On the flow structure of an inclined jet in crossflow at low velocity ratios

International Journal of Heat and Fluid Flow 58 (2016) 11–18

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On the flow structure of an inclined jet in crossflow at low velocity ratios C. Dai, L. Jia1, J. Zhang, Z. Shu, J. Mi∗ State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

a r t i c l e

i n f o

Article history: Received 3 May 2015 Revised 1 December 2015 Accepted 2 December 2015

Keywords: Flow structure Inclined jet Low velocity ratio Coherent structure

a b s t r a c t This study investigates the influence of different low velocity ratios on the flow structures of an inclined jet in crossflow (JICF). Experiments are conducted in a closed-loop water tunnel with a jet issuing from a round nozzle inclined at 35° with the streamwise direction of the crossflow. The flow structures are visualized using Laser Induced Fluorescence (LIF) and measured by Particle Image Velocimetry (PIV). Four velocity ratios of VR = 0.5, 1.0, 1.5, and 2.0 are considered with the density ratio ρ j /ρ ∞ = 1 and the Reynolds number Re = 1712 (based on the jet diameter and cross-flow velocity). Under the same conditions, Large-Eddy Simulations (LES) are operated for VR = 0.5 and 2.0, focusing on the three-dimensional dynamics of the JICF. Predictions by LES are found to agree well with the measurements. The qualitative and quantitative analyses suggest that the flow patterns and their unsteady behavior change with the velocity ratios considerably. When VR = 0.5, it is mainly hairpin vortices behaving like the classic counter-rotating vortex pair (CRVP) that dominate the JICF. As the velocity ratio increases, the classic JICF topology recovers and the ubiquitous CRVP becomes the characteristic feature of the JICF and persists far downstream for VR = 2.0. The LES results reveal that the coherent structures generated in the nozzle tube are initiated by the separation zone at the jet inlet sharp edge and play an important role in the formation of the hairpin vortices and the CRVP. © 2015 Elsevier Inc. All rights reserved.

1. Introduction The jet in crossflow refers to a jet of fluid emanating from a nozzle and interacting with the surrounding fluid that flows across the nozzle exit. This phenomenon or the like exists extensively in nature and also in many industrial applications, such as volcanic eruptions, pollutant in plumes, dilution jets in combustors, and cooling of turbine blades (Karagozian, 2014). Consequently, the control and understanding of JICF is of great industrial interest. Besides, the interaction between the jet and the crossflow generates a highly complex threedimensional, unsteady and nonlinear flow, making it an active subject of many experimental (Kelso et al., 1995; Cambonie and Aider, 2014), theoretical (Mcguirk and Rodi, 1978; Needham et al., 1988) and numerical studies (Le et al., 2011; Coletti et al., 2013) in fluid mechanics over the past few decades (Karagozian, 2010). Detailed reviews on this subject may refer to Margason (1993) and Mahesh (2013). Previously, most studies have been conducted on a jet initially at a right angle to crossflow. For example, Bidan and Nikitopoulos (2013) focused on the vortical structures encountered in steady and pulsed transverse jets at 0.15 ≤ VR ≤ 4.2. Kelso et al. (1996) studied

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Corresponding author. Tel.: +861062767074; fax: +861062767074. E-mail address: [email protected], [email protected] (J. Mi). The co-first author

http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.12.001 S0142-727X(15)00151-4/© 2015 Elsevier Inc. All rights reserved.

the structures of normal round jets in crossflow using flow visualization techniques and flying hot wire measurements with 2.0 ≤ VR ≤ 6.0. Based on the flow visualization of a round jet ejected vertically into the horizontal crossflow, Fric and Roshko (1994) documented four fundamental vortical structures involved in the JICF as shown in Fig. 1: the horseshoe vortex that forms upstream of the jet exit, the jet shear-layer formed primarily at the windward jet/crossflow interface, the counter-rotating vortex pair (CRVP) and the unsteady tornadolike wake vortices underneath the detached jet. Among them, the time-averaged defined CRVP is usually considered the most significant structure for the entrainment and mixture between the jet and crossflow. However, the flow structures in JICF are not always those four types of vortices when the velocity ratio changes and their formation mechanisms are different as well. Mahesh (2013) concluded that the JICF structures at low velocity ratios are different from those canonically at high ones. In the low ratio regime, the interaction of the jet with the crossflow is in fact dominated by hairpin vortices. Bidan and Nikitopoulos (2013) found that, at low velocity ratios, a stable leading-edge shear-layer rollup is identified inside the jet pipe. As the velocity ratio increases, this structure becomes destabilized and forms other transverse jet vortices. Kelso et al. (1996) showed that the unsteady upright vortices in the wake may form by different mechanisms for different velocity ratios. Recently, Cambonie and Aider (2014) conducted a study that was aimed at providing a

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the flow structures for the low-velocity-ratio JICF is to be presented late for better understanding of their origination and evolution as the velocity ratio is increased, especially for the hairpin vortex and CRVP structure. 2. Apparatus and procedures 2.1. Experimental details

Fig. 1. Schematic illusion of vortical structures of the JICF near the jet exit (Fric and Roshko, 1994).

complete transition scenario of the JICF topology from the lowest velocity ratios to high ones ranged between 0.16 and 2.13. According to the global evolution scenario of the round JICF topology proposed, the jet is almost attached and strongly interacts with the boundary layer for 0.3 ≤ VR ≤ 0.6, and it is also periodically swept by the crossflow when VR ≤ 0.3, due to the jet momentum being not sufficiently strong to sustain a steady obstacle for the crossflow. For VR > 1.25, the classical JICF vortical structures sketched in Fig. 1 are recovered. Compared to the normal JICF, the flow structures and their originations of an inclined jet into crossflow at low velocity ratios are very different. Surprisingly, the impact of low velocity ratios on the flow structures is less appreciated (Mahesh, 2013). Only a few articles have shown results on an inclined JICF for VR ≤ 2.0, and most of them are conducted numerically. Guo et al. (2006) studied the influence of the jet inclination on the flow field. They compared a normal and a 35° stream-oriented inclined jet at low velocity ratios of 0.1– 0.48 using LES. In their results, hairpin vortices are not mentioned; similar structures of recirculation, spanwise rollers at the windward jet/crossflow interface, and the counter-rotating vortex pair (CRVP) were observed for the normal and the inclined jets. At the lower velocity ratios, no horseshoe vortex was observed at the leading edge of the jet. They considered that the CRVP is originated from the shear layer of the jet/crossflow interaction and the streamwise vorticity contained in the boundary layer next to the jet exit. Tyagi and Acharya (2003) also performed an LES of a streamwise 35° round jet at low velocity ratios of 0.5 and 1, with the Reynolds number of Re = 15,000. Contrary to Guo et al. (2006), these investigators clearly showed the street of hairpin vortices in the wake of the jet exit and the far-field as they were convected downstream. It was concluded that the hairpin vortices were the origin of the CRVP. Recently, Fawcett et al. (2013) experimentally provided the visualization of the JICF structures and showed that the jet structure changes with the velocity ratio. The same conclusion was obtained by Sakai et al. (2014). For the CRVP origination, despite several initiation mechanisms have been proposed (Andreopoulos and Rodi, 1984; Marzouk and Ghoniem, 2007), relatively little attention has been paid to the effects of the supply plenum and nozzle flow on its development (Peterson and Plesniak, 2002; Peterson and Plesniak 2007). In the context of the above work, the present study is designated to focus on the vortical structures associated with an inclined jet in transverse flow at low velocity ratios and relatively lower Reynolds number, by means of both experiment and numerical computation. To this end, the flow structures of several selected planes are visualized by laser induced fluorescence (LIF) and quantitatively measured by particle image velocimetry (PIV). Since the consensus that the RANS models have a poor prediction for the anisotropy JICF problem and DNS has the limitation of huge computational cost, the present modeling uses LES for the numerical work. A detailed illustration of

Experiments are performed in a closed-loop low speed water tunnel with an 6 m long test section by an 0.4 m × 0.4 m cross-section, schematically described in Fig. 2(a). A set of five filter screens followed by a contraction with an area ratio of 2:1 is located directly upstream of the test section, removing large-scale secondary flows and providing stable inlet conditions during the experiments. The test section comprises three main parts made of acrylic: the test plate, the supply plenum and the inclined nozzle. The test plate served as boundary wall is 0.90 m (length) × 0.36 m (width) and is installed in the mainstream zone below the air/water shear layer. The round hole is drilled streamwise-oriented 35° in a thick disk, with a diameter D = 23 mm and a length L/D = 3.8, classified as the low stroke ratio (Sau and Mahesh, 2008). The jet exit center is mounted 13D downstream of the test plate leading edge and 26D upstream of the trailing edge. The jet from a supply plenum (10D in diameter and 6D in height) was fed by a secondary pump, which is monitored via a rotameter to make the velocity ratio accurate. In the supply plenum, the cells of the honeycomb are round (diameter d = 6 mm) and have a length of 20 cell diameters. The coordinates X, Y and Z correspond respectively to the streamwise, spanwise and vertical directions of the flow, as shown in Fig. 2(a) (left), with the origin taken at the center of the jet exit. The turbulence intensity of the crossflow at the test section entrance and the jet out of the honeycomb is 3% and 0.5% respectively. The main flow Reynolds number Re is 1712; where Re ≡ U∞ D/ν with D being the jet nozzle diameter, U∞ the bulk velocity and ν the viscosity. For different values of the velocity ratio Uj /U∞ , the rate of the jet flow is changed by modulating the rotameter while the mainstream velocity stays constant. The working fluid is water for both the mainstream and the jet at ambient temperature, thus obtaining that the density ratio ρ j /ρ ∞ = 1 and the blowing ratio BR ≡ ρ j Uj /ρ ∞ U∞ = Uj /U∞ . As the blowing ratio scales the thermal transport capacity of the coolant, it is arguably a more important parameter than the velocity ratio which scales the turbulent production for film cooling (Coletti et al., 2013). However, we take the velocity ratio as the only variable here, since it has the same value of the blowing ratio. Prior to the PIV measurements, LIF visualizations are conducted in both vertical and horizontal sectional planes (schematically shown in Fig. 2(b)) to obtain instantaneous tomographic images of the JICF. The jet plenum is filled with a dilute mixture of the rhodamine-6Gchloride and water. Planar sections are illuminated via a laser light sheet produced by a pulsed laser source passing through a negativefocal-length cylindrical lens. A long-focal-length cylindrical lens is used to focus the sheet, with the thickness of the light sheet being about 1 mm. The laser sheet beam is illuminated during 4 ns using a 15 mJ/pulse Nd: YAG laser, with the wavelength being 532 nm. An optical low-pass filter is used to isolate the fluorescence from the laser wavelength spectrally. The sheet is oriented to clearly view the jet trajectory and discern the vortex structures within the jet in the planes parallel and perpendicular to the plate. The fluorescence dye is supplied only into the jet flow; hence the coolant jet flow patterns are clearly recognized as the images. Fig. 2(b) shows the orthogonal planes with positions at which LIF measurements are taken. The symmetric plane (X–Z section, Y/D = 0) is measured to determine the trajectory of the JICF, also the windward and leeward vortical structures. For this, the laser is placed on a tripod horizontally under the water tunnel, with a mirror used to shift the light 90°. For the other planes

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Fig. 2. (a) Schematic of experimental configuration: test section (left) and the inclined nozzle (right); (b) Selective planes for LIF visualizations and 2D-PIV measurements. The coordinates X, Y and Z correspond respectively to the streamwise, spanwise and vertical directions of the flow.

in Fig. 2(b), the laser is installed on a three dimensional transverse system, so horizontal and vertical (perpendicular to the crossflow) light sheets can be obtained easily by changing the orientation of the cylindrical lens. For the transverse cross-sections, a mirror is placed downstream of the jet to make the recording possible. PIV is a global velocity measurement scheme (Adrian, 1991), whereby the velocity is computed by cross-correlating a pair of particle images taken at shot time interval. The PIV system used in the present study consists of a laser system, a synchronizer, and a 1 K by 1 K high resolution CCD camera connected to a Dell computer controlling the system. A Nikon 60 mm macro lens is placed in front of the CCD camera to prevent the image distortion error. One thousand images are acquired for each experimental configuration, after which post-processing is temporally averaged to obtain the final mean velocity data. The maximum recording frequency is 500 Hz. Solid glass balls of 10 micrometers in diameter are selected as the tracer particle, with a density ratio of 1.05 to fluid to ensure good tracking. These particles are seeded independently into the jet before passing through the magnetic pump and into the crossflow just upstream of the conditioning screens shown in Fig. 2(a). Since strong mixing occurs inside the pump, the particles distribution in the jet can be considered nearly uniform. The results obtained from these measurements are used to quantify the jet spread and the evolution of the flow structure. The interrogation of the velocity vector is carried out using the commercial software Davis 7.2. Interrogation window sizes of 32 × 32 pixels or 16 × 16 pixels, 75% overlapped are selected for different conditions. The images are cross-correlated using standard FFT algorithm and a Gaussian sub-pixel interpolation scheme. The physical dimension of the images ranges from 60 to 150 mm for different observation planes, resulting in a spatial resolution ranging from 0.02D to 0.05D. The uncertainty in the peak-finding algorithm is estimated to be 0.1 pixels, causing a typical uncertainty in velocity of 1.5%. For the flow rate, determined by the rotameter, the uncertainty is about 4%. 2.2. Computational details Large eddy simulations (LES’s) of the flows similar to those measured experimentally are implemented by the commercial solver Ansys Fluent. The purpose is to provide the three-dimensional

Fig. 3. Computation domain used in LES.

information on the vortical structures and their formation mechanisms for the velocity ratios of VR = 0.5 and 2.0, which is impossibly obtained by experiment. For the unsteady simulations, the incompressible LES using a WALE Subgrid-scale model with second-order accuracy for both spatial and temporal discretization (spectral synthesizer method) is selected as the turbulence model, through comparing different modeling strategies for this type of flow. Fig. 3 shows the computational domain, which consists of a crossflow channel, a film cooling nozzle and a plenum, similar to that in Section 2.1. The X, Y, Z axes are taken to be the same as the experimental configuration. The crossflow channel is 39D long, 6D wide and 6D high and counted 180 × 94 × 60 cells along the respective dimensions. The jet nozzle mesh comprises a dual O-grid type mesh with 8071 cells in the crosssection and 60 cells along the pipe axis. The whole mesh is structured and contained in total 4.2 million cells, 99.11% of which have a more than 0.9 quality by the Determinant criterion in ICEM. For the boundary layer meshes in the simulated domain, y+ < 1.0, where y+ is the dimensionless distance between the near-wall cell centroid and the boundary wall of the crossflow channel and film cooling tube, which is good enough for the LES computation. Mesh sensitivity is studied by running the same simulation at VR = 2.0 for a grid of about 8.4 million cells. By comparing the velocity and Reynolds stress profiles

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Fig. 4. (a) Lateral profiles of velocity and Reynolds stress in the symmetry planes at X/D = −0.5, 1.5 and 3.0 for VR = 2.0:  a grid of about 4.2 million cells, ———— 8.4 million; (b) Lateral profiles of Ux /U∞ in the symmetry planes at X/D = −0.5, 1.5 and 3.0 for VR = 0.5 and 2.0: ◦ experiment, ———— computation.

at different locations, see Fig. 4(a), it is validated that the simulations of 4.2 million are sufficiently accurate for this problem. Prior to the LES, an initial steady Reynolds averaged Navier–Stokes simulation is operated to initialize the flow domain and give a maximum viscous dissipation rate (ε ) estimate in the domain (Bidan and Nikitopoulos, 2013). The viscous dissipation is used to evaluate the time step used in LES according to the Kolmogorov time scale, i.e. √ τK = ν /ε. Hence in the LES computations, the time step varies from 1 ms at VR = 0.5 to 0.2 ms at VR = 2.0. Inlet boundary conditions of the computational domain are consistent with the experimental measurements. The bulk velocity of crossflow is set to ensure that Re = 1712, the same as for the experiments, and so is the turbulence intensity. The turbulence conditions at the coolant plenum inlet are taken as the turbulence intensity Tu = 0.5% and the turbulent length scale l = 6 mm, consistent well with those resulting from the PIV measurement. The crossflow temperature T∞ = 350 K, and the coolant jet Tc = 300 K. Then the density ratio is 1.0 as in the LES of Sakai et al. (2014). Flow time of 1.040 s (5200 time steps) is calculated to obtain the statistically significant data, using huge amounts of computer time for converging to residuals of less than 10−6 (about 13,824,000 CPU seconds per run, Intel W5590 at 3.33 GHz). Fig. 4(b) compares the lateral profiles of the dimensionless timeaveraged streamwise velocity Ux /U∞ , obtained from the LES prediction and the PIV measurement, for VR = 0.5 and 2.0. Three streamwise locations, X/D = −0.5, X/D = 1.5 and X/D = 3.0, in the symmetry plane (Y/D = 0) for the two velocity ratios are presented. It is obvious that some mismatches exist near the wall at X/D = −0.5 for VR = 0.5 and X/D = 3.0 for VR = 2.0, indicating the limitation of PIV in the boundary layer of the flow, due to the light reflection of the wall and the bad particle tracing characteristic in this field. However, the computed velocities at different locations, especially in the recirculation zone at X/D = 1.5, show a very good overall agreement with the measurements. Besides, the area-averaged turbulence intensity

calculated by LES is 29.8%, almost the same as Tu = 29.1% measured by PIV. Thus, this comparison suggests that the LES modeling can appropriately predict the present flow of investigation, so that both the measured and simulated results may be used below to explicate and understand the JICF problem of investigation. 3. Results and discussion JICF contains a few distinct flow structures as described by Frick et al. (1994), Cambonie et al. (2014) and Sakai et al. (2014). The typical vortices have long been identified, although their origins and dynamic roles are still under debate (Coletti et al. 2013). Since the present study is to resolve the influence of different low velocity ratios on the vortical structures in JICF, the flow topologies and the formation mechanisms of those vortex structures near the jet exit are examined for VR = 0.5–2.0. 3.1. Effects of velocity ratios on vortical structures To visualize the vortical structures, the -criterion method of vortex identification, firstly proposed by Dallmann (1983), is used here. This method is based on the principle that the vortex cores are associated with the minimum local pressure and is expressed through point-wise analysis of the velocity gradient tensor. In the present study, the flow is incompressible and hence for the -criterion, vortices are identified as flow regions with positive second invariant of the velocity gradient tensor, ∇ 2 P/ρ = i j i j − Si j Si j > 0, where i j = (ui, j − u j,i )/2 corresponds to the rotation-rate tensor and Si j = (ui, j + u j,i )/2 to the stress tensor. Fig. 5 displays the instantaneous vortical structures visualized by LIF at different planes for VR = 0.5– 2.0. Fig. 6 shows the iso-surfaces of ∇ 2 P/ρ obtained from LES to identify the vortical structures. It is obvious that the flow patterns change with the velocity ratio drastically.

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Fig. 5. Instantaneous LIF visualization images taken in the center plane at Y/D = 0 (a– d) and correspondingly in the horizontal plane at Z = 3 mm (e–h) for VR = 0.5, 1.0, 1.5 and 2.0 respectively, and in the vertical plane at X/D = 3.0 for VR = 0.5 (i, j), 2.0 (k, l).

Fig. 6. Instantaneous vortical structures near the nozzle exit for VR = 0.5 (∇ 2 P/ρ = 100/s2 ) and VR = 2.0 (∇ 2 P/ρ = 50/s2 ).

For VR = 0.5, the jet flow momentum is not strong enough to penetrate through the crossflow boundary layer, validated in Fig. 7(a) where the crossflow boundary layer overwhelms the jet and flows downstream together with the jet, and thus produces less complex vortical structures in the near field of the jet exit, which is intuitively reflected in Figs. 5 and 6. In Fig. 5(a, e), the jet bends towards the wall and then spreads over the wall, behaving like an attached jet. Due to the adverse pressure gradient and the push by the counter vortex displayed in Fig. 6, a steady horseshoe vortex with positive spanwise vorticity ωy is formed near the leading edge of the jet exit and wraps around the base of the jet and travels downstream, reorienting itself in the streamwise direction. The counter vortex with a negative ωy is formed mainly from the vorticity in the leading edge boundary layer of the nozzle. As the counter vortex grows, initiated by the high pressure zone shown in Fig. 6, the boundary layer of the crossflow separates on the leading edge of the nozzle, resulting in the horseshoe vortex. Note that only the horseshoe legs on the both sides of the jet are seen in Fig. 5(e). This is because the rhodamine-6G-chloride is added only into the jet while the horseshoe vortex comes from the crossflow boundary layer, so that the legs can be LIF-visualized only in the downstream region of the jet. Being consistent with the observation by Acarlar et al. (1987), it is the hairpin vortices that dominate the JICF, which is intuitively reflected in Fig. 6. The validation can be made also by comparing Fig. 5(a) and (i, j), where a side view and a

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Fig. 7. Contours of dimensionless vorticity: instantaneous spanwise vorticity ωy D/U∞ in the center plane at Y/D = 0 with stream traces of the crossflow in (a) and the jet and the vector field in (b); time-averaged streamwise vorticity ωx D/U∞ with the vector field in the vertical plane at X/D = 3.0 (c, d).

back view of the instantaneous hairpin vortex are seen correspondingly. Fig. 5(i) corresponds to the vertical plane penetrating the hairpin top and Fig. 5(j) to the hairpin leg. For the formation of the hairpin vortex, Sau et al. (2008) attribute it to the vorticity in the crossflow boundary layer inhibiting roll-up of the nozzle boundary layer at the leading edge. However, the results obtained in this study demonstrate that the above explanation is incomplete. A more accurate formation mechanism of the hairpin vortex for the inclined JICF at low velocity ratio will be amply illustrated in Section 3.2. It is emphasized that the hairpin vortex is different from the time-averaged defined CRVP, though its rotation direction shown in Fig. 5(i, j) is the same as the CRVP. Compared to the flow structures of the lowest velocity ratio, the canonical flow topologies recover and become more chaotic when VR = 2.0. From the LIF visualizations, the features of the attached jet disappears at VR = 1.0 and the flow structures are almost the same as the case of VR = 2.0 when VR = 1.5. All of the four significant vortex structures are observed in Figs. 5 and 7 for VR = 2.0. Strong shearlayer vortices are generated on the leading and trailing edges of the jet, as seen in Fig. 5(d) and Fig. 6, due to the high jet momentum causing an intense viscous shearing and instability at the jet/crossflow interface, which is quantitatively displayed in Fig. 7(b). In the low pressure wake region similar to the low pressure zone of VR = 0.5 in Fig. 6, wake vortices are visualized and shown in Fig. 5(d). The horseshoe vortex is not visualized apparently by LIF while the LES captures its head. This is caused by the suction of the low pressure region just downstream of the jet exit and the strong entrainment of the CRVP derived from the time-averaged inverse hairpin vortex in Fig. 6. The origin of the CRVP remains to be a subject of much debate, even though it is widely considered to be the most important mixing structure in JICF and quite a number of previous studies have focused on it. Of note, from the practical point of view, the presence of CRVP enhances the jet lift-off and then the entrainment of hot crossflow towards the wall, significantly degrading the film cooling effectiveness. Thus, it is necessary to clarify how the CRVP is formed. Fig. 7(c) and 8(d) together show that the CRVP structures from LES and experiment are quite similar in the plane of X/D = 3.0. This implies that LES can well capture the evolution of CRVP. So, it makes sense for us to provide a detailed illustration based on LES for the origination of the CRVP in Section 3.3.

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of X/D = 1.5, forming a bigger hairpin vortex than the inner hairpin vortex on the downstream edge of the jet together. Therefore, the formation of hairpin vortices is not only owing to the crossflow boundary layer vortices, the other coherent structures must be considered. Comparing the magnitudes of ωy from different sources suggest that the vortices generated in the nozzle tube may play a more important role in the hairpin vortex evolution. Nevertheless, we are presently unable to estimate the individual contributions from the three different types of vortices to the hairpin vortex formation, since we cannot determine their magnitude at their joint point. 3.3. Origination of CRVP at VR = 2.0

Fig. 8. Characteristic shedding frequency of shear vortex occurring in the symmetry plane of Y/D = 0.

Apart from the above, the velocity ratio also has impact on the unsteady behavior of the flow structures. The time series of the instantaneous vorticity ωy , obtained from the PIV velocity field of the central planes, are transformed into power spectrum density function by means of the discrete fast Fourier transform (FFT). Careful inspection of the successive LIF images suggests that the horseshoe vortex occurs and stays steadily at VR = 0.5, 1.0, and turns to eject off periodically at the frequency of 3.52 Hz when VR = 2.0. Differently, the shear vortices are shedding in all the cases. As VR increases from 0.5 to 2.0, the shedding frequency (f) increases from 1.56 Hz to 4.30 Hz while the corresponding Strouhal Number St (≡ fD/Uj ) decreases from 0.96 to 0.66. Fig. 8 shows the values of f and St against VR. Note that the decrease of St with VR is expected because the JICF would behave like a free jet if VR is sufficiently large. Typical values of St for a free jet range between 0.4 and 0.6. 3.2. Formation of hairpin vortices at VR = 0.5 For VR = 0.5, Fig. 9(a) shows the instantaneous distribution of the spanwise vorticity ωy in the iso-surface of ∇ 2 P/ρ = 100 /s2 and the center plane Y/D = 0 which cuts across the hairpin vortex. The rotation direction of the vortices in the head and leg of the hairpin vortex is marked out using the thick-dotted arrows. For the formation of the hairpin vortex, it seems to have reached a consensus that the hairpin vortex originates from the crossflow boundary layer, neglecting the likely effect of coherent structures forming within the nozzle tube. However, the present LES shows that, for the inclined JICF problem of investigation, the vortical structures developed in the nozzle tube play an important role in the hairpin vortex formation. Sau et al. (2008) have provided quite a detailed explanation for the evolution of the hairpin vortex due to the crossflow boundary layer separation. Here we would give more attention to the vortices within the nozzle. The formation of the hairpin vortex may be explained as follows. When VR = 0.5, the formation of the hairpin vortex results from merging the three vortices, one of which derives from the crossflow boundary layer noted above. At the sharp edge of the nozzle entrance, a separation region corresponding to a lower pressure is generated when the jet flows through it. Because of this separation region, the inner hairpin vortex is incepted from the jet boundary layer on the trailing edge of the nozzle wall, and is shed downstream. At the trailing edge of the jet exit, due to the lower pressure zone, a favorable pressure gradient accelerates the jet, resulting in a very strong shear between the jet and the trailing wall. Thus, lateral vortices with positive ωy are generated and shed away from the trailing edge of the exit in a periodic manner. As shown clearly in Fig. 9(a), the inner hairpin vortices merge with the shedding vortices from the trailing edge and the crossflow boundary vortices around the vertical plane

For VR = 2.0, Fig. 9(b) displays the instantaneous distribution of the spanwise vorticity ωy in the iso-surface of ∇ 2 P/ρ = 50 /s2 and the center plane Y/D = 0 which cuts across the inverse hairpin vortex. As seen on the plot, a series of apparent shear vortices are formed on the jet windward side due to the Kelvin–Helmholtz instability (Kelso et al., 1996; Andreopoulos and Rodi, 1984) whereas a street of inverse hairpin vortices are generated downstream from the plane of X/D = 3.0. In fact, these hairpin vortices are responsible for the timeaveraged CRVP as their instantaneous form is similar to the CRVP. The coherent structures of VR = 2.0 differ significantly from those of VR = 0.5 in the leading edge boundary vortices detached from the jet exit, due to the fierce shear effect as the jet flows more quickly. These leading vortices, with negative lateral vorticity, are shed from the leading jet exit and merge with the shear vortices with ωy in the same sign just above the exit. As indicated in the dotted rectangular zone of Fig. 9(b), a comparison is made between the two vortices with ωy in opposite sign, one of them is negative in the shear vortices and the leading nozzle boundary vortices, and the other is positive in the inner hairpin vortices, the trailing nozzle boundary vortices and the crossflow boundary vortices which have been stated in Section 3.2. By comparing the magnitudes of ωy of the two vortices in Fig. 9(b), it is inferred that ahead of the plane at X/D = 1.5, these two opposite vortices have compatible strength. However, downstream from the plane of X/D = 3.0, the negative vortices becomes dominant and a street of inverse hairpin vortices are generated. The legs of these inverse hairpin vortices are with ωx in the same sign as the temporally averaged CRVP. The inverse hairpin vortices flow downstream with the crossflow and their legs become longer. This is because near the windward jet/crossflow interface, due to the jet obstacle to the crossflow, the shear vortex head on the leading edge of the interface moves slower than the legs on lateral sides of the interface. Since the CRVP is a time-averaged structure, temporally averaged views of vorticities in several cross sections are shown in Fig. 10(a, b), where the horizontal nozzle sections are contoured by ωz and the vertical crossflow sections are colored by ωx . It is clearly shown that there exists a counter-rotating vortex pair (CRVP), both in the flow inside the jet tube and the flow downstream of the jet exit. In the following, the evolution of the CRVP from the jet hole to the downstream region is illustrated by means of the transport equation of the vorticity. For this incompressible JICF problem, the transport equation of the instantaneous streamwise vorticity ωx can be simplified as

d ωx ∂ Ux ∂ Ux ∂ Ux = ωx + ωy + ωz +υ dt ∂x ∂y ∂z



 ∂ 2 ωx ∂ 2 ωx ∂ 2 ωx + + . ∂ x2 ∂ y2 ∂ z2

(1) In (1), the first term on the right hand side represents the streamwise stretching; the second and third terms are responsible for the bending of the streamlines; the last term is for the viscous diffusion of streamwise vorticity. The first two terms abbreviated as ω · ∇ Ux . Fig. 9(c) shows the absolute ratio of ω · ∇ Ux to υ∇ 2 ωx . As demonstrated, the viscous term υ∇ 2 ωx is much smaller in magnitude than

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Fig. 9. Spanwise vorticity ωy on iso-surfaces of (a) ∇ 2 P/ρ = 100/s2 for VR = 0.5 and (b)∇ 2 P/ρ = 50/s2 for VR = 2.0; Instantaneous iso-surfaces of ∇ 2 P/ρ = 100 /s2 with (c) |ω · ∇ Ux /υ∇ 2 ωx | and (d)ω · ∇ Ux .

Fig. 10. (a) Time-averaged vorticity contours in the planes of Z/D = −1, 0 within the nozzle and the vertical planes of X/D = 1.5, 5.0 at VR = 0.5 and 2.0, respectively; (b) The pathlines of particles released from the jet inlet plane, colored by the instantaneous ωz at VR = 2.0.

ω · ∇ Ux . In other words, ω · ∇ Ux dominates the transport of ωx , par-

ticularly upstream from the plane of X/D = 3.0. This is also verified in Fig. 9(d). On the other hand, Fig. 10(a) shows that ωz of the CRVP at the nozzle exit has the same magnitude order with ωx of the CRVP in plane of X/D = 1.5. The viscous diffusion of the streamwise vorticity reduces ωx of the CRVP in the plane of X/D = 5.0 by about 70%. This is inconsistent with the previous conclusions that the vertical vorticity is provided to the CRVP by the folding of the shear layer vortices through their side arms (Kelso et al. 1996) and that the CRVP vorticity issues directly from the jet shear layer and reorients under the influence of the crossflow (Andreopoulos and Rodi, 1984). It is thus deduced that the commonly known time-averaged CRVP for VR = 2.0 may originate mainly from the coherent structures within the jet nozzle, which are deformed from the vertical vortices, i.e. ωz , into the streamwise vortices, i.e. ωx , by the folding and reorientation disciplined by Eq. (1). 3.4. Sub-large coherent structure Our LES calculations also find that there appears to be a sub-large coherent structure, named presently as the perturbation spiral structure (PSS), near the exit in the nozzle boundary layer, which has yet to be noted, to our best knowledge. Fig. 10(b) shows this finding. The PSS occurs within the nozzle tube around the horizontal plane of Z/D = −0.5, by comparing the particle pathlines of successive instants. As it approaches the nozzle exit, the PSS becomes stronger. It is hence inferred that the PSS may be initiated from the pressure fluctuation

near the leading edge of the jet exit. However, more comprehension on this interesting issue is needed from our further study on its formation mechanism and its effect on the flow structures outside the jet nozzle. 4. Conclusions Large-scale flow structures in an inclined JICF at different low velocity ratios have been investigated, using the experimental LIF and PIV methods and the numerical LES. It is demonstrated that the unsteady large-scale vortical structures change drastically with differing the velocity ratio. The present LES calculations show a good ability of LES in capturing the flow and mixing features for the JICF problem, which is hardly resolved by experiment. The analysis from LES calculations on the three-dimensional vortical dynamics, combining with the experimental observations, has revealed the origination of the time-averaged CRVP for different velocity ratios. The present work leads to the following conclusions: (1) At relatively low velocity ratios, the hairpin vortices are observed to dominate the JICF. As the velocity ratio rises, the canonical CRVP structure recovers and takes place of the hairpin vortices in controlling the evolution of the JICF. For unsteady behavior of the vortical structures, the horseshoe vortices stay steadily for VR = 0.5 and 1.0 but become periodically ejected off for the higher velocity ratios. Moreover, the shear vortices are always shedding and the shedding frequency

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increases with growing VR at the leading edge while the corresponding Strouhal number drops. (2) At VR = 0.5, the hairpin vortices result not only from the crossflow boundary layer vortices but also from the coherent structures within the jet nozzle tube. Through analyzing the magnitude order of ωy , it is found that the vortices generated in the nozzle tube contribute more to the hairpin vortex evolution. (3) The present LES results indicate that the CRVP defined from the temporally averaging for VR = 2.0 may originate mainly from the coherent structures within the jet nozzle tube. This is different from the previous results. Undergoing the folding and reorientation disciplined by the transport equation of vorticity, the coherent vortices within the jet nozzle tube are transformed from the vertical vortices into the streamwise vortices. The inverse hairpin vortices are responsible for the CRVP. (4) It appears that there exists a sub-large coherent structure around the horizontal plane of Z/D = −0.5 beneath the nozzle exit. Its formation may be due to the pressure perturbation at the leading edge. Whether or not this structure has a significant impact on the near field of the JICF is calling for a further study. Acknowledgments The support of National Natural Science Foundation of China (Coal Joint Fund) (Grant no.: U1361101) is gratefully acknowledged. The authors would also like to thank all the reviewers for their insightful comments and criticisms, the addressing of which has enhanced the paper substantially. References Acarlar, M.S., Smith, C.R., 1987. A study of hairpin vortices in a laminar boundary layer Part 2: hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83. Adrian, R.J., 1991. Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261–304. Andreopoulos, J., Rodi, W., 1984. Experimental investigation of jets in a cross-flow. J. Fluid Mech. 138, 93–127.

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