. This recirculation region becomes wider when separation distance increases, which agrees well with the wake region visualized earlier on. The streamwise velocity component contours, shown in Fig.7, represents a general receding trend in the velocity component distribution as the separation distance increases. This is likely due to the increased rates at which flow transits from laminar conditions to turbulent conditions with corresponding energy dissipation, when the separation distance increases. Furthermore, note that there are two interesting regions shown in the figure: one peak region at the impingement point and another just downstream but before the location of maximum cylinder diameter. Similar to the streamlines, the results show that the jet slows down along its way towards the impingement point, produces a stagnation point upon impingement, turns and follow the cylindrical contour. Mean vorticity contours presented in Fig. 8 follows a similar trend as what is observed in the streamwise velocity component distributions previously. The results show that considerably high jet shear layer vorticity impinges upon the cylindrical surface at the smallest separation distance used here, which gradually reduces as the separation distance increases. Vorticity regions associated with the wall boundary layer separation and formation of secondary vortices are also discernible. Furthermore, the mean vorticity level at - 6 -

Fig. 6 Mean streamlines of the Re=2000 jet impinging on a D/d=2 convex surface at a separation distance of (a) H/d=1, (b) H/d=2 and (c) H/d=4. PIV data were obtained both from locations slightly to the front and back of the test-cylinder in H/d=1 and 2 cases, due to the cylinder blocking the camera view during the experiments. Fig. 7 Mean streamwise velocity component contours of the Re=2000 jet impinging on a D/d=2 convex surface at a separation distance of (a) H/d=1, (b) H/d=2 and (c) H/d=4. the cylinder lee-side region is higher when smaller separation distances are used. These results are consistent with the earlier observations that primary vortices appear earlier and the vortex-pairs separate and break up sooner with increased separation distance. (b) Side-view of jet-impingement behaviour Mean velocity streamlines and vorticity contours for jet impingement upon the D/d=2 cylinder at separation distances of H/d=1, 2 and 4, taken along the side-views of the cylinder are presented in Fig. 9. After - 7 -

Fig. 8 Mean vorticity contours of the Re=2000 jet impinging on a D/d=2 convex surface at a separation distance of (a) H/d=1, (b) H/d=2 and (c) H/d=4. Fig. 9 Mean streamlines and vorticity contours of the Re=2000 jet impinging on a D/d=2 convex surface at a separation distance of (a) H/d=1, (b) H/d=2 and (c) H/d=4. impingement with the test-cylinder, recirculation flows as shown in the figure are produced at all separation distances. In particular for H/d=1 separation distance, there are a number of recirculation regions that cannot be determined which one is the recirculation region. This phenomenon is likely to be due to the fact that the - 8 -

cylinder was located quite close to the tank-wall at such a small separation distance. Similar to the results obtained from the top-view earlier, the mean vorticity levels adjacent to the impingement surface resulting from the jet shear layers decreases with larger separation distances. On the other hand, the vortex strength of the wall boundary layer separation and secondary vortex formation region is comparatively weaker than its counterpart as seen from the top-view. Again, this agrees well with our flow visualization results presented earlier and supports the notion that vortex-stretching phenomenon appears to be significantly more intense vortex-stretching around the convex cylindrical surface than along the flat cylindrical surface. 4. Conclusions An experimental study on the effects of separation distance on the impingement of a circular jet upon a D/d=2 convex cylinder has been carried out. Visualization results show that, while the impingement behaviour around the convex and flat surfaces of the cylinder share some similar trends, there are distinct changes when the separation distance is varied. For instance, the three characteristic impingement vortex locations are closer to the impingement point, spacing between consecutive vortices increases and vortexpair size increases when the separation distance increases from H/d=1 to 2 and 4. However, of particular interest is the formation of a narrower recirculation region at the lee-side of the convex cylinder in H/d=1 and 2 configurations. On the other hand, large-scale vortices resulting from the merging of several vortexpairs tend to form along the cylinder flat surface, with smaller separation distances leading to comparatively larger merged vortex entities. PIV results demonstrate that the jet flow follows more or less the convex cylindrical contour (observed from top-view) or flat cylindrical surface contour (observed from side-view), and that it moves away from the impingement point differently, depending on the exact location. Mean vorticity and streamwise velocity results show that a larger separation distance leads to lower vorticity levels impinging upon the cylinder surface, regardless of exact measurement plane. They also demonstrate the existence of a recirculation region at the cylinder lee-side which grows in size as the separation distance increases. Lastly, vortex strength of the wall boundary separation and secondary vortex formation region is discernibly weaker along the flat cylindrical surface, as compared to the convex cylindrical surface. Acknowledgements The authors would like to acknowledge the financial support provided by Nanyang Technological University for the research study. References Cornaro C, Fleischer AS and Goldstein RJ (1999) Flow visualization of a round jet impinging on cylindrical surfaces. Experimental Thermal and Fluid Science 20(2): 66-78. Fleischer AS, Kramer K and Goldstein RJ (2001) Dynamics of the vortex structure of a jet impinging on a convex surface. Experimental Thermal and Fluid Science 24(3-4): 169-175. Gilard V and Brizzi LE (2005) Slot jet impinging on a concave curved wall. Journal of Fluids Engineering 127(3): 595-603. Hammad KJ and Milanovic L (2011) Flow structure in the near-wall region of a submerged impinging jet. Journal of Fluids Engineering 133(9): 1445-1455. Hassan ME, Assoum HH, Sobolik V et al (2012) Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet. Exp Fluids 52: 1475-1489. Popiel CO and Trass O (1991) Visualization of a free and impinging round jet. Experimental Thermal and Fluid Science 4(3): 253-264. - 9 -

Sharif MAR and Mothe KK (2010) Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces. International Journal of Thermal Sciences 49(2): 428 442. Zuckerman J and Linor N (2006) Jet impingement heat transfer: physics, correlations and numerical modelling. Advances in Heat Transfer 39: 565-631. - 10 -