[American Institute of Aeronautics and Astronautics 40th Fluid Dynamics Conference and Exhibit -...

American Institute of Aeronautics and Astronautics

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Array Measurements of the Unsteady Surface Pressure in a Sharp-Edged Impinging Jet

W. Jiang1, K. Zhang2, A. Naguib3, Michigan State University, East Lansing, MI-44824, USA

and

M. El-Anwar4, A.M. Abouel-Fotouh5 National Research Centre, Giza, Egypt

Studied herein are the space-time characteristics of the surface-pressure fluctuations resulting from the impingement of an axisymmetric jet (at Reynolds number based on diameter of approximately 13500) on a flat wall. Unlike the bulk of existing literature, where the focus has been on jets emerging from a contoured nozzle or at the end of turbulent pipe flow, the present study examines a jet emerging from a sharp-edged circular opening. Pressure measurements are conducted using an array of thirty electret microphones embedded in the impingement plate. Data are acquired under normal- and oblique-impingement conditions. The results are compared to an earlier counterpart study of a jet exiting from a contoured nozzle. The comparison shows that significant fundamental differences in the observed pressure fluctuations and their spectral characteristics exist for the different jet exit conditions. Furthermore, it is found that alteration of the observed wall-pressure-field characteristics with change in the impingement angle may be explained through a hypothesis based on published work regarding the distortion of an isolated vortex ring impinging on an inclined wall. Future simultaneous measurements of the flow and wall-pressure fields are required to validate this hypothesis.

Nomenclature D = jet diameter f = frequency H = separation distance between jet exit and center of impingement plate m = integer representing a time offset (in number of data samples) between two time series N = total number of samples recorded in a time series n = integer representing the sample number in a time series Pd = dynamic pressure based on the jet exit velocity. Pd = ½Uj

2 p' = wall-pressure fluctuation p'rms = root mean square of the wall-pressure fluctuation q = pressure-generation source Rp1p2 = two-point wall-pressure cross correlation ReD = jet Reynolds number based on jet exit velocity and jet diameter r, = polar coordinates in the plane of the impingement plate t = time Uj = jet exit velocity uc = convection velocity of wall-pressure disturbances

1 Undergraduate student, Department of Mechanical Engineering 2 Graduate student, Department of Mechanical Engineering, student AIAA member 3 Associate Professor, Department of Mechanical Engineering, senior AIAA member 4 Researcher, Department of Mechanical Engineering 5 Researcher, Department of Mechanical Engineering

40th Fluid Dynamics Conference and Exhibit28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4851

Copyright © 2010 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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x,y,z = cartisian coordinates with origin at the center of the jet exit ij = strain-rate tensor p'p' = power spectrum of the wall-pressure fluctuation = inclination angle of impingement plate relative to the jet axis = fluid density i = vorticity vector

I. Introduction MPINGING jets are significant to many practical engineering applications, including heating, cooling and drying. Many studies of impinging jets have focused on the examination of the heat transfer from the impingement plate (e.g.

Yan et al.1, Viskanta2, Lytle and Webb3 and Webb and Ma4) and the flow field (Didden and Ho5, Popiel and Trass6 and Landreth and Adrian7). In contrast, there is little information regarding the space-time characteristics of the pressure fluctuations (p') acting on the impingement plate. The exceptions are two recent studies by Hall and Ewing: one (Ref. 8) where two-point wall-pressure measurements are employed and the other (Ref. 9) based on the use of extensive wall-pressure-sensor-array measurements. Such information has direct relevance to the unsteady loading on the impingement plate as well as flow-induced noise and vibration. Moreover, the intensity of p' is indicative of the strength of the associated turbulent flow structures, which are responsible for significant enhancement in heat transfer in impinging jets.

In the vicinity of the impingement plate, the flow field of a round normal impinging jet is typically divided into two regions: a stagnation region (r/D < 1; r is the radial coordinate measured from the centre of the jet and D is the jet diameter), where the turning of the jet to become parallel to the plate takes place, and a wall-jet region (r/D > 1). Using data from azimuthal wall-pressure arrays for the case of a jet exiting at the end of fully-developed turbulent pipe flow, Hall and Ewing9 found the dominant p' modes to be helical in the stagnation region. The strength of these modes, which the authors linked to the flow structures existing in the jet prior to its impingement on the plate, increased with increasing distance between the jet exit and impingement plate. In the wall-jet region, Hall and Ewing9 found axisymmetric and helical structures to be significant. Both modes had the same frequency, which was different from the much lower frequency of the helical modes found in the stagnation zone, and they decayed in strength with increasing separation between the jet exit and the plate. This led the authors to conclude that the helical modes identified for r/D > 1 were not the same as those originating in the jet and found in the stagnation zone. Instead, Hall and Ewing9 hypothesized that an asymmetric interaction of the jet’s flow structure with the impingement plate caused the formation of the helical modes observed in the wall jet.

More recently, El-Anwar et al.10 also utilized an extensive wall-pressure microphone array to measure the unsteady pressure caused by a jet exiting from a contoured nozzle and impinging on flat wall at normal and oblique incidence. The general characteristics of the wall-pressure rms (root mean square) and spectra were consistent with those found by Hall and Ewing9 in the case of normal impingement. In addition, El-Anwar et al. found that oblique impingement of an axisymmetric jet on a flat wall caused intensification of the wall-pressure fluctuations in the half plane where the jet experiences more obtuse turning relative to normal incidence, and vice versa. The intensified pressure fluctuations were associated with a larger convection velocity than in the normal-impingement jet.

In the present work, the study of El-Anwar et al.10 is extended to include a jet emerging from a sharp-edged opening (see Figure 1 for definition of the geometry). As will be seen in the results provided here, the change in the jet exit geometry causes fundamental changes in the wall-pressure characteristics. The objective of the current investigation is to document the spatio-temporal characteristics of the unsteady surface pressure acting on the impingement plate for the sharp-edged jet flow, and compare these characteristics to the results of El-Anwar et al.10 for a jet exiting from a contoured nozzle. Additionally, the effect of the impingement angle on the results will be examined.

II. Experimental Setup The experimental setup is illustrated in Figure 1: an axisymmetric air jet with a top-hat exit velocity profile and a

diameter D = 20.3 mm impinges on a flat, circular disc. The diameter of the disc is 15D, which is more than an order of magnitude larger than the jet diameter in order to minimize disc-edge effects on the measurements. The impingement disc is located at a distance H away from the jet exit and could be inclined to cause deviation from normal impingement by an angle (see Figure 1)

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Unsteady-surface-pressure (p') data are acquired using 30 microphones embedded in the impingement plate. Each microphone is a Panasonic WM-61A electret microphone with a package diameter of 6 mm and a sensing-hole diameter of 2 mm (approximately 0.1D). The frequency response of all microphones is obtained from calibration against a Brüel and Kjær ¼" microphone (model 4938-A-011) in a plane wave tube. The calibration procedure is similar to that employed by Daoud and Naguib11. The sensors are configured into one radial and two azimuthal arrays (at r/D = 1.25 and 2.91; referred to as inner- and outer-azimuthal arrays respectively) as depicted in Figure 2; also note the coordinate-system’s definition in the figure. The radial array contains eight microphones that are spaced 0.41D apart starting from r/D = 0. On the other hand, the azimuthal array at r/D = 1.25 contains eight uniformly distributed microphones, while the one at r/D = 2.91 has sixteen microphones with an angular spacing of 22.5o.

Microphone signals are sampled using two data-acquisition PC-boards: National Instruments PCI-6024E and PCMCIA-6062E. The boards have 12-bit resolution, maximum sampling rate of 200 and 500 kHz respectively, and they are synchronized by operating them in external-trigger mode and providing a common trigger signal from an Agilent 33120A function generator. The boards are configured for differential input, limiting the number of analog-input channels on each board to eight. Because of this limitation, two separate data recordings are necessary to capture the signals from all microphones: one for recording the signals of microphones in the radial and inner-azimuthal arrays, and the other for capturing the output of the outer-array microphones. Channel multiplexing of the analog-input channels produced a maximum time delay among the recorded time series of 35 s. During such period, a fluid particle translates a distance of 350 m at the jet exit velocity (Uj), which is more than fifty times smaller than the jet diameter. For the results presented here, data are acquired for a duration of 52.4 seconds at a rate

15D

D

x

zH

Figure 1. A schematic drawing of the investigated flow configuration.

Outer-Azimuthal Array:r = 2.91D

y

z

Inner-Azimuthal Array:r =1.25D

Radial Array

r

Figure 2. Microphone-array configuration: r and are in the plane of the impingement plate, while y and z are orthogonal to the jet’s axis (i.e. y and z are also in the plane of the plate for normal impingement).


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of 5000 samples/s. The sampling period is approximately four orders of magnitude larger than the time it takes a fluid particle to advect over a distance equal to the radial extent of the measurement domain. The flow and geometrical parameters are Uj = 10 m/s, H/D = 4, and = 0 and 30. The corresponding jet Reynolds number based on diameter is ReD 13550. Data are acquired for sixteen different azimuthal locations of the radial array (0 ≤ ≤ 337.5) in steps of 22.5 in order to get detailed information of the radial evolution of the wall pressure at different azimuthal angles.

III. Results and Discussion

A. Effect of Jet Exit Geometry The radial distribution of the

fluctuating-pressure rms (p'rms) in the case of normal impingement is plotted in Figure 3 using red circles. The results are compared to those obtained by El-Anwar et al.10 for a jet exiting from a contoured nozzle (black squares) at a comparable Reynolds number (ReD 16500). The random uncertainty of the measurements is less than 2% of the peak p'rms (based on two standard deviations). As seen from Figure 3, the sharp-edged geometry of the jet exit causes the level of pressure fluctuations to increase substantially relative to the contoured-nozzle exit (as well as relative to that reported by Hall and Ewing9 for a jet exiting at the end of a long pipe). The difference is particularly pronounced in the stagnation zone (r/D < 1). In fact, the maximum pressure fluctuations in the present study are found in the stagnation zone, whereas for the contoured nozzle, the peak p'rms is located in the wall jet zone (r/D = 1.67). The substantial rise in the rms level is believed to be caused by the larger initial mean shear associated with the much thinner shear-layer at separation in the sharp-edged geometry. Presumably the associated larger mean shear leads to the creation of more energetic vortex structures. The effect of these structures on wall-pressure generation is expected to be particularly strong in the stagnation zone where they “impinge” on the wall. At larger r, in the wall-jet zone, the pressure disturbances produced by the outward convection of these structure is only partly responsible for the observed p'rms. More specifically, another important pressure generating mechanism in the wall-jet region, which was discussed in Hall and Ewing9, is that resulting from structures generated from the interaction of the shear-layer vortices with the wall. Such interaction, in the case of an isolated vortex impinging on a wall, is found to result in the formation of secondary vortices of opposite sense of circulation to that of the vortices impinging on the wall (see Refs. 12-14 for example). Though they did not report velocity measurements, Hall and Ewing9 hypothesised that the local peak in p'rms found in the wall-jet zone results from the formation of secondary vortices. As discussed above, such a peak is found only for the jet exiting from the contoured nozzle. The absence of a similar peak in the sharp-edged jet is suggestive that the secondary vortices may not form in this case, or that the jet vortices are substantially stronger than the secondary ones.

Additional stark differences between the sharp-edged and contoured-nozzle jet geometry are seen when examining the frequency spectra (p'p'). Examples of such spectra obtained within the wall-jet zone are displayed for the former and latter cases at comparable, though not exact, radial locations in Figure 4. The spectra are obtained from 512 data records, leading to a random uncertainty of approximately 4%. In both jet-exit configurations, a broad spectrum peak, implying the association with a quasi-periodic flow structure, is evident in the spectra. In the case of the contoured-nozzle jet, the frequency of the peak remains at fD/Uj = 0.5 for the first two radial locations then it decreases by a “small” amount to 0.4 as r/D increases from 1.67 to 2.33. In contrast, for the sharp-edged jet, the peak frequency decreases monotonically with increasing radial coordinate over the entire range examined. This decrease is more substantial than in the contoured-nozzle case (as well as in the case of a jet at the exit of a long pipe; see Hall and Ewing9), corresponding to a change of fD/Uj from 0.7 at r/D = 1.25 to 0.3 at r/D = 2.5. As will be

Figure 3. Radial distribution of the rms pressure fluctuation for normal impingement ( = 0o): sharp-edged (red circles) and contoured-nozzle (black squares) exit. Pd is the dynamic pressure based on jet velocity: Pd = ½Uj

2.


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seen in section B below, the decrease in the peak frequency in the sharp-edged jet is predominantly caused by a drop in the convection velocity of the pressure-producing structures with increasing r. As discussed above, it is believed that these structures are primarily those originating from the jet shear layer and being advected in the outward radial direction by the mean flow. Presumably, the structures weaken as they travel (as reflected from the monotonic decrease in the spectrum peak in the left plot in Figure 4) due to dissipative influences. The more complex behavior of spectra for the contoured-nozzle jet, exhibiting non-monotonic behavior in both the spectrum peak magnitude and frequency with increasing r is likely due to the coexistence of multiple equally-important pressure-generating structures (such as the jet and secondary vorticies).

B. Effect of Impingement Angle In the remainder of the paper, the influence of the

jet impingement angle on the surface-pressure fluctuation is examined for the sharp-edged jet only. The reader is referred to El-Anwar et al.10 for similar results when the jet emerges from a contoured nozzle. The azimuthal distribution of the rms pressure-fluctuation obtained from the outer azimuthal array at r/D = 2.91 is depicted in Figure 5 for normal and oblique impingement ( = 0 and 30 respectively). As expected, normal impingement leads to a practically axisymmetric rms distribution (within 7% variation). In contrast, inclination of the impingement plate leads to an increase in p'rms in most of the left half-plane (where the jet turning angle is below 90), and vice versa. This effect is qualitatively consistent with that reported by El-Anwar et al.10 for the jet exiting from a contoured-nozzle. This suggests that although the pressure-generating flow structures in the sharp-edged jet seem to exhibit some differences from their counterpart in the contoured-nozzle jet, in both cases the impingement-plate inclination appears to have similar influence on the strength of the associated pressure fluctuations.

The largest decrease in p'rms relative to normal impingement is observed at = 0, which is the azimuthal direction along which the impingement causes the jet to turn through the largest angle. On the other hand, the largest increase in p'rms is found at =

Figure 4. Frequency spectra of the wall pressure in the wall-jet zone for normal impingement ( = 0o): sharp-edged (left) and contoured-nozzle (right) jet exit.

Figure 5. Effect of impingement angle on the azimuthal distribution of p'rms/Pd at r/D = 2.91. The magnitude of p'rms/Pd is indicated by the radial coordinate of the plot, and the azimuthal angle units are in degrees.


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180, where the jet turning angle is smallest. The radial distribution of p'rms along both of these azimuthal directions is depicted in Figure 6. Interestingly, the influence of oblique impingement on the level of pressure fluctuations observed in Figure 5 is not sustained over the entire radial extent of the measurement domain. Instead, this influence is only seen in the wall-jet zone (r/D approximately larger than unity), where the outer-azimuthal-array data in Figure 5 are captured. Within the stagnation area, the trends are reversed and p'rms increases relative to normal impingement at = 0, and decreases at = 180. In the former case, the increase is such that the level of pressure fluctuations becomes very strong, nearing 40% of the dynamic pressure based on the jet exit velocity.

A plausible explanation of the effect of oblique impingement on the level of pressure fluctuations may be arrived at by considering the pressure generation by the jet’s shear-layer vortices, and how the characteristics of these vortices are altered by interaction with the wall at oblique versus normal incidence. First, it is noted that regions of high vorticity in the flow are responsible for the generation of strong negative pressure. This can be explained through consideration of Poisson’s equation, governing the relationship between the hydrodynamic pressure and the velocity field for incompressible flows (e.g. see Townsend15, p. 43):

),,,(2 tzyxqp (1)

Where 2 is the Laplacian operator, p is the pressure, is the fluid density and q represents the spatial distribution of flow “sources” of pressure at time t. The pressure source term q is given by the inner product of the velocity-gradient tensor with itself. However, Bradshaw and Koh16 showed that q may be expressed in terms of the symmetric (strain rate, ij) and anti-symmetric (rotation) components of the velocity-gradient tensor. In turn, the anti-symmetric component can be re-written in terms of the vorticity vector (i), leading to the following form of q:

iijiijq

2

1 (2)

The solution to Eq. (1) is given by the following convolution integral:

s

sss

sss dVzzyyxx

tzyxqtzyxp222 )()()(

),,,(

2/

),,,(

(3)

Where xs, ys and zs represent the spatial coordinates of the pressure-generating source and the denominator of the integrand represents the distance between the location of the source and the point of observation of the pressure. Equation (3) shows that the pressure at a point located at x, y and z (e.g. at the location of a microphone in the present measurements) is the result of “summation” of all sources in the flow field, inversely weighted by their distance to the point of pressure observation. Since the cores of vortices are regions of high vorticity, they are also

Figure 6. Comparison between the radial distribution of p'rms for normal and oblique impingement. Data are shown for two azimuthal anlges along which the mean flow experiences the least ( = 180; left plot) and most ( = 0; right plot) turning. Some differences are seen between the normal-impingement data (red circles) in the left and right plots. These differences are within the quality of the flow axisymmetry observed (less than 7% variation).


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regions of strong negative pressure generation (see Eq. (2), noting the negative sign ahead of the positive definite vorticity source term). It is also important to note that a vortex with the same core vorticity would cause a wall-pressure signature that would decrease with increasing distance between the vortex and the wall (because of the denominator of the integrand in Eq. (3)).

Referring to Figure 6, it is reasonable to expect that, for the case of normal impingement ( = 0), the peak in the radial distribution of p'rms at r/D = 0.41 is the result of periodic/quasi-periodic impingement of the shear-layer vortices on the wall within the stagnation zone. As the plate is tilted, the pressure fluctuations at r/D = 0.41 are intensified on the side where = 0 and attenuated at = 180. Following the above discussion, this implies that the plate tilting causes the vorticity in the vortex core at = 0 to become larger than that at = 180 and/or the vortex core gets into closer proximity to the wall at = 0 than at = 180. The study by Lim17 of an isolated vortex ring impinging on an inclined wall shows that the wall inclination relative to the plane of the vortex causes an asymmetry in the vortex structure whereby the vortex core on the side that reaches the wall first (which would be at = 0 in the present study) does in fact get in closer proximity to the wall. Furthermore, because of the image-vortex effect, the closer the core gets to the wall, the stronger the vortex stretching it experiences leading to a smaller core size, and hence more intensification of the core vorticity. The combination of closer proximity to the wall and stronger core vorticity should enhance the wall-pressure signature of the side of the vortex reaching the wall first, as seen here at = 0, relative to that on the opposite side.

Farther out in the radial direction, in the wall-jet domain, the pressure fluctuations decay quickly with increasing r along the = 0 direction, while they remain fairly constant along the = 180 direction. The fast decay in the former direction is consistent with the idea that the vortex core is closest to the wall on the = 0 side. As described above, this proximity causes the core to become substantially smaller due to stronger stretching via the image vortex, leading to quicker annihilation through vorticity diffusion as the core travels outwards in the radial direction.

The effect of oblique impingement on the wall-pressure frequency spectra at = 0 and 180 may be examined from the results shown in Figure 7. Each of the two plots provided in the figure gives a comparison between spectra obtained under normal and oblique impingement conditions at r/D = 2.91. Overall, the spectrum shape remains fairly invariant with the change in impingement angle, exhibiting a broad peak, characteristic of an underlying quasi-periodic behavior. However, the frequency of the spectrum peak is shifted considerably, becoming lower on the side where = 0, and higher on the side where = 180. Oblique impingement also affects the spectrum magnitude in a manner consistent with the effect on p'rms found in Figures 5 and 6.

The reason for the shift in the spectrum-peak’s frequency seen in Figure 7 is explored by considering the convection velocity (uc) of pressure disturbances in the radial direction. Specifically, if p' is dominated by the passage of the shear-layer vortex structures as they convect outwards away from the stagnation zone, then the proper length and velocity scale for normalizing the frequency f are the local vortex-core diameter and convection velocity. That is, the larger the convection velocity the higher the frequency of the resulting pressure imprint. To calculate uc at a given r, the two-point cross correlation coefficient (Rp1p2) is computed between signals obtained from a microphone at that location and a neighboring microphone in the radial array. The specific equation used in the calculation is given by:

Figure 7. Comparison between the frequency spectra of p' for normal and oblique impingement at r/D = 2.91. Data are shown for two azimuthal angles along which the mean flow experiences the least ( = 180; left plot) and most ( = 0; right plot) turning.


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rmsrms

N

n

pp ppN

mnpnp

mR21

1

021

''

)(')('

)(21

(4)

Where n is an integer representing the sample number in the recorded time series, N is the total number of samples and m is an integer denoting the delay of signal p2 (measured at radial location r2) with respect to p1 (measured at r1) in data samples (the corresponding time offset is denoted by). An example of Rp1p2 obtained for r1/D = 2.5 and r2/D = 2.91 in the case of a normal-impinging jet is shown in Figure 8. A significant correlation peak of more than 0.5 is found at a non-zero time offset. The offset in the peak is indicative of the convective nature of the underlying pressure-generating disturbance. By dividing the spacing between the two microphones r = r2 – r1 by the time offset of the correlation peak, the convection velocity of the disturbance is obtained. The resulting values normalized by Uj at sixteen different azimuthal angles are plotted in Figure 9 for the normal and oblique impingement cases. In the former case, the convection velocity is uniform (though with some data scatter) and has a value of approximately half the jet exit velocity. In the case of oblique impingement, a strong asymmetry in the azimuthal distribution of uc develops. This asymmetry is such that at = 112.5 and 247.5, uc is the same as in normal impingement. For 112.5 < < 247.5 (which is practically most of the half plane where the jet turning angle becomes less than 90) uc increases beyond the normal-impingement value, becoming as high as 0.85Uj at = 180. In contrast, in the half plane where the jet turns more than 90, the convection velocity decreases below the normal-impingement magnitude reaching a minimum value of 0.25Uj at = 0. The change in uc value relative to normal impingement could, in part, be related to the azimuthal variation in the proximity to the wall of the core of the shear-layer vortices. As discuss earlier, based on the investigation by Lim17, it is expected that the core location will be closest to the wall at = 0 and farthest at = 180. Given the mean velocity gradient in the boundary layer developing over the impingement plate, the closer the vortex location to the wall, the lower is the local mean velocity, and hence the slower the advection of the vortex core. Thus, the convection velocity results appear to be consistent with the hypothesis that the wall-pressure fluctuations are dominated by the passage of the shear-layer vortices and their subsequent distortion due to the influence of the impingement plate.

With the knowledge of the convection velocity, the spectra in Figure 7 are plotted again in Figure

Figure 8. Cross-correlation between p' at r1/D = 2.5 and p' at r2/D = 2.91 for a normal-impinging jet.

Figure 9. Azimuthal distribution of uc/Uj for normal ( = 0o) and oblique ( = 30o) impingement. The magnitude of uc/Uj is indicated by the radial coordinate of the plot, and the azimuthal angle units are in degrees.


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10 after using uc instead of Uj to normalize the frequency. As hypothesized above, at = 180, the shift in the spectrum-peak’s frequency disappears with the use of the convection velocity to normalize the frequency. This implies that the rise in the peak’s frequency at = 180 when the impingement plate is tilted is caused by the resulting increase in the convection speed of the pressure-generating structures past the pressure measurement location. On the opposite side of the plate ( = 0; right plot in Figure 10), though the difference in the spectrum-peak’s frequency for = 0 and 30 does not completely disappear, it becomes much smaller (approximately 40% of the peak frequency for = 30 in Figure 10 in comparison to 300% in Figure 7). The remaining difference is likely the result of dissimilarity in the scale of the pressure-generating structures (e.g. the convecting vortex core’s diameter) between the two cases.

Decrease in the convection velocity also accounts for most of the reduction in the spectrum-peak’s frequency with increasing r in the case of normal impingement (see left plot in Figure 4). Specifically, in this case, the convection velocity is obtained at r1/D = 1.25, 1.67, 2.08 and 2.50 using cross-correlation of the pressure signal acquired at each of these locations with a signal measured at r2/D = 1.67, 2.08, 2.50 and 2.91. The resulting correlations, depicted in Figure 11, exhibit a correlation peak at a time offset that becomes progressively larger with increasing r. This implies that the convection velocity decreases monotonically in the radial direction, which is physically sensible given that the mean velocity for the radial wall-jet flow should decrease with increasing r because of mass conservation.

A reproduction of the spectra in the left plot of Figure 4 can be found in Figure 12 after normalization of the frequency using the convection instead of the jet exit velocity. As seen from the figure, the variation in the spectrum-peak’s frequency with increasing r is substantially reduced with this normalization. Some variation still remains, particularly at the largest radial location. It is believed that this variation is caused by changes in the length scale of the pressure-producing structures. Two primary, but opposing, mechanisms influence this change as the structures convect in the positive r direction. The first one is vortex stretching caused by the increasing diameter of the “ring” vortices originating from the jet’s shear layer. This mechanism causes reduction in the vortex core’s diameter. The second mechanism is diffusion, which leads to increase in the size of the structures with increasing r. Whether these mechanisms and the associated vortex diameter variation are in fact responsible for the residual variation of the spectrum-peak’s frequency in Figure 12 remains to be verified through concurrent velocity field measurements.

Figure 10. Spectra similar to those shown in Figure 7 but with normalization of the frequency using the convection velocity uc instead of Uj.

Figure 11. Cross-correlation of the wall-pressure at different radial locations in a normal-impinging jet.


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IV. Conclusions Measurements of the unsteady surface-pressure field are conducted using microphone arrays embedded in a flat

wall upon which an axisymmetric jet, emerging from a sharp-edged opening, impinges. Pressure data are recorded for normal and oblique impingement at a plate-to-jet distance of four jet diameters and a jet Reynolds number of approximately 13500 (based on jet exit diameter). Analysis of the results leads to the following conclusions:

1. For normal impingement, fundamental differences are found in the wall-pressure characteristics of the jet exiting from a sharp-edged orifice in comparison to those for a jet exiting from a contoured nozzle or at the end of fully-developed turbulent pipe flow. First, the level of peak pressure fluctuations in the sharp-edged jet is found to be more than twice that found in the latter jet types at comparable Reynolds number and similar plate-to-jet distance. Second, for the sharp-edged jet, the behavior of the frequency spectrum of the wall pressure in the wall-jet region is found to imply a quasi-periodic, pressure-generating flow structure that is advected outwards in the radial direction while decelerating and decaying in strength. In contrast, the wall-pressure spectrum in the other types of jet is found to have a more complex behavior that might imply the co-existence of multiple types of pressure-generating structures in the wall-jet region. Overall, the results lead to the hypothesis that the thinness of the boundary layer at the exit of the sharp-edged jet, in comparison to other jet types at a comparable Reynolds number, results in the development of more energetic vortical structures that dominate the pressure generation process not only within the stagnation zone (as is the case of other types of jet) but also in the wall-jet region as well. Future concurrent velocity-field and pressure measurements are planned to confirm this hypothesis.

2. Oblique impingement is found to cause strong asymmetry in the azimuthal distribution of the surface-pressure fluctuation level, frequency spectrum and convection velocity. The asymmetry is such that stronger level of pressure fluctuations, relative to normal impingement, is found in the half plane where the jet turns through an angle larger than 90; the opposite takes place in the other half plane. This intensification of the pressure fluctuation is only found within the stagnation zone. At larger radial locations, in the wall-jet domain, the increased fluctuations decay fairly quickly becoming less than their counterpart in the half plane where the jet turns through an angle less than 90. A hypothesis to clarify the physical reasons leading to these observations is proposed. The hypothesis is based on published work on the impingement of an isolated vortex ring on a wall normal to the ring’s axis, and how the characteristics of the vortex ring are altered by the inclination of the impingement wall. Velocity-field measurements are required to further examine these ideas.

Acknowledgments This work is funded by US-Egypt Joint Board on Scientific and Technological Cooperation through contract no.

OTH10-028-002 and NSF grant number OISE-0611984.

Figure 10. Spectra similar to those shown in the left plot of Figure 4 but with normalization of the frequency using the convection velocity uc instead of Uj.


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