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TURBULENT JET INJECTED INTO A CROSS FLOW – FLOW STRUCTURE, PRESSURE FLUCTUATIONS AND RESULTING STRUCTURAL VIBRATIONS

Shridhar Gopalan Department of Mechanical Engineering

Johns Hopkins University Baltimore, MD 21218

Bruce Abraham Anteon Corporation Mystic, Connecticut

Joseph Katz Department of Mechanical Engineering

Johns Hopkins University Baltimore, MD 21218

http://www.me.jhu.edu/~lefd

ABSTRACT This study characterizes the velocity, vorticity, wall

pressure fluctuations and resulting structural vibrations caused by injection of a round, turbulent jet into a fully-developed, flat-plate, turbulent boundary layer. Considerable effort is invested in reducing the background noise in the water channel to levels that are well below the local pressure fluctuations. One of the channel walls is replaced by a vibration isolated, 1m long, aluminum plate from which the 1cm-diameter jet is injected. The cross flow velocity is fixed at 2 m/s and the velocity ratio, r (ratio of mean jet velocity to the cross flow), varies from 0.5 to 2.5 (jet Reynolds numbers up to 50,000 and Re based on cross flow speed and jet diameter =20,000)). High-resolution PIV is used to measure the flow field and low-noise, high sensitivity pressure sensors are used for the wall pressure measurements. These piezoresistive sensors have a thin film of polyurethane coating that enables employment in water for the first time. The flush-mounted transducers are installed at several locations ranging from 2-15 diameters behind the jet.

Auto-spectra of the pressure signals show the effect of the jet in the 15-100Hz range, and peak rise up to 25dB for r=2.5. The fluctuations increase with velocity ratio and decrease with distance from the jet, although there is only a 6dB increase in overall levels at r=2.5 as compared to r=1. Hilbert-Huang “amplitude” spectrum shows the frequency content of the signal as it evolves in time, and is found to be a useful tool to characterize such unsteady phenomena. Using a Stream Store data acquisition system, velocity and pressure measurements have been made simultaneously and thousands of frames have been recorded. Analysis of these frames demonstrates the relationship between the pressure fluctuations and the vortical structures. Several striking differences in the flow structure between high and low velocity ratios are described in the paper.

INTRODUCTION The injection of a fluid jet into a turbulent boundary

layer has many engineering applications. Some examples are fuel injection for internal combustion engines, chemical mixing, chimney emissions, and overboard discharge from piping systems on marine vessels or aircraft. Related unsteady phenomena include vortex shedding, flow separation and reattachment. The resulting unsteady pressure and shear stresses excites unwanted structural vibrations. This investigation seeks to characterize the steady-state and fluctuating velocity field and resulting wall pressure and acceleration from the injection of a fully-developed, round, turbulent jet into a fully-developed, flat-plate, turbulent boundary layer. High-resolution Particle Image Velocimetry (PIV) is used to measure the flow field around the jet and pressure transducers the effect of the jet on the wall pressure fluctuations. A key objective is to understand the relationship between the presence of flow structures and the wall pressure fluctuations (excitation) and the resulting plate acceleration (structural response).

The flow field created by a jet injected into a cross-flow has received much attention. Fric and Roshko (1994) present flow visualization results and mostly study higher velocity ratios (r>2). Their carefully conducted flow visualization has shown that there is a wake structure behind the jet. At high velocity ratios the wake structure is made of vorticity generated at the wall boundary layer. As will be shown in this paper, our present experiments for r>2, concur with their finding. However at lower velocity ratios, the flow picture is very different. Yuan et al. (1999) perform LES of a jet in a cross flow at velocity ratios of 2 and 3.3 at low Re. They report that the spanwise rollers on the upstream and downstream edges of the jet account for most of the TKE production in the near field. They also comment on the formation of the counter rotating vortex pair (CVP) along the lateral edges of the jet. Kelso et al. (1998) show striking flow visualization pictures at a velocity ratio of 5, illustrating many features of the jet-cross flow

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interaction. The inception of the CVP can be well understood from their pictures. Haven and Kurosaka (1997) study the effect of hole exit geometry on the near-field characteristics of cross-flow jets. They track the vorticity around the circumference of the jet to identify its relative contribution to the nascent stream wise vortices. Smith and Mungal (1998) perform extensive imaging of the planar concentration field of a jet in crossflow using PLIF with acetone vapor. These experiments are performed for r ranging from 5 to 200 and they present length scales to characterize the jet-cross flow interaction and mixing.

Most of the earlier works have focused on higher velocity ratios (r>2). This research focuses on velocity ratios ranging from 0.5-2.5 and find striking differences in the flow structure between low and high velocity ratios.

Figure 1: Experimental facility 1. Experimental setup

The experiments are performed in a specially designed closed-loop water tunnel located at The Johns Hopkins University (figure 1). The transparent, lucite test chamber is 2m long and has a cross-section of 14.5x14.5 cm2. Boundary layer suction and tripping is provided as shown in figure 1. The flow is driven by two 15 HP centrifugal pumps, each controlled by a variable frequency drive, with a maximum combined flow of about 47.5 lps. The pumps are located a floor below the test section and are separated from the test section by long flexible hoses. Combined with the reservoir (figure 1), these measures are effective in minimizing the effect of pump-induced vibrations, unsteady flow and pressure pulses at the blade rate and shaft rate frequencies. Consequently, the acoustic contamination in the tunnel is minimized and turbulent pressure measurements can be performed. In this study the cross flow in

the test-section is 2 m/s. An aluminum test plate 1m long, 6.35 mm thick and 9.7 cm wide replaces part of the sidewall of the channel and is vibration isolated from the channel walls and sealed using thick neoprene gaskets. As noted in the introduction, we intend to measure the vibrations of the Al-plate (test plate) caused by the jet-cross flow interaction. A 9.5mm diameter (D) jet is injected from the Al plate in to the cross flow, 71 cm downstream of the suction/trip location with velocities ranging from 1 to 5 m/s as shown in figure 2. The corresponding velocity ratios are r=0.5 to 2.5. A fully developed turbulent pipe flow is established in the pipe prior to injection. Thus, both the jet boundary layer (separating shear layer) and the cross flow boundary layer are turbulent.

Figure 2: Setup for PIV experiments and the coordinate system. 2. Pressure measurements

Four high-sensitivity, differential type, piezoresistive pressure transducers with a measurement range of 7kPa are flush mounted on the Al-plate, downstream of the jet exit as shown in figure 3 and table 1. These sensors, manufactured by Endevco (model 8510B-1), are coated with a thin film of polyurethane that enabled them to be used in water. To the best of our knowledge this is the first time that such coated sensors are used successfully in water. Furthermore their small size (2.5mm diameter sensor) combined with high sensitivity and low noise floor makes them unique for turbulence measurements. Auto spectra of the pressure data, averaged over 100 instantaneous data of sensor 1 for various velocity ratios are shown in figure 4. The low electronic noise floor of the sensor is also shown in figure 4. With no jet injection, i.e. r=0 shows the pressure fluctuations generated by the turbulent boundary layer on the test wall. When the jet is turned on, the

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Figure 3: Location of flush-mounted pressure sensors on the Al plate.

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Figure 4: Auto spectrum of pressure signals at sensor location 1 for different velocity ratios. effect of the jet is distinctly seen in the 15-100Hz range and peak fluctuations increase up to 25dB for r=2.5.

Interestingly, in figure 4 we see a systematic increase in levels from r=0.5 only up to r=2. The levels for r=2 and 2.5 are almost the same. As will be shown later in the paper, this diminishing effect is caused by the fact that at higher velocity ratios (r > 2) the wall boundary layer vorticity is the source for the wake structures that are responsible for the pressure fluctuations. Hence there is a weaker dependence on the velocity of the jet, whereas at lower velocity ratios the jet vorticity plays a big role in the wake region. This flow behavior is explained in detail in the following sections.

Figure 5 shows the auto-spectra of the wall pressure fluctuations for r=1, at several downstream locations. Clearly

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Figure 5: Auto spectrum of wall pressure fluctuations for r=1. the fluctuations decrease with increasing distances from the jet exit. At 15 diameters from the jet exit, the levels are only about 4dB higher than that of the turbulent boundary layer for r=0 at the same location. 3. PIV and combined PIV - Pressure measurements

PIV measurements with procedures described in several previous publications (Sridhar & Katz 1995, Roth & Katz 1999, 2001, Gopalan & Katz 2000) are performed with the light sheet perpendicular and parallel to the test plate as shown in figure 2. The coordinate system is also shown in figure 2. The PIV measurements performed parallel to the test plate were combined with the pressure measurements. In this process velocity frames from a 2K x 2K-pixel2 camera operating at 3 fps are streamed directly to hard disk arrays using a Stream-Store data acquisition system (Nimmo-Smith et al. 2002). Simultaneously pressure data is acquired at a sampling rate of 5000Hz and the timing of each velocity frame appears as a positive spike (recorded along with the pressure signals) as shown in figure 9b, for example.

Figures 6 and 7 show sample velocity and vorticity fields at the z=0 plane, for r=1 and r=2.5 respectively. This plane represents the center plane of the jet. At r=1, the lower momentum jet bends close to the wall at about y/D=1.2. Negative vorticity is seen all along the inner boundary of the jet, and at the wall-boundary layer upstream of the jet exit. Positive vorticity in lower magnitudes is observed along the forward edge of the jet. For r=2.5, the jet has higher momentum and bends only around y/D=4.5. Negative and positive vorticity of much higher magnitudes as compared to r=1, is seen along the inner and forward edges of the jet. Figures 8a & 8b show instantaneous samples of the region behind the jet exit

Location of pressure sensors

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x (cm) 1.88 3.75 8.75 13.75

x/D 2 4 9.3 14.6 z (cm) 0 0 -1.25 0

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Figure 6: Sample instantaneous velocity and vorticity for r=1 at z=0. The jet extends from –0.5≤≤≤≤x/D≤≤≤≤0.5. at the plane y/D=0.8, for r=1.0. Pressure data were simultaneously recorded for these frames. The formation of a separated region (region with almost zero velocity) or a “dead zone” is clearly evident. This region is bounded by positive and negative vortical layers. At z>0, there is positive vorticity and at z

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Figure 9: (a) Region downstream of the jet exit for r=1, 4mm away from the wall (i.e. y/D=0.4). Purple circles are the pressure sensors. (b) Corresponding pressure signals and velocity frame timing. Figure 9a is another example showing the region downstream of the jet exit at y/D=0.4. The “dead zone” is evident, bounded by positive and negative vorticity layers. Since the light sheet is closer to the wall than for y/D=0.8, no part of the jet core is cut, resulting in an unbroken “dead zone”. The width of the dead zone for r=1 is about 1.5D and the length persists till about x/D=5. The two circles shown in figure 9a at z=0, (and also figures 11a and 12a) represent the pressure sensors and the corresponding pressure signals are shown in figure 9b. In this figure (and all other cases too) the velocity frame timing is the horizontal line at zero with a positive spike. Analysis of the pressure data is presented in the next section.

Figure 10 is a flow visualization picture at r=1, where only the jet fluid is densely seeded with fluorescent particles that appear yellow in the picture. The illumination is a laser light sheet at y/D=0.4 and it is evident from the picture that the bounding vorticity layers in figures 8a, 8b and 9a are made of jet fluid. Thus the wake region near the wall for lower velocity ratios is made of jet vorticity. Figure 11a shows the wake region for r=1.5 at y/D=0.8. Clearly this flow is similar to that of r=1 but with a much wider dead zone, about 2D.

Figure 10: Light sheet at y/D=0.4, showing jet fluid (that appear yellow) in the bounding vorticity layers. Cross flow is from left to right and r=1.

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Figure 11: (a) Region downstream of the jet exit for r=1.5 at y/D=0.8 showing the “dead zone”. (b) Pressure signals and velocity frame timing. Figure 11b is the pressure signal from sensors 1 and 2 and its discussion is presented in the next section.

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Figure 12a shows the wake region at y/D=0.4, for r=2.5 along with the pressure data (figure 12b). In contrast to the results in figures 8a, 8b, 9a and 11a there is no “dead zone”. Distinct rolled-up vortical structures of alternating signs and high speed flow between them are clearly evident, compared to counter rotating vorticity layers bounding a dead zone for the lower velocity ratios. Flow visualization performed at r=2.5 similar to that shown in figure 10 confirms Fric and Roshko’s observation that the source of vorticity in the structures seen in figure 12 is the wall boundary layer. Note the pressure signal (sensor 1) in figure12b, which shows a minimum when the frame was recorded consistent with the presence of the strong vortex above sensor 1.

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Figure 12: (a) Region downstream of the jet exit for r=2.5 at y/D=0.4 showing vortical structures and absence of the “dead zone”. (b) Pressure signals and velocity frame timing. Thus, for lower velocity ratios, namely r≤1.5, the flow downstream of the jet exit is characterized by a separated region or a “dead zone”. The width of this separated region increases with velocity ratio and is up to 2D at r=1.5 and the length persists up to 5D. The dead zone is bounded on either side by vorticity layers of opposite signs that are shed from the jet. The cross flow moves around and over this separated region. Conversely for higher velocity ratios, namely r>2, the flow is

remarkably different with no dead zones. There are rolled-up vortical structures of alternating signs in the wake with high speed flow between them. The source of vorticity for these structures is the wall boundary layer. The jet vorticity remains confined to the jet and is located far away from the wall due to the higher momentum of the jet, eventually forming the CVP. 4. Hilbert-Huang Spectra

The pressure signals were analyzed using a commercially available add-on to Matlab that computes the Hilbert-Huang spectra (HHS) (Huang et al. 1998). HHS describes the amplitude-frequency content of a signal as a function of time. Figure 13 shows the zoomed-in HHS (0.1s long) of part of the pressure signals in figure 9b. Horizontal axis represents time, vertical axis the frequency and the colors represent the amplitude. The dashed vertical line in the HHS indicates the velocity frame timing. HHS enables us to identify features of the flow that a conventional spectra cannot, since it provides the frequency content of the signal as it evolves in time. For example, consider the frequency contents of the sensor 1 signal, indicated by the dashed circle in figure 13a. It can be argued that these pressure fluctuations are sensed by sensor 2 at slightly different frequencies, a short time later as indicated by the displaced dashed circle in figure 13b. The unsteady convecting vortical structures that cause the pressure fluctuations change as they pass from sensor 1 to sensor 2. The convection speed of these structures can also be estimated from the time delay between the dashed circles in figure10. In this example it is about 0.5m/s, i.e. 25% of the cross flow. Recall that the convection speed here refers to the instabilities or structures in the vorticity shed from the jet that travel on either sides of the “dead zone” (figure 8a, 8b, 9a or 11a). A conventional Fourier spectra would have simply given broad frequency peaks for the signals and the time displacement of the frequency contents cannot be seen.

The instantaneous HHS vary considerably with time. The present example illustrates the unsteady behavior of the jet-crossflow interaction. It also exhibits the usefulness of HHS, allowing us to identify and follow convecting structures even in highly unsteady flows. Note that the signals also have a low frequency content (

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from the above examples, the convecting structures leave a signature in the 30-60Hz range. The frequencies in the 20Hz range and below (but above 10 Hz) are associated with the meandering of the wake region and the jet. The variability in frequency with time causes broad averaged Fourier spectra as seen in figure 4 or 5.

Figure 13: Instantaneous sample zoomed-in Hilbert-Huang spectra for r=1, for the pressure signals in figure 9b - (a) Sensor 1 (b) Sensor 2. 5. Summary The flow structure caused by a jet in a cross flow is highly unsteady and depends strongly on the velocity ratio and shows two clear patterns. Pattern 1 occurs at low velocity ratios, namely at r ≤ 1.5 and Pattern 2 occurs at high velocity ratios, namely at r ≥ 2. At low velocity ratios, the jet creates a

Figure 14: Instantaneous sample zoomed-in Hilbert-Huang spectra for r=1.5, for the pressure signals in figure 11b- (a) Sensor 1 (b) Sensor 2. separated region or a “dead zone” bounded by the counter rotating vorticity sheets shed from the jet. A 2-D slice of this enclosed region appears as shown in figure 9a, for example. The paper provides clear evidence that these bounding vorticity layers are made of jet fluid. The cross flow moves around this enclosed region. A schematic description of this flow pattern is sketched in figure 15. Conversely at higher velocity ratios, the high-momentum jet bends far away from the wall and the jet vorticity remains confined with it. On bending, this jet vorticity leads to a counter rotating vortex pair (CVP) identified by many earlier works (e.g. Fric & Roshko, Kelso et al. 1998, Kelso et al. 1995). The region behind the jet, near the wall is now made of large-scale vortical structures (or “legs”) containing wall boundary layer vorticity, a slice of which is shown in figure 12a.

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Hilbert Huang spectra prove useful to analyze the wall pressure fluctuations and follow the advection of unsteady large-scale structures. Two examples shown in this paper indicate the complex nature of the wall pressure fluctuations, the frequencies involved, the causes for the fluctuations and the convection speed of wake structures. Vibration measurements of the test plate coupled with these pressure and flow measurements will soon be performed.

Figure 15: Schematic representation of the jet-cross flow interaction for velocity ratios ≤≤≤≤ 1.5.

ACKNOWLEDGMENTS The authors like to thank Endevco (www.endevco.com), who engineered the coatings on their pressure sensors enabling use in water. Special thanks Dr. Bo Tao of Purdue University, who was involved in the pressure measurements. This research is made possible by funding from ONR - Dr. Steven Schreppler and NSWC - Dr. William Martin. The authors express their gratitude to them.

REFERENCES FRIC T F & ROSHKO A Vortical structure in the wake of a transverse jet. J. Fluid Mech. 1994, 279. GOPALAN, S., KATZ, J., KNIO, O. 1999 The flow structure in the near field of jets and its effect on cavitation inception, Journal of Fluid Mechanics, 398, 1-43. HAVEN B A & KUROSAKA M Kidney and anti-kidney vortices in crossflow jets. J. Fluid Mech. 1997, 352. HUANG, N. E. et al. 1998 The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis. Proc. R. Soc. London 454, 903-995. KELSO R M, LIM T T, PERRY A E New experimental observations of vortical motions in transverse jets. Phys. Fluids 1998, 10.

KELSO R M, LIM T T, PERRY A E An experimental study of round jets in cross-flow. J. Fluid Mech. 1996, 306. ROTH, G., & KATZ, J. 2001 Five techniques for increasing the speed and accuracy of PIV interrogation, Meas. Sci. Technol. 12, 238. SMITH S H & MUNGAL M G Mixing, structure and scaling of the jet in crossflow. J. Fluid Mech. 1998, 357. SRIDHAR, G. & KATZ, J. 1995 Lift and drag forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7, 389–399. YUAN L L, STREET R L, FERZIGER J H Large-eddy simulations of a round jet in crossflow. J. Fluid Mech. 1999 379.