Investigation of Crossflow Interaction of an Oscillating Jet

10.2514/6.2017-1690 AIAA SciTech Forum 9 - 13 January 2017, Grapevine, Texas 55th AIAA Aerospace Sciences Meeting

Investigation of Crossflow Interaction of an Oscillating Jet

Downloaded by Tonya Maniaci on December 18, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-1690

Mohammad A. Hossain1, Robin Prenter2, Ryan K. Lundgreen3, Lucas M. Agricola4, Ali Ameri5, James W. Gregory6, Jeffrey P. Bons7 The Ohio State University, Columbus, OH, 43235

Numerical investigations were conducted to evaluate the interaction of an oscillating jet with a crossflow. A conventional curved fluidic oscillator with an aspect ratio of unity is used. The flow interaction is investigated at three different inclination angles to the crossflow free stream direction ( = , , ) and at three blowing ratios ( = , , ). An Unsteady Reynolds Averaged Navier-Stokes (URANS) model was used to evaluate the flowfield. Models were validated by comparing key flow features and oscillating frequency reported in the literature. Time averaged and time resolved flow fields are presented. Two alternating streamwise vortices are observed at all blowing ratios. The sense of rotation of these alternating vortices is opposite to the traditional counter rotating vortex pair (CRVP) found for a steady jet in crossflow. A larger lateral jet spreading is observed for = at higher blowing ratio. The trajectory envelope of a sweeping jet is shallower than the lowest limit of the steady jet trajectory envelope for all cases due to rapid decay in velocity magnitude. An investigation of the alternating vortices is presented at various phase angles of the jet.

Nomenclature AR BR CRVP D HSV HPV RLVS SWV Ut U∞

∅ Ω

= = = = = = = = = = = = = = = =

aspect ratio, (W/H) blowing ratio counter rotating vortex pair hydraulic diameter, (10mm) horseshoe vortex hairpin vortex ring like vortical structure streamwise vortices throat velocity freestream velocity non-dimensional wall distance inclination angle streamwise vorticity, (1/s) phase angle vorticity magnitude strain rate tensor

I. Introduction

T

he unsteady nature of an oscillating jet provides great potential for use as a flow control device, especially since the frequency of oscillations is controllable by the designer. Since it involves no moving parts while generating the oscillating jet, it is getting increased attention among the flow control community. Potential applications of such 1

Graduate Research Associate, Mechanical Engineering, Student Member AIAA. Graduate Research Associate, Aerospace Engineering, Student Member AIAA. 3 Postdoctoral Researcher, Aerospace Research Center, Member AIAA. 4 Graduate Research Associate, Aerospace Engineering, Student Member AIAA. 5 Research Scientist, Mechanical and Aerospace Engineering. 6 Associate Professor, Aerospace Engineering, 201 W. 19th Ave, Associate Fellow AIAA. 7 Professor, Aerospace Engineering, 2300 West Case Road, Email: [email protected], Associate Fellow AIAA. 1 2

American Institute of Aeronautics and Astronautics Copyright © 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


a device include separation control1, drag reduction2, noise control3 and turbine film cooling4. Extensive research56 has been performed on the development of active flow control technologies that force controlled reattachment of separated flows over lifting surfaces, showing that aerodynamic performance can be improved by reattaching flow with these devices. With pulsing, an effective separation control can be achieved while reducing the required injected mass flow7-8 at the control surface. Two techniques that have been used successfully include synthetic jets, zero-net-mass-flux devices that consist of enclosed cavities where alternating periods of blowing and suction are created9 and high frequency plasma actuators. One of the main challenges in the design and development of active flow control is a greater actuation power required to maintain effectiveness at full scale with higher free stream velocities. Also, the majority of unsteady blowing actuators employ mechanical or piezoelectric devices which are often large in size, and employ numerous moving parts with associated reliability issues and limited lifetime. For this reason, in recent years there has been an increasing interest in fluidic actuator development10, which is a purely passive system. A significant amount of work has been done to understand the flowfield associated with jets in a crossflow. Figure 1 shows the dominating flow structures of a transverse jet in a crossflow that includes shear layer vortices, wake vortices, horseshoe vortices and a counter rotating vortex pair (CRVP). Shear layer vortices and wake vortices are unsteady vortices that are strongest in the near field of the jet. Horseshoe vortices and the CRVP are more stable, and convect downstream influencing the freestream11.

Figure 1. Different vortex system associated with the jet in a crossflow12. The flow features of this fluidic oscillator have not been fully characterized especially the boundary layer interaction and the effects of crossflow on the jet oscillation. Lacarelle et al13 showed improved mixing by four fluidic oscillators in a generical jet in crossflow configuration compared to standard non oscillating jets. Ostermann et al14 have studied the internal and external flow features of a fluidic oscillator in a quiescent environment using phase averaged Particle Image Velocimetry (PIV). Later Osterman et al15 reported time-resolved PIV data and three dimensional flow field for the same device in a crossflow environment where they studied a single blowing ratio (BR = 3) at a single inclination angle ( = 90 ). According to their findings, oscillating jet is bent by the crossflow and the trajectory of the sweeping jet is shallower than that of a steady jet in crossflow. In addition, spatial oscillation creates a pair of counter-rotating vortex system and the sense of rotation is opposite to that of the counterrotating vortex pair of a steady jet in crossflow. The primary goal of this study is to investigate the interaction between an oscillating jet in a cross flow at different inclination angles and various blowing ratios where blowing ratio is defined by –

(

) =

The fluidic oscillator used in this study was invented by Bowles Fluidic Corporation16. It is a conventional feedback type fluidic oscillator which includes a fluidic circuit. The fluidic circuit consists of a power nozzle, two feedback loops and an exit aperture, or throat. Figure 2 shows the schematic of a typical feedback type fluidic oscillator. The general working principle of such a device is as follows. A jet enters into the cavity from a pressurized plenum via the power nozzle. Then the power jet expands to fill the throat and the feedback channels. Two opposite vortices begin to form on both sides of the power jet. As the intensity of the vortices increase, one 2 American Institute of Aeronautics and Astronautics


vortex becomes dominant. This causes the power stream to deflect against the opposite wall. When the power stream deflects to the side wall, it attaches to the wall according to the Coanda effect. This allows a portion of the fluid to enter into the feedback loop. This fluid carries pressure waves back to the control port, which helps the power stream detach from the side wall. The power stream then switches to the opposite wall and the same process repeats, which results in an oscillatory fluid motion at the throat.

Figure 2.Schematic of a feedback type fluidic oscillator.

II. Numerical Investigation Computational Domain and Grid generation Three different geometric configurations were developed based on the inclination angle ( ) of the oscillator with the main stream. Figure 3 shows each geometry, with the fluidic oscillator and the direction with the freestream. The exit of the oscillator was modified based on the inclination angle ( ). The exit opening area of the oscillator increases as α becomes shallower with the streamwise flow direction. At = 90 , the exit section has a rectangular opening which is extended 3.5D in the spanwise (z-axis) direction. For = 60 , the exit opening becomes a trapezoidal shape. The exit area is approximately 90% of the actual rectangular opening used for = 90 . However, the distance between the windward and the leeward edge remains constant (1D). For = 30 , the exit opening is approximately 220% larger than the actual rectangular opening ( = 90 case). In addition, the distance between the windward and the leeward edge is approximately 2D for this configuration. Figure 4 shows the computational domain which is extended 40D in the streamwise direction and 20D (±10 from the centerline) in the spanwise direction. The domain is extended 15D in the vertical direction (y-axis).The main flow inlet is located 10D upstream of the oscillator windward edge. Hybrid grids including prism layers at the wall and polyhedral cells in the core of the domain were used. Three grids were examined for this study. Table 1 shows the properties of each grid in terms of a non-dimensional wall distance, .

Figure 3.Geometric configurations and oscillator exit geometry. 3 American Institute of Aeronautics and Astronautics


Figure 4.Computational domain and grid generation. Table 1.Details of the computational grid and cases CFD Case α = 90o α = 60o α = 30o

BR 1 2 3 1 2 3 1 2 3

Cells (million) 2.42 2.42 2.42 2.69 2.69 2.69 2.74 2.74 2.74

y+ 4.75 4.75 4.75 3.25 3.25 3.25 3.50 3.50 3.50

Time step Δt,(Sec) 2.0E-04 1.0E-04 5.0E-05 2.0E-04 1.0E-04 5.0E-05 2.0E-04 1.0E-04 5.0E-05

Model Validation An unsteady RANS (URANS) simulation was performed in this study using the commercial code FLUENT to predict the time averaged and time resolved flow fields. The flow equations were discretized by a second order upwind scheme and spatial gradients were reconstructed by a least square cell based method. The k-ω SST model by Menter et al.18 was employed to model the effects of turbulence. A second order implicit discretization in time has been adopted for the unsteady calculation. A velocity inlet ( = 15 / ) boundary condition was assumed at the main inlet and a massflow inlet condition was assumed at the inlet of the oscillator. The massflow was calculated based on the theoretical throat velocity of the oscillator. The main flow inlet turbulence intensity was 0.4%, and the oscillator inlet turbulent length scale was 0.01m. The outlet temperature and pressure were assumed ambient. The model is validated with experimental results reported by Ostermann et al.15. Since the flowfield of the fluidic oscillator is inherently unstable, predicting the frequency of the oscillation is important. The oscillation frequency of the fluidic device reported by Ostermann et al.15 was 67 Hz at BR = 3, while the model predicted an oscillation frequency of 71Hz at BR = 3, within 5% of the actual frequency. Figure 5 shows experimental and computational instantaneous velocity vectors for BR = 3 in a crossplane at x/D = 14. The contours are colored by streamwise velocity normalized by freestream velocity. The left column shows the experimental results reported by Ostermann et al.15 at three phase angles of the jet, and the right column shows the data from this model. Many similarities were observed in the velocity fields. The CFD prediction of jet spreading in the spanwise direction and jet penetration height is qualitatively similar to the experimental results. In addition, the location and the size of the vorticies are similar compared to experimental results. The sign of the vorticity is also matched in both cases. It is important to note that the boundary layer profile reported by Ostermann et al.15 was fully turbulent at the exit of the oscillator. However, a uniform velocity inlet condition was used for the CFD in this study. The boundary layer thickness ( ) 4 American Institute of Aeronautics and Astronautics


was approximately 15mm (3D) in the experimental case while in CFD, the boundary layer thickness was approximately 5mm (0.5D) at the leeward edge of the oscillator exit.

Figure 5.Instantaneous crossplane velocity vectors overlaid on contours of normalized streamwise velocity at x/D = 14, BR = 3 and = Another qualitative validation was made by comparing the 3D flowfield at BR = 3. Figure 6 shows the time resolved isosurface of Q = 130,000 s-2 for four different phase (∅) angles with data from Ostermann et al.15 and the current model. Here Q is defined as a function of vorticity magnitude (Ω ) and strain rate sensor ( ). (Eq. 1) =

1 Ω − 2

(1)

The presented phase angles of ∅ = 0 , 45 , 90 and135 make up one “sweep” of the jet, starting attached to one side of the oscillator and switching to the other. Due to symmetry, the data for ∅ = 180 , 225 , 270 and 315 is theoretically identical, in the reversed direction. It is evident that CFD was able to predict the dominant flow structures such as the alternating streamwise vortices and their directions. However, some small structures are also predicted by the current CFD model that are not seen in the experimental data. The primary reason for this is that the PIV data presented by Ostermann et al.15 are phase-averaged which involves spatial smoothing. The phaseaveraging has 2 dominant effects: 1) if the vortex appears in a slightly different place each time, the averaging will make it look more diffuse than it really is in a single snap-shot and 2) random smaller vortices that spin off from the larger structure probably appear at different places each time and will be lost in the phase averaging. There’s also spatial smoothing in any PIV system due to the minimum box size in the processing and any smoothing that was used to get rid of spurious vectors. In contrast, the CFD data presented here is essentially (is it, or not) time accurate. In addition, the current RANS turbulence model does not have enough dissipation to transfer energy from large structures to relatively small structures. The term “coherent structure” is used to describe the dominant streamwise vortex (SWV) structures in the flow field downstream of the fluidic oscillator, before they mix out into the main 5 American Institute of Aeronautics and Astronautics

Figure 6. Instantaneous flow field (top view) at various phase angle(∅). Isosurface of Q = 130,000s-2 colored by streamwise vorticity at BR = 3 and  = 90°.

III. Results This section discusses the time averaged velocity field of the fluidic device for three different inclination angles ( = 90 , 60 and 30 ) and three blowing ratios (BR = 1,2,3). In addition, the time resolved vortical structures are presented at four different phase angles (∅ = 0 , 45 , 90 and 135 ). Figure 7 shows the oscillation frequency of the jet at the exit of the device. As expected, the oscillation frequency increases with the increase of blowing ratio. Since the sweeping mechanism is dominated by the internal geometry of the oscillator, the frequency of the jet does not change when it interacts with the cross stream flow. The frequency estimated by CFD is also compared with experimental frequency reported by Ostermann et al.15 for a similar curved feedback type fluidic oscillator. A slightly higher frequency (71 Hz at BR = 3) was predicted by CFD compared to the experimental frequency (67 Hz). 100 80 Frequency(Hz)


flow. These large coherent structures are observed in the near wall region for all cases. In addition, some other important flow structures such as ring-like vortices (RLVS) and horseshoe vortices (HSV) are also visible in the CFD results and identified in Fig. 6.

60 40 0

CFD (  = 30 ) 0

CFD (  = 60 ) 0 CFD (  = 90 )

20

0

Exp (  = 90 ) (Ostermann et al. 2016)

0 0

1

2 3 4 Blowing ratio (BR) Figure 7. Oscillation frequency at various blowing ratios.

6 American Institute of Aeronautics and Astronautics


Figure 8 shows the time-resolved flow field (top view) for = 90 case at three blowing ratios for half an oscillation period. The flow field is presented by isosurfaces of = 220,000 colored by streamwise vorticity. Each column of Figure 7 represents a single oscillation phase (∅) at various blowing ratios and each row shows a sequence of phases for half an oscillation. As one might expect, two alternating streamwise vortices were found as the most dominant flow structure. The alternating behavior of the vortices is generated by the sweeping action of the jet interacting with the main flow. The sense of rotation of these two streamwise vortices are opposite from each other, which was also reported by Ostermann et al.15. It is important to note that the sense of rotation of these streamwise vortices is opposite to the counter rotating vortex pair (CRVP) found in a steady jet in crossflow. The strength of these streamwise vortices decreases due to the sweeping action of the jet which enhances mixing as they convect downstream. It was also observed that the flow field is most dynamic near the leeward side of the hole. As soon as the jet begins interacting with the mainflow, it starts to break down into smaller structures that augment mixing. With the sweeping action of the jet, this mixing can cover a larger surface area making it attractive for applications such as film cooling. A noticeable ring-like vortical structure was observed at the highest blowing ratio (BR = 3) where the jet penetrates the furthest from the wall. These ring-like vortices are also common in transverse jets in crossflow17. However, it is not well understood how they interact with the two alternating streamwise vortices.

Figure 8. Instantaneous flow field (top view) for = configuration at various phase angles(∅) and blowing ratios (BR = 1-3). Isosurface of Q = 220,000s-2 colored by streamwise vorticity. The effects of blowing ratio on the flow field are also shown in Figure 8. As blowing ratio decreases (BR = 2 and 1), the lateral spreading of the jet also decreases. This happens due to lack of momentum required to penetrate into the main flow. However, the alternating vortices still dominate the flow field as they convect downstream. The ringlike vortices (RLVS) appeared slightly ( = 2 , ∅ = 0 and 90 ), but did not continue with the streamwise vortices. Strong mixing was not observed in these cases compared to BR = 3 case. At the lowest blowing ratio (BR = 1) the jet spreading was the least and horseshoe vortices and hairpin vortices were visible at this blowing ratio. Sau and Mahesh17 reported the presence of these hairpin vortices at low blowing ratios in a steady jet case. More details of the jet spreading mechanism are explained with streamlines later in this section.



Figure 9. Instantaneous flow field (top view) for = configuration at various phase angles(∅) and blowing ratios (BR = 1-3). Isosurface of Q = 220,000s-2 colored by streamwise vorticity

Figure 10. Instantaneous flow field (top view) for = configuration at various phase angles(∅) and blowing ratios (BR = 1-3). Isosurface of Q = 220,000s-2 colored by streamwise vorticity Figure 9 and 10 show a similar time-resolved flow field (top view) for = 60 and 30 cases at three blowing ratios for half an oscillation period. The flow fields are also presented by isosurface of = 220,000 colored by streamwise vorticity. The exit opening of the device changes, as the inclination angle becomes shallower ( = 8 American Institute of Aeronautics and Astronautics


60 and 30 ). The exit opening takes a trapezoidal shape from a rectangular shape. Two alternating streamwise vortices are visible. No significant variation was observed in jet spreading since the oscillation frequency and blowing ratio remain the same in these cases and all other parameters such as boundary layer thickness and freestream velocity remain constant. With similar blowing ratios, the momentum carried out by the jet is similar for both cases that are responsible for the jet spreading. However, there are some noticeable differences in coherent structures. For = 60 case, the coherent structures survive a larger streamwise distance compared to = 90 . As seen in the previous case ( = 90 , = 3 , ∅ = 0 ), the coherent structures cover approximately 8D in the streamwise direction. In contrast, these structures remain coherent approximately 11D in the streamwise direction for this ( = 60 , = 3 , ∅ = 0 ) case. A similar trend was also observed for = 30 case where the coherent structures cover 14D along the streamwise direction (Figure 10). A lower convective velocity near the wall due to boundary layer and higher streamwise velocity due to hole inclination is responsible for these structures to remain coherent for a longer period of time. The ring-like vortices (RLVS) were observed at BR = 3 for = 60 . However, no RLVS were observed for = 30 case as the inclination angle is such that the jet is not penetrating enough to generate those RLVS. Figure 11-12 show the instantaneous streamlines of all three cases at three blowing ratios released from the point of maximum velocity at the throat. The streamlines presented here are colored by instantaneous phase angle of the jet. Since the jet is oscillating spatially, the streamlines will change with time. Figure 11 shows the top view of the instantaneous streamlines where each column of the figure show streamlines at different blowing ratios (BR) and each row show the streamlines at different inclination angles ( ). It is evident that the streamlines are bent towards the streamwise direction at the far field (x/D > 5) due to the presence of a wake behind the oscillating jet and oppositely signed streamwise vortices. However, the sweeping of the jet causes the near-hole streamlines to deflect and spread laterally. The maximum spreading is restricted by the freestream flow compared to the jet spreading in a quiescent environment. Therefore, high blowing ratio causes higher lateral spreading (Fig.11 first column) of the jet due to its high momentum compared to the local freestream momentum. During a single oscillation cycle the streamline exhibits significant bending in the spanwise direction when the jet has minimum defection (∅ ≈ 90 ). Ostermann et al.15 suggested that this bending happens due the presence of a local vortex trailing the jet during the sweeping motion. The bending pattern of the streamlines changes with different inclination angle ( ). For = 90 , the maximum bending of the streamline occurs approximately at x/D = 2 while this bending location moves further downstream from the hole as decreases ( = 60 , 30 ). As previously discussed, the vortical structures remain coherent at = 60 , 30 for a longer period of time and the bending of the streamlines is delayed. Figure 12 shows the jet trajectories by instantaneous streamlines of all three cases at three blowing ratios released from the point of maximum velocity at the throat. As discussed earlier, the streamlines presented here are colored by instantaneous phase angle of the jet. Each column of the figure show streamlines at different blowing ratios (BR) and each row show the streamlines at different inclination angle ( ). These jet trajectories are compared with the envelope of steady jet trajectory available in the literature12. It is evident that the streamlines are shallower than the lowest limit of the steady jet trajectory envelope. This happens due to the sweeping action of the jet that causes a rapid decay in velocity magnitude14. Moreover the streamline bends toward the wall due to the streamwise vortices at the downstream edge of the hole. As the blowing ratio (BR) decreases, the streamlines become shallower and remains closer to the wall. Similar behavior was observed for the = 60 , 30 case. Figure 12 also shows the jet penetration height for each case. It is evident that the maximum jet penetration occurs at the highest blowing ratio for a corresponding . As the blowing ratio decreases, the jet penetration height is also reduced due to the lack of momentum. For = 90 , the estimated maximum jet penetration was 4D from the wall. The jet penetration height reduces 100% for this case when the blowing ratio reduces from 3 to 1. Figure 13 shows the time averaged velocity vectors in a crossplane at x/D = 14 colored by streamwise vorticity. Some key features were observed from these time averaged results. The dominant alternating vortices are visible for all cases and the sense of rotation is opposite to the CRVP found in a steady jet in crossflow. The lateral jet spreading is also visible in Fig. 13. The highest jet spreading was found at = 90 , = 3 which is approximately 8D (±4 from the centerline).This lateral jet spreading is reduced significantly as the blowing ratio decreases ( = 1). Moreover, the strength of vortices decreases significantly compared to the steady jet due to the sweeping action of the jet that causes a rapid decay in velocity magnitude. This might be advantageous for applications such as film cooling where relatively weak streamwise vortices are required to prevent the hot flow from penetrating close to the cold coolant flow.



Figure 11.Instantaneous streamlines (xz-plane) colored by phase angle releases from the throat for , , configuration at various blowing (BR) ratios.

=

Figure 12.Instantaneous streamlines (xy-plane) colored by phase angle releases from the throat for , , configuration at various blowing (BR) ratios.

=



Figure 13.Time averaged velocity vectors in a crossplane at x/D = 14 colored by streamwise vorticity.

IV. Conclusion Unsteady RANS calculations were conducted to evaluate the crossflow interaction of a sweeping jet emitting at various inclination angles. A conventional curved fluidic oscillator with an aspect ratio of one was studied at several blowing ratios. The time averaged and time resolved velocity fields were examined to understand the development of the dominant flow structures. Oscillation frequency, jet spreading and jet penetration were estimated at several blowing ratios. Some key findings are listed below1. 2.

3. 4.

The oscillation frequency of the jet does not change with interaction of the crossflow. The jet lateral spreading and jet penetration height depends on the blowing ratio. High blowing ratio improves mixing and a faster decay of the jet. Two alternating streamwise vortices dominate the flow. In addition, high blowing ratio flows exhibit important flow structures such as ring-like vortices and horseshow vortices. The trajectory envelope of a sweeping jet is shallower than the lowest limit of the steady jet trajectory envelope for all cases due to rapid decay in velocity magnitude. The streamline bends toward the wall due to the streamwise vortices at the downstream edge of the hole. As the blowing ratio (BR) decreases, the streamlines become shallower and remain close to the wall.

Future studies will investigate the effect of the incoming boundary layer, streamwise pressure gradient and rate of entrainment.

Acknowledgement This work has been funded by the US Department of Energy (DOE - NETL) under award no. DE-FE0025320 with Robin Ames as program manager. Computational resources were provided by the Ohio Supercomputer Center (OSC). The views expressed in the article are those of the authors and do not reflect the official policy or position of the Department of Energy or U.S. Government. 11 American Institute of Aeronautics and Astronautics

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18

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