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A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets
Accepted Manuscript A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets
Kemal Bülent Yüceil
PII: DOI: Reference:
S1270-9638(17)30527-8 http://dx.doi.org/10.1016/j.ast.2017.03.034 AESCTE 3973
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
7 March 2014 27 February 2017 27 March 2017
Please cite this article in press as: K.B. Yüceil, A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets, Aerosp. Sci. Technol. (2017), http://dx.doi.org/10.1016/j.ast.2017.03.034
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A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets Kemal Bülent Yüceil* Istanbul Technical University, Faculty of Aeronautics and Astronautics, Maslak, Istanbul 34469, Turkey
Abstract Velocity measurements were made in the near field of underexpanded sonic air jets using particle image velocimetry (PIV), interferometric Rayleigh scattering and total pressure tubes. Shadowgraph technique was also used to visualize the shock waves generated due to underexpansion in the near field of the jets. The two main objectives were to study the effect of underexpansion ratio on the flow structure and to determine the suitability of the PIV technique in high-speed flows with shock waves. The jets were produced by a convergent nozzle connected to a settling chamber. Different underexpansion conditions were obtained by changing the chamber (jet total) pressure against the atmospheric ambient. Jet exit-to-ambient pressure ratios ranged between 1 and 20.32 corresponding to fully-expanded jet Mach numbers between 1 and 3.03, respectively. The PIV measurements of the streamwise and transverse velocities in the near field up to ten nozzle diameters were made, from which distributions of mean velocities, turbulence intensities and turbulent shear stress were obtained. In order to check the accuracy of the PIV measurements (particularly, the particle lag effects) an interferometric Rayleigh scattering technique was also used to obtain the streamwise velocity for *
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certain jet conditions. Additionally, some pressure measurements were made using a total pressure tube to provide a comparison with the two optical techniques. In general, the PIV method provided good velocity data in the jet near field and allowed the identification of flow structures and their respective locations such as shock waves, expansion regions, slip lines and shear layers. However, when compared to the Rayleigh scattering data, the effect of particle inertia was evident in certain locations in the jets. This effect was most dramatic just downstream of the Mach disk (barrel shock) in the case of highly underexpanded jets.
Keywords: Underexpanded Jet, Rayleigh scattering, PIV, Mach disk
Nomenclature: dp
Particle diameter (ȝm)
D
Nozzle diameter (m)
Kn
Knudsen number (-)
Mj
Jet Mach number (-)
M
Mach number (-)
p0
Chamber pressure (Pa)
pa
Ambient pressure (Pa)
pe
Jet exit pressure (Pa)
St
Stokes number (-)
T0
Chamber temperature (K)
Te
Jet exit temperature (K)
U
Streamwise velocity (m/s)
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Ue
Nozzle exit velocity (m/s)
u
Underexpansion ratio (-)
u'
Turbulent streamwise velocity (m/s)
V
Transverse velocity (m/s)
v'
Turbulent transverse velocity (m/s)
x
Streamwise distance from the jet exit (m)
y
Transverse distance from the jet centerline (m)
ǻU
Characteristic velocity difference (m/s)
Ȝ
Mean free path (m)
ȝ
Dynamic viscosity (Pa·s)
ȡp
Particle density (g/cm3)
IJf
Characteristic flow time (ȝs)
IJp
Particle response time (ȝs)
1. Introduction A thorough understanding of the structure and dynamics of sonic and supersonic jets is important in the development of air and space propulsion systems with high-performance nozzle designs. These nozzles are expected to provide not only improved thrust but also enhanced jet plume mixing for reduced thermal signature and environmental impact. However, detailed baseline data on the structure of sonic and supersonic jets are needed for a range of operating pressures. Of particular interest is the structure of underexpanded jets. In these jets, the pressure at the nozzle exit is larger than that of the ambient. Such situations are encountered, for example, in rockets that operate through the atmosphere
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at varying altitudes. Another example is related to the power generation industry. The accidental discharge of a high-pressure gas into the atmosphere from a vessel through a small opening is an underexpanded sonic jet until the vessel pressure has become sufficiently low.
Measurements in sonic/supersonic jets are difficult even for small-scale ground testing. In general, physical probes are not well suited for measurements in these flows as they can significantly alter the flow. Further, the quantity measured by the probe needs a certain interpretation in order to infer the actual property of the flow without the probe in place. Therefore, non-intrusive optical techniques are the preferred methods for the diagnostics of these flows. Further, laser-based optical techniques can be used to obtain time-frozen images of flow properties such as velocity, temperature and density. Recently, several techniques have been developed and implemented which show promise for the quantitative characterization of supersonic jets. For velocity, these include Particle Image Velocimetry (PIV), planar Doppler velocimetry, filtered Rayleigh scattering and interferometric Rayleigh scattering. For the past 20 years PIV has been very popular and effective in optical diagnostics of flows at low and high speeds and there is vast amount of work in the literature for the application of this technique to such flows. In particular, PIV is applied to investigate supersonic jet flows in many studies. These involve studies [1-20] of over- or under-expanded supersonic free or mixing jets for their importance in STOVL aircraft applications. Velocity measurements in supersonic jet flows have also been performed using planar Doppler velocimetry [21-23], filtered Rayleigh scattering [24-25] and interferometric Rayleigh scattering [26-30].
Among the optical techniques, PIV is one of the most convenient, providing instantaneous twodimensional data with relative ease. It has received wide attention in recent years and has been
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successfully applied to a range of laminar and turbulent flows. With the recent developments in realtime PIV, the technique has become even more attractive as a two-dimensional velocity imaging method. Further, using a stereoscopic approach, it is possible to obtain two-dimensional images of all three components of the velocity field simultaneously. Today, the use of PIV in most low speed flows is straightforward. Its application to high-speed and supersonic flows, on the other hand, presents certain challenges. One of these challenges is associated with the inertia of particles used as scatterers in the flow [31-34]. Supersonic jet flows, unless ideally expanded, contain shock cells through which the flow accelerates and decelerate rapidly. Therefore, particles with larger mass and smaller slip drag cannot follow the flow with adequate accuracy. In order to minimize the particle lag problem particles with proper size (as suggested by Samimy and Lele [31]) and type should be used in flows having shock waves and shear layers with strong velocity gradients.
In the present study, PIV measurements were performed in the near field of ideally- and underexpanded sonic jets with a range of exit-to-ambient pressure ratios. Further, in order to assess the particle lag and the associated measurement error, PIV streamwise velocity data were compared to those obtained from total pressure probe measurements and to those obtained using an interferometric Rayleigh scattering technique (Bivolaru et al. [27]) which relies on scattering from particles that are much smaller than the interrogating laser’s wavelength.
2. Experimental set-up 2.1. Facility The experimental set-up was part of the Aerodynamic Research and Testing Facility at Polytechnic University. Details of this facility and the supersonic jet are provided in previous studies [4,27,7]. A
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schematic of the facility along with the PIV set up is shown in Fig. 1. Briefly, a convergent nozzle (diameter of D = 8.9 mm) connected to a settling chamber provided the jet flow. Dried, compressed air was provided to the settling chamber at different pressures and flow rates through multi-stage regulators. The jet could be run continuously for several hours without interruption. A seeding system introduced the special scattering particles into the jet fluid. The seeding system was composed of a high-pressure fluidized bed, containing the suspended seed particles, and a mixing chamber with multiple opposing jet injection ports. The mixing chamber was located in the high pressure line, approximately 9 m upstream of the jet settling chamber. The mass/volume percentage of the seeding was negligibly small compared to the supply air of the jet that the flow had not become a two-phase flow. The ambient air is seeded using a smoke generator. The settling chamber is instrumented with thermocouples and pressure transducers that provide information on jet total conditions. Prior to the quantitative measurements, the general structure of the flow was determined by using schlieren and shadowgraph systems for optimal utilization of the measurement techniques.
2.2. PIV system In this study a commercial PIV system (FlowMap) from Dantec was used for measurements. The PIV system consisted of a laser, light sheet optics, a CCD camera, a PIV processor, a personal computer and a traversing system (Fig. 1). The laser was a dual-cavity Nd:YAG laser whose output was frequency doubled using a KDP crystal to obtain the 532 nm green line. The two laser cavities were inserted into a housing that contained optics to combine the two beams into one and then frequency double it. Each laser was operated in single Q–switch mode and signals generated by the synchronization module in the PIV processor (DANTEC PIV 2000) controlled the firing of the laser cavities and hence the time interval between pulses. Laser pulses were separated in time by 2.00 μs and
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the laser repetition rate was set to 4.5 Hz which was the maximum frame rate of the camera for double imaging.
The laser output was formed into a light sheet and directed through the test area by using mirrors and a cylindrical lens. The thickness of the light sheet at the measurement area was about 1 mm. A Dantec 80C60 HiSense PIV/PLIF camera with 1280¯1024 pixels is used with a Nikon Micro-Nikkor 60/2.8 lens to obtain the PIV images. The system was controlled by Dantec FlowMap Software 3.2 running on a standard Pentium processor-based personal computer. The camera was arranged to capture a field of view of 65 mm (7.3D) long (along the jet axis) by 52 mm (5.8D) high (in the transverse direction). PIV images were processed with the Dantec FlowManager Software 3.2. Correlations were then computed using the standard cross correlation function with an interrogation window size of 32¯32 pixels which corresponded to a linear resolution of 1.63¯1.63 mm. An overlap of 50% was used resulting in a final field of 79¯63 vectors and an effective spatial resolution of 0.82¯0.82 mm. Single correlation pass was used to calculate the final vector field. For vector validation, a signal-to-noise filter removed vectors with a ratio of highest correlation peak to second highest correlation peak ratio less than 1.2 (within the range suggested by Keane and Adrian [35]). In addition, the velocity data were filtered with a standard 3¯3 moving average filter. In the moving average filter, the magnitude of the velocity vector in question was compared with the average velocity magnitude of the neighboring vectors. Vectors having a velocity magnitude with a deviation outside the range of 0.1 times the maximum deviation of magnitude of all vectors from the average were removed. Missing vectors were interpolated using a 3¯3 local average technique. The percentage of valid vectors in the PIV data was seen to vary according to the jet case being measured but it was 85%
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or above in all cases. 100 image pairs were acquired for each jet flow case and used in the averaging process to obtain mean quantities.
The laser, transmitting optics and the camera were all placed on a milling machine that was used as a manual traverse system. Therefore, the complete PIV system could be traversed on the milling machine to obtain measurements at different regions of the stationary jet. The resolution of the traverse system was better than 0.1 mm in each direction. However, the PIV system was stationary to make the near field measurements in the underexpanded jet for the present study. Further details of the optical system and the jet facility can be found in Otugen et al. [4].
In the present PIV measurements, porous silica particles were used as scatterers in order to minimize the particle lag problem. The particles had a nominal diameter of 2.42 μm while their equivalent density was in the range between 0.18 and 0.2 g/cm3 depending on the porosity of each particle. A source of bias error can arise in PIV if the particles do not faithfully track flow velocity changes. A measure of the particles’ ability to track velocity changes in the flow is the particle response time, IJp [33]. By definition, a particle experiencing a step change in velocity will take a time IJp to reach 63% of the velocity step change. The particle response time due to a sudden velocity change can be estimated by the relation for IJp given by Poggie et al. [34]: ߬ ൌ
ߩ ݀ଶ ሾͳ ݊ܭሺʹǤͶͻʹ ͲǤͺͶሺെͲǤͶ͵ͷȀ݊ܭሻሻሿሺͳሻ ͳͺߤ
where ȝ is dynamic viscosity of the gas (calculated herein using Sutherland’s formula), ȡp is the particle density, dp is the particle diameter and Kn is the Knudsen number, which is defined as the ratio of the mean free path (Ȝ) to the particle diameter. This work includes PIV measurements in the near field of ideally- and under-expanded sonic jets with a range of exit-to-ambient pressure ratios. To get
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an estimate of the particles’ ability to track velocity changes within these flows, particle response time was calculated using Eq. (1) and for the particle diameter of 2.42 ȝm. The response time was for the flow through a normal shock wave representing the Mach disk or the barrel shock at the downstream end of the expansion region at the sonic jet exit. For this flow at the highest underexpansion ratio case, Mach number before the normal shock was about 2.75 in which case the particle Kn = 0.0034 and IJp computes to be 9.8 ȝs. Note that the relatively large diameter of the particles causes the calculated particle response time to be almost equal to the value that would correspond to pure Stokes drag. Samimy and Lele [31] suggested that for particles to reliably follow velocity fluctuations in a turbulent mixing layer, the Stokes number, which is defined as St = IJp / IJf, where IJf is the characteristic flow timescale, must be less than about 0.5. The characteristic timescale in this Stokes number criterion was based on the vorticity thickness as the characteristic length scale. In the current work, in the expansion region near the exit of jet nozzle, the characteristic length scale is taken to be jet nozzle diameter, D. Therefore, the flow timescale is taken to be IJf = D/ǻU, where ǻU is the characteristic velocity difference. The velocity difference between the upstream and downstream of the normal shock were about 440 m/s. Taking this as the characteristic velocity difference gives IJf = 20 ȝs and St = 0.48. Therefore, although this value is close to the limit specified by Samimy and Lele [31], the particles should be able to track the sudden velocity changes across the normal shock in the expansion region with reasonable accuracy. In addition, the response time of particles with flow conditions behind the Mach disk shock was calculated. Using the flow conditions behind a normal shock at Mach 2.75 (Kn = 9.4¯10-4) and Eq. (1) gives a response time IJp of 4.4 ȝs. This corresponds to a distance of 0.7 mm that the particles will travel to reach 63% of the velocity step change. This suggests that the ability to resolve the barrel shock will be limited by the spatial resolution of the data and not the particle response time.
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Uncertainties in the PIV measurements associated with measurement technique/configuration, flow field and data reduction process combined were estimated to be on the order of 1.5% a given velocity value. Although these type of uncertainties are relatively small, the turbulence effects and shear layers which interact with shock and expansion waves in the flow field cause some relatively large scatter in velocity values given in profile plots as can be seen in the next section. However, the presence of regions with relatively large scatter in velocity distributions for some cases does not change the overall or expected trend of the profiles or variations.
2.3. Interferometric Rayleigh Scattering System The interferometric Rayleigh scattering technique for high-speed gas velocity measurements is described in detail in Bivolaru et al. [27]. The schematic of the experimental setup is shown in Fig. 2a. The technique is based on the analysis of the Rayleigh scattered light for the Doppler shift due to the bulk motion of the gas. The Doppler shift and hence, a given velocity component is measured by using a Fabry-Perot interferometer that is operated in the imaging mode. A fast image processing technique is used to determine the time-frozen Doppler shift in signal coming from a single location in the flow. The 532 nm second harmonic of a line-narrowed (injection seeded), pulsed Nd:YAG laser was used to interrogate the jet flow. The laser beam passed through the jet at a 45 deg. angle. The scattered light from the probe volume was collected at 90 deg. to the laser beam, allowing the measurement of the streamwise component of velocity. The Rayleigh scattered signal, along with a reference laser light, was passed through the Fabry-Perot interferometer. The output of the interferometer was then focused on the CCD camera where the concentric rings of the interference pattern were formed (Fig. 2b). The double ring patterns from the interferometer containing both the reference and the Doppler-shifted
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signal were analyzed using an auto-correlation image processing method specifically developed by Bivolaru et al. [27] for this purpose. Details of the image processing algorithm for Rayleigh scattering measurements can be found in Ref. [27].
2.4. Pitot Pressurre Measurements For the pitot measurements, a syringe-type stainless steel tube with inner and outer diameters of 0.8 and 1 mm, respectively was used to measure the total pressure. The local velocity was obtained as follows. First, from the measured pitot total pressure and jet total pressure (jet plenum pressure), the local Mach number was determined using normal shock relations. Then using this local Mach number and jet total temperature (plenum temperature) the local static pressure and velocity were determined. The pitot measurements were limited to the supersonic flow region, upstream of the Mach disk since the measurement of static pressure was not available in the subsonic region behind shock.
3. Results and Discussion Measurements were made for four different chamber pressures with the same sonic nozzle. The conditions for each jet studied are summarized in Table 1. Subscripts “0”, “e” and “a” refer to chamber, jet exit and ambient conditions, respectively. u = pe / pa is the jet exit-to-ambient pressure ratio and Mj is the equivalent fully (isentropically) expanded jet Mach number. In the table, u = 1 corresponds to the ideally expanded jet and it forms a baseline for comparison with the other underexpanded jets.
Table 1 Summary of experimental conditions u
p0 (kPa)
T0 (K)
pe (kPa)
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Te (K)
p0/pa
Mj
1
191.50
282
101.33
235
1.89
1
7.55
1444.90
282
764.50
235
14.26
2.28
15.53
2974.90
282
1574.02
235
29.36
2.85
20.32
3891.89
282
2059.20
235
38.41
3.03
First, in order to have an estimate for the size of the near field structure of the underexpanded jets shadowgraph measurements were made in the jet near field for various underexpanded jets. Fig. 3 shows shadowgraphs images having a streamwise extend of about nine jet exit diameter (x/D = 9, where x is the streamwise distance measured from the jet exit) for five different underexpansion ratios of which three correspond to those used in the PIV measurements. The image shown on the top left corner with a ruler (dimensions in inches) is given for dimensional reference. Images given for underexpansion ratios 7.5 and above show the “Mach disk” which is a well-known characteristic for the highly underexpanded jets. Shadowgraph image given for u = 1.5, though slightly underexpanded, can be approximated for the ideally expanded case (u = 1) with respect to higher u values given in Table 1 for the highly underexpanded cases. Location of the Mach disk obtained from these shadowgraph images is used along with PIV results for comparison which will be discussed next.
Figure 4 shows the flow structure in the near field of the highly underexpanded jet of u = 20.3 obtained by both qualitative (shadowgraph) and quantitative (PIV) measurements. Shadowgraph image in Fig 4a clearly depicts the jet expansion region which is terminated by a normal shock (the so-called “Mach disk” or “barrel shock”) and the slip lines emanating from the edges of the Mach disk. The region shown on the image extends downstream to about seven nozzle exit diameters. Fig. 4b and 4c show the normalized streamwise velocity (U/Ue) contours and the normalized velocity vectors,
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respectively, obtained with PIV. 100 image pairs were used to obtain the average vector field and the corresponding velocity contours. Jet exit velocity Ue is used to normalize the measured velocities. The dark area in the center portion of the contour plot which begins at about x/D = 3.8 to 4.0 and extends downstream corresponds to the subsonic flow region behind the Mach disk. Although the PIV results are usually susceptible to particle lag in flows with strong shocks, the rapid change in contour levels clearly indicates the large drop in velocity across the barrel shock of the Mach disk. The shadowgraph image shows that the barrel shock is at about x/D = 3.8 whereas PIV contours indicate supersonic velocities up to about x/D = 4. Nevertheless, both measurements agree quite well with each other in terms of the overall flow structure and size. Velocity vector field in Fig. 4c shows the divergence of the flow in the areas of the high expansion region upstream of the Mach disk as well as the shear layers extending downstream from the edges of the Mach disk. A unit vector is shown over the top right corner of the vector map to provide a scale for the normalized velocity vectors. Flow is mainly parallel to x-direction in the center portion of the jet within about -0.2 < y/D < 0.2 but exhibits high divergence beyond this within the expansion region.
Centerline distribution of the mean streamwise velocity obtained from the PIV measurements are shown in Fig. 5 for all the jets studied. The centerline velocity, U, is normalized by the nozzle exit velocity Ue. When the jet is ideally expanded (u = 1), the centerline streamwise velocity stays nearly constant up to a streamwise location of about five jet nozzle diameters downstream of the exit plane. Further downstream, shear layer penetrates the jet core and the centerline velocity starts decaying. On the other hand, for all underexpanded jets the streamwise velocity first increases with increasing distance until it reaches a maximum and then abruptly collapses. The initial increase in velocity is due to the jet expansion process and the adjustment of the static pressure to that of the ambient. Through
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this expansion, the flow becomes supersonic. For the largest underexpansion case of u = 20.32, the maximum velocity is nearly 90 percent larger than the exit velocity while for the smallest underexpanded jet of u = 7.55, the maximum velocity is about 70 percent larger than the jet exit velocity. The streamwise distance where the maximum velocity is reached increases with increasing underexpansion ratio, u. Further downstream, the flow goes through the Mach disk and becomes subsonic. Although the actual region where the flow goes through the Mach disk is a very thin region formed by the barrel shock it appears as a finite region in PIV measurements possibly due to particle lag and the unsteadiness of the barrel shock. As can be seen from Fig. 5 this region can be as wide as 1.5 exit diameters. As mentioned earlier, streamwise location of the Mach disk is obtained from the shadowgraph images (Fig. 3) by measuring the distance from the nozzle exit to the barrel shock. The distances normalized by the jet exit diameter are shown on the plot for velocity distributions for each underexpanded jet case with vertical dashed lines that begin and end with the corresponding symbols. Vertical line for u = 7.55 case (shown by the open diamond symbol) corresponds to the location where the velocity drops after reaching its maximum implying that the agreement for the Mach disk location from both measurements is quite good. Mach disk locations obtained from the shadowgraph measurements for the other underexpansion cases lie within the region of velocity drop showing a reasonable agreement of PIV and shadowgraph results. Downstream of the Mach disk, the flow again accelerates, although less rapidly, as it goes through a second expansion region.
Figs. 6 and 7 compare the mean streamwise velocity distributions obtained by the PIV, to those obtained by the Rayleigh scattering technique and a pitot tube for u = 20.32 and u = 7.55, respectively. A shadowgraph image corresponding to each underexpansion case is also shown as an inset. For both jets, all three types of measurements agree fairly well except for the region around the Mach disk. The
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PIV measurements show that the velocity drop across the normal shock takes place over an axial distance of about one nozzle diameter (~ 9 mm). Clearly, the seed particle lag prevents accurate measurement of velocity in this region. By comparison, the Rayleigh scattering measurements (which depend on gas molecules as scatterers) show a much steeper drop in velocity immediately downstream of the Mach disk. However, even the Rayleigh scattering measurements do not show a discontinuity across the normal shock; Fig. 6 indicates that the drop in velocity takes place over a distance more than 1 mm. A major contribution to this is the finite volume of the Rayleigh scattering probe (which is approximately 1.5 mm in the stream direction). Also, the possible unsteady (jittery) motion of the Mach disk may have contributed to the finite distance for the velocity drop. In Fig. 7 (u = 7.55), both the Rayleigh scattering and the PIV results show a convergent-divergent passage inside the jet, downstream of the Mach disk that is indicated by the peak in velocity at x/D = 3.8. It is also observed that the peak velocity at this location is higher for the Rayleigh scattering measurement again perhaps indicating PIV particle lag.
The flow Mach number just upstream of the Mach disk can be estimated from the measured velocity assuming adiabatic flow on jet axis. Taking the average of the velocity measured by the three methods, the centerline flow Mach numbers upstream of the disk are estimated to be M ≈ 2.75 and 2.17 for u = 20.32 and 7.55, respectively. These values are slightly smaller than the fully-expanded jet Mach numbers of Mj = 3.03 and 2.28 for the two jets possibly indicating that the jets have not yet been fully adjusted to the ambient pressure at this axial position. These Mach numbers can be used to estimate the flow velocity immediately downstream of the Mach disk. Using normal shock relations U/Ue can be obtained as 0.527 and 0.586, for u = 20.32 and 7.55, respectively. These estimates are comparable to the corresponding experimental measurements of 0.5 and 0.55 for U/Ue.
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The evolution of the mean streamwise velocity profiles (from the PIV measurements) for the perfectly expanded jet as well as the underexpanded jets of u = 15.53 and 20.32 are shown in Figs. 8, 9 and 10, respectively. x/D locations corresponding to PIV surveys along the jet centerline are shown in the shadowgraph images next to velocity profiles with horizontal lines in each figure. The shadowgraph image shown next to u = 1 profile actually corresponds to a slightly underexpanded case, u = 1.5, but it is considered as an adequate representation of the ideally expanded case. For the ideally expanded jet (Fig. 8), the near field evolution of the profiles is similar to that of a low-speed jet. There is a slight lateral growth in the velocity profiles in the region x/D < 8. By contrast, Figs. 9 and 10 show that the velocity profiles grow rapidly in the axial direction for the underexpanded jets. This initial growth is primarily due to the expansion process rather than turbulent momentum transport. Immediately downstream of the Mach disk, a “wake” region is observed that is characterized by relatively uniform low velocity (subsonic). For the u = 20.32 case (Fig. 10), at x/D = 4 although there is an overall drop in velocity near the jet axis, the PIV profile near the center is not uniform. This axial location is just downstream of the Mach disk (indicated by the Rayleigh scattering results in Fig. 6) however, due to the particle lag (and most likely coupled with a slight curvature in the Mach disk), the PIV results show a peak in the velocity located on jet axis. If the Mach disk is not perfectly planar and is slightly bulging downstream at the center, this could lead to the non-uniform near center velocity distribution measured on a straight line (the measurement line would not perfectly coincide with the disk as can be seen in the shadowgraph image).
Fig. 11 compares the PIV profile to the Rayleigh scattering profile for the mean streamwise velocity at x/D = 5 for u = 20.32. A shadowgraph image corresponding to the same underexpansion
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ratio is also included next to the velocity profile. Transverse (y/D) boundaries of the region where velocity profile is obtained are also shown on the shadowgraph image with two short vertical line segments on the horizontal line that represents the streamwise location of the velocity profiles for PIV and Rayleigh scattering measurements. It is well known that in a free highly-underexpanded jet, downstream of the Mach disk, slip lines form at the edges of the disk. Inside of the slip lines, the flow is subsonic while on the outside it is supersonic. However, in Fig. 11 neither the Rayleigh scattering nor the PIV measurements show a discontinuous change in the velocity profile. However, the Rayleigh scattering velocity profiles show a steeper gradient than those measured by the PIV method with a higher velocity peak on each side again, indicating the difficulty with the latter technique due to particle lag. However, based on the fact that the Rayleigh scattering results do not show a discontinuous jump in velocity, it is concluded that by x/D = 5, the slip lines have been replaced by a shear layer. In any case, with the exception of the inner shear layer regions, there is good agreement between the two types of measurements.
Fig. 12 shows the near field mean transverse velocity (V/Ue) profiles for the underexpanded jet with u = 20.32, obtained by the PIV method. x/D locations corresponding to PIV surveys are shown in the shadowgraph image next to velocity profiles with horizontal lines. The most downstream x/D location (x/D = 9.8) falls outside the top edge of the shadowgraph image but it is still marked by a horizontal line. The transverse edges of the survey region (-4 < y/D < 4) are also indicated by the two vertical lines in the shadowgraph image to give an idea about the extent of the profiles with respect to the initial expansion region and the Mach disk. In the figure, the transverse velocity is normalized by the jet exit velocity. The transverse velocity is large even at jet exit (showing an inner peak maximum magnitude that is 10 percent of the jet exit velocity). The transverse velocity inner peaks reach 20
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percent of the exit velocity by x/D = 1.2 but start a slow decay thereafter. The inner peaks dominate the outer ones up to about x/D = 4 indicating that the entrainment velocity at the boundary of the jet is dominated by the initial expansion of the underexpanded jet. However, by x/D = 9.8, the expansion process has been completed and the entrainment velocity starts dominating.
Figs. 13 and 14 show the turbulent shear (Reynolds) stress profiles, u 'v ' , obtained from the PIV measurements for the ideally expended jet (u = 1) and the underexpanded jet with u = 20.32, respectively, along with the corresponding shadowgraph images. Product of fluctuating velocity components from 100 image pairs acquired at 4.5 Hz were averaged to obtain the Reynolds stress giving a total recording time of 22.2 s. The shadowgraph image shown next to u = 1 profile again corresponds to a slightly underexpanded case, u = 1.5. x/D locations corresponding to PIV surveys are shown in the shadowgraph image next to velocity profiles with horizontal lines. The transverse edges of the survey region (-2 < y/D < 2 for u = 1 and -3 < y/D < 3 for u = 20.32) are also indicated by the two vertical lines in the shadowgraph. The magnitudes of the maximum turbulent shear stress are much larger for the underexpanded jet. Further, the growth trends for u 'v ' are opposite for the two jets. Similar to a low-speed jet, the turbulent shear stress grows with axial distance in the ideally expanded jet reaching its highest measured value at x/D = 9.8. By contrast, for the underexpanded jet, u 'v ' reaches its peak values at x/D = 1.2 and starts a slow decay thereafter. By x/D = 9.8, the peak values of the underexpanded jet are similar to those for the ideally expended jet at the same location. Clearly, there is a significant difference in the structure of turbulence of the two jets.
4. Conclusion
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The near field velocity structure of underexpanded sonic jets was studied using a digital PIV technique with additional measurements using an interferometric Rayleigh scattering method and total pressure tubes. An objective of the study was the investigation of the suitability of the PIV technique in high-speed flows with shock waves. In general, the PIV technique, in conjunction with the seed particles used, provided satisfactory results in all the jets studied except for the Mach disk region and the region directly downstream of the slip lines in the highly-underexpanded jets where the particle inertia prevented accurate quantitative information. Nevertheless, the PIV measurements provided insightful information on the velocity structure of these jets once it is understood that absolute magnitudes in the vicinity of shock waves may have relatively large errors. Of course, these types of measurements can be further improved with new types of particles with smaller mass-to-slip drag ratios.
In the underexpanded jets, the initial expansion process results in large transverse velocity magnitudes that tend to dominate the entrainment velocity at the jet boundary. Further, in the initial expansion region of these jets, the maximum turbulent shear stress values are much higher than in the sonic jet operated at design condition.
Acknowledgments The author would like to thank Dr. Volkan Otugen and Dr. Engin Arik for their support, valuable contributions and guidance during the course of this study.
References
19
[1] L.M. Lourenco, A. Krothapalli, Particle image displacement velocimetry measurements of a 3D jet, Physics of Fluids, Vol. 31, No. 07, July 1988, pp 1835-1837. [2] A. Krothapalli, D.P. Whishart L.M. Lourenco, Nearfield structure of a supersonic jet: on-line PIV study, Proc. 7th International Symp. Appl. Laser Tech. Fluid Mech., Vol. 2, p.26, Lisbon, Portugal, July 1994 [3] M.P. Wernet, PIV for turbomachinery applications, Presented at the SPIE Conf. On Optical Diagnostics in Fluid and Thermal Flow, San Diego, CA, 1997 (NASA TM 107525) [4] M.V. Otugen, D. Bivolaru, E. Arik, K. Jensen, PIV Study of a Mach 1.6 Supersonic Jet, Proc. VSI_SPIE 98, December 6-9 1998, Yokohama, Japan. [5] M.B. Alkislar, L.M. Lourenco, A. Krothapalli, Velocity Field Measurements in a Screeching Rectangular Jet By Means of PIV, AIAA Paper 1999-0607, 1999. [6] M.B. Alkislar, L.M. Lourenco, A. Krothapalli, Stereoscopic PIV Measurements of a Screeching Supersonic Jet, Journal of Visualization, Vol. 3, Nos. 2, 2000, pp. 135-143. [7] K.B. Yuceil, M.V. Otugen, E. Arik, Underexpanded Sonic Jets: A PIV Study, 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 10-13 July, 2000 [8] A. Jeronimo, M.L. Riethmuller, O. Chazot, PIV Application to Mach 3.75 Overexpanded Jet, 11th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 8-11, 2002 [9] M.B. Alkislar, I. Choutapalli, A. Krothapalli, L.M. Lourenco, J.H. Arakeri, The Structure of a Pulsed Jet - A PIV Study, AIAA Paper 2005-1274, 2005.
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[10] C. Chauveau, D.M. Davidenko, B. Sarh, I. Gokalp, V. Avrashkov, C. Fabre, PIV Measurements in an Underexpanded Hot Free Jet, 13th International Symposium on the Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2006. [11] D. Mitchell, D. Honnery, J. Soria, Study of Underexpanded Supersonic Jets with Optical Techniques, 16th Australasian Fluid Mechanics Conference, Gold Coast, Australia, 2007. [12] R. Kumar, A. Krothapalli, I. Choutapalli, Near-Field Acoustic Characteristics of a Turbulent Axisymmetric Pulsed Jet, AIAA Journal, Vol. 48, No. 6, 2010, pp. 1256-1260. [13] A. Wroblewski, R. Locke, M. Wernet, J. Bridges, Validating PIV Measurements in Supersonic Jets Using Shadowgraph Optical Imaging, AIAA Paper 2011-1163, 2011. [14] J. Bridges, M. Wernet, PIV Measurements of Supersonic Internally-Mixed Dual-Stream Jets, AIAA Paper 2011-2786 (2011). [15] R. Elavarasan, L. Lourenco, L. Venkatakrishnan, A. Krothapalli, Application of PIV to Large Scale STOVL Supersonic Jet Facility, AIAA Paper 1999-0271, 1999. [16] A. Krothapalli, E. Rajkuperan, F. Alvi, L. Lourenco, Flow Field and Noise Characteristics of a Supersonic Impinging Jet, Journal of Fluid Mechanics, vol. 392, 1999, pp. 155-181. [17] R. Elavarasan, L. Venkatakrishnan, A. Krothapalli, L. Lourenco, A PIV Study of a Supersonic Impinging Jet, Journal of Visualization, Vol. 2, Nos. 3/4, 2000, pp. 213-221. [18] F. Alvi, J. Ladd, W. Bower, Experimental and computational investigation of supersonic impinging jets, AIAA Journal, Vol. 40, No. 4, 2002, pp. 599–608. [19] H. Lou, C. Shih, F.S. Alvi, A PIV Study of Supersonic Impinging Jet, AIAA Paper 2003-3263, 2003.
21
[20] B. Henderson, J. Bridges, M. Wernet, An Experimental Study of the Oscillatory Flow Structure of Tone-Producing Supersonic Impinging Jets, Journal of Fluid Mechanics, vol. 542, 2005, pp. 115–137. [21] J.G. Santiago, J.C. Dutton, Velocity Measurements for a Sonic Underexpanded Transverse Jet Injected Into a Supersonic Flow, AIAA Paper 1995-0525, 1995. [22] P.S. Clancy, M. Samimy, Two-Component laser Doppler velocimetry in high-speed flows, AIAA Journal, Vol. 35, pp. 1729-1738, Nov. 1997 [23] P.S. Clancy, M. Samimy, W.R. Erskine, Planar Doppler Velocimetry: Three-component velocimetry in supersonic jets, 36th Aerospace Science Meeting and Exhibit, January 12-15, 1998, Reno, NV. [24] R.B. Miles, R.W. Lempert, Two dimensional measurement of density, velocity, and temperature, in turbulent high speed flows by UV Rayleigh scattering, Applied Physics B, Vol. 51, 1 (1990). [25] R.B. Miles, R.W. Lempert, J. Forkey, Instantaneous velocity fields and background suppression by filtered Rayleigh scattering, AIAA 29th Aerospace Sciences Meeting, Reno, NV. AIAA Paper No: 91-0357, 1991 [26] H.E. Kouros, R.G. Seasholtz, Fabry-Perot interferometer measurement of static temperature and velocity for ASTTOVL model tests, Symp. on Laser Anemometry: Advances and Applications, Ed: Otugen, M.V., Huang, T.T., (FED-Vol. 1, 1994) [27] D. Bivolaru, M.V. Otugen, A. Tzes, G. Papadopoulos, Image processing for interferometric Mie and Rayleigh scattering velocity measurements, AIAA Journal, Vol. 37, No. 6, June 1999 [28] D. Bivolaru, P.M. Danehy, K.D. Grinstead Jr., S. Tedder, A.D. Cutler, Simultaneous CARS and Interferometric Rayleigh Scattering, AIAA Paper 2006-2968, 2006.
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[29] S.A. Tedder, D. Bivolaru, P.M. Danehy, M.C. Weikl, F. Beyrau, T. Seeger, A.D. Cutler, Characterization of a Combined CARS and Interferometric Rayleigh Scattering System, AIAA Paper 2007-871, 2007.
[30] A. Bivolaru, A.D. Cutler, P.M. Danehy, R.L. Gaffney Jr, R.A. Baurle, Spatially and Temporally Resolved Measurements of Velocity in a H2-air Combustion-heated Supersonic jet, AIAA Paper 200927, 2009.
[31] M. Samimy, S.K. Lele, Motion of Particles with Inertia in a Compressible Free Shear Layer, Physics of Fluids A, Vol. 3, No. 8, 1991, pp. 1915-1923.
[32] C.B. Ross, L.M. Lourenco, A. Krothapalli, Particle Image Velocimetry Measurements in a ShockContaining Supersonic Flow, AIAA Paper 1994-0047, 1994.
[33] A. Melling, Tracer Particles and Seeding for Particle Image Velocimetry, Measurement Science and Technology, Vol. 8, No. 12, 1997, pp. 1406-1416.
[34] J. Poggie, P.J. Erbland, A.J. Smits, R.B. Miles, Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering, Experiments in Fluids, Vol. 37, 2004, pp. 438–454.
[35] R.D. Keane, R.J. Adrian, Theory of Cross-Correlation Analysis of PIV Images, Applied Scientific Research, Vol. 49, No. 3, 1992, pp. 191–215.
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Figure Captions: Fig. 1: Schematic of Test Facility and the PIV System Fig. 2: (a) Schematic of Interferometric Rayleigh Scattering System, (b) Concentric rings of the interference pattern obtained at the CCD camera Fig. 3: Near field shadowgraph images (corresponding underexpansion ratios are shown on the images) Fig. 4: Near field flow structure of the underexpanded jet for u = 20.3. (a) shadowgraph image, (b) PIV normalized streamwise velocity (U/Ue) contours, (c) PIV normalized velocity vectors Fig. 5: Mean streamwise velocity on jet axis for different underexpansion cases with corresponding Mach disk locations shown by vertical dashed lines. Fig. 6: Comparison of PIV, Rayleigh scattering and pitot mean streamwise velocity measurements for u = 20.32 Fig. 7: Comparison of PIV, Rayleigh scattering and pitot mean streamwise velocity measurements for u = 7.55 Fig. 8: Mean streamwise velocity profiles for u = 1 and the shadowgraph image for u = 1.5 Fig. 9: Mean streamwise velocity profiles and the shadowgraph image for u = 15.53 Fig. 10: Mean streamwise velocity profiles and the shadowgraph image for u = 20.32 Fig. 11: Comparison of PIV and Rayleigh scattering mean streamwise velocity profiles along with the shadowgraph image for u = 20.32 (horizontal line on image is at x/D = 5) Fig. 12: Mean transverse velocity profiles and the shadowgraph image for u = 20.32
24
Fig. 13: Turbulent shear stress profiles for u = 1 and the shadowgraph image for u = 1.5 Fig. 14: Turbulent shear stress profiles and the shadowgraph image for u = 20.32
25
Pressure Regulator Injection Ports
Air Storage Tanks Seeding Reservoir
Control
Sonic Nozzle
p0
Compressor
Laser Sheet
T0
y
N2 x
PC
Cylindrical Lens
Lasers and Transmitting Optics
Mirror From CCD Camera
PIV Processor
Fig. 1
1 Fig1
(a)
(b)
Fig. 2
2 Fig2
Ruler scale: inches
Mach disk
Mach disk
Fig. 3
3 Fig3
Mach disk
(a) U/Ue: 0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80
2
y/D
1
0
-1
-2
(b)
0
1
2
3
x/D
4
5
6
7 1
2
y/D
1
0
-1
-2
(c)
0
1
2
3
x/D
Fig. 4
4 Fig4
4
5
6
7
2.4
Mach u=7.55 u=15.53 disk 2 locations
u=20.32
u=1 u=7.55 u=15.53 u=20.32
U / Ue
1.6
1.2
0.8
0.4
0 0
1
2
3
4
x/ D
Fig. 5
5 Fig5
5
6
7
8
2.4
PIV Ray leigh Scattering
2
Pitot
U / Ue
1.6
1.2
0.8
0.4
Mach disk location 0 0
1
2
3
4
x/ D
Fig. 6
6 Fig6
5
6
7
8
2.4
P IV 2
Rayleigh Scattering P ito t
U / Ue
1.6
1.2
0.8
0.4
Mach disk location 0 0
1
2
3
x/ D
Fig. 7
7 Fig7
4
5
6
2 x/D 7
x/D = 1 x/D = 2
1.5
6
x/D = 3
U /Ue
1
x/D = 4
5
x/D = 5
4
x/D = 6
3
x/D = 7
2
0.5
1
0
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 8
8 Fig8
3
2 x/D 7
x/ D = 2 x/ D = 3
1.5
U /Ue
1
x/ D =4 x/ D = 5
6
x/ D = 6
4
5
x/ D = 7
3 2
0.5
0
-0.5 -3
-2
-1
0
y /D
1
2
Fig. 9
9 Fig9
3
2
x/ D = 2 x/ D = 3 x/ D =4 x/ D =5 x/ D = 6 x/ D = 7
1.5
x/D 7 6 5 4
U /Ue
1
3 2
0.5
0
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 10
10 Fig10
3
2
1.5
x/D 5
U /Ue
1
0.5 PIV
0
R ayleig h Scat t er ing
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 11
11 Fig11
3
y/D 4
0.3 x/D = 0
-4
x/D 9.8
x/D = 1.2
0.2
x/D = 2.05 4.9
x/D = 4.9
0.1
V /Ue
x/D = 9.8
0
2.05 1.2
-0.1 0
-0.2
-0.3 -4
-3
-2
-1
0
y /D
1
2
Fig. 12
12 Fig12
3
4
x/D = 0 x/D = 1.2 x/D = 2.05
0.002
x/D = 3.26 x/D = 4.09 x/D = 9.83
-u'v' /Ue 2
0.001
4.9
0 2.05
-0.001
1.2
-0.002
0
-0.003 -0.004 -2
-1.5
-1
-0.5
0
0.5
1
y /D
Fig. 13
13 Fig13
-2
0.003
y/D 2
x/D 9.8
1.5
2
y/D 3
0.2 x/D = 0
0.15
x/D = 1.2 x/D = 2.05
0.1
4.9
-u'v' /Ue 2
x/D = 4.9
0.05
x/D = 9.8
0
2.05 1.2
-0.05
0
-0.1 -0.15 -0.2 -3
-2
-1
0
1
2
y /D
Fig. 14
14 Fig14
-3
x/D 9.8
3
Kemal Bülent Yüceil
PII: DOI: Reference:
S1270-9638(17)30527-8 http://dx.doi.org/10.1016/j.ast.2017.03.034 AESCTE 3973
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
7 March 2014 27 February 2017 27 March 2017
Please cite this article in press as: K.B. Yüceil, A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets, Aerosp. Sci. Technol. (2017), http://dx.doi.org/10.1016/j.ast.2017.03.034
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A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets Kemal Bülent Yüceil* Istanbul Technical University, Faculty of Aeronautics and Astronautics, Maslak, Istanbul 34469, Turkey
Abstract Velocity measurements were made in the near field of underexpanded sonic air jets using particle image velocimetry (PIV), interferometric Rayleigh scattering and total pressure tubes. Shadowgraph technique was also used to visualize the shock waves generated due to underexpansion in the near field of the jets. The two main objectives were to study the effect of underexpansion ratio on the flow structure and to determine the suitability of the PIV technique in high-speed flows with shock waves. The jets were produced by a convergent nozzle connected to a settling chamber. Different underexpansion conditions were obtained by changing the chamber (jet total) pressure against the atmospheric ambient. Jet exit-to-ambient pressure ratios ranged between 1 and 20.32 corresponding to fully-expanded jet Mach numbers between 1 and 3.03, respectively. The PIV measurements of the streamwise and transverse velocities in the near field up to ten nozzle diameters were made, from which distributions of mean velocities, turbulence intensities and turbulent shear stress were obtained. In order to check the accuracy of the PIV measurements (particularly, the particle lag effects) an interferometric Rayleigh scattering technique was also used to obtain the streamwise velocity for *
Tel: +90 (212) 285 3137, Fax: +90 (212) 285 3139 Email address: [email protected]
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certain jet conditions. Additionally, some pressure measurements were made using a total pressure tube to provide a comparison with the two optical techniques. In general, the PIV method provided good velocity data in the jet near field and allowed the identification of flow structures and their respective locations such as shock waves, expansion regions, slip lines and shear layers. However, when compared to the Rayleigh scattering data, the effect of particle inertia was evident in certain locations in the jets. This effect was most dramatic just downstream of the Mach disk (barrel shock) in the case of highly underexpanded jets.
Keywords: Underexpanded Jet, Rayleigh scattering, PIV, Mach disk
Nomenclature: dp
Particle diameter (ȝm)
D
Nozzle diameter (m)
Kn
Knudsen number (-)
Mj
Jet Mach number (-)
M
Mach number (-)
p0
Chamber pressure (Pa)
pa
Ambient pressure (Pa)
pe
Jet exit pressure (Pa)
St
Stokes number (-)
T0
Chamber temperature (K)
Te
Jet exit temperature (K)
U
Streamwise velocity (m/s)
2
Ue
Nozzle exit velocity (m/s)
u
Underexpansion ratio (-)
u'
Turbulent streamwise velocity (m/s)
V
Transverse velocity (m/s)
v'
Turbulent transverse velocity (m/s)
x
Streamwise distance from the jet exit (m)
y
Transverse distance from the jet centerline (m)
ǻU
Characteristic velocity difference (m/s)
Ȝ
Mean free path (m)
ȝ
Dynamic viscosity (Pa·s)
ȡp
Particle density (g/cm3)
IJf
Characteristic flow time (ȝs)
IJp
Particle response time (ȝs)
1. Introduction A thorough understanding of the structure and dynamics of sonic and supersonic jets is important in the development of air and space propulsion systems with high-performance nozzle designs. These nozzles are expected to provide not only improved thrust but also enhanced jet plume mixing for reduced thermal signature and environmental impact. However, detailed baseline data on the structure of sonic and supersonic jets are needed for a range of operating pressures. Of particular interest is the structure of underexpanded jets. In these jets, the pressure at the nozzle exit is larger than that of the ambient. Such situations are encountered, for example, in rockets that operate through the atmosphere
3
at varying altitudes. Another example is related to the power generation industry. The accidental discharge of a high-pressure gas into the atmosphere from a vessel through a small opening is an underexpanded sonic jet until the vessel pressure has become sufficiently low.
Measurements in sonic/supersonic jets are difficult even for small-scale ground testing. In general, physical probes are not well suited for measurements in these flows as they can significantly alter the flow. Further, the quantity measured by the probe needs a certain interpretation in order to infer the actual property of the flow without the probe in place. Therefore, non-intrusive optical techniques are the preferred methods for the diagnostics of these flows. Further, laser-based optical techniques can be used to obtain time-frozen images of flow properties such as velocity, temperature and density. Recently, several techniques have been developed and implemented which show promise for the quantitative characterization of supersonic jets. For velocity, these include Particle Image Velocimetry (PIV), planar Doppler velocimetry, filtered Rayleigh scattering and interferometric Rayleigh scattering. For the past 20 years PIV has been very popular and effective in optical diagnostics of flows at low and high speeds and there is vast amount of work in the literature for the application of this technique to such flows. In particular, PIV is applied to investigate supersonic jet flows in many studies. These involve studies [1-20] of over- or under-expanded supersonic free or mixing jets for their importance in STOVL aircraft applications. Velocity measurements in supersonic jet flows have also been performed using planar Doppler velocimetry [21-23], filtered Rayleigh scattering [24-25] and interferometric Rayleigh scattering [26-30].
Among the optical techniques, PIV is one of the most convenient, providing instantaneous twodimensional data with relative ease. It has received wide attention in recent years and has been
4
successfully applied to a range of laminar and turbulent flows. With the recent developments in realtime PIV, the technique has become even more attractive as a two-dimensional velocity imaging method. Further, using a stereoscopic approach, it is possible to obtain two-dimensional images of all three components of the velocity field simultaneously. Today, the use of PIV in most low speed flows is straightforward. Its application to high-speed and supersonic flows, on the other hand, presents certain challenges. One of these challenges is associated with the inertia of particles used as scatterers in the flow [31-34]. Supersonic jet flows, unless ideally expanded, contain shock cells through which the flow accelerates and decelerate rapidly. Therefore, particles with larger mass and smaller slip drag cannot follow the flow with adequate accuracy. In order to minimize the particle lag problem particles with proper size (as suggested by Samimy and Lele [31]) and type should be used in flows having shock waves and shear layers with strong velocity gradients.
In the present study, PIV measurements were performed in the near field of ideally- and underexpanded sonic jets with a range of exit-to-ambient pressure ratios. Further, in order to assess the particle lag and the associated measurement error, PIV streamwise velocity data were compared to those obtained from total pressure probe measurements and to those obtained using an interferometric Rayleigh scattering technique (Bivolaru et al. [27]) which relies on scattering from particles that are much smaller than the interrogating laser’s wavelength.
2. Experimental set-up 2.1. Facility The experimental set-up was part of the Aerodynamic Research and Testing Facility at Polytechnic University. Details of this facility and the supersonic jet are provided in previous studies [4,27,7]. A
5
schematic of the facility along with the PIV set up is shown in Fig. 1. Briefly, a convergent nozzle (diameter of D = 8.9 mm) connected to a settling chamber provided the jet flow. Dried, compressed air was provided to the settling chamber at different pressures and flow rates through multi-stage regulators. The jet could be run continuously for several hours without interruption. A seeding system introduced the special scattering particles into the jet fluid. The seeding system was composed of a high-pressure fluidized bed, containing the suspended seed particles, and a mixing chamber with multiple opposing jet injection ports. The mixing chamber was located in the high pressure line, approximately 9 m upstream of the jet settling chamber. The mass/volume percentage of the seeding was negligibly small compared to the supply air of the jet that the flow had not become a two-phase flow. The ambient air is seeded using a smoke generator. The settling chamber is instrumented with thermocouples and pressure transducers that provide information on jet total conditions. Prior to the quantitative measurements, the general structure of the flow was determined by using schlieren and shadowgraph systems for optimal utilization of the measurement techniques.
2.2. PIV system In this study a commercial PIV system (FlowMap) from Dantec was used for measurements. The PIV system consisted of a laser, light sheet optics, a CCD camera, a PIV processor, a personal computer and a traversing system (Fig. 1). The laser was a dual-cavity Nd:YAG laser whose output was frequency doubled using a KDP crystal to obtain the 532 nm green line. The two laser cavities were inserted into a housing that contained optics to combine the two beams into one and then frequency double it. Each laser was operated in single Q–switch mode and signals generated by the synchronization module in the PIV processor (DANTEC PIV 2000) controlled the firing of the laser cavities and hence the time interval between pulses. Laser pulses were separated in time by 2.00 μs and
6
the laser repetition rate was set to 4.5 Hz which was the maximum frame rate of the camera for double imaging.
The laser output was formed into a light sheet and directed through the test area by using mirrors and a cylindrical lens. The thickness of the light sheet at the measurement area was about 1 mm. A Dantec 80C60 HiSense PIV/PLIF camera with 1280¯1024 pixels is used with a Nikon Micro-Nikkor 60/2.8 lens to obtain the PIV images. The system was controlled by Dantec FlowMap Software 3.2 running on a standard Pentium processor-based personal computer. The camera was arranged to capture a field of view of 65 mm (7.3D) long (along the jet axis) by 52 mm (5.8D) high (in the transverse direction). PIV images were processed with the Dantec FlowManager Software 3.2. Correlations were then computed using the standard cross correlation function with an interrogation window size of 32¯32 pixels which corresponded to a linear resolution of 1.63¯1.63 mm. An overlap of 50% was used resulting in a final field of 79¯63 vectors and an effective spatial resolution of 0.82¯0.82 mm. Single correlation pass was used to calculate the final vector field. For vector validation, a signal-to-noise filter removed vectors with a ratio of highest correlation peak to second highest correlation peak ratio less than 1.2 (within the range suggested by Keane and Adrian [35]). In addition, the velocity data were filtered with a standard 3¯3 moving average filter. In the moving average filter, the magnitude of the velocity vector in question was compared with the average velocity magnitude of the neighboring vectors. Vectors having a velocity magnitude with a deviation outside the range of 0.1 times the maximum deviation of magnitude of all vectors from the average were removed. Missing vectors were interpolated using a 3¯3 local average technique. The percentage of valid vectors in the PIV data was seen to vary according to the jet case being measured but it was 85%
7
or above in all cases. 100 image pairs were acquired for each jet flow case and used in the averaging process to obtain mean quantities.
The laser, transmitting optics and the camera were all placed on a milling machine that was used as a manual traverse system. Therefore, the complete PIV system could be traversed on the milling machine to obtain measurements at different regions of the stationary jet. The resolution of the traverse system was better than 0.1 mm in each direction. However, the PIV system was stationary to make the near field measurements in the underexpanded jet for the present study. Further details of the optical system and the jet facility can be found in Otugen et al. [4].
In the present PIV measurements, porous silica particles were used as scatterers in order to minimize the particle lag problem. The particles had a nominal diameter of 2.42 μm while their equivalent density was in the range between 0.18 and 0.2 g/cm3 depending on the porosity of each particle. A source of bias error can arise in PIV if the particles do not faithfully track flow velocity changes. A measure of the particles’ ability to track velocity changes in the flow is the particle response time, IJp [33]. By definition, a particle experiencing a step change in velocity will take a time IJp to reach 63% of the velocity step change. The particle response time due to a sudden velocity change can be estimated by the relation for IJp given by Poggie et al. [34]: ߬ ൌ
ߩ ݀ଶ ሾͳ ݊ܭሺʹǤͶͻʹ ͲǤͺͶሺെͲǤͶ͵ͷȀ݊ܭሻሻሿሺͳሻ ͳͺߤ
where ȝ is dynamic viscosity of the gas (calculated herein using Sutherland’s formula), ȡp is the particle density, dp is the particle diameter and Kn is the Knudsen number, which is defined as the ratio of the mean free path (Ȝ) to the particle diameter. This work includes PIV measurements in the near field of ideally- and under-expanded sonic jets with a range of exit-to-ambient pressure ratios. To get
8
an estimate of the particles’ ability to track velocity changes within these flows, particle response time was calculated using Eq. (1) and for the particle diameter of 2.42 ȝm. The response time was for the flow through a normal shock wave representing the Mach disk or the barrel shock at the downstream end of the expansion region at the sonic jet exit. For this flow at the highest underexpansion ratio case, Mach number before the normal shock was about 2.75 in which case the particle Kn = 0.0034 and IJp computes to be 9.8 ȝs. Note that the relatively large diameter of the particles causes the calculated particle response time to be almost equal to the value that would correspond to pure Stokes drag. Samimy and Lele [31] suggested that for particles to reliably follow velocity fluctuations in a turbulent mixing layer, the Stokes number, which is defined as St = IJp / IJf, where IJf is the characteristic flow timescale, must be less than about 0.5. The characteristic timescale in this Stokes number criterion was based on the vorticity thickness as the characteristic length scale. In the current work, in the expansion region near the exit of jet nozzle, the characteristic length scale is taken to be jet nozzle diameter, D. Therefore, the flow timescale is taken to be IJf = D/ǻU, where ǻU is the characteristic velocity difference. The velocity difference between the upstream and downstream of the normal shock were about 440 m/s. Taking this as the characteristic velocity difference gives IJf = 20 ȝs and St = 0.48. Therefore, although this value is close to the limit specified by Samimy and Lele [31], the particles should be able to track the sudden velocity changes across the normal shock in the expansion region with reasonable accuracy. In addition, the response time of particles with flow conditions behind the Mach disk shock was calculated. Using the flow conditions behind a normal shock at Mach 2.75 (Kn = 9.4¯10-4) and Eq. (1) gives a response time IJp of 4.4 ȝs. This corresponds to a distance of 0.7 mm that the particles will travel to reach 63% of the velocity step change. This suggests that the ability to resolve the barrel shock will be limited by the spatial resolution of the data and not the particle response time.
9
Uncertainties in the PIV measurements associated with measurement technique/configuration, flow field and data reduction process combined were estimated to be on the order of 1.5% a given velocity value. Although these type of uncertainties are relatively small, the turbulence effects and shear layers which interact with shock and expansion waves in the flow field cause some relatively large scatter in velocity values given in profile plots as can be seen in the next section. However, the presence of regions with relatively large scatter in velocity distributions for some cases does not change the overall or expected trend of the profiles or variations.
2.3. Interferometric Rayleigh Scattering System The interferometric Rayleigh scattering technique for high-speed gas velocity measurements is described in detail in Bivolaru et al. [27]. The schematic of the experimental setup is shown in Fig. 2a. The technique is based on the analysis of the Rayleigh scattered light for the Doppler shift due to the bulk motion of the gas. The Doppler shift and hence, a given velocity component is measured by using a Fabry-Perot interferometer that is operated in the imaging mode. A fast image processing technique is used to determine the time-frozen Doppler shift in signal coming from a single location in the flow. The 532 nm second harmonic of a line-narrowed (injection seeded), pulsed Nd:YAG laser was used to interrogate the jet flow. The laser beam passed through the jet at a 45 deg. angle. The scattered light from the probe volume was collected at 90 deg. to the laser beam, allowing the measurement of the streamwise component of velocity. The Rayleigh scattered signal, along with a reference laser light, was passed through the Fabry-Perot interferometer. The output of the interferometer was then focused on the CCD camera where the concentric rings of the interference pattern were formed (Fig. 2b). The double ring patterns from the interferometer containing both the reference and the Doppler-shifted
10
signal were analyzed using an auto-correlation image processing method specifically developed by Bivolaru et al. [27] for this purpose. Details of the image processing algorithm for Rayleigh scattering measurements can be found in Ref. [27].
2.4. Pitot Pressurre Measurements For the pitot measurements, a syringe-type stainless steel tube with inner and outer diameters of 0.8 and 1 mm, respectively was used to measure the total pressure. The local velocity was obtained as follows. First, from the measured pitot total pressure and jet total pressure (jet plenum pressure), the local Mach number was determined using normal shock relations. Then using this local Mach number and jet total temperature (plenum temperature) the local static pressure and velocity were determined. The pitot measurements were limited to the supersonic flow region, upstream of the Mach disk since the measurement of static pressure was not available in the subsonic region behind shock.
3. Results and Discussion Measurements were made for four different chamber pressures with the same sonic nozzle. The conditions for each jet studied are summarized in Table 1. Subscripts “0”, “e” and “a” refer to chamber, jet exit and ambient conditions, respectively. u = pe / pa is the jet exit-to-ambient pressure ratio and Mj is the equivalent fully (isentropically) expanded jet Mach number. In the table, u = 1 corresponds to the ideally expanded jet and it forms a baseline for comparison with the other underexpanded jets.
Table 1 Summary of experimental conditions u
p0 (kPa)
T0 (K)
pe (kPa)
11
Te (K)
p0/pa
Mj
1
191.50
282
101.33
235
1.89
1
7.55
1444.90
282
764.50
235
14.26
2.28
15.53
2974.90
282
1574.02
235
29.36
2.85
20.32
3891.89
282
2059.20
235
38.41
3.03
First, in order to have an estimate for the size of the near field structure of the underexpanded jets shadowgraph measurements were made in the jet near field for various underexpanded jets. Fig. 3 shows shadowgraphs images having a streamwise extend of about nine jet exit diameter (x/D = 9, where x is the streamwise distance measured from the jet exit) for five different underexpansion ratios of which three correspond to those used in the PIV measurements. The image shown on the top left corner with a ruler (dimensions in inches) is given for dimensional reference. Images given for underexpansion ratios 7.5 and above show the “Mach disk” which is a well-known characteristic for the highly underexpanded jets. Shadowgraph image given for u = 1.5, though slightly underexpanded, can be approximated for the ideally expanded case (u = 1) with respect to higher u values given in Table 1 for the highly underexpanded cases. Location of the Mach disk obtained from these shadowgraph images is used along with PIV results for comparison which will be discussed next.
Figure 4 shows the flow structure in the near field of the highly underexpanded jet of u = 20.3 obtained by both qualitative (shadowgraph) and quantitative (PIV) measurements. Shadowgraph image in Fig 4a clearly depicts the jet expansion region which is terminated by a normal shock (the so-called “Mach disk” or “barrel shock”) and the slip lines emanating from the edges of the Mach disk. The region shown on the image extends downstream to about seven nozzle exit diameters. Fig. 4b and 4c show the normalized streamwise velocity (U/Ue) contours and the normalized velocity vectors,
12
respectively, obtained with PIV. 100 image pairs were used to obtain the average vector field and the corresponding velocity contours. Jet exit velocity Ue is used to normalize the measured velocities. The dark area in the center portion of the contour plot which begins at about x/D = 3.8 to 4.0 and extends downstream corresponds to the subsonic flow region behind the Mach disk. Although the PIV results are usually susceptible to particle lag in flows with strong shocks, the rapid change in contour levels clearly indicates the large drop in velocity across the barrel shock of the Mach disk. The shadowgraph image shows that the barrel shock is at about x/D = 3.8 whereas PIV contours indicate supersonic velocities up to about x/D = 4. Nevertheless, both measurements agree quite well with each other in terms of the overall flow structure and size. Velocity vector field in Fig. 4c shows the divergence of the flow in the areas of the high expansion region upstream of the Mach disk as well as the shear layers extending downstream from the edges of the Mach disk. A unit vector is shown over the top right corner of the vector map to provide a scale for the normalized velocity vectors. Flow is mainly parallel to x-direction in the center portion of the jet within about -0.2 < y/D < 0.2 but exhibits high divergence beyond this within the expansion region.
Centerline distribution of the mean streamwise velocity obtained from the PIV measurements are shown in Fig. 5 for all the jets studied. The centerline velocity, U, is normalized by the nozzle exit velocity Ue. When the jet is ideally expanded (u = 1), the centerline streamwise velocity stays nearly constant up to a streamwise location of about five jet nozzle diameters downstream of the exit plane. Further downstream, shear layer penetrates the jet core and the centerline velocity starts decaying. On the other hand, for all underexpanded jets the streamwise velocity first increases with increasing distance until it reaches a maximum and then abruptly collapses. The initial increase in velocity is due to the jet expansion process and the adjustment of the static pressure to that of the ambient. Through
13
this expansion, the flow becomes supersonic. For the largest underexpansion case of u = 20.32, the maximum velocity is nearly 90 percent larger than the exit velocity while for the smallest underexpanded jet of u = 7.55, the maximum velocity is about 70 percent larger than the jet exit velocity. The streamwise distance where the maximum velocity is reached increases with increasing underexpansion ratio, u. Further downstream, the flow goes through the Mach disk and becomes subsonic. Although the actual region where the flow goes through the Mach disk is a very thin region formed by the barrel shock it appears as a finite region in PIV measurements possibly due to particle lag and the unsteadiness of the barrel shock. As can be seen from Fig. 5 this region can be as wide as 1.5 exit diameters. As mentioned earlier, streamwise location of the Mach disk is obtained from the shadowgraph images (Fig. 3) by measuring the distance from the nozzle exit to the barrel shock. The distances normalized by the jet exit diameter are shown on the plot for velocity distributions for each underexpanded jet case with vertical dashed lines that begin and end with the corresponding symbols. Vertical line for u = 7.55 case (shown by the open diamond symbol) corresponds to the location where the velocity drops after reaching its maximum implying that the agreement for the Mach disk location from both measurements is quite good. Mach disk locations obtained from the shadowgraph measurements for the other underexpansion cases lie within the region of velocity drop showing a reasonable agreement of PIV and shadowgraph results. Downstream of the Mach disk, the flow again accelerates, although less rapidly, as it goes through a second expansion region.
Figs. 6 and 7 compare the mean streamwise velocity distributions obtained by the PIV, to those obtained by the Rayleigh scattering technique and a pitot tube for u = 20.32 and u = 7.55, respectively. A shadowgraph image corresponding to each underexpansion case is also shown as an inset. For both jets, all three types of measurements agree fairly well except for the region around the Mach disk. The
14
PIV measurements show that the velocity drop across the normal shock takes place over an axial distance of about one nozzle diameter (~ 9 mm). Clearly, the seed particle lag prevents accurate measurement of velocity in this region. By comparison, the Rayleigh scattering measurements (which depend on gas molecules as scatterers) show a much steeper drop in velocity immediately downstream of the Mach disk. However, even the Rayleigh scattering measurements do not show a discontinuity across the normal shock; Fig. 6 indicates that the drop in velocity takes place over a distance more than 1 mm. A major contribution to this is the finite volume of the Rayleigh scattering probe (which is approximately 1.5 mm in the stream direction). Also, the possible unsteady (jittery) motion of the Mach disk may have contributed to the finite distance for the velocity drop. In Fig. 7 (u = 7.55), both the Rayleigh scattering and the PIV results show a convergent-divergent passage inside the jet, downstream of the Mach disk that is indicated by the peak in velocity at x/D = 3.8. It is also observed that the peak velocity at this location is higher for the Rayleigh scattering measurement again perhaps indicating PIV particle lag.
The flow Mach number just upstream of the Mach disk can be estimated from the measured velocity assuming adiabatic flow on jet axis. Taking the average of the velocity measured by the three methods, the centerline flow Mach numbers upstream of the disk are estimated to be M ≈ 2.75 and 2.17 for u = 20.32 and 7.55, respectively. These values are slightly smaller than the fully-expanded jet Mach numbers of Mj = 3.03 and 2.28 for the two jets possibly indicating that the jets have not yet been fully adjusted to the ambient pressure at this axial position. These Mach numbers can be used to estimate the flow velocity immediately downstream of the Mach disk. Using normal shock relations U/Ue can be obtained as 0.527 and 0.586, for u = 20.32 and 7.55, respectively. These estimates are comparable to the corresponding experimental measurements of 0.5 and 0.55 for U/Ue.
15
The evolution of the mean streamwise velocity profiles (from the PIV measurements) for the perfectly expanded jet as well as the underexpanded jets of u = 15.53 and 20.32 are shown in Figs. 8, 9 and 10, respectively. x/D locations corresponding to PIV surveys along the jet centerline are shown in the shadowgraph images next to velocity profiles with horizontal lines in each figure. The shadowgraph image shown next to u = 1 profile actually corresponds to a slightly underexpanded case, u = 1.5, but it is considered as an adequate representation of the ideally expanded case. For the ideally expanded jet (Fig. 8), the near field evolution of the profiles is similar to that of a low-speed jet. There is a slight lateral growth in the velocity profiles in the region x/D < 8. By contrast, Figs. 9 and 10 show that the velocity profiles grow rapidly in the axial direction for the underexpanded jets. This initial growth is primarily due to the expansion process rather than turbulent momentum transport. Immediately downstream of the Mach disk, a “wake” region is observed that is characterized by relatively uniform low velocity (subsonic). For the u = 20.32 case (Fig. 10), at x/D = 4 although there is an overall drop in velocity near the jet axis, the PIV profile near the center is not uniform. This axial location is just downstream of the Mach disk (indicated by the Rayleigh scattering results in Fig. 6) however, due to the particle lag (and most likely coupled with a slight curvature in the Mach disk), the PIV results show a peak in the velocity located on jet axis. If the Mach disk is not perfectly planar and is slightly bulging downstream at the center, this could lead to the non-uniform near center velocity distribution measured on a straight line (the measurement line would not perfectly coincide with the disk as can be seen in the shadowgraph image).
Fig. 11 compares the PIV profile to the Rayleigh scattering profile for the mean streamwise velocity at x/D = 5 for u = 20.32. A shadowgraph image corresponding to the same underexpansion
16
ratio is also included next to the velocity profile. Transverse (y/D) boundaries of the region where velocity profile is obtained are also shown on the shadowgraph image with two short vertical line segments on the horizontal line that represents the streamwise location of the velocity profiles for PIV and Rayleigh scattering measurements. It is well known that in a free highly-underexpanded jet, downstream of the Mach disk, slip lines form at the edges of the disk. Inside of the slip lines, the flow is subsonic while on the outside it is supersonic. However, in Fig. 11 neither the Rayleigh scattering nor the PIV measurements show a discontinuous change in the velocity profile. However, the Rayleigh scattering velocity profiles show a steeper gradient than those measured by the PIV method with a higher velocity peak on each side again, indicating the difficulty with the latter technique due to particle lag. However, based on the fact that the Rayleigh scattering results do not show a discontinuous jump in velocity, it is concluded that by x/D = 5, the slip lines have been replaced by a shear layer. In any case, with the exception of the inner shear layer regions, there is good agreement between the two types of measurements.
Fig. 12 shows the near field mean transverse velocity (V/Ue) profiles for the underexpanded jet with u = 20.32, obtained by the PIV method. x/D locations corresponding to PIV surveys are shown in the shadowgraph image next to velocity profiles with horizontal lines. The most downstream x/D location (x/D = 9.8) falls outside the top edge of the shadowgraph image but it is still marked by a horizontal line. The transverse edges of the survey region (-4 < y/D < 4) are also indicated by the two vertical lines in the shadowgraph image to give an idea about the extent of the profiles with respect to the initial expansion region and the Mach disk. In the figure, the transverse velocity is normalized by the jet exit velocity. The transverse velocity is large even at jet exit (showing an inner peak maximum magnitude that is 10 percent of the jet exit velocity). The transverse velocity inner peaks reach 20
17
percent of the exit velocity by x/D = 1.2 but start a slow decay thereafter. The inner peaks dominate the outer ones up to about x/D = 4 indicating that the entrainment velocity at the boundary of the jet is dominated by the initial expansion of the underexpanded jet. However, by x/D = 9.8, the expansion process has been completed and the entrainment velocity starts dominating.
Figs. 13 and 14 show the turbulent shear (Reynolds) stress profiles, u 'v ' , obtained from the PIV measurements for the ideally expended jet (u = 1) and the underexpanded jet with u = 20.32, respectively, along with the corresponding shadowgraph images. Product of fluctuating velocity components from 100 image pairs acquired at 4.5 Hz were averaged to obtain the Reynolds stress giving a total recording time of 22.2 s. The shadowgraph image shown next to u = 1 profile again corresponds to a slightly underexpanded case, u = 1.5. x/D locations corresponding to PIV surveys are shown in the shadowgraph image next to velocity profiles with horizontal lines. The transverse edges of the survey region (-2 < y/D < 2 for u = 1 and -3 < y/D < 3 for u = 20.32) are also indicated by the two vertical lines in the shadowgraph. The magnitudes of the maximum turbulent shear stress are much larger for the underexpanded jet. Further, the growth trends for u 'v ' are opposite for the two jets. Similar to a low-speed jet, the turbulent shear stress grows with axial distance in the ideally expanded jet reaching its highest measured value at x/D = 9.8. By contrast, for the underexpanded jet, u 'v ' reaches its peak values at x/D = 1.2 and starts a slow decay thereafter. By x/D = 9.8, the peak values of the underexpanded jet are similar to those for the ideally expended jet at the same location. Clearly, there is a significant difference in the structure of turbulence of the two jets.
4. Conclusion
18
The near field velocity structure of underexpanded sonic jets was studied using a digital PIV technique with additional measurements using an interferometric Rayleigh scattering method and total pressure tubes. An objective of the study was the investigation of the suitability of the PIV technique in high-speed flows with shock waves. In general, the PIV technique, in conjunction with the seed particles used, provided satisfactory results in all the jets studied except for the Mach disk region and the region directly downstream of the slip lines in the highly-underexpanded jets where the particle inertia prevented accurate quantitative information. Nevertheless, the PIV measurements provided insightful information on the velocity structure of these jets once it is understood that absolute magnitudes in the vicinity of shock waves may have relatively large errors. Of course, these types of measurements can be further improved with new types of particles with smaller mass-to-slip drag ratios.
In the underexpanded jets, the initial expansion process results in large transverse velocity magnitudes that tend to dominate the entrainment velocity at the jet boundary. Further, in the initial expansion region of these jets, the maximum turbulent shear stress values are much higher than in the sonic jet operated at design condition.
Acknowledgments The author would like to thank Dr. Volkan Otugen and Dr. Engin Arik for their support, valuable contributions and guidance during the course of this study.
References
19
[1] L.M. Lourenco, A. Krothapalli, Particle image displacement velocimetry measurements of a 3D jet, Physics of Fluids, Vol. 31, No. 07, July 1988, pp 1835-1837. [2] A. Krothapalli, D.P. Whishart L.M. Lourenco, Nearfield structure of a supersonic jet: on-line PIV study, Proc. 7th International Symp. Appl. Laser Tech. Fluid Mech., Vol. 2, p.26, Lisbon, Portugal, July 1994 [3] M.P. Wernet, PIV for turbomachinery applications, Presented at the SPIE Conf. On Optical Diagnostics in Fluid and Thermal Flow, San Diego, CA, 1997 (NASA TM 107525) [4] M.V. Otugen, D. Bivolaru, E. Arik, K. Jensen, PIV Study of a Mach 1.6 Supersonic Jet, Proc. VSI_SPIE 98, December 6-9 1998, Yokohama, Japan. [5] M.B. Alkislar, L.M. Lourenco, A. Krothapalli, Velocity Field Measurements in a Screeching Rectangular Jet By Means of PIV, AIAA Paper 1999-0607, 1999. [6] M.B. Alkislar, L.M. Lourenco, A. Krothapalli, Stereoscopic PIV Measurements of a Screeching Supersonic Jet, Journal of Visualization, Vol. 3, Nos. 2, 2000, pp. 135-143. [7] K.B. Yuceil, M.V. Otugen, E. Arik, Underexpanded Sonic Jets: A PIV Study, 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 10-13 July, 2000 [8] A. Jeronimo, M.L. Riethmuller, O. Chazot, PIV Application to Mach 3.75 Overexpanded Jet, 11th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 8-11, 2002 [9] M.B. Alkislar, I. Choutapalli, A. Krothapalli, L.M. Lourenco, J.H. Arakeri, The Structure of a Pulsed Jet - A PIV Study, AIAA Paper 2005-1274, 2005.
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[10] C. Chauveau, D.M. Davidenko, B. Sarh, I. Gokalp, V. Avrashkov, C. Fabre, PIV Measurements in an Underexpanded Hot Free Jet, 13th International Symposium on the Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2006. [11] D. Mitchell, D. Honnery, J. Soria, Study of Underexpanded Supersonic Jets with Optical Techniques, 16th Australasian Fluid Mechanics Conference, Gold Coast, Australia, 2007. [12] R. Kumar, A. Krothapalli, I. Choutapalli, Near-Field Acoustic Characteristics of a Turbulent Axisymmetric Pulsed Jet, AIAA Journal, Vol. 48, No. 6, 2010, pp. 1256-1260. [13] A. Wroblewski, R. Locke, M. Wernet, J. Bridges, Validating PIV Measurements in Supersonic Jets Using Shadowgraph Optical Imaging, AIAA Paper 2011-1163, 2011. [14] J. Bridges, M. Wernet, PIV Measurements of Supersonic Internally-Mixed Dual-Stream Jets, AIAA Paper 2011-2786 (2011). [15] R. Elavarasan, L. Lourenco, L. Venkatakrishnan, A. Krothapalli, Application of PIV to Large Scale STOVL Supersonic Jet Facility, AIAA Paper 1999-0271, 1999. [16] A. Krothapalli, E. Rajkuperan, F. Alvi, L. Lourenco, Flow Field and Noise Characteristics of a Supersonic Impinging Jet, Journal of Fluid Mechanics, vol. 392, 1999, pp. 155-181. [17] R. Elavarasan, L. Venkatakrishnan, A. Krothapalli, L. Lourenco, A PIV Study of a Supersonic Impinging Jet, Journal of Visualization, Vol. 2, Nos. 3/4, 2000, pp. 213-221. [18] F. Alvi, J. Ladd, W. Bower, Experimental and computational investigation of supersonic impinging jets, AIAA Journal, Vol. 40, No. 4, 2002, pp. 599–608. [19] H. Lou, C. Shih, F.S. Alvi, A PIV Study of Supersonic Impinging Jet, AIAA Paper 2003-3263, 2003.
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Figure Captions: Fig. 1: Schematic of Test Facility and the PIV System Fig. 2: (a) Schematic of Interferometric Rayleigh Scattering System, (b) Concentric rings of the interference pattern obtained at the CCD camera Fig. 3: Near field shadowgraph images (corresponding underexpansion ratios are shown on the images) Fig. 4: Near field flow structure of the underexpanded jet for u = 20.3. (a) shadowgraph image, (b) PIV normalized streamwise velocity (U/Ue) contours, (c) PIV normalized velocity vectors Fig. 5: Mean streamwise velocity on jet axis for different underexpansion cases with corresponding Mach disk locations shown by vertical dashed lines. Fig. 6: Comparison of PIV, Rayleigh scattering and pitot mean streamwise velocity measurements for u = 20.32 Fig. 7: Comparison of PIV, Rayleigh scattering and pitot mean streamwise velocity measurements for u = 7.55 Fig. 8: Mean streamwise velocity profiles for u = 1 and the shadowgraph image for u = 1.5 Fig. 9: Mean streamwise velocity profiles and the shadowgraph image for u = 15.53 Fig. 10: Mean streamwise velocity profiles and the shadowgraph image for u = 20.32 Fig. 11: Comparison of PIV and Rayleigh scattering mean streamwise velocity profiles along with the shadowgraph image for u = 20.32 (horizontal line on image is at x/D = 5) Fig. 12: Mean transverse velocity profiles and the shadowgraph image for u = 20.32
24
Fig. 13: Turbulent shear stress profiles for u = 1 and the shadowgraph image for u = 1.5 Fig. 14: Turbulent shear stress profiles and the shadowgraph image for u = 20.32
25
Pressure Regulator Injection Ports
Air Storage Tanks Seeding Reservoir
Control
Sonic Nozzle
p0
Compressor
Laser Sheet
T0
y
N2 x
PC
Cylindrical Lens
Lasers and Transmitting Optics
Mirror From CCD Camera
PIV Processor
Fig. 1
1 Fig1
(a)
(b)
Fig. 2
2 Fig2
Ruler scale: inches
Mach disk
Mach disk
Fig. 3
3 Fig3
Mach disk
(a) U/Ue: 0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80
2
y/D
1
0
-1
-2
(b)
0
1
2
3
x/D
4
5
6
7 1
2
y/D
1
0
-1
-2
(c)
0
1
2
3
x/D
Fig. 4
4 Fig4
4
5
6
7
2.4
Mach u=7.55 u=15.53 disk 2 locations
u=20.32
u=1 u=7.55 u=15.53 u=20.32
U / Ue
1.6
1.2
0.8
0.4
0 0
1
2
3
4
x/ D
Fig. 5
5 Fig5
5
6
7
8
2.4
PIV Ray leigh Scattering
2
Pitot
U / Ue
1.6
1.2
0.8
0.4
Mach disk location 0 0
1
2
3
4
x/ D
Fig. 6
6 Fig6
5
6
7
8
2.4
P IV 2
Rayleigh Scattering P ito t
U / Ue
1.6
1.2
0.8
0.4
Mach disk location 0 0
1
2
3
x/ D
Fig. 7
7 Fig7
4
5
6
2 x/D 7
x/D = 1 x/D = 2
1.5
6
x/D = 3
U /Ue
1
x/D = 4
5
x/D = 5
4
x/D = 6
3
x/D = 7
2
0.5
1
0
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 8
8 Fig8
3
2 x/D 7
x/ D = 2 x/ D = 3
1.5
U /Ue
1
x/ D =4 x/ D = 5
6
x/ D = 6
4
5
x/ D = 7
3 2
0.5
0
-0.5 -3
-2
-1
0
y /D
1
2
Fig. 9
9 Fig9
3
2
x/ D = 2 x/ D = 3 x/ D =4 x/ D =5 x/ D = 6 x/ D = 7
1.5
x/D 7 6 5 4
U /Ue
1
3 2
0.5
0
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 10
10 Fig10
3
2
1.5
x/D 5
U /Ue
1
0.5 PIV
0
R ayleig h Scat t er ing
-0.5 -3
-2
-1
0
1
2
y /D
Fig. 11
11 Fig11
3
y/D 4
0.3 x/D = 0
-4
x/D 9.8
x/D = 1.2
0.2
x/D = 2.05 4.9
x/D = 4.9
0.1
V /Ue
x/D = 9.8
0
2.05 1.2
-0.1 0
-0.2
-0.3 -4
-3
-2
-1
0
y /D
1
2
Fig. 12
12 Fig12
3
4
x/D = 0 x/D = 1.2 x/D = 2.05
0.002
x/D = 3.26 x/D = 4.09 x/D = 9.83
-u'v' /Ue 2
0.001
4.9
0 2.05
-0.001
1.2
-0.002
0
-0.003 -0.004 -2
-1.5
-1
-0.5
0
0.5
1
y /D
Fig. 13
13 Fig13
-2
0.003
y/D 2
x/D 9.8
1.5
2
y/D 3
0.2 x/D = 0
0.15
x/D = 1.2 x/D = 2.05
0.1
4.9
-u'v' /Ue 2
x/D = 4.9
0.05
x/D = 9.8
0
2.05 1.2
-0.05
0
-0.1 -0.15 -0.2 -3
-2
-1
0
1
2
y /D
Fig. 14
14 Fig14
-3
x/D 9.8
3